Frontiers in

Orthopaedic
Biomechanics

Cheng-Kung Cheng
Savio L-Y. Woo
Editors

123
Frontiers in Orthopaedic Biomechanics
Cheng-Kung Cheng • Savio L-Y. Woo
Editors

Frontiers in Orthopaedic
Biomechanics
Editors
Cheng-Kung Cheng Savio L-Y. Woo
School of Biomedical Engineering Musculoskeletal Research Center,
Shanghai Jiao Tong University Department of Bioengineering
Shanghai University of Pittsburgh
China Pittsburgh, PA
USA

ISBN 978-981-15-3158-3    ISBN 978-981-15-3159-0 (eBook)

https://doi.org/10.1007/978-981-15-3159-0

© Springer Nature Singapore Pte Ltd. 2020

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Foreword

A good understanding of biomechanics is beneficial for orthopaedic surgeons as the

majority of the diseases being treated start when the normal biomechanical environ-
ment in the body is disturbed. For this reason, orthopaedic surgeons are now required
to undergo training in biomechanics, which is important for evaluating joint condi-
tions, planning interventional treatments, and planning postoperative rehabilitation
regimes. A number of textbooks have been published in recent years on the princi-
ples of orthopaedic biomechanics, but few texts to date have presented in-depth
discussions of each area of the field of orthopaedics, from basic biomechanical prin-
ciples through to direct clinical applications. The content of this book covers recent
breakthroughs in the field of orthopaedic biomechanics, primarily focusing on clini-
cally relevant developments and challenges in this field. I highly recommend this
book be read by orthopaedic surgeons, biomedical engineers and researchers, and
related personnel in the field of orthopaedic biomechanics. It is also my hope that
this book will be a vital source of information on the latest advances in biomechan-
ics for younger practitioners that may not yet have significant experience in the field.

Kerong Dai
Ninth People’s Hospital
Shanghai, China
Shanghai Jiao Tong University School of Medicine
Shanghai, China

v
Contents


Biomechanics of Bone and Cartilage������������������������������������������������������    1
Yi-Xian Qin, Minyi Hu, and Xiaofei Li

Biomechanics of Skeletal Muscle and Tendon��������������������������������������   37
Yuan-Hung Chao and Jui-Sheng Sun
Biomechanics of Ligaments��������������������������������������������������������������������   75
Jie Yao, Zizhan Lian, Bin Yang, and Yubo Fan
Hand and Wrist Biomechanics ��������������������������������������������������������������   89
Steven Regal, Steven Maschke, and Zong-Ming Li

Biomechanics of the Elbow �������������������������������������������������������������������� 105
Su-Ya Lee and Fong-Chin Su

Biomechanics of the Shoulder���������������������������������������������������������������� 131
Min Zhang and Chih-Hwa Chen
Biomechanics of Spine ���������������������������������������������������������������������������� 147
Lizhen Wang, Zhongjun Mo, Yuanjun Zhu, Enze Zhou,
and Yubo Fan

Biomechanics of the Hip�������������������������������������������������������������������������� 169
Bolun Liu, Jia Hua, and Cheng-Kung Cheng

Biomechanics of the Knee ���������������������������������������������������������������������� 189
Huizhi Wang, Bolun Liu, Xinzheng Qi, Savio L-Y. Woo,
and Cheng-Kung Cheng

Biomechanics of Foot and Ankle������������������������������������������������������������ 219
Duo Wai-Chi Wong, Ming Ni, Yan Wang, and Ming Zhang

vii
viii Contents


Biomechanics of Human Motion������������������������������������������������������������ 265
Rongshan Cheng, Zhongzheng Wang, Cong Wang, Fuping Li,
Yifei Yao, Yan Yu, and Tsung-Yuan Tsai

Biomechanics of the Fracture Fixation�������������������������������������������������� 301
Yingze Zhang, Hongde Wang, Tianrui Wang, Wei Chen,
and Yanbin Zhu
Biomechanical Principles in Designing Custom-Made
Hip Prosthesis������������������������������������������������������������������������������������������ 339
Jia Hua

Biomechanics of Orthopedic Rehabilitation������������������������������������������ 357
Ayman A. Mohamed, Yih-Kuen Jan, Ian M. Rice, Fang Pu,
and Cheng-Kung Cheng
Biomechanics of Osteo-Synthetics���������������������������������������������������������� 397
Chia-Ying James Lin, Heesuk Kang, and Scott J. Hollister
Introduction

The primary function of the musculoskeletal system is to produce force to move

joints and limbs. It also serves to protect vital organs in the body. As such, the heavy
burden placed on the system can often lead to injury and degeneration. Orthopaedics
is a surgical discipline that is frequently used in conjunction with rehabilitation to
manage musculoskeletal ailments.
About 50 years ago, a number of leading orthopaedic surgeons began to work
with early bioengineers to introduce engineering practices to the medical field.
These bioengineers introduced the principles of mechanics to the analysis of the
structure and functional relationship of the musculoskeletal system, offered a better
understanding on the mechanism of injuries, and collaborated to design new and
more effective treatment procedures. Indeed, the contribution of orthopaedic biome-
chanics to advancing the management of musculoskeletal injuries has been signifi-
cant and has greatly benefited patients around the world.
More recently, novel methods of production and processing of biomaterials,
together with the application of advanced mechanical instrumentation, have revolu-
tionized the development of orthopaedic devices, such as with customized anatomi-
cal prosthesis, implants with increased longevity, and arthroscopic and robot-assisted
surgical instruments. Therefore, this book offers a systematic and comprehensive
review of current clinical best practice as well as novel research on offer to further
enhance patient outcomes.
This book is aimed towards younger orthopaedic surgeons, biomedical engi-
neers, and rehabilitation scientists who are looking for a solid review of the current
field of orthopaedic biomechanics. The book presents an in-depth analysis of the
fundamental principles of orthopaedic biomechanics as well as the clinical applica-
tions across the musculoskeletal system—including fracture healing, design of cus-
tomized orthopaedic implants, and evidence-based methods of orthopaedic
rehabilitation. Moreover, the application of innovative biomaterials in clinical prac-
tice is also covered in this book. Thus, the main feature of the book is that it clearly
shows the relationship between the musculoskeletal anatomy and design of ortho-
paedic and rehabilitation treatments. Sound mechanical theories are presented to

ix
x Introduction

explain how the musculoskeletal system works, what causes musculoskeletal inju-
ries, and how various treatment methods can improve the outcome.
There are 15 chapters in this book. Following Introduction, Chaps. 1–10 detail
important biomechanical concepts relevant to surgical and clinical practice, includ-
ing cartilage, muscles and tendons, ligaments, and joints. Chapter 11 introduces the
biomechanics of human motion, and the following three chapters discuss various
orthopaedic injuries and treatment methods. The last chapter focuses on orthopae-
dic bio-synthetics. Each chapter is contributed by experts in the respective research
fields and presents advanced approaches to orthopaedic biomechanics. Key features
of each chapter are highlighted as follows. The introductory section outlines the
target and contents of the book. Chapter 1 discusses how mechanical biology and
biomechanical signal transduction attenuate musculoskeletal degeneration, as
knowledge of specific cellular responses is critical to understanding the underlying
mechanism which has the potential to regulate bone and cartilage adaptation.
Chapter 2 introduces the anatomy of muscles and tendons and demonstrates how
these tissues act to produce mechanical force. Chapter 3 presents mechanical meth-
ods for measuring forces in ligaments, in addition to detailing the mechanism of
ligament injury and treatment methods available. Chapter 4 provides a review of the
anatomy and biomechanical function of the hand and wrist. This chapter also dis-
cusses the pathomechanics of the hand and wrist after injury, i.e. arthritis of the
thumb, distal radius fracture, and malunion carpal tunnel syndrome. The functional
and musculoskeletal anatomy of the elbow is illustrated with pictures in Chap. 5.
This chapter also details the pathomechanics of the elbow, including elbow fracture
and arthritis. Chapter 6 contains a systematical review of the musculoskeletal and
functional anatomy of the shoulder, as well as a description of shoulder arthroplasty.
Chapter 7 emphasizes on the repair of the lamina and related ligaments, using exam-
ples to illustrate the design of spinal arthroplasty to restore the function of the spine
and improve the stability and longevity of implants. In Chap. 8, significant param-
eters relating to the function and kinematics of the hip are introduced, as well as an
analysis of reaction forces in the hip joint. Chapter 9 focuses on knee disorders,
namely knee osteoarthritis and osteotomy, and discusses the design of knee arthro-
plasties with the aim of restoring knee function. Chapter 10 includes a biomechani-
cal assessment of the foot and ankle based on computational models, in addition to
detailing methods of applying finite element analysis to the study of injuries, pros-
thetic design, surgical approaches, and orthotics. Chapter 11 discusses the structural
anatomy that contributes to stability and mobility of joints. In this chapter, common
pathologies and hip arthroplasties are introduced. Chapter 12 focuses on the intro-
duction of fracture fixation methods. Biomechanical principles of screw and plate
fixation for fracture healing are described comprehensively in this section. Chapter
13 introduces the concept of customized hip stems for individual patients based on
their unique bone geometry, deformities, and pathological conditions. This chapter
may be of interest to surgeons and researchers who regularly interact with such
custom implants but need additional information on the development methods.
Chapter 14 details methods for improving the effectiveness of orthopaedic rehabili-
tation. This section investigates the biomechanical principles of exercises as well as
Introduction xi

appropriate assistive devices (splints, walkers, crutches, and canes) for orthopaedic
rehabilitation. The final chapter, Chap. 15, focuses on the introduction of osteo-­
synthetics to the field of biomedical engineering. Design parameters such as implant
microstructural and materials for osteo-synthetics are discussed, as well as a new
design strategy termed Topology Optimization. This final chapter presents novel
research that could readily be applied in clinical settings, such as materials that pos-
sess the solid-fluid bi-phasic properties of native bone.
We are truly grateful for the contributions made by all the authors of this book.
Each is a distinguished leader in their respective areas of orthopaedic biomechanics.
Their wealth of knowledge and experience makes this book a true representation of
“the Frontiers in Orthopaedic Biomechanics”. We thank each author for presenting
the materials in each chapter in a comprehensive manner. We are also indebted to
Springer Nature and the editorial team for their kind assistance with making this
publication possible.

Shanghai, China  Cheng-Kung Cheng

Pittsburgh, PA, USA  Savio L-Y. Woo
Chapter 1
Biomechanics of Bone and Cartilage

Yi-Xian Qin, Minyi Hu, and Xiaofei Li

Abstract The use of mechanical biology and biomechanical signal transduction

is a novel approach to attenuate musculoskeletal degeneration, whereas the under-
standing of specific cellular responses is critical to delineate the underlying mech-
anism. Dynamic mechanical signals with optimized loading signals, i.e., intensity
and frequency, have been shown to have the potential to regulate bone and carti-
lage adaptation. Mechanotransduction pathways are of great interests in elucidat-
ing how mechanical signals produce such observed effects, including reduced
bone loss, increased bone formation, and osteogenic cell differentiation. The
objective of this review is to develop a molecular understanding of the mechano-
transduction processes in tissue regeneration, which may provide new insights
into bone physiology. In this chapter, we discuss the potential for mechanical
loading to induce dynamic bone fluid flow, i.e., generated by the intramedullary
pressure (ImP) and strains in bone, regulation of bone adaptation, and optimiza-
tion of stimulation parameters in the loading regimen. The potential for mechanical
loading to regulate bone fluid flow and microcirculation is also discussed.
Particular attention is allotted to the responses of mechanical loading, including
potential cellular and molecular pathways, osteocytes associated with Wnt signal-
ing, the elevation of marrow stem cells and suppression of adipose cells, as well as
the roles of LRP5 and microRNA. Altogether, these discussed data highlight the
complex yet highly coordinated process of mechanotransduction in bone tissue
regeneration.

Keywords Biomechanics and mechanobiology · Bone adaptation · Osteopenia

Mechanical loading · Muscle atrophy · Stem cell differentiation · Loading
frequency · Ultrasound treatment · Cartilage regeneration · Bone remodeling

Y.-X. Qin (*) · M. Hu · X. Li

Stony Brook University, Stony Brook, NY, USA
e-mail: Yi-Xian.Qin@StonyBrook.edu

© Springer Nature Singapore Pte Ltd. 2020 1

C.-K. Cheng, S. L-Y. Woo (eds.), Frontiers in Orthopaedic Biomechanics,
https://doi.org/10.1007/978-981-15-3159-0_1
2 Y.-X. Qin et al.

1 Background

Bone mineral density (BMD) and muscle strength are highly biomechanically
related to each other [1, 2]. High physical activity level has been associated with
high bone mass and low fracture risks, and is therefore recommended to reduce
fractures at old age [3–7]. As a direct consequence of exposure to microgravity,
astronauts experience several physiological changes, which can have serious medi-
cal complications. Most immediate and significant are the musculoskeletal implica-
tions in bone and muscles [8–11]. Results of the joint Russian/US studies of the
effect of microgravity on bone tissue from 4.5 to 14.5 month-long missions have
demonstrated that bone mineral density (BMD, g/cm2) and mineral content (BMC,
g) are decayed in the whole body of the astronauts [12]. The greatest BMD losses
have been observed in the skeleton of the lower body, i.e., in pelvic bones
(−11.99 ± 1.22%) and in the femoral neck (−8.17 ± 1.24%), while there is no evi-
table decay found in the skull region. Overall changes in bone mass of the whole
skeleton of male cosmonauts during the period of about 6 months on a mission
made up −1.41 ± 0.41% and suggest the mean balance of calcium over flight equals
to −227 ± 62.8 mg/day. On average, the magnitude and rate of the loss are stagger-
ing; astronauts lose bone mineral in the lower appendicular skeleton at a rate
approaching 2% per month with muscle atrophy [5, 6, 13–15]. In simulated or
actual microgravity, human postural muscles undergo substantial atrophy: after
about 270 days, the muscle mass attains a constant value of about 70% of the initial
one. Most animal studies have reported preferential atrophy of slow-twitch fibers
whose mechanical properties change towards the fast type. After microgravity, the
maximal force of several muscle groups has showed a substantial decrease (6–25%
of pre-flight values) [8, 10, 16–19]. The mechanism that explains both muscle and
bone decays in the function disuse environment is still unclear. In recent years,
considerable attention has focused on identifying particular parameters and exer-
cise paradigms to ameliorate the deficits of muscle atrophy and bone density.
Perhaps microcirculation and interstitial fluid flow that link with exercise and mus-
cle contraction can identify the interrelationship between muscle and bone flow in
response to loading and disuse environment. The headward shift of body fluids and
the removal of gravitational loading from bone and muscles have led to progressive
changes in the musculoskeletal systems. The underlying factor producing these
changes may be primarily due to the fluid flow and circulations in both muscular
and bone tissues.
The ability of musculoskeletal tissues to respond to changes in its functional
milieu is one of the most intriguing aspects of such living tissue, and certainly con-
tributes to its success as a structure. The ability of bone and muscle to rapidly
accommodate changes in its functional environment ensures that sufficient skeletal
mass is appropriately placed to withstand the rigors of functional activity, an attri-
bute described as Wolff’s law [20, 21]. This adaptive capability of musculoskeletal
tissues suggests that biophysical stimuli may be able to provide a site-specific,
exogenous treatment for controlling both bone mass and morphology. The premise
1 Biomechanics of Bone and Cartilage 3

of a mechanical influence on bone morphology has become a basic tenet of bone

physiology [22–26]. Absence of functional loading results in the loss of bone mass
[22, 27–31], while exercise or increased activity results in increased bone mass
[32–36].
Similarly, the increasing exercise of musculo-tissues can significantly increase
blood flow, oxygen, and exchange fluid in muscle. During muscle contraction, sev-
eral mechanisms regulate blood flow to ensure a close coupling between muscle
oxygen delivery and metabolic demand [8, 10, 16–19, 37–44]. To define the formal
relationship between the mechanical milieu, the adaptive response, and the relation-
ship between muscle pump and interstitial fluid flow will prove instrumental in
devising a mechanical intervention for musculoskeletal disorders, such as osteopo-
rosis, muscle fatigue, and atrophy, designing biomechanical means to accelerate
fracture healing, and promoting bony ingrowth.

2 Bone Structure, Physiology, and Basic Biomechanics

Similar to most of the biological tissues, bone has its unique structure and serves as
a functional unit [45–47] (Fig. 1.1). In general, the basic structure of mature long
bone includes both cortical (or compact) bone and trabecular (or cancellous) bone.
Within the mature cortical bone, the skeleton shows the lamellar structure. Such a
plate structure is centered with the Haversian canal, mostly aligned longitudinally
and connected with the Volkmann’s canals that is running horizontally in the cor-
tex. These two conduits are rich in vascular tissue; two-thirds of the vascular supply
is provided through the medullary cavity, and the other one-third is provided
through the periosteum. Bone cells that present in the bone lacunae are intercon-
nected by the canaliculi, tubules structure, and communicate with each other
through the gap junction. Each concentric structure is consisted of a capillary tube,
a concentric plate structure, lacuna, and canaliculi. Such a unique bone unit is
called osteon.
The Haversian canals, canaliculi, and lacunae occupy 13.3% of the volume of the
cortical bone [48, 49]. The rest solid portion is the matrix, which is occupied by
mineral material containing the hydroxyapatite crystal and collagen fiber. The solid
bone matrix of the bone contains pores of the order of 0.01–0.1 μm in diameter
[48–52]. The primary constituents of an osteon are collagen (organic), hydroxyapa-
tite (inorganic), and fluid. Fluid flows through the various microstructural spaces to
transfer metabolites to the osteocytes, ensuring that bone tissue remains viable. This
continuous perfusion allows the remodeling processes to continue in perpetuity. The
requisite nutrition of the cells and essential disposal of their waste products are car-
ried by this dynamic fluid stream. Because of the intricate microstructure of cortical
bone, transportation between cells would be very poor if it relied solely on fluid
diffusion. Indeed, a complex network of very thin (~1 μm) and quite long (up to
100 μm) canaliculi must employ a more active policy of nutrient allocation and
signal dispersion [48–52].
4 Y.-X. Qin et al.

Bone (femur)

Lamellae

Periosteum

Marrow Cavity

Haversian & Volkmann’s

Canals

Endosteum

Osteocyte Bone Matrix Structure

with Hydroxyapatite
and Collagen
Canaliculi

Fig. 1.1 Cortical bone and osteon structure. The general structure of cortical bone includes mar-
row cavity, periosteum, and endosteum. The microstructure includes Haversian Canals, Volkmann’s
canal, osteocyte, and lacuna and canaliculi system

Regarding the potential mechanotransduction in bone induced by fluid flow,

Cowin [50, 51] summarized that there are three primary levels of bone porosities
within cortical microstructure, which might mediate fluid flow. Firstly, an osteon,
the basic structure of bone with dominant cylindrical structures of 100–150 μm
radii running primarily along the long axes of bone, contains at its center an osteo-
nal canal (OC), including blood vessels, a nerve, and surrounding fluid. There are
cells attached on the walls of the OC. At the level of the osteon, fluid transduction
from the Haversian canal to the cement line or its surrounding micropores, whether
1 Biomechanics of Bone and Cartilage 5

via perfusion or convection, appears to be significantly influenced by the pathway

of the fluid flow. Secondly, an osteon contains lacunae structure of 3–10 μm in
radius surrounding the OC, which connects to the OC via canaliculi. Osteocytes
(~2 μm radii) are contained within the lacunae. Thirdly, canaliculi, a capillary with
0.1–0.5 μm in radius, run radially, and surround and connect the lacunae, OC, and
cement lines together. In addition, the microstructures of collagen-apatite porosity
(100–300 Å) contain fluid in the collagen matrix. The cortical vascular supply
begins primarily at the marrow cavity and passes through the endosteum, accom-
modating approximately 2/3 of the vascular supply in the cortex. These levels of
porosities participate in and interact with each other in fluid diffusion/perfusion,
and fluid pathways may include vascular canals, the lacunar-canalicular spaces, and
collagen-apatite spaces.

3 Mechanical Properties and Characterization

of Biological Tissues

The mechanical strength of biological tissue or a sample can be defined and quanti-
fied by its mechanical parameters, such as stress, strain, and modulus. These
mechanical parameters are defined as follows.

3.1 Stress

In one-dimensional testing status, the stress is defined as the axial loading on

the perpendicular cross-sectional area. The load and force per unit area is the
response to externally applied loads on a structural section. In general, a unit
point can experience three-dimensional loads. External forces and moments can
be applied to the structure in different directions, resulting in tensile, compres-
sive, bending, torsional, shear, and composite stresses. Fractures often clinically
occur at the location where the principal stress exceeds the mechanical strength
of the tissue. The unit of stress is defined as N/m2 or Pa, MPa (106 Pa), and GPa
(109 Pa).

3.2 Strain

External loading on a structure can induce the change of dimension of the structure,
which is called deformation. The strain is defined as the structural deformation
against the original shape of the structure caused by an applied load. There are two
6 Y.-X. Qin et al.

types of strains, one of which is the normal strain, which causes a change in the
length of the specimen, and another is the shear strain, which causes a change in the
angular relationship within the structure. Strain has no unit quantity, but is usually
expressed in %, ε, and με.

3.3 Elastic Modulus

It is the relation between strain and stress, such as the ratio of stress to strain, as the
basic material constants that reflect the mechanical properties of a material. The
relationship between stress and strain can be defined as stress/strain = elastic modu-
lus, the value of which is the ratio of stress to strain. The unit of elastic modulus is
also Pa, MPa, or GPa. The larger the value of elastic modulus, the higher the strength
of the material (Fig. 1.2).
Bone intensity is referred to the ability of bone tissue to resist structural damage
after being loaded. It is a comprehensive index that integrates bone structure, bone
mass, and material properties.
The mechanical properties of the tissue can be quantified by various mechanical
loading and evaluations. The mechanical strength testing instruments can be used to
obtain the test results of the tissue strength, stiffness, hardness, and toughness. The
mechanical properties of bone are usually assessed by mechanical testing of the

130
Ultimate stress
120
110
100
90
80
Stress (MPa)

Yield point
70
60
50 E, slope of linear portion
40
30
20
10
0
0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.0
Strain (%)

Fig. 1.2 Strain–stress relation under mechanical loading

1 Biomechanics of Bone and Cartilage 7

3-point Bending 4-point Bending Torsion

Fig. 1.3 Long bone under loading of 3-point bending, 4-point bending, and torsion

bone using a 3- or 4-point bending device (Fig. 1.3). The shear mechanical test of
bone can be achieved by torsional testing (Fig. 1.3). The choice of the test type is
determined by various technical and physiological factors. For example, in the study
of healing of long bone fractures, bending and torsion tests are a logical choice
because they can test the bending and torsional strength of the tissue. The torsional
test subjects each cross-section of the bone to the same torque, while the 4-point
bending test creates a uniform bending moment [53] for the entire epiphysis.
For the torsional test, an additional parameter, twisting to failure (fracture), can
be used as a measure of the callus ductility. Although it can only be measured once
for a given callus, it is possible to obtain multiple measurements on hardness and
stiffness before reaching failure. Multilevel testing methods have been reported to
test the loading model by performing a noninvasive load on bone. Within these
methods, bending strength or torsional and compressive stiffness can be quantified
in multiple planes.

4 Musculoskeletal Tissue Response to Dynamic

Mechanical Signals

High physical activity level has been associated with high bone mass and low frac-
ture risks, and is therefore recommended to reduce fractures [3, 4, 6]. The ability of
musculoskeletal tissues to respond to changes in its functional milieu is one of the
most intriguing aspects of such living tissue, and certainly contributes to its success
as a structure. Bone and muscle rapidly accommodate changes in its functional
environment to ensure that sufficient skeletal mass is appropriately placed to with-
stand the regions of functional activity, an attribute described as Wolff’s law [20,
21]. This adaptive capability of musculoskeletal tissues suggests that biophysical
stimuli may be able to provide a site-specific, exogenous treatment to control both
bone mass and morphology. The premise of mechanical influence on bone morphol-
ogy has become a basic tenet of bone physiology [24–26]. Based on the Muscle
Pump Theory, vascular arteries and veins within skeletal muscles are compressed
upon muscle contraction, and therefore increasing the arteriovenous pressure gradi-
ent and promoting capillary filtration [54–56].
8 Y.-X. Qin et al.

Modeling (formation) and remodeling (coupling of resorption and formation)

responses are sensitive only to dynamic (time-varying) strains; static strains are
ignored as a source of osteogenic stimuli [57]. With that said, it is also clear the
osteogenic potential of mechanical signals is defined by a strong interdependence
between cycle number, strain magnitude, and frequency. In cortical bone, 2000 με
induced at 0.5 Hz (one cycle every 2 s) maintains bone mass and achieves this with
just four cycles of loading encompassing 8 s/day [30]. Reducing this strain to
1000 με at 1 Hz requires 100 cycles, and 100 s, to maintain bone mass [58]. Raising
the loading frequency to 3 Hz, bone mass can be retained with 1800 cycles of only
800 με [53], while at 30 Hz, the same 600 s requires only 200 με to maintain cortical
bone, a protocol employing 18,000 cycles of loading. Increasing the 30 Hz signal to
1 h/day (108,000 cycles), only 70 με is necessary to inhibit bone loss. These data
demonstrate the sensitivity of bone to mechanical loading goes up quickly with the
total number of loading cycles, which closely associated with the loading frequency,
i.e., extremely low levels of strain will maintain bone mass if sufficient numbers
induced by relatively higher frequency are applied. This relation between the load-
ing cycle and resultant bone strain can be plotted in a nonlinear response curve [53]
(Fig. 1.4). It is suggested that a nonlinear governing relationship between the daily

10000
Net bone ±s.e.
formation

m=3.5
Anabolic 1000
m=5
Microstrain

m=2.5
Low exercise
m=4.5
Med exercise
100 High freq loading m=1
Maintain Electrical field
Bone therapy
resorption
LIPUS
10
0.1 1 10 100 1000 10000 100000 1000000
Number of Daily Loading Cycles
Resorb

Fig. 1.4 Nonlinear interrelationship of cycle number and daily strain magnitude following a gov-
erning equation (Eq. 1.1). It appears that bone mass can be retained through a number of distinct
strategies: (1) bone is preserved with extremely low daily loading cycles and extremely high fre-
quency, i.e., 4 cycles per day of 2000 με, (2) bone mass is maintained with 100 cycles per day of
1000 με, or 10,000s of cycles of signals well below 100 με (each represented as a star), (3) bone is
responded to extremely high frequency and extremely low strain magnitude, such as electrical field
induced muscle contraction and low-intensity pulsed ultrasound (LIPUS). It is proposed that fall-
ing below this “daily strain energy” would stimulate bone loss, or any combination exceeding this
relationship would stimulate net bone gain [53]
1 Biomechanics of Bone and Cartilage 9

loading cycles and the peak bone strain magnitude generated in the body can be
generated using curve fitting analysis [53].

S = 10 2.28 ( 5.6 - log10 C )

1.5
(1.1)

where S represents the peak bone strain, and C represents the total daily loading
cycles. Such higher loading cycles can be achieved using higher frequency daily
loading regimen.
It is well accepted that overloading will damage the bone and lead to failure, just
as too much light, noise, or pressure will overwhelm sight, hearing, and touch,
respectively. Although the skeleton’s primary responsibility is structural support in
nature, its overall responsibilities are broader than first presumed, and even include,
a critical role of the acoustic sensory organ in elephants [3]. Emphasizing this point,
bone’s ­adaptation to mechanical signals is nonlinear, such that it can be influenced
by a very few high-magnitude strain events, or by many thousands of low-magni-
tude strain events.
To adapt to the changing demands of mechanics, bone mass and bone morphol-
ogy can be regulated via bone remodeling at specific sites. This crucial process of
structural remodeling of the bone involves bone resorption and the subsequent bone
formation. However, difficulties to determine specific mechanical components will
hamper our understanding of bone remodeling related diseases, as well as limiting
our judgments on bone fractures and healing capacity. Therefore, continuous stud-
ies of the bone remodeling process, for example, to determine the mechanical model
of this remodeling process, can ultimately benefit the intervention on prevention
and treatment of musculoskeletal disorders.

5 Functional Disuse-Induced Bone Loss and Muscle Atrophy

Disuse osteoporosis is a common skeletal disorder in patients subjected to pro-

longed immobility or bed rest, e.g., fracture and spinal injury. In addition to bone
loss, functional disuse and microgravity can cause muscle atrophy. These physio-
logical changes generate additional health complications, including increased risk
of falls and fracture, and poor long-term recovery. Analyses of spinal cord injury
(SCI) patients showed a reduction in bone mineral density (BMD) in disused limbs
[59–61] and a higher incidence of fracture [62–65]. More than 1 year after SCI,
30–40% of demineralization was observed in the femoral neck, distal femur, and
proximal tibia [60]. It has been reported that SCI induced osteopenia/osteoporosis
reaches the fracture threshold (BMD of 1 g/cm [66]) 1–5 years after the injury, with
a fracture frequency of 5–34% [62, 67–69]. These patients were also observed to
have significant reductions in muscle mass [70]. Analyses from space missions of
4–12 months duration have shown that weightlessness can induce 1–2% BMD loss
per month in the spine, hip, and the lower extremities [5, 71]. The reduction in tra-
10 Y.-X. Qin et al.

becular BMD in both hip and femur regions was greater than 2% per month, while
there was only minimally decrease in cortical bone [72]. Similar results were
observed in animal studies. Burr et al. [73] showed an increase in the bone turnover
rate in cast-immobilized animals that received muscle stimulation for 17 days.
Lower extremity muscle volume was also altered by disuse. Exposure to a
6-month space mission resulted in a decrease in muscle volume of 10% in the quad-
riceps and 19% in the gastrocnemius and soleus [6, 74]. Computed tomography
measurements of the muscle cross-sectional area (CSA) indicated a decrease of
10% in the gastrocnemius and 10–15% in the quadriceps after short-term missions
[15, 75]. Similar results were concluded after SCI, where patients suffered signifi-
cant 21%, 28%, and 39% reductions in CSA at the quadriceps femoris, soleus, and
gastrocnemius muscles, respectively [76, 77]. In addition to the effects on whole
muscle volume, muscle fiber characteristics were also modified due to inactivity
[78–80]. There are two primary muscle fibers: slow (type I) fibers play an important
role in maintaining body posture while fast (type II) fibers are responsive during
physical activity. Under disuse conditions, all fiber types were decreased in size,
16% for type I and 23–36% for type II [79–81]. The atrophied soleus muscles also
underwent a shift from type I (−8% in fiber numbers) to type II fibers [79, 81, 82].
Clinical muscle stimulation has been examined extensively in SCI patients to
strengthen skeletal muscle and alleviate muscle atrophy with promising outcomes
[83–86]. A few physical training studies further investigated this electrical stimulation
technique to determine its effect on osteopenia. These studies showed mixed results
with respect to bone density data [83, 87–90]. Using dual-energy X-ray absorptiom-
etry (DXA), BeDell et al. found no change in BMD of the lumbar spine and femoral
neck regions after functional electrical stimulation-induced cycling exercise, while
Mohr et al. showed a 10% increase in BMD in the proximal tibia following 12 months
of similar training [91–93]. In a 24-week study of SCI patients in whom 25 Hz electri-
cal stimulation was applied to the quadriceps muscles daily, Belanger and colleagues
reported a 28% recovery of BMD in the distal femur and proximal tibia, along with
increased muscle strength [92]. A number of reported animal studies also indicated
that muscle stimulation can not only enhance muscle mass, but bone mineral density
as well [94, 95]. Both animal and human studies seem to strongly support that func-
tional disuse can result in significant bone loss and muscle atrophy.

6 Frequency-Dependent Marrow Pressure and Bone Strain

Generated by Muscle Stimulation

A recent study has revealed that induced marrow fluid pressure and bone strain by
muscle stimulation were dependent on dynamic loading parameters and optimized
at certain loading frequencies [96]. Adult Sprague Dawley retired breeder rats with
a mean body weight of 387 ± 41 g (Taconic, NY) were used to measure the relation-
ships between ImP, bone strain, and induced muscle contraction. Rats were anesthe-
tized using standard isoflurane inhalation. A micro-cardiovascular pressure
transducer (Millar Instruments, SPR-524, Houston, TX) was inserted into the femo-
 1 Biomechanics of Bone and Cartilage 11

ral marrow cavity, guided via a 16-gauge catheter. A single element strain gauge
(120 Ω, factor 2.06, Kenkyojo Co., Tokyo) was firmly attached onto the lateral
surface of the same femur at the mid-diaphyseal region, with minimal disruption to
the quadriceps, for measuring bone strains during the loading. The MS was applied
at various frequencies (1, 2.5, 5, 10, 15, 20, 30, 40, 50, 60, and 100 Hz) to induce
muscle stimulation.
Normal heartbeat generated approximately 5 mmHg of ImP in the femur at a
frequency of 5.37 ± 0.35 Hz. The ImP value (peak-peak) was increased significantly
by dynamic MS at 5, 10, 15, 20, 30, and 40 Hz (p < 0.05 for 5, 10, 30, and 40 Hz,
p < 0.01 for 15 and 20 Hz). The response trend of the ImP against frequency was
nonlinear; the ImP reached a maximum value of 45 ± 9.3 mmHg (peak-peak) at
20 Hz (Fig. 1.5), although there was no significant difference between 10, 20, and

a 60 b b
a
50 a
PRESSURE (mmHg)

a
40
a
30

20

10

0
0 10 20 30 40 50 60 70 80 90 100
FREQUENCY (Hz)
b
160 a
140
STRAIN (microstrain)

a
120
100 b
80
60
40 c
c c
20 c c
0
0 10 20 30 40 50 60 70 80 90 100
FREQUENCY (Hz)

Fig. 1.5 (a) ImP in rat femur increased significantly with electrical frequency at 5, 10, 15, 20, 30,
and 40 Hz. In the loading spectrum from 1 to 100 Hz, stimulation at 1 Hz generated an ImP of
18 mmHg. A maximum ImP of 45 mmHg was measured at 20 Hz, which was 2.5-folds higher than
1 Hz. ap < 0.05 vs. baseline ImP; bp < 0.01 vs. baseline ImP. (b) Bone surface strain measurement.
Dynamic muscle stimulation applied at various frequencies significantly increased bone strain. In
the loading spectrum from 1 to 100 Hz, stimulation at 1 Hz produced a strain of 62 με. Peak strain
of 128 με was recorded at 10 Hz stimulation. The strain magnitude was reduced by >75% of the
peak strain for stimulation frequencies greater than 30 Hz. ap < 0.01 vs. 1, 2.5, and 5 Hz; bp < 0.01
vs. 10 Hz; cp < 0.001 vs. stimulation 20 Hz and below
12 Y.-X. Qin et al.

30 Hz. In the range from 5 to 40 Hz, the ImP was shown approximately 60% of the
maximum ImP. The MS generated ImP in the marrow cavity with values of
17.4 ± 6.2, 24 ± 5.4, 37.5 ± 11.0, 26.3 ± 11.1, and 3.7 ± 1.5 mmHg at frequencies of
1, 5, 10, 40, and 100 Hz, respectively.
The response of matrix strain to the MS frequency also was nonlinear (Fig. 1.5).
The MS generated femoral matrix strains of 61.8 ± 6.2, 87.5 ± 5.1, 128.4 ± 19.2,
78.3 ± 6.8, 18.7 ± 1.3, and 10.1 ± 1.8 με at frequencies of 1, 5, 10, 20, 40, and 100 Hz,
respectively. While the ImP trend indicated that the peak ImP value was observed at
20 Hz, the maximum matrix strain was measured at 10 Hz. Bone strain induced by
MS at 10 Hz was significantly different (p < 0.01) comparing to all other stimulations
with the exception of 15 Hz. In addition, the strains generated by MS above 30 Hz
were significantly lower than those values loaded at and below 20 Hz (p < 0.005), in
which matrix strains, when loaded above 30 Hz, decreased by more than 75% of the
peak strain measured at 10 Hz. For frequencies from 40 to 100 Hz, MS induced
matrix strain were less than 20 με. These results suggest that MS with a relatively
high rate and small magnitude can trigger significant fluid pressure in the skeleton.

7 Dynamic Muscle Stimulation Induced Attenuation

of Bone Loss

These findings were verified in an in vivo experiment under functional disuse condi-
tions [97]. Fifty-six 6-month-old female Sprague-Dawley retired breeder rats
(Taconic, NY) were used to investigate the effects of frequency-dependent dynamic
muscle stimulation (MS) on skeletal adaptation under disuse environment. Animals
were randomly assigned to seven groups with n = 8 per group: (1) baseline control,
(2) age-matched control, (3) HLS, (4) HLS + 1 Hz MS, (5) HLS + 20 Hz MS, (6)
HLS + 50 Hz MS, and (7) HLS + 100 Hz MS. Functional disuse was induced by an
HLS, setup modified from Morey-Holton and Globus [98, 99]. An approximately
30° head-down tilt was set to prevent contact of the animal’s hind limbs with the
cage bottom. The body weight of each animal was weighed 3 times per week
throughout the study.
Throughout the entire experimental period, the body weights were not signifi-
cantly different between groups at the beginning of the study, with an average of
320 ± 47 g. Age-matched control animals were able to maintain a steady body
weight throughout the study, with only a −0.15% difference between the start and
end date. Animals subjected to 4-week functional disuse lost a significant amount of
body mass. These weight reductions were similar in HLS and HLS + MS groups,
with −10% for HLS (p < 0.05), −8% for 1 Hz (p = 0.07), −9% for 20 Hz (p < 0.05),
−11% for 50 Hz (p < 0.01), and −8% for 100 Hz (p = 0.09).
Trabecular bone structure changes by MS stimulation seem to be sensitive to the
fluid pressure magnitude experienced by the tissue, where a larger response occurred
at the region near the marrow cavity, and attenuated at the region near the growth
1 Biomechanics of Bone and Cartilage 13

plate. For example, M1 is the distal metaphyseal region 1.5 mm above the growth
plate. The lack of weight-bearing activity for 4 weeks significantly reduced trabecu-
lar bone quantity and quality, demonstrated by a 70% decreases in BV/TV, an 86%
decrease in Conn.D, a 28% decrease in Tb.N, a 57% increases in SMI, and a 43%
increase in Tb.Sp compared with baseline (p < 0.001). Similar results were observed
when compared with age-matched control (p < 0.001); decreases in BV/TV (66%),
Conn.D (86%), and Tb.N (26%), as well as increases in SMI (39%) and Tb.Sp
(39%) were observed. Trabecular BV/TV in electrically stimulated animals, with
the exception of 1 Hz, was significantly greater than that of disused bone. Animals
with MS at 20 Hz and 50 Hz showed an increase in BV/TV by 143% (p < 0.05) and
147% (p < 0.01), respectively. Stimulation at 100 Hz showed an 86% increase in
BV/TV, but this change was not statistically different from the HLS group. The
other outcome measures of Conn.D, Tb.N, and Tb.Sp were also significantly affected
by MS at 20, 50, and 100 Hz frequencies. There were up to 600% and 38% increases
for Conn.D and Tb.N, and up to a 36% decrease for trabecular separation (20 Hz
p < 0.01, 50 Hz p < 0.001, and 100 Hz p < 0.05). SMI and Tb.Th were not affected
by the stimulus, regardless of its frequency. The animals subjected to 4 weeks of
1 Hz MS showed the same level of bone loss and structural deterioration as did the
HLS animals without MS, and showed significant differences compared to
­stimulation at higher frequencies. M3, the distal metaphyseal portion directly above
the growth plate, is a region with the most abundant trabecular network with
0.3 ± 0.05 BV/TV and 4.72 ± 0.64 Tb.N (Fig. 1.6). Disuse induced a 38% bone loss,
75% decrease in Conn.D, 30% reduction in Tb.N, and 43% more spacing within this
region. Similar to the results reported for the M2 portion, 50 Hz MS resulted in the
greatest preventive effects against disuse osteopenia, with increased BV/TV (40%;
p < 0.05), Conn.D (305%; p < 0.001), and Tb.N (41%; p < 0.001), and reduced
Tb.Sp (31%; p < 0.001). While BV/TV was not significantly altered by MS at 20 Hz
(+26%) and 100 Hz (+20%), trabecular qualities, Conn.D, Tb.N, and Tb.Sp, were
improved (up to 226%, 28%, and 24%, respectively, p < 0.001). Like the other
metaphyseal regions, SMI and Tb.Th were not affected by the stimulation. With the
exception of 1 Hz, stimulation frequencies at 20, 50, and 100 Hz had greater effects
on the trabecular bone 2.25 cm away from the growth plate, closer to the diaphysis.
Also, BV/TV inhibition at M1 was significantly higher (p < 0.05) than that of M3
with 20 Hz MS. Although following a trend similar to that of the above indices, at
50 and 20 Hz MS, the percent changes of the μCT measurements were not statisti-
cally significant between the three metaphyseal regions.
While trabecular bone responded to MS showing structural property changes, the
epiphyseal trabecular bone was not significantly affected by the 4-week HLS. The
percentage changes were minor versus the metaphyseal regions, with −5% BV/TV,
−44% Conn.D, −7% Tb.N, and +4% Tb.Sp. In this region, MS did not induce any
measurable effect on the bone volume and trabecular integrity at any stimulation
frequency. All stimulated values were comparable to age-matched and HLS ani-
mals, with up to 10% greater in BV/TV, 8% greater in Tb.N, and a 9% reduction in
Tb.Sp. These changes were not statistically significant.
14 Y.-X. Qin et al.

Age-Matched HLS 1 Hz MS 20 Hz MS 50 Hz MS 100 Hz MS

0.25 80
70
***
0.2 * ** **
60

Conn.D (1/mm^3)
**
50
0.15
BV/TV

40
#+ #+
0.1 30 #+ #+
20
0.05 10
0
0 Baseline Age- HLS 1Hz 20Hz 50Hz 100Hz
Baseline Age- HLS 1Hz 20Hz 50Hz 100Hz matched **
matched
0.5 #+ #+
4.5
0.45
4 ** *** ** *** *
0.4
#+ #+

Tb.Sp (mm)
3.5 0.35 ***
3 0.3
Tb.N

2.5 0.25
2 0.2
1.5 0.15
1 0.1
0.5 0.05
0 0
Baseline Age- HLS 1Hz 20Hz 50Hz 100Hz Baseline Age- HLS 1Hz 20Hz 50Hz 100Hz
matched matched

Fig. 1.6 MS induced ImP maintained bone mass at higher loading frequency, indicated by μCT
images of trabecular bone in distal femur. Graphs show mean ± SD values for bone volume frac-
tion (BV/TV, %), connectivity density (Conn.D, 1/mm3), trabecular number (Tb.N, 1/mm), and
separation (Tb.Sp, mm). MS at 50 Hz produced a significant change in all indices, compared to
HLS. #p < 0.001 vs. baseline; +p < 0.001 vs. age-matched; ∗p < 0.05 vs. HLS and 1 Hz MS;
∗∗
p < 0.01 vs. HLS and 1 Hz MS; ∗∗∗p < 0.001 vs. HLS and 1 Hz MS

The μCT data were correlated with the histomorphometry analyses. In the
metaphyseal trabecular bone, BV/TV measured by the 2-D histomorphometric
method was 43% lower in the HLS group than in age-matched controls (p < 0.001).
Animals subjected to MS also experienced 22–29% of bone loss (p < 0.01). The
result was correlated with the BV/TV values from the μCT analysis, giving an R2
value of 0.84 (p < 0.05). In other bone formation indices, HLS animals also showed
significant decline in MS/BS (76%, p < 0.001), MAR (80%, p < 0.001), and BFR/
BS (92%, p < 0.001). Disuse had an insignificant effect on the trabecular BV/TV
(−10%) at the epiphyseal region, similar to the results of the μCT analysis. Bone
formation indices were reduced due to HLS (52% for MS/BS, 147% for MAR, and
59% for BFR/BS), and daily MS failed to prevent such reduction of bone formation
activity.
These data imply that MS, applied at a high frequency with low magnitude and
for a short duration, is able to mitigate bone loss induced by the functional disuse.
There was, however, no evidence to suggest that such loading would enhance over-
all new bone formation, e.g., the total bone mass was less than age-match animals.
However, further studies related to cellular activities, e.g., osteoclast and osteo-
blast, and linked either bone resorption and bone formation, may be necessary to
further explore the balance of resorption and formation in such functional dis-
use model.
1 Biomechanics of Bone and Cartilage 15

8 Cellular and Molecular Pathways of Bone in Response

to Mechanical Loading

Bone remodeling involves all related cell types, i.e., osteoblast, osteoclast, osteo-
cyte, T-cells, B-cells, megakaryocyte, and lining cells. Thus, all these cells are
potentially mechano-sensitive and even interrelated. These cells respond to mechan-
ical loading and can express specific molecular pathways. This section will discuss
several potential pathways involved in mechanical stimulation induced adaptation.

8.1 Basic Multicellular Units (BMU)

To explore the interrelation among overall bone cells, a cluster of bone forming and
bone resorption cells among dynamic and temporal adaptation structures are pro-
posed, known as “basic multicellular units” (BMUs) [100]. Bone adaptation occurs
constantly and each cycle may take over several weeks. Such processes are ­performed
with a combination of resorption and formation. Each phase can involve targeted
molecular and gene activations. An active BMU consists of a leading front of bone-
resorbing osteoclasts. Reversal cells, of unclear phenotype, follow the osteoclasts,
covering the newly exposed bone surface, and prepare it for deposition of replace-
ment bone, following deposition of an unmineralized bone matrix known as osteoid.
Related molecular factors are represented in this temporal sequence (Fig. 1.7).
In response to mechanical loading, the first stage of remodeling reflects the
detection of initiating triggering signals such as fluid flow and any other of physical
stimulation, e.g., pressure, electrical, and acoustic waves. Prior to activation, the
resting bone surface is covered with bone-lining cells, including preosteoblasts. B
cells are present in the bone marrow and secrete osteoprotegerin (OPG), which sup-
presses osteoclastogenesis.
During the Activation phase, the endocrine bone-remodeling signal parathyroid
hormone (PTH) binds to the PTH receptor on preosteoblasts. Damage to the miner-
alized bone matrix results in localized osteocyte apoptosis, reducing the local
transforming growth factor β (TGF-β) concentration and its inhibition of
­
osteoclastogenesis.
In the resorption phase, in response to PTH signaling, preosteoclasts are recruited
to the bone surface. Additionally, osteoblast expression of OPG is decreased, and
the production of CSF-1 and RANKL is increased to promote the proliferation of
osteoclast precursors and differentiation of mature osteoclasts. Mature osteoclasts
anchor to RGD-binding sites, creating a localized microenvironment (sealed zone)
that facilitates degradation of the mineralized bone matrix.
In the Reversal phase, reversal cells engulf and remove demineralized undigested
collagen from the bone surface. Transition signals are generated that halt bone
resorption and stimulate the bone formation process.
During the Formation phase, formation signals and molecules arise from the
degraded bone matrix, mature osteoclasts, and potentially reversal cells. PTH and
16 Y.-X. Qin et al.

Activation Resorption Reversal Formation Termination Quiescence

Hematopoietic
stem cells

Mesenchymal
stem cells
RANKL Monocyte
Csf-1
Preosteoclast

OPG
PTH Preosteoblast
Osteoclast

Macrophages Osteoblasts
Bone-lining cells

sclerostin Osteoid

New bone

Old bone
Osteocytes

Osteocytes

Fig. 1.7 Bone remodeling cycle and its associated molecular pathways. Three primary cell types
are involved in bone modeling and remodeling, including osteoblast, osteoclast, and osteocyte. The
remodeling cycle of bone is composed of sequential phases of resorption and formation, including
the activation of precursor cells, osteoclasts activation generating bone resorption, bone formation
by osteoblasts after mineral removal and reversal, and mineralization. The osteoblasts that are
buried within the newly formed mineral matrix yield to osteocytes. Other osteoblasts that rest on
the bone surface become bone lining cells [47]

mechanical activation of osteocytes reduce sclerostin expression, allowing for Wnt-­

directed bone formation to occur.
Finally, in the Termination phase, sclerostin expression likely returns, and bone
formation ceases. The newly deposited osteoid is mineralized, the bone surfaces
return to a resting state with bone-lining cells intercalated with osteomacs, and the
remodeling cycle concludes.
Mechanical stimulation is likely involved in each of these phases and eventually
regulates related molecular and genetic factors. This unique spatial and temporal
arrangement of cells within the BMU is critical to bone remodeling, ensuring coor-
dination of the distinct and sequential phases of this process: activation, resorption,
reversal, formation, and termination.

9 Mechanical Signal Induced Marrow Stem Cell Elevation

and Adipose Cell Suppression

The data from disuse osteopenia and clinical osteoporosis have shown significant
reduction of bone density and structural integrity, culminating in an elevated risk of
skeletal fracture. Concurrently, a marked reduction in the available bone-marrow-­
1 Biomechanics of Bone and Cartilage 17

derived population of mesenchymal stem cells (MSCs) [101] jeopardizes the regenera-
tive potential that is critical to recovery from bone loss, musculoskeletal injury, and
diseases. A potential way to combat the deterioration involves harnessing the sensitivity
of bone to mechanical signals, which is crucial in defining, maintaining, and recovering
bone mass. As discussed above, bone cells, i.e., osteoblast, osteoclast, and osteocyte,
may sense external mechanical loading directly and perform the balance of formation
and resorption in the remodeling process; specific mechanotransductive signals may
also bias MSC differentiation towards osteoblastogenesis and away from adipogenesis.
Mechanical targeting of the bone marrow stem-cell pool might, therefore, represent a
novel, drug-free means of slowing the age-related decline of the musculoskeletal system.
Considering the importance of exercise in stemming both osteoporosis and obe-
sity, combined with the fact that MSCs are progenitors of both osteoblasts and adi-
pocytes (fat cells), as well as the anabolic response of the skeletal system to
mechanical loadings, it was hypothesized that mechanical signals anabolic to bone
would invariably cause a parallel decrease in fat production. In an in vivo setting,
7-week-old C57BL/6J mice on a normal chow diet were randomized to undergo low
magnitude high-frequency loading (90 Hz at 0.2 g for 15 min/day) or placebo treat-
ment [102]. At 15 weeks, with no differences in food consumption between groups,
in vivo CT scans showed that the abdominal fat volume of mice subjected to loading
was 27% lower than that of controls (p < 0.01) [103, 104]. Wet weights of visceral
and subcutaneous fat deposits in loading mice were correspondingly lower.
Confirmed by fluorescent labeling and flow cytometry studies [103, 104], these data
indicated that mechanical signals influence not only the resident bone cell (osteo-
blast/osteocyte) population, but also their progenitors, biasing MSC differentiation
towards bone (osteoblastogenesis) and away from fat (adipogenesis). In a follow-up
test of this hypothesis, mice fed on a high-fat diet were subjected to low magnitude
loading or placebo treatment [103, 104]. Suppression of adiposity by the mechani-
cal signals was accompanied by a “mechanistic response” at the molecular level
showing that loading significantly influenced MSC commitment to either an osteo-
genic (Runx2, a transcription factor central to osteoblastogenesis) or adipogenic
(peroxisome proliferator-activated receptor [PPAR]γ, a transcription factor central
to adipogenesis) fate. Runx2 expression was greater and PPARγ expression was
decreased in mice that underwent LMMs compared with controls. The PPARγ tran-
scription factor, when absent or present as a single copy, facilitates osteogenesis at
least partly through enhanced canonical Wnt signaling [105, 106], a pathway criti-
cally important to MSC entry into the osteogenic lineage and expansion of the
osteoprogenitor pool. Notably, low magnitude mechanical loading treatment also
resulted in a 46% increase in the size of the MSC pool (p < 0.05) [103, 104]. These
experiments, although not obviating a role for the osteoblast/osteocyte syncytium,
provide evidence that bone marrow stem cells are capable of sensing exogenous
mechanical signals and responding with an alteration in cell fate that ultimately
influences both the bone and fat phenotype. Importantly, the inverse correlation of
bone and fat phenotype has increasing support in the clinical literature. Although
controversial, and despite the presumption that conditions such as obesity will
inherently protect the skeleton owing to increased loading events, data in humans
evaluating bone–fat interactions indicate that an ever-increasing adipose burden
comes at the cost of bone structure and increased risk of fracture [107].
18 Y.-X. Qin et al.

10 Osteocyte and Its Response to Mechanical Signals

Coupled with Wnt Signaling

Osteocytes, cells embedded within the mineralized matrix of bone, are becoming the
target of intensive investigation [100, 108–110]. Osteoblasts are defined as cells that
make bone matrix, and are thought to translate mechanical loading into biochemical
signals that affect bone modeling and remodeling. The interrelationship between
osteoblasts and osteocytes would be expected to have the same lineage, yet these cells
also have distinct differences, particularly in their responses to mechanical loading
and utilization of the various biochemical pathways to accomplish their respective
functions. Among many factors, Wnt/β-catenin signaling pathway may be recognized
as an important regulator of bone mass and bone cell functions [100, 110]. While
osteocytes are embedded within the mineral matrix, Wnt/β-catenin signaling pathway
may serve as a transmitter to transfer mechanical signals sensed by osteocytes to the
surface of bone. Further, new data suggest that the Wnt/β-catenin pathway in osteo-
cytes may be triggered by crosstalk with the prostaglandin pathway in response to
loading which then leads to a decrease in expression of negative regulators of the
pathway such as Sclerostin (Sost) and Dickkopf-related protein 1 (Dkk-1) [66, 110].
Figure 1.8 indicates the potential pathway in response to mechanical loading.
It has been shown that the Wnt pathway is closely involved in bone cell differen-
tiation, proliferation, and apoptosis [110, 111]. Regulation of the Wnt/β-catenin sig-
naling pathway is vested largely in proteins that either act as competitive binders of
Wnts, notably the secreted frizzled-related proteins (sFRP) family, or act at the level
of low-density lipoprotein receptor-related protein 5 (LRP5), including the
osteocyte-­specific protein, sclerostin (the Sost gene product), and the Dkk proteins,
particularly Dkk-1 and Dkk-2 [110–114]. Sclerostin has been shown to be made by
mature osteocytes and inhibits Wnt/β-catenin signaling by binding to LRP5 and
preventing the binding of Wnt. Dkk-1 is highly expressed in osteocytes [112–114].
Clinical trial studies using antibodies to sclerostin have also shown increased bone
mass, suggesting that targeting of these negative regulators of Wnt/β-catenin signal-
ing pathway might be anabolic treatments for diseases such as osteoporosis [112].
Finally, mechanical loading has been shown to reduce sclerostin levels in bone
[112], suggesting that one of the targets of the pathways, activated by the early
events after mechanical loading, is the genes encoding these negative modulators of
the Wnt/β-catenin signaling pathway.
There is still much to be learned regarding how the bone cells, i.e., osteocyte,
sense and transmit signals in response to or absence of loading and further elevate
the activity of other cells. Although fluid shear stress is proposed as a triggering
force, the identity of these particular mechanical signals is still a challenging area to
study. The osteocyte is joining the osteoblast and osteoclast as targets for therapeu-
tics to treat or prevent bone disease. Clearly targeting the Wnt/β-catenin pathway in
osteocytes because of its central role in bone mass regulation and bone formation in
response to mechanical loading may prove useful for designing new paradigms and
pharmaceuticals to treat bone disease in the future.
1 Biomechanics of Bone and Cartilage 19

10
Lrp5
3
EP2/4
4 Wnt
11 Fz
Inte Akt
grin
s 5
ILK
GSK-3β
β-Cat
Cs43 HC

2 ERα β-Cat
6
9
7
PGE2

Sost↓
β-Cat
Dkk↓
1 Tcf
8
Wnt↑
ε

Fig. 1.8 Mechanical loading, e.g., fluid shear stress, induced Wnt signaling activation [110]. The
mechanical load applied to bone (ε) is perceived by the osteocyte through an unknown mechanism,
although fluid flow induced through the lacunar-canalicular system may be a critical component of
this perception, “step 1.” Perception of load (strain) triggers a number of intracellular responses
including the release of PGE2, “2” through a poorly understood mechanism into the lacunar-­
canalicular fluid where it can act in an autocrine and/or paracrine fashion. Connexin-43 hemichan-
nels (CX43 HC) in this PGE2 and integrin proteins appear to be involved. Binding of PGE2 to its
EP2 and/or EP4 receptor, “3,” leads to a downstream inhibition of GSK-3β, “5” (likely mediated
by Akt, “4”) and the intracellular accumulation of free β-catenin, “6.” (Integrin activation can also
lead to Akt activation and GSK-3β inhibition.) New evidence suggests that ER may participate in
the nuclear translocation of β-catenin, “7” which leads to changes in the expression of a number of
key target genes “8.” One of the apparent consequences is the reduction in sclerostin and Dkk1, “9”
with increased expression of Wnt, “10” (which one or ones is unknown). The net result of these
changes is to create a permissive environment for the binding of Wnt to Lrp5-Fz and amplification
of the load signal, “11.” (With permission of Bone)

10.1 The Role of LRP5 in Bone Responding

to Mechanical Loading

LRP5 has been shown to have important functions in the mammalian skeleton.
Experimental evidence has pointed LRP5 as a critical factor in translating mechan-
ical signals into the proper skeletal response. For example, loss-of-function muta-
tions in LRP5 have been reported to cause the autosomal recessive human disease
Osteoporosis-Pseudoglioma syndrome (OPPG), which leads to a significant reduc-
tion of BMD, and are more susceptible to skeletal fracture and deformity [115–
20 Y.-X. Qin et al.

117]. Moreover, the mechanical importance of LRP5 has been demonstrated in

LRP5−/− mice, which were found with an almost complete ablation in the ulnar
loading-induced bone formation compared to wild-type controls [117, 118].
Multiple single nucleotide polymorphisms (SNPs), located in exons 18 and 10,
have been reported, which can significantly affect the interconnection between
physical activity and bone mass [117, 119]. A high bone mass (HBM) phenotype
in humans was reported to be caused by certain missense mutations near the
N-terminus of LRP5 [120, 121]. An LRP5 overexpression mutation is, on the other
hand, associated with high bone mass and induced osteoblast proliferation [120].
Increased sensitivity to load due to a lower threshold for initiating bone formation
was also reported with this mouse [121]. A recent study done by Zhong et al.
showed that in vitro tension on MC3T3-E1 cells increased LRP5 gene expression
at 1, 3, and 5 h of loading [122].

10.2 MicroRNA and Its Role in Mechanotransduction

in Tissue

The newly discovered MicroRNAs (miRNAs) are short noncoding RNAs, which
can be complementary to messenger RNA (mRNA) sequences to silence gene
expression by either degradation or inhibitory translation of target transcripts [123,
124]. Regulation of Runx2, bone morphogenic protein (BMP), and Wnt signaling
pathways is by far the most well-studied miRNA-related osteoblast function.
Positive and negative regulations of miRNAs on Runx2 expression have been shown
to affect skeletal morphogenesis and osteoblastogenesis [125]. Inhibition of osteo-
blastogenesis can result from miRNA-135 and miRNA-26a regulated BMP-2/Smad
signaling pathway [126]. Activation of Wnt signaling through miRNA-29a-targeted
Wnt inhibitors is upregulated during osteoblast differentiation [127]. In addition,
studies have been done to investigate the miRNA function on self-renewal and lin-
eage determination for tissue regeneration via human stromal stem cells [128, 129].
Moreover, extensive studies have also been done to access the effects of miRNAs on
osteogenic functions in committed cell lines including osteoprogenitors, osteo-
blasts, and osteocytic cell lines. In general, actions of miRNA may affect bone cell
differentiation in either positive or negative ways [123, 129].
Recent research has gained interests in studying the transcription and microRNA
regulation to better understand gene expression regulation in a mechanical loading
model. Transcription factors can bind to motifs in the promoter of genes and directly
affect their expression; therefore, mechanotransduction in bone may result in tran-
scription factors alteration for regulation. Using a predictive bioinformatics algo-
rithm, a recent study investigated the time-dependent regulatory mechanisms that
governed mechanical loading-induced gene expression in bone. Axial loading was
performed on the right forelimb in rodents. A linear model of gene expression was
created and 44 transcription factor binding motifs and 29 microRNA binding sites
were identified to predict the regulated gene expression across the time course. It
1 Biomechanics of Bone and Cartilage 21

may be important in controlling the loading-induced bone formation process via the
time-dependent regulatory mechanisms.

10.3 Mechanotransductive Implication in Bone

Tissue Engineering

Development of artificial scaffold for musculoskeletal applications could take

advantages of the mechanotransduction phenomena to achieve its integrity and
function, which can lead to tissue healing. Mechanical signals delivered to bone
cells may be interfered by the scaffold deformation, and should be taken into
account. Fortunately, mechanotransduction could be used to control the prolifera-
tion and differentiation of bone cells [130–134]. Fluid flow has been proposed as an
important mechanical aspect to be considered when developing bone scaffolds
[132–136]. Studies using bioreactors have helped us understand the phenomena of
mechanotransduction used in scaffold design [130]. For example, rotating bioreac-
tors, flow perfusion bioreactors, and other mechanical stimuli such as strain have
been designed to increase mass transfer by inducing dynamic flow conditions in
culture, to create osteoinductive factors on mesenchymal stem cells by the gener-
ated fluid shear stress [137], and to induce the osteogenic differentiation of mesen-
chymal stem cells [138], respectively. Among all, mimicking the natural bone strain
to favor osteogenesis is one of the most rational aims for scaffold development.
Matching of the strain histograms of a scaffold and the actual bone can be per-
formed using microCT measurements and finite element method [132, 139, 140].

11 Biomechanics of Articular Cartilage

11.1 The Composition of Articular Cartilage

As a kind of connective tissue, articular cartilage is a white, smooth, and thin layer
that covers the surfaces of bones in diarthrodial joints [94]. Its primary function is
to bear physical stress, distribute the mechanical load, absorb the shock, and lubri-
cate the friction between bones in a joint during daily activities [141–143].
Articular cartilage has a highly organized layered structure. And it can be divided
into four zones based on the cell shape, size, and collagen direction (as shown in
Fig. 1.9) [142, 143]: (1) superficial zone (10–20%), elongated chondrocytes and
thin collagen fibrils are parallel to the surface of joints in this zone; (2) middle zone
(40–60%), spherical chondrocytes and larger collagen fibrils are randomly ori-
ented; (3) deep zone (30–40%), spherical chondrocytes and larger collagen fibrils
are perpendicular to the joint surface; (4) calcified zone (5%), the main components
of the calcified zone are calcium salts deposition without chondrocytes or colla-
gens [143].
22 Y.-X. Qin et al.

Articular Cartilage surface

Superficial Zone (10%-20%)

Chondrocytes
Middle Zone (40%-60%)
Collagen fibrils

Deep Zone (30%-40%)

Tidemark
Calcified Zone (~5%)
Subchondral bone

Fig. 1.9 The stratified structure of articular cartilage and the arrangement of chondrocytes and
collagen fibrils in each zone. There are three primary layers in normal articular cartilage. The cell
shapes are shown specific shapes in various zones, e.g., flat in the superficial zone, round in the
middle zone, and column-like in the deep zone

Articular cartilage consists of chondrocytes and an extracellular matrix (ECM)

[144, 145]. Chondrocytes are the sole type of cells in articular cartilage, and only
make up 2% of the volume of articular cartilage [141–143]. They originate from
mesenchymal stem cells (MSCs), and are highly specialized cells. And they vary in
shape, size, and number in different zones of articular cartilage [141–143].
ECM is mainly composed of macromolecules including proteoglycans (PGs)
(5–10% wet weight), collagen (10–20% wet weight), and water (60–80%) [142,
145]. Almost 90% Collagen in ECM is type II collagen, and they form a firm col-
lagen network in articular cartilage [141–145]. Collagen types I, IV, V, VI, IX, and
XI contribute only a minor proportion. PGs primarily exist as aggregates formed by
a high density of negative charge sulfated glycosaminoglycan (sGAG) [146] (as
shown in Fig. 1.10).

11.2 The Effect of Mechanical Load on the Metabolism

of Articular Cartilage

Compared with other tissues such as bone and muscle, articular cartilage in diar-
throdial joints does not contain blood vessels, lymphatic vessels, and nerves, and
therefore the nutrients are transported to the chondrocytes from the synovial fluid in
joint movements. The capacity of articular cartilage self-repair is very limited, and
could not be able to heal on its own. During daily activities, articular cartilage expe-
riences the mechanical environment changes caused by joint movements. And it can
respond to a variety of mechanical stress, strain, and pressure generated by normal
load-bearing activities in the walking, running, and other daily exercises [145]. The
1 Biomechanics of Bone and Cartilage 23

Collagen Fabric
Negatively
charged sGAG
Proteoglycan

Chondrocyte

Extracellular Matrix

Fig. 1.10 The proteoglycan, collagen, and chondrocyte in the extracellular matrix of the articular
cartilage

chondrocytes and ECM play a unique role in the anabolism and catabolism of artic-
ular cartilage, and are responsible for the maintenance of the structural integrity and
mechanical function of articular cartilage.
Chondrocytes are sparsely embedded in the ECM [141–143, 145]. They have a
low level of metabolic activity and replication due to the limited nutrition transporta-
tion from the synovial fluid [145]. For each chondrocyte, it can establish its micro-
environment and trap itself in its matrix, which could prevent their migration to the
adjacent area of cartilage. And the communication between cells and direct cell-to-­
cell signal transduction is limited under this microenvironment trap. The survival of
chondrocytes in ECM mainly depends on the mechanical and chemical environment
provided by articular cartilage, and they can regulate ECM in their vicinity area by
sensing the mechanical force in their surrounding microenvironment and responding
to mechanical stimuli caused by the physical load of joints, such as compressive,
tensile, and shear stress.
Moreover, the negatively charged sGAG in ECM can attract ions, and provide
articular cartilage with the osmotic imbalance in the ionic interstitial fluid, which
leads to absorb water and induces a swelling pressure to resist compression loads
[143, 145]. The collagen network in ECM enables articular cartilage to resist ten-
sion and shear forces. The mechanical balance between sGAG and collagen in ECM
is responsible for the stable micromechanical environment for chondrocytes [143,
145]. Taken together, the chondrocytes could sense mechanical signals to synthe-
size and maintain the turnover of ECM. In turn, the ECM could protect chondro-
cytes from potentially damaging biomechanical forces and enables articular
cartilage to support the physical load in our daily life. The interactions between
chondrocytes and ECM are crucial for the homeostasis of articular cartilage.
24 Y.-X. Qin et al.

11.3 The Degeneration of Articular Cartilage Caused by Joint

Overuse/Disuse

Articular cartilage could maintain its structural integrity and mechanical func-
tion under joint normal loading conditions during routine daily activity.
However, the homeostasis of articular cartilage is interrupted when it is exposed
to insufficient or excessive mechanical loading conditions, and could cause car-
tilage degeneration with a consequence of joint diseases, such as osteoarthritis.
Previous studies have found that the synthesis of proteoglycan decreased and
cartilage degeneration was observed under joint overuse conditions in marathon
runners or animal with running exercises (as shown in Table 1.1) [147–153].
Besides, prolonged joint disuse or joint immobilization can cause joint atrophy
and AC degeneration [153–157]. Progressive thinning of AC and the degrada-
tion of the extracellular matrix (ECM) has been reported in both immobilized
patients and unload animal models [153–157]. And the animal studies also dem-
onstrated that the thickness of cartilage became thinner and the underlying sub-
chondral bone increased in osteoarthritis group induced by anterior cruciate
ligament transection; moreover, in hind limb suspension group, the irregular
and lose distributions of chondrocytes in cartilage were found due to mechani-
cal functional disuse. However, low-intensity ultrasound stimulation could gen-
erate acoustic pressure waves with mechanical energy, and it could mitigate the
cartilage degeneration [5, 143, 145] (as shown in Fig. 1.11).

Table 1.1 Safranin O intensity of cartilage in the lateral middle section of tibia (ratio = experimental/
control) [147]
Immobilization/remobilization Running
Strenuous Endurance
Moderate (20 km/ (40 km/
Cartilage Immobilization Remobilization Remobilization (4 km/day, day, 15 day, 15
zones for 11 weeks for 15 weeks for 50 weeks 15 weeks) weeks) weeks)
Superficial 0.58∗ 0.82 0.81 0.81 0.95 0.62∗∗
zone
Middle 0.80 1.00 0.81 0.90 1.02 1.00
zone
Deep zone 0.82 0.95 0.93 0.90 1.00 1.00
Calcified 1.00 1.00 0.80 1.20 1.01 0.98
zone
Changes of Safranin O intensity in different cartilage zones of the canine knee joints in the inter-
mediate section of the latéral condyle of the tibia under immobilization/remobilization conditions
and running conditions. The two-tailed Mann-Whitney U-test or Wilcoxon’s matched-pairs signed-
ranks tests was used for statistical analysis
∗
p < 0.05
∗∗
p < 0.01
1 Biomechanics of Bone and Cartilage 25

100 µm

Age-matched OA OA+US
100 µm

HLS HLS+OA HLS+OA+US

Fig. 1.11 The toluidine blue and fast green staining of cartilage in right tibial plateau in different
groups (OA osteoarthritis, US ultrasound, HLS hind limb suspension) [158]

12 Discussion

These data have suggested that dynamic stimulation generates fluid pressure in bone
with simultaneously low-level bone strain. MS adjacent to the rat femur induces a
peak ImP at 20–30 Hz. The increase in bone fluid pressure suggests that hyperten-
sion in the skeletal nutrient vessels may increase ImP and regulate fluid flow in bone
[56]. Similarly, the bone strain was highest at approximately 10 Hz. Stimulus-­
induced bone fluid and matrix deformation are dependent on stimulation frequency.
It appears that the oscillatory MS stimulates relatively high fluid pressure at the
frequency range between 20 Hz and 50 Hz in the tested frequencies up to 100 Hz.
In such optimized loading rate (e.g., 20–50 Hz), relatively high ImP and relatively
low bone strain were observed in response to the MS loading, which may be critical
to regulating fluid flow, and adaptation in bone as a functional loading frequency-­
dependent manner. It is also noted that both ImP and strain at 10 Hz and 20 Hz are
26 Y.-X. Qin et al.

higher than the value at a lower frequency, i.e., 1 Hz. There is a significant strain
difference between 10 Hz and 20 Hz, while no significant ImP difference was
observed between 10 Hz and 20 Hz. At an optimal frequency, MS can produce high
fluid pressure gradients within the femoral marrow cavity and a high strain value in
bone. It is possible that loading generated matrix strain and fluid pressure in bone
may have combined effects in adaptation if loaded at relatively high frequencies.
Dynamic muscle stimulation was able to inhibit bone loss and trabecular archi-
tectural deterioration caused by a lack of daily weight-bearing activities. The impor-
tance of selecting an effective loading regimen was investigated in this study, in
which a wide range of stimulation frequencies was tested to determine their effects
on skeletal adaptive responses. Throughout this study, we have referred 1 Hz as low
frequency, 20 Hz and 50 Hz as mid frequency, and 100 Hz as high frequency. From
our results, we concluded that the effectiveness of dynamic MS was greatly depen-
dent on the stimulation frequency. The optimized frequency, which resulted in a
strong adaptive response in the disuse osteopenia model, was in the range of 50 Hz.
While the strain level generated at 50 Hz by MS was relatively low, e.g., approxi-
mately 10 με, the adaptive response may be mainly contributed by induced fluid
flow, and uncoupled to strain [159]. The degree of effectiveness of MS in attenuating
bone loss varied in different regions of the distal femur. Such spatial response may
also depend on the fluid pressure generated in the local region as a dose-­dependent
manner. While low-frequency MS was unsuccessful in preventing osteopenia, mid-
frequency MS applied to the quadriceps was able to maintain trabecular bone mass.
These results were consistent with previous in vivo results in which mechanical
loading at frequencies between 20 Hz and 50 Hz was shown to be anti-catabolic to
bone [53, 160–162]. This sensitivity was even more apparent in trabecular bone,
perhaps due to the increased surface area in the trabecular network, which exposes
it to rapid changes in fluid pressure [163]. For example, trabecular osteoblast sur-
face in the tibia was increased by 26% when an MS protocol at 10 Hz was applied
for 3 weeks [162]. Likewise, whole body vibration at 45 Hz increased the rate of
formation of the growing skeleton by 30% [164].
Both ImP and matrix strain have indicated a nonlinear response in the MS spec-
trum between 1 Hz and 100 Hz, though peaked differently at 20 Hz (ImP) and 10 Hz
(strain). While no obvious muscle fatigue was observed, perhaps due to the rest
period during the stimulation, the mechanism behind such a nonlinear response is
not clear. From the characteristics of tissue material point of view, e.g., the visco-
elastic property of the tissues, both muscle and bone could quickly dampen the
response at high frequencies through the MS loading. But, due to the difference in
densities and viscosities between muscle and bone, MS induced ImP, and matrix
strain could result in different frequency responses or optimized/resonant patterns
for different tissues against the loading. In addition, mechanotransduction of MS
through different connective tissues may attenuate the high-frequency response in
bone, e.g., via the connective pathway from muscle, tendon to bone, thus resulting
in peak strain and peak ImP at varied frequencies. Future research on such complex
interrelations between muscle kinematics, bone fluid flow, and matrix strain is nec-
essary to elucidate the mechanism further.
1 Biomechanics of Bone and Cartilage 27

Even in the absence of bone matrix strain, previous data have shown that ImP
alone can induce bone adaptation [161]. Using a turkey ulna osteotomy model, dis-
use alone resulted in a 5.7% loss of cortical bone. Direct fluid loading at 20 Hz for
4 weeks increased cortical bone mass by 18% by enhancing the formation of bone
at both periosteal and endosteal surfaces [161]. Transcortical fluid pressure gradient
and total bone formation were strongly and positively correlated. Bone fluid flow
plays an important role in triggering bone remodeling [165–167]. Strong evidence
suggests that interstitial fluid flow in bone interacts strongly with external muscular
activities via various mechanisms [168, 169]. According to a muscle pump hypoth-
esis, an arteriovenous pressure gradient enhances muscle perfusion [54, 170]. This
process may, in turn, increase the hydraulic pressure in skeletal nutrient vessels and
amplify the capillary filtration in bone tissue [54–56].
As a clinical application, MS on spinal cord-injured patients can cause a partial
reversal of disuse osteopenia and recovery of muscular strength [92]. Other in vivo
studies have also reported positive effects of using muscle stimulation to inhibit
muscle atrophy. Immobilization studies using MS at 50–100 Hz have shown to min-
imize the reduction of the cross-sectional area of muscle fiber and to restore
mechanical properties [171, 172]. Previous data showed that stimulation of distal
nerve stumps had similar action potential response between normal and innervated
muscle [173]. Although the response of ImP and bone mass by MS under such
periphery nerve block conditions still remains unknown, MS could serve as a miti-
gating agent to retain bone mass under chronic nerve damage conditions, e.g., spinal
cord injury. Taken together with the results from our current study, dynamic MS
may be applied as both a skeletal therapy and a muscular therapy to prevent osteo-
penia and sarcopenia.
Loading-induced fluid flow in the musculoskeletal tissues may ultimately
enhance interstitial flow and mechanotransduction in bone. Furthermore, dynamic
loading, if applied at an optimal frequency, has been shown to have preventive
potential in osteopenia in a functional disuse environment as a biomechanically
based intervention for preventing and treating osteoporosis and muscle atrophy.

Acknowledgments This research was supported by the National Institutes of Health (R01
AR52379, AR61821, and AR49286), and the National Space Biomedical Research Institute
through a NASA Cooperative Agreement NCC 9-58. The authors are grateful to Ms. Alyssa Tuthill
for her technical assistance and all the members in the Orthopaedic Bioengineering Research Lab,
particularly for their tireless assistance in the study.

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Chapter 2
Biomechanics of Skeletal Muscle
and Tendon

Yuan-Hung Chao and Jui-Sheng Sun

Abstract Skeletal muscle is the biological tissue able to transform chemical energy
to mechanical energy. Skeletal muscle has three basic performance parameters that
describe its function: structure and composition, force production, and movement
production. From a mechanical perspective, the musculotendinous unit behaves as
an elastic-contractile component (muscle fibers) in series with another elastic com-
ponent (tendons) to move human body. Due to their unique hierarchical structure
and composition, tendons possess characteristic biomechanical properties, includ-
ing high mechanical strength and viscoelasticity, which enable them to carry and
transmit mechanical loads (muscular forces) effectively. Tendons are also mechano-­
responsive by adaptively changing their structure and function in response to altered
mechanical loading conditions. The production of movement and force is the
mechanical outcome of skeletal muscle contraction. The focus of this chapter is on
the biomechanical behavior of skeletal muscle and tendon as they contribute to
function of the musculoskeletal system.

Keywords Skeletal muscle · Tendon · Structure and composition

Extracellular matrix · Viscoelastic behavior · Active muscles force production
Mechanotransduction

Y.-H. Chao
School and Graduate Institute of Physical Therapy, College of Medicine, National Taiwan
University, Taipei City, Taiwan
e-mail: yuanhungchao@ntu.edu.tw
J.-S. Sun (*)
Department of Orthopedic Surgery, College of Medicine, National Taiwan University,
Taipei City, Taiwan
Department of Orthopedic Surgery, National Taiwan University Hospital, Taipei City, Taiwan

© Springer Nature Singapore Pte Ltd. 2020 37

C.-K. Cheng, S. L-Y. Woo (eds.), Frontiers in Orthopaedic Biomechanics,
https://doi.org/10.1007/978-981-15-3159-0_2
38 Y.-H. Chao and J.-S. Sun

1 Skeletal Muscle

1.1 Structure and Composition

1.1.1 Muscle Fiber

The fiber of the skeletal muscle is a long, cylindrical, multinucleated cell that is
filled with smaller units of filaments. The largest of the filaments is the myofibril,
which is composed of the sarcomeres that are arranged from end to end through the
length of the myofibril. Each sarcomere also contains filaments, which is known as
myofilaments. There are two types of myofilaments within each sarcomere, namely,
thicker myofilaments and thinner myofilaments. The thicker one is composed of
myosin protein molecules. The thinner one is composed of molecules of the protein
actin. Sliding of the actin myofilament on the myosin chain is the basic mechanism
of muscle contraction.
Connective tissue within the muscle, called intramuscular connective structure
(IMCT), consists of predominantly collagen protein and proteoglycans [1]. It covers
skeletal muscle fiber in layers, providing mechanical support for blood vessels and
nerves deep in every muscle fiber. As muscle fiber generates mechanical tension, the
IMCT transmits muscular passive force [2–4]. Extending from tendon, epimysium
embraces every individual muscle. Fascicles within the muscle are layered by the
perimysium, and individual muscle fibers are covered by the endomysium. IMCT
comprises various proportion of collagen fiber, proteoglycans, and other substances.
According to the location and ingredients, IMCT plays various functional roles.
Endomysium with better elasticity can adapt with more deformation. Perimysium
with better stiffness can transmit force produced by muscle fibers more efficiently.
Endomysium is directly in contact with the sarcolemma and muscle fiber,
accounting for only 0.47–1.2% of the muscle dry weight. The main collagen fiber
type of endomysium is type III, IV, V, and lesser percentage of type I is also found.
Due to lesser proportion of type I collagen, endomysium is more elastic and less
stiff for transmitting force. When force is produced by muscle fibers, the adjacent
endomysium adapts itself with various angle between collagen fibers of endomy-
sium and muscle fibers. Because of this adaptation, the endomysium can resist elon-
gation deformation up to 150% change of its original physiological length. This
adaptation and continuity of endomysium let muscle fibers not recruited during a
movement render tendon transmitting force without changing length.
Different with endomysium, perimysium is multilayered, consisting of collagen
fibers type I, III, IV, V, VI, and XII and proteoglycans, elastin fiber [1, 4]. Due to
collagen fiber type I, perimysium is able to resist more traction force and has an
important role in transmitting force. According to studies on bovine muscle, peri-
mysium accounts for 0.4–4.8% muscle dry weight with different functions. The
ratio of weight of perimysium in different muscles is more various than endomy-
sium. This variance may indicate that perimysium plays a main role in defining
functional differences in multiple muscle groups [1].
2 Biomechanics of Skeletal Muscle and Tendon 39

The epimysium, formed by collagen fibers type I and III, with larger diameter is
thicker than endo- and perimysium [3]. It covers all muscle belly and consists of two
layers of wavy collagen fibrils in contact with tendon surface [1, 4]. When tension
takes place along the direction of the fiber, epimysium provides resistance. When
the force is orthogonal, the epimysium will show a discrete yielding. When epimy-
sium of two different muscles connects, it provides a membrane for vessels and
nerves to transport into muscles and a surface for sliding in all directions when
muscle contracts. Epimysium receives forces directly from perimysium and muscle
fibers sometimes, and transmits the force to the tendons or the aponeurotic expan-
sions. In conjunction with different muscles, it provides a fluent phase for sliding.

1.1.2 Mononuclear Cells

Fibroblast is the primary mononuclear cell in normal muscle ECM which is respon-
sible for producing collagen, fibronectin, MMPs, and PGs [5]. Being sensitive to
mechanical loading, fibroblasts are responsible for transforming mechanical signals
into altered gene expression. Once experienced an altered mechanical environment,
fibroblasts proximal to the myotendinous junction signal for increased collagen pro-
duction to help in the development and maintenance of tendon. Laminins and talins
are also produced to link the ends of muscle fibers to the basement membrane at the
myotendinous junction [6]. A recent study by Archile-Contreras et al. showed that
fibroblasts isolated from different muscle types possess distinct in vitro growth
capability and express different levels of MMP-2 [5]. In this animal study, fibro-
blasts cultured from semitendinosus and sternomandibularis muscles showed higher
growth capacity compared to that of longissimus dorsi. Active MMP-2 expression
was highest in semitendinosus fibroblast cultures and lowest in sternomandibularis
fibroblast cultures. The mechanical properties and collagen content were not ana-
lyzed in these muscles; therefore, these observed differences could not be correlated
with muscle function or ECM turnover.
Satellite cells (SCs) are shown by Guerin et al. to be capable of synthesizing and
secreting MMP-2 and MMP-9. This study suggested the skeletal muscle cells could
participate in remodeling the ECM during myogenesis and the regeneration of skel-
etal muscle through assisting MMPs’ migration through the ECM to muscle injury
site [7]. A recent study by Hoedt et al. even showed that myogenic differentiation
factor (myoD) could be induced by erythropoietin (Epo) treatment to prevent apop-
tosis of satellite cells in murine and in vitro models. In addition, satellite cell content
in type II myofibers as well as the content of MyoD+ SCs increased through endur-
ance training. Epo receptor mRNA expression in human SCs also suggested that
Epo treatment could regulate human SCs in vivo [8]. Crameri et al. showed that a
single bout of high intensity exercise could induce SCs re-entry into the cell growth
cycle though a single bout was not sufficient for the SCs to undergo terminal dif-
ferentiation [9].
40 Y.-H. Chao and J.-S. Sun

1.1.3 Extracellular Matrix (ECM)

Skeletal muscle collagens, which accounts for 1–10% of muscle dry weight mass,
is the major structural protein in skeletal muscle ECM. In the various types of col-
lagens, type I and III predominate in adult endo-, peri-, and epimysium with type I
being the predominant collagen in perimysium and type III evenly distributed
between endomysium [10]. Type V collagen forms a core for type I collagen fibrils
in peri- and endomysium [11]. Type XII and XIV collagen are fibril-associated col-
lagens with interrupted triple helices (FACITS) localized primarily to perimysium
and appeared to link fibrillary collagen to other ECM components without precisely
known function [12]. Muscle basement membrane consists mainly of type I colla-
gen network though type VI, XV, and XVIII are also present [13]. Types XV and
XVIII are multiplexins that can bind growth factors and assist in linking the base-
ment membranes of glycoproteins and endomysium [14]. The basement membrane
and endomysium are closely connected, involving in the transmission of force from
the myofiber to the tendon [15].
Many of the proteoglycans (PGs) in muscle ECM belong to the family of small
leucine-rich proteoglycans (SLRPs), including decorin, biglycan, fibromodulin, and
lumican with decorin and biglycan being the most abundant. Other PGs comprised
approximately 30% in muscle ECM includes the heparin sulfate PGs collagen
XVIII, perlecan, and agrin which bind to growth factors. Growth factors can be
stored and released by negatively charged glycosaminoglycans (GAGs) in the base-
ment membrane and endomysium surrounding muscle fibers. Enzymes in the ECM
cleave the GAG chains with their associated growth factors allowing interaction in
cell signaling and mechanotransduction [16, 17].
Comprising the major structure of ECM, collagen and proteoglycans interacts
uniquely to maintain the structure and organization of the matrix. Decorin, the
major PG in the perimysium, has been proposed to be a regulator of type I collagen
fibrillogenesis due to its binding interaction with type I collagen. It inhibits the lat-
eral growth of collagen fibrils through its core protein presumably. Biglycan also
binds to type I collagen in a similar way with decorin. The binding and the location
of collagen crosslinks might be key factors determining the structural organization
of the ECM since collagen fibril diameter in tendon becomes irregular in the absence
of these two materials. In mice absent of biglycan, mild muscular dystrophic pheno-
type is found implicating that these PGs are vital in maintaining normal tissue func-
tion and mechanical properties [18].
Various glycoproteins in the ECM functions in linking type IV collagen (base-
ment membrane) and sarcolemma (muscle fiber membrane). Laminins are bound by
intergrins and α-dystroglycan where integrins are bound to fibronectin [13].
Laminins are also bound to type IV collagen directly and indirectly linked to fibro-
nectin or nidogen. These glycoproteins interact to provide lateral force transmis-
sions from the myofiber, and with the network formed with type IV collagen, form
the basic structure of basement membrane [19].
Matricellular proteins in skeletal muscle include osteopontin, secreted protein
acidic and rich in cysteine (SPARC), thrombospondin, and tenascin-C. Osteopontin
2 Biomechanics of Skeletal Muscle and Tendon 41

possesses cytokine-like functions that appears during muscle regeneration but sel-
dom observed in normal skeletal muscle. It is typically secreted by inflammatory
cells and may also be secreted by myoblasts [20]. SPARC has been observed to bind
collagen and accompany its interaction in extracellular matrix [21]. The role of
thrombospondin is assumed to prevent excessive capillary formation in skeletal
muscle ECM as evidenced in the mice model [22]. Tenascin-C is indicated to play
a role in maintaining neuromuscular junction architecture by binding to perlecan
and agrin [23]. The major function of these proteins is not structural, but they are
vital in ECM signaling and maintaining ECM organization.
Skeletal muscle ECM composition and its mechanical properties are regulated
by matrix remodeling enzymes. Matrix metalloproteinase (MMP) levels are gener-
ally low in uninjured muscle. In this, MMP-2 and MMP-9 are gelatinases expressed
in muscle that degrade type IV collagen, fibronectin, proteoglycans, and laminin.
Collagenases MMP-1 and MMP-13 degrade types I and III collagens. Membrane
type I MMP not only activates MMP-2 but also functions proteolytically near mus-
cle cell surface. Tissue inhibitors of matrix metalloproteinases (TIMPs) 1–3 bind to
active MMPs or stabilize inactive MMPs to inhibit their enzymatic activities.
Through these enzymes, ECM of skeletal muscle is strictly regulated [13].
To define ECM mechanical properties, Meyer et al. first showed in their study
that isolated muscle fiber stress–strain behavior was linear, and that of muscle bun-
dle was nonlinear. To further differentiate and distinguish the source of nonlinearity
(ECM itself vs. numerous individual muscle fibers with different linear material
properties), numerous single fibers were isolated from ECM and grouped into a
bundle to compare among groups of multiple muscle fibers with and without
ECM. The results showed that the modulus of a fiber group was nearly the same as
that of single fibers while the modulus of bundle was about five times higher. These
results demonstrate that ECM is inherently stiffer than muscle fibers and its material
properties are highly nonlinear [24].

1.2 Passive Muscles

1.2.1 Elastic Behavior

The property of elasticity has a central role in a diverse range of physiological and
pathophysiological processes in skeletal muscle. Skeletal muscle is anisotropic due
to its microstructural arrangement. Its structure is divided into many levels—epimy-
sium, perimysium, and endomysium, as stated. Each muscle fiber contains actin,
myosin, and titin filaments. According to the sliding filament theory, muscle con-
traction occurs when actin and myosin interacts with a cross-bridge, and consume
one ATP (adenosine triphosphate) per cross-bridge cycle.
Elasticity describes a material property in which the material returns to its origi-
nal shape after stress applied and then removed. Muscle elastic behavior is nonlin-
ear. There are three main features to its viscoelasticity: First, when the muscle is
42 Y.-H. Chao and J.-S. Sun

stretched and relaxed, the tension decreases over time until the muscle reaches a
new steady state (stress relaxation). Second, when the muscle is stretched with a
constant tension, the length of muscle increases over time until it reaches a new
steady state (creep). Third, muscle exhibits different length–tension relationship
curve if repeatedly stretched. This is called “effect of cyclic loading” [25].
A relaxed skeletal muscle, referring to the passive muscle, will act as a deform-
able body when stretched beyond the resting length. However, the muscle deforma-
tion in response to the stretching does not follow Hooke’s law, which means it is not
linear. The passive muscle elasticity is mainly attributed to the connective tissues
content within the muscle [26]. The more proportion of the connective tissue within
the muscle, the stiffer the muscle will become [27]. Thus, lower extremity muscles,
containing more intramuscular connective tissue, are usually stiffer, compared to
the muscles from upper extremity. In addition, the muscles derived in vitro is usu-
ally shorter than the natural muscle length in vivo because of the lack of muscle tone
from neural supply and the difference in intrinsic mechanical properties.
When muscle is stretched to more than its resting length, it will exhibit passive
resistance to the stretching force without any metabolic energy requirement. The
resistance to deform is mainly from the following three structural components: con-
nective tissue within and around the muscle, intramuscular cross-links, and the non-
contractile proteins [26, 28]. The connective tissues provide general support of the
muscle structure. The binding sites of the cross-bridges between the actin and myo-
sin filaments provide the resistance to stretching during attached state. The giant
protein molecules such as titin help to maintain the integrity of sarcomere. By keep-
ing the myosin in the center between the Z discs, the proteins form the elastic con-
nections of the myosin and the Z-line. The part close to the fiber ends of the
sarcomere is less deformable than that at other sites. The length of the sarcomere
can be extended to a maximum of 3.5–4.0 μm [29].
However, from a macro perspective in joint motion, the changes in muscle–ten-
don complex length are much more than in the muscle length itself because the
tendons will generate little resistance to stretch in the toe region of the stress–strain
curve. On average, tendon changes account for almost more than half of the mus-
cle–tendon complex length changes [30]. Moreover, the passive resistance in joints
can be the interaction results of two components, including the joint angle and the
displacement. The passive resistance produced regarding the joint angle is negligi-
ble in the middle range of the motion, but significantly increase around the end
range of the motion [26]. The relationship between the passive resistance and the
joint angle is presented as the following equation:

( )
k e l (α −α0 ) − 1 , if α ≥ α
T =
0

 0, if α < α 0

where T refers to the passive joint torque, k and l are constants, α is the joint angle,
and α0 is the joint angle threshold; joint angles below this value are slack and do not
produce much passive resistance. On the other hand, the antagonist muscle, such as
2 Biomechanics of Skeletal Muscle and Tendon 43

the triceps brachialis when performing elbow flexion, will not contribute much
resistance to the deformation during joint motion. Although the antagonist muscle
does not activate, a little tension exerted by the muscle tone still contains energy for
elastic deformation, which stores some space for structural extensibility without
generating too much resistance to deformation.

1.2.2 Viscoelastic Behavior

Passive muscles are viscoelastic material that exhibit both viscous and elastic char-
acteristics when subjected to tensile and compressive deformation [31].
Viscoelasticity is the stress and strain experienced in the passive muscle dependent
on the rate of loading; hence, the timing of the force application affects the strain
response of the passive muscle. The viscoelasticity displayed during tensile loading
is contributed by the passive properties of the protein titin [32, 33]. Lengthening
velocity affects the passive properties of muscle fibers significantly [34]. As length-
ening rate increases, the peak transient stress within the muscle fiber also increases,
even at very slow velocities. In passive muscles, a high rate of stretch results in a
higher stiffness than a slow stretch. This is one of the reasons that slow stretching
exercises are capable of minimizing the increase in force in the muscle–tendon unit
for a given amount of stretch.
There are other important properties of viscoelastic materials, including creep,
stress relaxation, and hysteresis. Hysteresis is the phenomenon that a stretched pas-
sive muscle returns to its pre-stretched length. It is found when length–tension char-
acteristics of passive muscle differ during loading (imposition of an external force)
and unloading response [35]. The hysteresis area between the loading and unload-
ing represents the amount of mechanical energy loss (dissipated to heat) in the
recovery from that stretch.
The more mechanical energy dissipated, the more obvious the hysteresis phe-
nomenon. In general, the relation between hysteresis and muscle stretch speed (or
rhythmic deformation frequency) can be presented as:

E = kω n

where E is the dissipated mechanical energy (the hysteresis area), ω is the oscilla-
tion frequency, and k and n are empirical constants. If n = 1, the dissipated energy is
proportional to velocity, and when n = 0, the dissipated energy is velocity indepen-
dent. In the latter case, the resistance acts like friction and is the same at any veloc-
ity. In human joints, the exponent n is typically close to zero. Therefore, muscle
hysteresis is relatively independent of oscillation frequency compared to “classic”
viscoelastic bodies, such as rubber. This indicates that the amount of mechanical
energy converted to heat is relatively independent of the rate of muscle length
change. Recent study has examined the effects of aging and gender on muscular
viscoelastic characteristics in athletes [36]. Increased tone and muscular stiffness
are found associated with aging, which can potentially lead to increased risk of falls,
44 Y.-H. Chao and J.-S. Sun

injuries, general muscle performance deficits, and a consequent limitation of the

ability to perform daily activities.
When a constant load is applied for a sufficiently long period, the muscle exhib-
its creep (lengthening relaxation) [37]. Rapid elongation occurs initially followed
by a slower increase in deformation. Stress relaxation is the declination of resis-
tance (the tension recorded at the muscle end) over time when a constant deforma-
tion is applied [38]. For example, holding a static stretch at a specific joint position
results in a gradual decrease in tension in the muscle from stress relaxation. Creep
and stress relaxation have important implications for stretching and risk of injury in
repetitive tasks.
Muscles also possess thixotropic, or sticky friction, properties which is distinct
from muscle’s elastic and viscous properties and which is contraction history depen-
dent [39]. Thixotropy appears as semisolid fluids under resting conditions but tem-
porarily becomes more fluid when it is shaken or stirred to decrease its viscosity.
Thixotropy is a consequence of long-term stable cross-bridges between the myofila-
ments of both extrafusal and intrafusal muscle fibers. Synovial fluid (found in
human joints) contains thixotropic property as well. Under some conditions, the
proprioception, including the senses of limb position, limb movement and muscle
force are subjected to the influence of thixotropy as evidenced [40]. The influence
of muscle and joint thixotropy in our daily life may appear in morning stiffness,
especially in seniors and in patients with rheumatoid arthritis. Several movements
are required when waking up in the morning, to make joints more flexible.
Thixotropy increases as muscle fatigues. Moreover, a recent study showed that a
movement-dependent change in passive ankle stiffness is caused by thixotropic
properties of the calf muscle, which may increase the levels of ankle sway [41].
Shear modulus is used to calculate the tissue modules. The shear modulus’s
equation is presented as:

µ = ρν 2 λ 2

where μ is the shear modulus, ρ is the density of the tissue, v is frequency of the
vibration, λ is the local wavelength.
Elastography is a newly developed image-based technique for measuring passive
mechanical properties of skeletal muscles. Using MRI or ultrasound, stiffness and
elastic properties are determined based on one of the following two principles: (1)
For a given stress (force), stiffer tissue strains (deforms) less. (2) Mechanical waves
(specifically shear waves) travel (wave propagation) faster through stiffer tissue. In
vivo methods for measuring muscle mechanical properties are developing. There
are inverse finite analysis (FEA) for determining muscle mechanical properties in
human [42] and 3-in-1 Whole Animal Muscle System (Aurora Scientific) for mea-
suring in vivo, in situ, and in vitro muscle function. However, there are still some
uncertainties and limitations to these methods such that further studies are needed.
Understanding the normal mechanical properties of muscle is beneficial to differen-
tiate the abnormal pattern and figure out the problems. This must be especially
2 Biomechanics of Skeletal Muscle and Tendon 45

considered in long-term therapy to provide the appropriate stimulus for normal

muscle mechanical properties.

1.3 Active Muscles

1.3.1 Muscle Force Production

The relationship between muscle force production and movement speed has been
described by Hill [43]. As pushing and lifting speed varies with the mass of the
object under fixed amount of force. Equation established by Hill simulates the ther-
mic generation during muscle contraction. This formation is: (v + b)
(F + a) = b(F0 + a), where F means the tension in the muscle, v means the velocity
of the contraction of the muscle, a is the Hill’s coefficient which correlated with the
heat generated during muscle shortening, and F0 means the tension of the muscle
when the contraction velocity is zero (isometric contraction).
In this model, where a and b are constant, the tension of the muscle and the
velocity of the contraction are inversely proportional. In fast contraction, the tension
generated by the muscle would be less than that in slow contraction under the same
environmental setting. While in vivo, the environment varies and influenced by
many factors. So, Hill-type model has been widely studied and modified into differ-
ent models implicated in different situations for more accurate simulation through-
out the years; however, the accuracy of the model in vivo remains unknown [44].
Biewener and his colleagues demonstrated a two-element Hill-type model in goats’
gastrocnemius muscles with EMG and found this model more accurate at predicting
muscle forces [44]. Further research to investigate more accurate models to simulate
the muscle force–velocity relationship within different situations is required since it
is multifactorial.
Features of muscle force–velocity in different types of muscle contractions are
distinguished. In concentric contraction, the maximal force production decreases as
the muscle contraction velocity increases. In isometric contraction, the length of the
muscle stays unchanged. Therefore, the velocity of muscle contraction is zero. The
eccentric contraction means the length change of the muscle is positive during mus-
cle contraction. The amount of force production increases while the contraction
velocity increases, which is converse to the situation in concentric contraction. The
maximum force generated by the eccentric contraction is about 1.5 times the value
of isometric contraction, and the plateau speed is also higher on isolated frog mus-
cles [45]. However, the experiment showed that the phenomenon did not have the
same effect on voluntary eccentric contraction on human body. In addition, EMG
activation did not change much while the eccentric velocity changes; it is even
lower than concentric contraction. Westling and his colleagues thought that might
be due to a protective neural inhibitory mechanism from too much tension on the
muscle [46]. Voukelatos et al. used electrical stimulation to train quadriceps mus-
cles for 3 weeks and found the overall torque output in eccentric contraction
46 Y.-H. Chao and J.-S. Sun

increases [47]. The results might indicate that the protective mechanism is change-
able. However, the enhancement of the peak value of voluntary eccentric contrac-
tion did not correlate with the increasing of angular velocity, which, to some extent,
might be due to the protective mechanism, though the mechanism remained unclear.
Typically, Hill-type model contains three elements: a contractile element with
force-length and force–velocity relations, a serial and a parallel elastic element. For
simulating the proper biomechanics in eccentric contraction, based on Hill-type
model, Haeufle et al. established a four-element model composed of a contractile
element, a parallel elastic element, a series elastic element, and a serial damping
element. This model considered serial damping and eccentric force–velocity rela-
tion. Thus, it is thought to be more suitable for simulating eccentric contraction in
human movements [48].
The decreasing of isometric force, maximum velocity of muscle shortening, and
an increase curvature of the force–velocity relationship are three main factors con-
tributing to the power loss in mammalian muscles after fatigue. The underlying
mechanism of muscle physiologic change needs further exploration. Jones [49]
reviewed recent articles and found there were two main discussion aspects: First,
the relationship between excitation-contraction coupling and force, and the other is
the slowing of contractile properties [50]. The contraction velocity was found slow-
ing down when muscle was fatigued comparing to the same force output generated
by non-fatigue muscle. On the other hand, under the same amount of velocity, the
force output was also decreased [51].

1.3.2 Muscle Size and Force Production

Normal muscle contraction, no matter the length or types of muscle contraction,

undergoes respective mechanisms. Multiple factors, such as physical property, neural
activation, motor control, environment, and even psychology, affect force produc-
tion. However, the muscle strength is directly associated with muscle size (physical
property) in general. Skeletal muscle changes in size and in ways including weight,
circumference, and length during muscle growth. Two major sources of muscle
weight increment are water and protein content. Human fetal muscle contains about
90% water. It decreased to about 78.5% by 4–7 months of age before attaining about
76% in the adult. There are major changes in the protein content of muscle during
muscle growth [52]. The more portion of fibrillar protein in skeletal muscle is, the
greater the muscle strength can be produced during muscle contraction.
Muscle strength is also proposed to be closely related to changes in fiber cross-­
sectional area, especially the maximal strength. Tonson et al. found that maximal
isometric strength exerted by the forearm muscles in human is proportional to their
size whatever the age [53]. Muscle fiber circumference can increase with newly
synthesized myofibrils located near or at the surface of the fibers through use, a
phenomenon called hypertrophy. Overall, increase in muscle strength are accompa-
nied by more fiber cross-sectional area in muscle although Krivickas et al. ­mentioned
that force is proportional to fiber diameter, rather than to cross-sectional area [54].
2 Biomechanics of Skeletal Muscle and Tendon 47

Muscle fascicle length is the other way of measuring muscle force. Arnold et al.
stated that the length and velocity of muscle fibers can have a large effect on muscle
force generation [55]. As muscle fibers increase in length, the number of sarcomeres
added to the ends of the myofiber increases. With longer muscle fascicle length,
more sarcomeres with cross-bridges produce more force.
Besides muscle growth with age, the influence of exercise on muscle plays an
important role between muscle size and muscle strength. In general, immobilization
can reduce muscle size and mass within 1–2 weeks. Kawakami et al. found that
subjects who performed isometric and bilateral leg extension exercise every day
after bed ridden for 20 days suffered less decrease in muscle strength and fiber
cross-sectional area [56]. The fiber cross-sectional area decreased in control group
by −7.8% while in exercise group it showed a lower tendency of −3.8% decrement.
This implies that exercise can reduce muscle atrophy and influence muscle size.
For more accurate evaluation of the change in muscle circumference (muscle
size), fiber cross-sectional area is usually employed. It can be measured using
anthropometric measurements or magnetic resonance imaging (MRI), with the lat-
ter being more accurate [53]. Therefore, MRI becomes the major tool for measuring
the fiber cross-sectional area.

1.3.3 Force Production and Muscle’s Moment Arm

Body movements depend on the contraction of muscles and the consequent motion
of the bone moving through the joint. When muscle contracts, the force produced
acts on muscle attachment (usually attached to bone). After receiving the force, the
bone starts moving around the joint. The relation between moment arm and force
can be simplified in the equation: T = F × R (Fig. 2.1), where T means the torque, F
means the force (N), R means movement arm, the perpendicular distance from the
pivot (rotation center) to the line of force F.

T = F×R

When it comes to body (a three-dimensional structure) movement, the force

becomes force vector and movement arm becomes movement arm vector to define
muscle movement model of moment of force vector. In the human muscle contrac-
tion model (3D model), moment of force vector (Mt) is obtained as a cross product

Fig. 2.1 Definition of

torque (T)
48 Y.-H. Chao and J.-S. Sun

of force vector (F) and the position vector (r), which is from pivot to any point along
the line of F.

Mt = F × r

Force vector (F) could be divided into magnitude force (f) and unit force
vector (u).

F = fu

Mt = fu × r = f ( u × r )

Moment arm vector (d) comes from the cross of unit force vector (u) and posi-
tion vector (r). In this equation, moment arm vector (d), also called normalized
moment vector, means moment of force vector per unit scalar of force acts on the
bone. The direction of moment arm vector (d) can be defined by right-hand rule.
When circling the right hand second to fourth finger from the direction of position
vector (r) to the direction of unit force vector (u), the direction of the right-hand
thumb is the same as the direction of vector d.
In the muscle movement model, the magnitude of moment arm vector (d) was
equal to the perpendicular distance from the pivot (joint center) to the line of force.
However, when the force line was not perpendicular to the position vector (r), the
magnitude of moment arm vector (d) is equal to r sin θ, θ means the angle between
vectors r and u (when the force line is perpendicular to r, θ is 90° and sinθ = 1). In
the below picture, vector r and u are on the same plate o. d is moment arm vector.
As the cross production of r × u, moment arm vector d is perpendicular to the r and
u simultaneously. The direction of d is counterclockwise which can be defined by
right-hand rule (Fig. 2.2).

Mt = fd
d = (r × u )
d = r sin θ

When it comes to human movement, XYZ 3D system can be used to analyze the
muscle and joint action. Below is an elbow flexion example. Take elbow joint as a

Fig. 2.2 Definition of

moment arm vector (d)
2 Biomechanics of Skeletal Muscle and Tendon 49

Fig. 2.3 Analysis of the

muscle and joint action
during human movement

center of 3D model, the movement arc produced by brachialis on humerus and ulna
bone is then defined. rA and rB are the position vectors of the brachialis origin and
insertion. F is the contraction force line and direction of the brachialis. u is the unit
force vector of F. d is the moment arm vector of the brachialis on elbow joint. d is
the magnitude of moment arm vector and it is equal to the length of the shortest
distance from center (elbow joint) to the brachialis (Fig. 2.3).
u can be calculated by brachialis position vector (rA − rB) and the length of
brachialis (|rA − rB|).
--- ---
- rA − rB
u = --- ---
rA − rB

In the movement of elbow contraction, humerus bone and body is considered to

be immobilized. The real moving bone is ulna bone. Thus, moment arm of action is
rB. Moment arm vector d is the cross product of rB and u. Its direction can be
defined by right-hand rule through u and r. The moment of force vector of brachia-
lis on elbow joint can be calculated by Mt = fd.
In this 3D model, moment arm vector is continuously changing in the whole
movement. When the brachialis keeps shortening, the angle between ulna and hum-
mer bone becomes smaller, and the direction of the force vector F keep changing at
the same time. Since we assume the force of muscle does not change in the whole
movement, the length of muscle, moving traction of the bone, and the angle of the
joint will influence the moment arm instantly.
The length of movement arm depends on the muscle attachment of the bone. The
shorter movement arm is, the faster the joint movement than the longer movement
arm muscle may produce under the same speed. Shorter movement arm may have a
shorter angular excursion. When the joint comes to the rotation angle of θ, the mov-
ing distance of shorter movement arm is shorter than the longer movement arm one
(when circling around the same angle θ, long radius circle has a longer arc length).
The muscle with shorter movement arm can induce larger angular excursions than
50 Y.-H. Chao and J.-S. Sun

Fig. 2.4 Determination of

the length of movement
arm during human
movement

the muscle with longer movement arm at the same shortened length of muscle con-
traction (Fig. 2.4).
In the figure, θ1 is the angle produced by the contraction of muscle 1. When the
muscle is relaxed, the bone is lying on the X-axis (X = 0). The blue line is the bone
situation when muscle 1 shortens (half of initial length). The yellow line is the bone
situation when the muscle 2 shortens (half of initial length), which has a longer
movement arm. Under the same shortening ratio (half of initial length in figure), θ1
is larger than θ2. Thus, if muscle 1 and muscle 2 have similar shortening speed,
muscle 1 can induce more angular excursions than muscle 2.
However, the interaction between the muscle force and the movement arm length
should be considered when discussing muscle function on joint movement in real
life. The force produced by muscle relies on the type and the number of muscle
fiber. In general, the muscle with more muscle fiber can produce larger force with
contraction. Muscle types can be morphologically divided into parallel and pennate
types. Parallel type muscle has liner muscle fiber. Parallel type has two subgroups,
fusiform and strap type. Because the parallel type muscle is composed of long
fibers, they can shorten more than the pennate muscle. More shortened length is
able to induce larger angular excursion. However, the pennate type muscle is easy
to induce large force in contraction. The movement arm could be confirmed with
anatomical analyzation or the calculation of movement arm vector.
The method of measuring movement arm can be simply divided into geometric
models and functional model. In early studies, geometric model was employed
using cadaver and anatomical approach that may not apply to the living models and
their complex movements. With technological advancement, high performance
computer, and precise imaging system (X-ray, MRI), the measurement of move-
ment arm improved. Thus, 3D geometric models and imaging geometric models
2 Biomechanics of Skeletal Muscle and Tendon 51

occurred. Researchers can observe muscle movement in the living situation, and
calculation through the computer software can be done. In functional model, the
actual movement arm is not important. The effective moment arm could be defined
through calculation of the equation. The effective moment arm could be defined
through calculation from the equation, Moment of Force = Force × Moment Arm.
Functional model applies when the joint type, muscle structure, muscle length, joint
angle are too complex to measure by geometric model.
The muscle moment arm vector is important in studying biomechanics and kine-
siology. Combining the muscle force, contraction speed joint angle, and muscle
moment arm human body movement can be analyzed precisely and in detail.
Advance theory of biomechanics and kinesiology could be thus derived.

1.3.4 Force Production and Level of Recruitment of Motor Units

Motor unit is considered the functional unit of the neuromuscular system which
work together to coordinate the contractions of a single muscle. A motor unit con-
sists of a motor neuron and the skeletal muscle fibers innervated by that motor
neuron’s axonal terminals [57]. A group of motor units within a muscle is called
motor pool. In human, there are no direct measures of the number of motor neurons
innervating any muscle [58]. It can be counted by anatomical [59] or electrophysi-
ological [60] method, but with some error. The number of muscle fibers within a
single motor unit varies both within a particular muscle and from muscle to muscle
as well. Muscles that act on the larger body masses usually contain more muscle
fibers and hence more motor units [57]. For example, triceps brachii muscle has
more muscle fibers in each motor unit than brachioradialis muscle.
Muscle produces force by regulating recruitment of motor units and by modulat-
ing the firing rates of recruited motor units [61]. Force production is controlled by
three neuromuscular mechanisms: the number and type of recruited motor unit and
their firing rate [62]. Increasing speed, force, or duration of movement involves
progressive recruitment of motor units with larger size and higher activation thresh-
olds. In 1965, Henneman et al. proposed a size principle of motor units recruitment
[63]. Neurons within the central nervous system vary widely in size. The larger cell
has larger surface area, and it should have some correlation with function. Finally,
they found the motor units were recruited from the smallest to the largest based on
the size of the load. As a result, the order is from slow twitch, low-force, fatigue-­
resistant muscle fibers to fast twitch, high-force, and less fatigue-resistant muscle
fibers. The size principle is discussed in relation to the organization of the motor
neuron pools. “Fractionation,” “discharge zone,” “subliminal fringe,” “facilitation,”
and “occlusion” are redefined abbreviated terms of the sizes and excitabilities of the
cells in a pool. Cell size is assumed to be the determinant of the overall frequency
of discharge or usage of a motor neuron [63].
The relation between the recruitment and firing rate of motor units is organized
in an inverse hierarchical structure—the onion skin scheme [61]. Hence, the firing
rates of earlier-recruited motor units have a greater value than those of the
52 Y.-H. Chao and J.-S. Sun

l­ater-­recruited motor units at any time and force during an isometric muscle con-
traction [64–66]. Also, the same pool of all the motor units of a muscle receives a
common excited signal, known as common drive [64], and modulates their firing
rate in unison. The later-recruited, higher-threshold motor units have shorter-dura-
tion, higher-­amplitude force twitches compared with the earlier-recruited, lower-
threshold motor units. The higher threshold motor units were driven by lower firing
rate because of the nature of fatigue. It seems that the neuromuscular system is
designed to optimize some combination of force and duration over which the force
is sustained. The firing rate has a large range from very low frequencies to produce
a series of single twitch contractions to high frequencies to produce a fused tetanic
contraction. In general, there will be a 2 to 4-fold change in force. The firing rate of
each individual motor unit increases with increased muscular effort until a maxi-
mum rate is reached [67].
As each individual level of analysis of the neuromuscular system structure has a
unique frequency, there are also robust relations in the frequency domain between
different levels [68]. Elble and Randall found a strong coherence between force
output and EMG at 8–12 Hz, and they also found coherence at a similar frequency
between single motor units and EMG [69]. Farmer et al. have found coherence
between motor units in 1–12 and 16–32 Hz bandwidths during volitional force
­output [70].

1.3.5 Force Production and Fiber Type

Skeletal muscles are categorized into: (1) slow oxidative fibers, (2) fast oxidative–
glycolytic fibers, and (3) fast glycolytic fibers, in terms of energy utilization. They
can also be classified as type I fibers, type IIA fibers, and type IIB fibers, respec-
tively. Most skeletal muscles contain a mixture of all three fiber types. Their propor-
tions vary with the typical action of the muscle. Each type of muscle fiber harbors a
unique feature. Slow oxidative fibers are the smallest in diameter and the least pow-
erful type of muscle fibers. Fast oxidative–glycolytic fibers are intermediate in
diameter between the other two types of fibers. Fast glycolytic fibers are the largest
in diameter and produce most power. Other characteristics include myoglobin con-
tent, color, contraction velocity, method for generating ATP, fatigue resistance,
order of recruitment, and primary functions [71].
The above classification classifies muscle fiber types as being fast or slow based
on the speed of shortening and utilization of aerobic/anaerobic cellular respiration.
Muscle fibers can also be typed using two other different methods: (1) histochemi-
cal staining for myosin ATPase and (2) myosin heavy chain isoform identification
[72]. Classification for myosin ATPase staining, which based on staining intensities
and differences in pH sensitivity, leads to 7 muscle fiber types. According to the
speed of muscle contraction (from the slowest to the fastest): types I, IC, IIC, IIAC,
IIA, IIAB, and IIB. Difference of myosin heavy chain isoform in muscle is also used
to distinguish different muscle type. Although the human genome contains at least
10 genes for myosin heavy chains, only three are expressed in adult human limb
2 Biomechanics of Skeletal Muscle and Tendon 53

muscles [73]. MHC I, MHC IIA, and MHC IIB correspond to the isoforms identi-
fied by the speed of muscle shortening as types I, IIA, and IIB, respectively.
Skeletal muscle can be typed into different categories in different ways. However,
skeletal muscle not only changes in size in response to demands, but also converts
from one type to another (muscle fiber plasticity). Fiber conversions between type
IIB and type IIA are the most common, but type I to type II conversions are possible
in pathologic conditions. Aging can also influence the conversion between the pro-
portion of muscle fiber type. Older muscle was found to have a greater percentage
of fibers that co-express MHC I and MHC IIA (28.5%) compared with younger
muscle (5–10%) [74]. Exercise, the common prescription in physical therapy, is the
other way to change the proportion of muscle fiber type.

2 Tendon

2.1 Structure and Composition

Tendon is a highly dense connective tissue, composed of a range of multiple hierar-

chical components, which connect and transmit force from muscle to bone. The
minimum unit of tendon is called tropocollagen molecules, which are then cross-­
linked into collagen molecules. Collagen molecules aggregate into microfibrils and
lead to the formation of collagen fibrils. Coupling with multiple collagen fibrils,
collagen fiber, the basic unit of a tendon, is formed. Each collagen fiber is sur-
rounded by a connective tissue compartment named the endotenon, sometimes
referred to as the interfascicular matrix (IFM). The well-established function of
endotenon is to allow collagen fiber to glide with each other and to provide a canal
with the supplement of vessels, nerves, and lymphatics into the deeper portion of
tendon [75]. Then, the collagen fibers packed together to form primary fiber bun-
dles, also termed subfascicles. Fascicles, secondary fiber bundles, are visible groups
of collagen fibers with a wide variety of shapes and diameters, ranges from 150 to
500 μm [76]. Above this layer, groups of fascicles constitute the whole tendon, that
is, the tertiary bundle, with a diameter of 1000–3000 μm surrounded by the epitenon
[75]. These highly aligned collagen bundles arrange in a longitudinal axis parallel
to the direction of mechanical stretch and allow tendon to withstand high tensile
strength.

2.1.1 Cell Population within Tendon

Tendon cells, also named tenocytes, are the foremost fibroblast-like cells reside
between either the intrafascicles or the interfascicles. With a highly developed endo-
plasmic reticulum, tenocytes are responsible to sense and respond to the changes of
the microenvironment, including synthesis and degradation of the extracellular
matrix (ECM) [77]. Although tendon cells seem to have a similar morphology, the
54 Y.-H. Chao and J.-S. Sun

diversity of tenocytes is classified into several types according to their location and
cell morphology. The first type is the “chondrocytic” type. The chondrocytic type
presents in the entheses, where tendon attaches to bone. This type of tenocyte is
characterized with round nuclei with the ability to produce chondrocyte-like matrix,
such as type II collagen and aggrecan [78, 79]. The second type is the “external”
type. The external-type tenocytes are more similar to the synovial cells; they reside
in epitenon and interfascicles of endotenon and paratenon. Thus, they can provide
adequate lubrication to facilitate the gliding of collagen bundles [80]. Another type
is the “internal” type. The internal-type tendon cells can be found between the col-
lagen fibers; they have fusiform morphology and a spindle-shaped nucleus that are
responsible for producing the collagenous and non-collagenous ECM [80, 81]. Till
now, the role of different cell populations on tendon healing is still in debate. After
laceration of the flexor profundus tendons from adult monkeys, tenocytes from the
epitenon first migrated and proliferated to the wound site at day 4 while the response
of cells from the endotenon was postponed to day 9. Both cells demonstrated the
ability to synthesize type I procollagen [82]. Gelberman et al. revealed the epitenon
fibroblasts migrated to the injured spot and removed the cellular debris and collagen
fragments through phagocytosis while the collagen anabolism occurred within the
endotenon cell layer [83]. Recently, Cadby et al. indicated that both cells from peri-
tenon and endotenon had multi-differentiated potency; the peritenon-derived cells
migrated and proliferated more quickly with increased expression of alpha-smooth
muscle actin (α-SMA), a specific gene marker of myofibroblast [84]. From the
above information, tendon is consisted of multiple fibroblasts with different mor-
phologies and biochemical characteristics, and it has the ability of intrinsic healing.
In this decade, tendon stem/progenitor cells (TSPCs) were first named and iso-
lated from human and mouse tendons. These cells account for only 3–4% of total
cells and possess divergent characteristics compared with tendon cells. TSPCs har-
bor several criteria of stem cells, including clonogenicity, multipotency, and self-­
renewal. Besides differentiating into tenocytes, TSPCs have the differentiating
potential toward osteogenesis, adipogenesis, and chondrogenesis. Consequently,
TSPCs are also named tendon-derived mesenchymal stem cells [85]. Similar to ten-
don cells, TSPCs can be classified into several types depending on the designated
niches. In the study of Mienaltowski, tendon stem cells were isolated from the
Achilles tendon and the surrounding peritenon (paratenon and epitenon) of C57Bl/6
mice. Interestingly, stem cells from tendon portion had higher colony forming units
and a higher expression of tendon-related gene markers, such as tenomodulin
(Tnmd) and scleraxis (Scx). Stem cells from peritenon displayed a higher level of
endomucin (Emcn), a vascular endothelial marker, as well as Cd133 and Musashi-1
(Msi1), pericyte stem cell markers. These findings indicated that tendon tissue con-
tains separate progenitor pools with distinct features. Thus, different kinds of TSPCs
may play distinct role in tendon healing. For example, intrinsic healing is related to
the expression of tendon-related gene markers while extrinsic repairing is achieved
through recruiting the perivascular cells from peritenon [86]. Although the applica-
tion of TSPCs into the research of tendon regeneration has drawn much interest, the
use of TSPCSs still has several dilemmas. Due to their scarcity and the tendency to
2 Biomechanics of Skeletal Muscle and Tendon 55

lose their phenotype and function with passaging, several factors have been found
to maintain their stemness [87]. For instance, matrix composition, substrate confor-
mation, growth factor and cytokine supplement, mechanical loading as well as oxy-
gen tension may affect their differentiated trend [88]. Thus, more studies are needed
for further investigation of TSPCs in tendon pathology and tissue engineering.

2.1.2 Extracellular Matrix

In human body, collagen is the most plentiful protein with 25 subtypes. Among
them, fibrillar types I, III, V, and XI collagen are essential for providing the connec-
tive tissue with its original stiffness and strength [76, 89]. In tendon, collagen com-
poses 60–85% of tendon dry weight and type I collagen accounts for 95% of total
collagen [90]. Besides type I collagen, there is little and varied amount of other
collagens, including type III, V, VI, XI, XII, and XIV [76]. Type I collagen is a triple
helix structure which comprises two α1 chains and one α2 chain. Thus, it is encoded
by two genes: Col1a1 and Col1a2. During collagen synthesis, procollagen is trans-
lated and folded into triple helix in the rough endoplasmic reticulum and then trans-
ported to the Golgi apparatus. Next, procollagen is modified into bundles and
packed into secretory vacuoles and then secreted to the extracellular matrix [91].
Type III collagen accounts for the remaining 5% of total collagen. Pertaining to
the fibrillar type collagen, the structure of type III collagen is similar to type I col-
lagen, wherein the difference is that type III collagen is composed by homotrimeric
molecules; type I collagen consists of heterotrimeric units. Coinciding with type I
collagen, Type III collagen is well known for its regulatory role in type I collagen
fibrogenesis. The interaction between type I and III collagen modulates the diameter
of collagen fibrils. Through tendon maturation, type III collagen assembles and
gathers into the endotenon or tendon sheath [91]. Increased type III collagen was
observed during tendon regeneration [92, 93].
Proteoglycans are a category of glycoprotein consisting of a core protein to
which at least one glycosaminoglycan (GAG) chain is attached. PGs can be divided
into two classes. One is the small leucine-rich proteoglycans (SLRPs), such as deco-
rin (Dcn), biglycan (Bgn), fibromodulin (Fmod), and lumican. The other type is the
large PGs, including aggrecan and versican [94]. Decorin is the most plentiful PGs
in tendon, accounting for 80% of total PGs content. It is a horse-hoof like protein
constituted by three domains. An N-terminal region is attached by a single dermatan
or chondroitin sulfate side chain. A central region is composed of ten leucine-rich
repeats which harbor a binding site of other proteins, including type I, II, III, VI
collagen, and TGF-β, etc. A C-terminal region contains several cysteine residues
[94, 95]. The central portion binds to the collagen fibril with the GAG side chain
lying parallel or perpendicular to the axis of the collagen fibril. By doing so, the
GAG side chain can interact with the other side chain of another Dcn molecule
which binds to a collagen fibril nearby, connecting to adjacent collagen fibril with
an inter-fibrillar bridge [96]. This is the way that Dcn maintains the spatial arrange-
ment of collagen fibrils and regulates the diameter of collagen fibrils. Dcn−/− mice
56 Y.-H. Chao and J.-S. Sun

showed disability in the regulation of collagen fibril diameter with increasing pres-
ence of enormous fibrils. In the studies of Halper and Reed et al., the packing of
collagen fibrils was sabotaged, thus resulting in a decrease of tendon mechanical
properties. These findings suggested that Dcn regulated the diameter of collagen
fibrils through inhibiting abnormal lateral fusion of collagen fibrils [94, 95]. With
two chondroitin or dermatan sulfate side chains, biglycan shares a similar collagen
binding site with Dcn. Knockout of Bgn or Dcn leads to morphological defects of
collagen fibrils. However, the lack of Bgn losses its ability to suppress bone mor-
phogenetic protein-2 (BMP-2), resulting in ectopic tendon ossification [18, 94].
With keratin side chains, lumican and fibromodulin share the same binding site on
fibrillar collagen, different from the binding site of Dcn and Bgn [94, 96].
Glycoproteins are a variety of proteins which are covalently attached by carbo-
hydrate groups. The glycoproteins mainly found in tendon include tenomodulin
(Tnmd), tenascin-C (Tnc), collagen oligomeric matrix component (COMP), and
lubricin. As a potential candidate for tendon markers, tenomodulin is a type II trans-
membrane glycoprotein which highly presents in late developing and mature ten-
dons. Tnmd−/− mice demonstrated a decrease in tendon cell density. Also, a reduce
in cell proliferation was found without the presence of cell apoptosis. As a regulator
of collagen architecture and fibrogenesis, Tnmd−/− mice showed uneven fibrillar
surfaces and abnormally increased diameter of collagen fibrils [97]. Knockout of
Tnmd in TSPCs inhibited self-renew capacity, and tendon stem cells tended to cease
cell cycle inducing early cellular senescence [98].
As a hexameric extracellular matrix glycoprotein, tenascin-C (Tnc) is highly pre-
sented in the circumstances below. High concentration of Tnc was found during the
embryogenesis of the musculoskeletal system, containing tendon, skin, ligament,
muscle, articular cartilage, and bone [99, 100]. However, the Tnc−/− mice did not
express a particular phenotype and revealed an ordinary wound healing process in
skin and nerve tissues [101, 102]. Interestingly, upregulation of Tnc was discovered
in mechanosensitive tissues that transmit forces from muscle to bone, such as myo-
tendinous junction and osteotendinous junction [100, 103]. Therefore, the expres-
sion of Tnc is modulated by mechanical stimulus and has been postulated with the
increase of elasticity in the ECM [104].

2.2 Basic Mechanics

2.2.1 Elastic Behavior

Elasticity is the tendency of tissue to resist deformation with an applied force [105].
Tendon is made up of collagen fibrils with highly consistent alignment. The colla-
gen fibrils are the basic load-bearing units. Traditional material testing can be used
to test the elasticity of the tendon. By fixing an isolated tendon specimen to a mate-
rial testing machine, recording the loading of tensile stretch applied to the tendon
and the amount of tendon elongation under each load, the elasticity of the tendon
2 Biomechanics of Skeletal Muscle and Tendon 57

can be calculated. Stiffness is an extensive property of a matter, which is calculated

by dividing the tensile force by the amount of extension of the tendon. Elastic mod-
ulus, which is an intensive property of a matter, is the ratio of stress to strain. In
tendon, the stress is the ratio of the force to the cross-sectional area, and the strain
is the ratio of the change in length to the original length. When a tendon specimen
is stretched, the length–tension relationship is nearly linear only at the mid-tension
portion before tissue damage and failure. At the beginning, there is a toe-region
because of the crimp structure of the collagen fibrils. The waviness of the fibrils is
first straightened and then start to behave their elasticity [106].
Muscle–tendon unit should be viewed as a whole since tendon is connected to
the muscle and caused by muscle contractions in real life. Therefore, when it comes
to the elastic behavior of the tendon in vivo, the condition of the muscle is not
negligible.
One of the methods for measuring tendon elasticity in vivo is through measuring
the lengthening of the tendon or deep aponeurosis during maximal voluntary iso-
metric contraction (MVIC) [107]. Force acting on the tendon is calculable using the
moment arm length and torque data. Fitting the force and tendon elongation to a
linear regression equation, the slope of the equation is considered to be an index of
the tendon stiffness [107]. Another feasible method for measuring tendon elasticity
in vivo is strain elastography. In this, tendon tissue is manually compressed.
However, manual compression is not quantifiable; therefore, it provides only quali-
tative information (i.e., relative elasticity). Shear wave elastography produces shear
wave into the tissue through its excitation transducer [108]. The information about
shear wave propagation velocity can be collected by detectors and imaging trans-
ducers. Shear modulus can then be calculated by the following equation [109]:

µ = c2 ρ

where μ is the shear modulus, c is the shear wave propagation velocity, and ρ is the
density of the tissue. The density of all soft tissue can be assumed to be 1000 kg/m3.
Ultrasound and magnetic resonance imaging (MRI) are imaging modalities that
can also be used to detect shear waves [108]. When force is imposed on a stiffer
tendon, it will shorten rapidly and bear less load. A stiffer tendon will transmit more
of the imposed force to the muscle, while a more compliant tendon will be more
prone to involuntary oscillations. Tendon stiffness is influential by diet. In an animal
experiment, the rats fed on diets containing advanced glycation end products
(AGEs) for 88 days had stiffer tendons than those in the control group. Glycation
has effect on collagen cross-linking, and this may result in change in integrity and
elastic property of tendon tissue [110].
The slack of the muscle–tendon unit may influence the elastic behavior of tendon.
Fukutani et al. applied supramaximal electrical stimulation at the tibial nerves of eight
young healthy male volunteers [111]. The joint torque (plantar-flexion) was signifi-
cantly larger when the ankle joint was positioned in 20° of dorsiflexion than posi-
tioned in 20° of plantar-flexion. However, the magnitude of Achilles tendon elongation
measured by ultrasound was significantly smaller in the 20° dorsiflexed position.
58 Y.-H. Chao and J.-S. Sun

Assuming a 20° dorsiflexed position, the influence of the slack is zero and the tendon
elongation was resulted from muscle force only; at 20° plantar-flexed position, 20%
of the tendon elongation was resulted from muscle force, and 80% of tendon elonga-
tion could be caused by elimination of slack due to different positioning [111].
Konow et al. investigated the lateral gastrocnemius muscle–tendon interaction
during landing, and found that the muscle–tendon unit lengthened significantly dur-
ing the last one-third of landing with increased range of motion of the joints, while
the muscle fascicles behaved isometrically during the first two-thirds of landing
without any observable muscle–tendon unit lengthening [112]. This result indicates
that during the first two-thirds of landing, the tendon lengthened rapidly, storing the
energy through elongation, and it recoiled, releasing the energy and lengthened the
muscle fascicles during the last one-third of the landing. In such situations, tendon
plays a role in power attenuation, which may be a protective mechanism that reduces
the risk of muscle fascicle damage during rapid lengthening [112].
Farris et al. recruited young male participants to observe the muscle–tendon
interaction during walking with constant speed and walking with acceleration. The
amount of triceps surae muscle fascicles shortening was larger in early stance phase
during the accelerative walking than during the constant walking, and the amount of
fascicle shortening was not consistent to the muscle–tendon unit length change.
This indicates that the energy produced by the fascicle shortening was stored in the
tendon through elongation. In other words, the contractile work was stored in series
elastic elements in the form of elastic energy [113]. The tendon then released the
energy for the movement of the desired tasks. In the task of two-legged hopping,
both adults and children presented maximal tendon excursion and minimal muscle
excursion at their preferred self-selected hopping speed, which is in consistent with
the optimal energy-saving strategy in theory [114]. This experimental result implies
that elastic behavior of tendon plays an important role in movement efficiency.

2.2.2 Viscoelastic Behavior

Tendon is viscoelastic, meaning that their mechanical properties such as stiffness

are time-dependent. Viscoelastic materials exhibit phenomena such as creep and
stress-relaxation. Creep is strain increase (not large enough to cause any structural
damage) over time with constant application of stress. This phenomenon exhibits
most significantly early and reached plateau gradually during muscle contraction.
Stress-relaxation is a phenomenon presented as decreased stress over time with
constantly applied strain. Both creep and relaxation are properties presented as a
nondestructive change in tendon. If given sufficient time to recovery, and the load
and strain removed, the tendon will return to the initial condition. The viscoelastic
materials also demonstrate a variation between the loading and unloading curves,
which is called hysteresis, wherein energy absorbed during loading is greater than
dissipated during unloading [115].
An accurate measurement is crucial to understand the mechanical properties of
tendon. Recently, ultrasound-based testing is widely used, because it is a noninva-
2 Biomechanics of Skeletal Muscle and Tendon 59

sive method and applicable under physiological condition. In vivo experiment,

B-mode ultrasonography is mostly used to document tendon deformation during a
ramp isometric contraction, and tendon force is calculated simultaneously. The
load-deformation relationship is obtained in consequence. However, this measure-
ment uses manual tracking to analyze, and manual tracking is extreme depending on
the consistency of delineating in these patterns [116]. Shear wave elastography is
considered a more accurate method to detect local change in tendon since it detects
the velocity of transverse wave with established methodology [117].
O’Brien et al. reported that human patellar tendon with a 22-N peak load showed
a 42% drop after 15 min, and with a 66-N peak load, a 35% drop was showed [118].
In contrast, Graf et al. reported the primate patellar tendon with a 39.6 ± 5.1 N of
peak load and showed a 69.8% drop after 10 min [118]. Such differences may be
due to species variation. However, Shepherd et al. reported species variation is less
influential than functional requirement in determining fascicle fatigue behavior
[119]. Different types of tendon were differentiated based on their function: the
positional tendon (position joints and facilitate movement) and the energy-storing
tendon (store high stresses when stretched, e.g., loading). Positional tendon tends to
exhibit higher failure strength than energy-storing tendon. However, when fatigue
properties were taken into consideration, energy-storing tendon showed signifi-
cantly greater lifetimes under the same cyclic loading [119]. Furthermore, the strain
distributions are varied among tendons. One study showed that the insertional
regions of Achilles tendon are more capable of withstanding high strains than other
regions without failing [120]. However, Suydam et al. showed that the cross-­
sectional area of tendon is unrelated to either the shear or viscosity modulus [121].
The exact factors affecting tendon behavior remain unknown.
In cyclic stress relaxation test, after 300, 900, and 1800 cycles, human semiten-
dinosus showed stress decrease by 29.11%, 35.11%, and 38.5%, respectively, and
cyclic creep test showed significant damage particularly in 900–1200 cycles. During
cyclic creep, fiber bundles of the tendon are stretched out progressively, and the
progressive recruitment pattern would not occur under stress relaxation [119].
Cyclic loading is seen to be more close to the mechanism of tendon injury. When
tendon fibers responded to creep loading, isolated fiber kinks exhibited in low-level
fatigue. In the case of moderate-level fatigue similar changes occurred but in a
larger distribution. The situation of high-level fatigue showed severe matrix disrup-
tion [122]. Furthermore, Wren et al. found that tendon lifetime under cyclic loading
was related to the magnitude of stress and the amount of initial strain [120].
Low hysteresis is beneficial for tendon, because it makes high elastic energy
return and makes heat damage minimal [123]. Peltonen et al. reported hysteresis of
Achilles tendon to be on an average of 5 ± 2% between 10–80% of maximum vol-
untary contraction [123]. However, hysteresis would increase after cyclic load the
change may be caused by progressive extension of toe region and increasing cyclic
energy dissipation [120]. In addition, hysteresis of tendon depends on the physio-
logical capability of stress resistance in which high-stressed tendon (e.g., Achilles
and patella tendon) showed higher fatigue resistance over low-stressed tendon. This
is due to a functional requirement that these tendons are of different materials.
60 Y.-H. Chao and J.-S. Sun

Several factors alter tendon viscoelastic properties, such as strengthening and

stretching, and the physiological conditions like aging or preconditioning.
Plyometric training reduces hysteresis without significant alteration in the cross-­
sectional area of Achilles tendon. This implies that regular engagement in physical
activities could help to achieve or maintain a low hysteresis in Achilles tendon
[123]. Stretching can also reduce hysteresis and stiffness. The change depends pri-
marily on the duration rather than the number of stretches without alteration in
maximum voluntary contraction. The present results suggest that stretching could
decrease viscosity, but increase elasticity in tendon structure [115]. Stretching, in
consequence, is considered an effective way to improve reused energy during
exercise.
Preconditioning in the primate model is proved to reduce the acute tendon ten-
sion loss in the graft due to viscoelastic relaxation. Graf et al. showed that isometric
conditioning is as effective as cyclic stretching for preconditioning [118]. Bed rest
is another factor of increased hysteresis. Kubo et al. showed that 20 days bed rest
reduced stiffness and increased hysteresis of vastus lateralis tendon. However, these
changes were not found in plantar flexor [124]. Finally, research showed that age
did not have significant effect on viscoelastic properties of the patellar tendon. The
authors inferred that may be because patellar tendon is high loading dependent in
daily activities; therefore, it harbors the properties that are not easily weakened [125].

2.3 Mechano-responses of Tendon

2.3.1 Physiological Mechano-responses

Adequate mechanical loading is essential for the maintenance of tendon homeosta-

sis and enhancement of the biomechanical properties of tendon. For instance, uphill
running exercise for 12 weeks significantly increased the modulus and failure stress
per body weight in rat Achilles tendons [126]. In addition, swimming exercise for 8
weeks markedly increased the maximum tension, maximum force, and modulus of
the rat Achilles tendons [127]. Since increase in modulus represents smaller defor-
mation with a stationary mechanical stress in tendon; thus, a higher modulus indi-
cates a stiffer tendon as a material [128]. Moreover, tendon can alter its structure in
response to the mechanical loading to which it withstands. Treadmill exercise for 8
weeks increased the cross-sectional area (CSA) of collagen fibril of rat Achilles
tendon [129]. Treadmill exercise for 4 weeks can also enhance the alignment of col-
lagen fibril through the reorganization of the ECM into a close-packed condition
[130, 131].
While appropriate exercise leads to the enhancement of tendon mechanical prop-
erties, we may consider the increase in tendon biomechanics, which is essentially
related to the concentration and cross-links of collagen fiber. Curwin et al. showed
a 46% increase in collagen deposition and a 50% decrease in pyridinoline cross-­
links, following 8-week strenuous treadmill exercise in the Achilles tendons of
2 Biomechanics of Skeletal Muscle and Tendon 61

p­ remature roosters [132]. These findings indicated the turnover of collagen enhance-
ment but a decrease in quality after strenuous endurance exercise of collagen fiber.
A 12-week uphill running exercise increased the expression of type III collagen and
insulin-like growth factor I (IGF-I). Type III collagen forms thinner and disorga-
nized fiber. Increased type III collagen can be found in tendon lesion site [133, 134].
IGF-I is an effective stimulator of collagen anabolism and cell proliferation [135,
136]. These results indicate that exercise promotes metabolism of the ECM while
the following mechanical consequences still need to be defined.
Several models were employed to mimic the mechanical stimulus during the
locomotion of the body segment. In addition, tendons were loaded and unloaded,
causing changes in the influx and extrusion of the interstitial fluid, and the intersti-
tial fluid flow toward the organized extracellular matrix with low permeability
[137]. Thus, fluid shear stress was used to mimic the shear force the tendon with-
stood. Shear stress at 1666 μm/s, approximately 0.02–0.1 Pa, increased the intracel-
lular calcium concentration. Combining shear stress and uniaxial tension strain at
4% enhanced the percentage of tenocytes exhibiting transient calcium response
[137]. Shear stress at 0.41 Pa reduced the expression of Col I, Col III and several
profibrotic factors in rat palmar flexor tendon cells. Shear stress also downregulated
TGF-β2, TGF-β3 and TGF-β receptors, except for TGF-β1. Increase in the expres-
sion of vascular endothelial growth factor (VEGF) as well as MMPs, and decrease
in the expression of TIMPs, MMP inhibitors, were found under shear stress
­condition. These findings suggested shear stress had an antifibrotic effect and pro-
moted tendon catabolism [138].
Besides shear stress, tensile loading has been exerted to evaluate how tenocytes
regulated cell behaviors and homeostasis of the ECM in response to tensile strain.
Yang et al. investigated the effect of cyclic mechanical stretching on the prolifera-
tion and collagen mRNA expression and protein production of human patellar ten-
don fibroblasts under serum-free condition [139]. The role of TGF-β1 in collagen
production by cyclically stretched tendon fibroblasts was also investigated. The
results suggest that increase in the cellular production of collagen type I is at least
in part mediated by TGF-β1. Uniaxial cyclic strain at the parameter of 4%, 0.5 Hz
enhanced the expression of tendon-related genes in TSCs, such as Col1 and Tnmd,
while 8%, 0.5 Hz strain upregulated the expression of LPL, Sox-9, and Runx2,
which, respectively, represented a specific gene marker of adipocytes, chondro-
cytes, and osteocytes. The findings were in accordance with the in vivo treadmill
running model. Moderated treadmill running elevated the expression of tendon-­
related genes, including Col1 and Tnmd. The expression of IGF-1 was enhanced
and TSCs proliferation increased with moderate exercise as well. Additionally,
intensive exercise induced tendon anabolism through the expression of Col1 and
Tnmd with the concomitant increase of non-tendon-related genes [140, 141]. This
suggested that proper mechanical loading promoted the maintenance of tendon phe-
notype and facilitated TSCs differentiation into tendon lineage.
On the contrary, the following studies show different types of tendons and different
tendon tissue response under unloading or detraining. Kubo et al. found that the ten-
don structure and collagen content of Achilles tendon showed gradual improvement
62 Y.-H. Chao and J.-S. Sun

after 3 months of isometric training (15 repetitions of 80% MVC, 4 times/week).

After another subsequent 3 months of detraining, the tendon experienced rapid
decrease in tendon elongation and stiffness. With a significant detraining change
showed in MRI, but not the ultrasound echo-intensity, the authors deduced the effect
of detraining is more significant on tendon structure, but the tendon cell number may
preserve to an amount [142].
In recent studies, compressive loads are under investigations because the com-
pression effect on tendon grafts fixed to the bone via suture anchors is unneglect-
able. In an animal study, flexor digitorum tendons were harvested and subjected to
compressive loads. Results showed that, the tendon had geometric changes with a
volume decrease of up to 30%, mainly from extracellular water excretion. The ten-
don itself also experienced indirect elongation of 5–10% due to compressive force
[143]. This result offers the clinical implication of preloading the tendon as a prepa-
ration to avoid post-surgical failure of grafting tendon tissues.
Recently, tendon mechanobiological studies gain more and more attention. With
advanced technological conditions, scientists are able to investigate tenocyte reac-
tion under various modes of external forces. Be it tensile, compressive, shear load
or even unloading, tendon cells or extracellular matrix seems to have good response
on healing and proliferate under various external forces. Although under external
loading, tissue quality often has a better result, the biochemical strength seems to
show no difference among various circumstances. With heterogeneous results
shown in various conditions, it is crucial to continue study the dose of external loads
under specific conditions of tendon for further in-depth knowledge of tendon
mechanobiology.

2.3.2 Pathological Mechano-responses

It is well established that appropriate mechanical loads are beneficial to enhance the
mechanical properties of the tendon. However, excessive mechanical loads on ten-
dons may result in tendon injuries. Tendon injuries are classified into acute and
chronic injury. Lacerations and ruptures are two common acute injuries. As for the
chronic tendon injury, tendinopathy can be the representative [144].
Tendinopathy, which is usually termed tendinitis, tendinosis, and paratenonitis,
has been found to be a result of a failed healing response according to recent histo-
pathological studies [145]. It may cause degenerative changes with increased levels
of prostaglandin E2 (PGE2), deoxyribonucleic acid, and protein synthesis in vitro
within tendon [146, 147]. Every single microtrauma a tendon experienced may
accumulate over time and cause tendinopathy. Previous study has found that loading
on the tendon fibroblasts will increase PGE2 and leukotriene B4 expression. The
correlation of tendon breakdown and the enhanced activities of vascular endothelial
growth factor (VEGF) and matrix metalloproteinase (MMP) was evidenced in the
study of Schwartz [148]. When comparing the histological characteristics of tendi-
nopathy to those of the normal tendons, it shows an increased number of tenocytes
and concentration of glycosaminoglycans in the ground substance, and disorganiza-
2 Biomechanics of Skeletal Muscle and Tendon 63

tion and fragmentation of the collagen, and neovascularization [145]. Moreover, the
increased expression of type III collagen, fibronectin, tenascin C, aggrecan, and
biglycan are the molecular changes found in the patients with chronic Achilles ten-
dinopathy. These changes might be an adaptive response to changes in mechanical
loading [149].
Overloading might be the cause of tendinopathy. Human patella tendon fibro-
blasts underwent cyclic uniaxial stretching of strain conditions: 4%, 8%, 12% ran-
domly for 4 h and rested 4 h to observe the inflammatory response of mediators
PGE2 and LTB4. Results showed that, under higher stress loads (12%) PGE2 and
LTB4 levels were higher with significant difference. This may imply the possible
mechanism of overuse inflammatory tendinitis [150, 151]. In tendon cells, repeti-
tive, small-magnitude stretching, e.g., 4% strain at a frequency of 0.5 Hz, increased
Col I, TGF-β production and reduced inflammatory mediators through downregula-
tion of the expression of COX-2 and PGE2. Whereas large-magnitude stretching,
e.g., 8% strain at a frequency of 0.5 Hz, also increased Col I, TGF-β and MMP-1
production but had a pro-inflammatory effect [139, 152, 153]. The above studies
indicated change in tendon anabolism with excessive mechanical loading may have
a pathological inference on tendinopathy.
Insufficient mechanical loads, such as disuse or immobilization can also have some
effects on tendons [146]. Immobilization has been associated with decreased levels of
extracellular matrix protein expression, alterations in tenocyte m
­ orphology, and loss of
normal extracellular matrix architecture, resulting in impaired function and healing
capacity [154–158]. Deprived of stress, tendon tissues underwent dramatic changes in
tendon cell shape, cell number, and collagen fiber alignment, and eventually caused
tendon degeneration [155]. Stress deprivation-initiated metabolic alterations, such as
decrease in anabolic activities but increase in catabolic activities of the tendon matrix
are likely responsible for certain degenerative changes in tendons [159].
Non-physiological loading may induce tendinopathy as well, by altering TSPC
function and fate at both the proliferation and differentiation levels. Tendon stem/
progenitor cells (TSPCs) is responsible for preserving adequate tenocyte numbers
in the tissue throughout life and replenishing them after injury. Studies supported
that mechanical loading critically affects the fate of TSPCs. An in vitro study
showed that mechanical loading at physiological levels promoted TSPC prolifera-
tion and differentiation into tenocytes, while excessive levels of loading led TSPCs
to differentiate into non-tenocytes, such as adipocytes, chondrocytes, and osteo-
cytes, in addition to tenocytes [159]. An in vivo study using treadmill running fur-
ther found that tendons subjected to repetitive strenuous mechanical loading
produced high levels of PGE2, which was associated with decreased TSPC prolif-
eration and induced TSPCs to differentiate into adipocytes and osteocytes [160].
These studies suggest that non-physiological loading may induce tendinopathy by
altering TSPC function and fate at both the proliferation and differentiation levels.
Better understanding of these mechanisms may provide a new strategy for the pre-
vention and treatment of tendinopathy.
Aging accounts for tendinopathy as well which is termed “age-related tendi-
nopathy.” Morphologically, increased lipid deposition and ossification and PGE2
64 Y.-H. Chao and J.-S. Sun

accumulation are characterized in aging tendon [146]. Altered morphology of ten-

don fibroblasts from aging was observed [161]. Cell nuclei are flattened in tendon
cells and the shape of the tendon cell nuclei elongated significantly with age, espe-
cially at 3 and 12 months in rat [162]. Functional deficit in the biomechanical prop-
erties of tendons resulted from aging was reported by Ensey et al. In this study,
tendons from aging rats showed lower Young’s modulus and lower total strain than
younger ones and have higher tensile modulus [163]. Moreover, the exposure to
repetitive mechanical loading also had an effect on their biomechanical properties
[162]. However, one study found that the modulus was not significantly different
between 1 and 4–5 years old rabbits. Both normal and repaired tissues exhibited
non-linear stress–strain curves, which are typical of collagenous materials [164].
The results of the mechano-response of aging tendons are heterogenous which
require further elucidation.

2.3.3 Mechanotransduction

Tenocytes are mechanoresponsive through mechanotransduction mechanisms by

which tenocytes convert mechanical signals into a series of biological events such
as expression of numerous genes, including those responsible for extracellular
matrix. In vitro, the earliest responses to mechanical stimuli are recorded at the
proximities of the cell–ECM contacts; these include the opening of stretch-activated
ion channels, the phosphorylation of focal adhesion kinase (FAK), the activation of
small guanosine triphosphatases (GTPases), and generation of reactive oxygen spe-
cies [165]. Multiple intracellular signaling pathways are subsequently triggered
such as mitogen-activated protein kinases (MAPKs), protein kinase C, and NF-kB
[166–170]. As a result, an ECM component could be regulated at the gene transcrip-
tion level.
One candidate for mechanotransduction mechanisms are stretch-activated ion
channels (SACs), which are suggested to interact directly with cytoskeleton and
thus can sense the cell stretch [171]. Opening of SACs causes an increase in intra-
cellular Ca2+ concentration and other ions (e.g., sodium and potassium) to influx
followed by membrane depolarization. Tendon and ligament fibroblasts respond to
mechanical loads by increasing their intracellular Ca2+ levels. Ligament fibroblasts
subjected to mechanical stretch propagated Ca2+ wave better than cells that were not
subjected to mechanical stretch [172]. In human flexor digitorum profundus tendon
cells, transient increase in intracellular calcium level was found under fluid-induced
shear stimuli [173, 174]. While tensile stretch at 0.5 Hz, 4% for 10 cycles increased
the percentage of tendon cells with transient calcium response. When combining
fluid shear stress and cyclic mechanical stretch, greater calcium activity was gener-
ated compared to the single model application [137]. In human mesenchymal stem
cells, uniaxial mechanical stretch at 1 Hz, 8% for 6, 24, 48, and 72 h enhanced the
production of ECM proteins and expression of tendon-related gene markers, includ-
ing Scx, tenascin-C, tenomodulin, decorin, Col I, and Col III. However, these effects
were eliminated by inhibiting the SACs with gadolinium [175]. The above findings
2 Biomechanics of Skeletal Muscle and Tendon 65

suggested that tendon cell responded to tensile mechanical stimuli through increas-
ing the intracellular calcium level via the SACs. Taken together, these studies sug-
gest that calcium is an important mediator in cellular mechanotransduction.
MAPKs constitute key steps in many intracellular signaling pathways. They usu-
ally function as final effectors of signal transduction pathways directly to activate
transcription factors in the cytoplasm and nucleus. MAPKs are serine/threonine-­
specific protein kinases that respond to extracellular stimuli (mitogens) and regulate
various cellular activities such as gene expression, mitosis, differentiation, and cell
survival/apoptosis. MAPK is crucial for the conversion of mechanical load to tissue
adaptation inducing signaling from the cytosol to the nucleus. It is well described
that several cell types and subsets of MAPKs such as extracellular signal-regulated
kinase 1 and 2 (ERK1/2), MAPK-p38, and stress-activated protein kinases/c-jun
NH2-terminal kinase (SAPK/JNK) can be activated by mechanical stress, as well as
by lowered pH, growth factors, hormones, and reactive oxygen species [1]. ERK-­
mediated pathways are mostly involved in proliferation and differentiation and gen-
erally considered anti-apoptotic. JNK and p38-signaling pathways are activated by
stress stimuli, many of which induce apoptosis, but in some cellular systems they
have been implicated in proliferation and differentiation as well. Each is proved to
have major roles in the regulation of intracellular metabolism and gene expression
and integral actions in many areas including growth and development, disease,
apoptosis, and cellular responses to external stresses [176]. For example, cyclic
strain resulted in an immediate activation of JNK in patellar tendon fibroblasts
which was regulated by a magnitude-dependent response and appeared to be medi-
ated through a calcium-dependent mechanotransduction pathway [177]. Our recent
study demonstrated that mechanical stretch with 8% strain at 1 Hz rate improves
tenocyte characteristics via reversing the fibroblast-to-adipocyte phenotypic transi-
tion induced by high glucose through inhibition of Akt and activation of ERK [178].

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Chapter 3
Biomechanics of Ligaments

Jie Yao, Zizhan Lian, Bin Yang, and Yubo Fan

Abstract The ligaments are important tissues that connect the bones in the
human body. The main function is to transmit the tensile load by playing an
important role in maintaining the stability and restraint excessive joint motion
in musculoskeletal system. Their unique composition and structure let liga-
ments to guide joints to articulate smoothly and to protect other soft tissues in
and around the joints. These ligaments have biomechanical properties designed
for this important function. As such, understanding the biomechanical behavior
of ligaments is important. Also, these fundamental knowledges are helpful in
preventing ligament injury and improving the treatment method. In this chapter,
the ligament composition, structure, and function are introduced. Then the bio-
mechanical properties of the ligaments and the method to obtain them are
described by using the anterior cruciate ligament (ACL) of the knee as an exam-
ple. And finally, injury, as well as current surgical treatment and postoperative
rehabilitation, is reviewed.

J. Yao · Z. Lian
Key Laboratory for Biomechanics and Mechanobiology of Ministry of Education, School
of Biological Science and Medical Engineering, Beihang University, Beijing, China
Advanced Innovation Center for Biomedical Engineering, Beihang University, Beijing, China
B. Yang
Orthopedics Department, Peking University International Hospital, Beijing, China
Y. Fan (*)
Key Laboratory for Biomechanics and Mechanobiology of Ministry of Education, School
of Biological Science and Medical Engineering, Beihang University, Beijing, China
Advanced Innovation Center for Biomedical Engineering, Beihang University, Beijing, China
National Research Center for Rehabilitation Technical Aids, Beijing, China
e-mail: yubofan@buaa.edu.cn

© Springer Nature Singapore Pte Ltd. 2020 75

C.-K. Cheng, S. L-Y. Woo (eds.), Frontiers in Orthopaedic Biomechanics,
https://doi.org/10.1007/978-981-15-3159-0_3
76 J. Yao et al.

Keywords Ligaments · Anterior cruciate ligament · Tensile properties

Viscoelastic properties · Injury · Reconstruction

1 Ligament Composition, Structure, and Function

1.1 Composition

The ligament is a fibrous connective tissue that is mainly composed of fibroblasts. Its
extracellular matrix is rich in collagen, proteoglycans, and water, which determines the
biomechanical characteristics of the ligament. Water accounts for about 60–70% of the
mass of the cytoplasmic matrix. Collagen accounts for about 70–80% of its dry weight,
and is a most important component of bearing loading. In addition, other components
such as elastin and proteoglycan are also included in the cytoplasmic matrix [1, 2].
Collagen is the main component of the ligament extracellular matrix and is
mainly composed of type I collagen. In addition, type II, type III, type V, and type
XI collagen also account for a certain proportion. For example, Type II collagen
usually exists at the junction of the ligament and bone; the proportion of type III
collagen in the ligament gradually decreases as the embryo develops. A small
amount of type V and type XI collagen is often accompanied by type I, II, and III
collagen in fibrous cell surfaceome [3, 4].
The content of elastin varies among different types of ligaments, generally less
than 1% of dry weight. It can impart ligament elasticity and tensile strength together
with collagen. There is no continuous repetitive cycle throughout the peptide chain
in its amino acid sequence structure. But there are alternating hydrophobic and
hydrophilic segments [5]. Proteoglycans consist of small amounts of protein bound
to negatively charged polysaccharide chains referred to as GAGs. Proteoglycans
account for a small proportion of ligaments, about 0.5%. It can bind to water and
improve the stability and strength between ligament fibers. In addition, there are a
variety of other chemicals, including intracellular DNA, proteases, lipoproteins,
etc., which together maintain the survival of cells in the ligament.
The distribution of the biochemical components that make up the ligament is
nonuniform. For example, the collagen proportions of the four ligaments (anterior
cruciate ligament (ACL), posterior cruciate ligament (PCL), medial collateral liga-
ment (MCL), and lateral collateral ligament (LCL)) in knee joint are different, the
hydroxyproline densities are: 15.1 ± 0.4, 18.3 ± 0.3, 17.6 ± 0.4, 17.6 ± 0.4 mg/μm3.
On the same ligament, the collagen distribution is nonuniform. The collagen pro-
portion in the anterior sites of the above four ligaments is higher than the posterior
sites. Along the longitudinal axis of ACL and PCL, the collagen proportions at the
middle regions are greater than those at both ends near the bone [6]. Furthermore,
there are also capillaries in the ligament, which provide blood for the growth of the
ligament, as well as the repair after injury. Blood vessels growing in some ligaments
can also nourish surrounding bones and other soft tissues.
3 Biomechanics of Ligaments 77

1.2 Structure

Microscopically, the collagen of the ligament is a layered structure. The triple helix-­
shaped collagen molecules aggregate to form collagen fibers. Macroscopically, the
ligaments can be divided into visceral ligament and joint ligament. They are distrib-
uted in different locations, which makes their structure varying. The visceral liga-
ment is formed by a single layer or double layers of peritoneal folds. It is connected
to the visceral layer of the liver, kidneys, and other organs. The ends of the joint
ligament are attached to the surface of the bone or fused to the joint capsule. At the
ligament’s insertion site on the bone, the collagen fibers bind to the bone cells and
form the skeletal junction of the ligament. The middle part of the ligament is a dense
connective tissue composed of a large number of fiber bundles. The length and
thickness of the fiber bundles are nonuniformly and irregularly distributed. The fiber
bundles interact with each other, and each bundle of fibers is at an angle of 0–30° to
the longitudinal direction of the ligament.
Take the PCL as an example. 95% of the fiber bundles are aligned and distributed
consistent with the longitudinal axis of the ligament. The other 5% is arranged
obliquely from the proximal posterior end to distal medial, at an angle of 15–20° to
the longitudinal axis of the ligament. The fiber bundles in the middle part of the liga-
ment are tightly connected to each other, and looks like a twisted rope. The fiber
bundles near the femoral and tibial attachments are relatively loose and can be sepa-
rated. These fiber bundles are composed of elastin and collagen, which are inter-
twined to form the overall structure of PCL.

1.3 Function

Physiological functions of the ligament include transmitting loads and limiting

excessive movement. The ligaments are distributed in and around the joint cavity,
and between the body’s organs and the peritoneum. Due to the difference in ana-
tomical location and structure, the ligaments’ functions vary.
The joint ligament is connected to the bones. The joint tracking is mostly deter-
mined by the restraints of ligament and articular cartilages. The ligament can pre-
vent the joint from over-extension and over-flexion, and generally bears the load
within its elastic limit to ensure the joint is stable. Injury occurs when the ligament
is extended to its yield stress. The consequences of ligament injury include joint
instability, dislocation, and changes in the mechanical environment of the joint, and
will lead to subsequent joint tissue injury, arthritis, and other symptoms. In addition,
the visceral ligament fixes the internal organs in a normal position and limits their
range of motion, thereby protecting the organs. The composition and structure of
the ligaments make it exhibit typical nonlinear anisotropic mechanical behavior. For
example, when the loading is small, the collagen fibers in the ligament are in a
“crimp” state, and the ligament is relatively compliant, which is represented by the
78 J. Yao et al.

“toe” region of the loading-elongation curve. When the load is increased, the col-
lagen fibers are elongated, and the sliding between each other is reduced, the stiff-
ness of the ligament is increased. Ligament maintains approximately linear elastic
until the collagen fibers reach the yield threshold. In addition, the mutual sliding
action between the fiber bundles can contribute to the viscoelastic effect of the liga-
ment. All these characteristics provide the basis for the physiological function of the
ligament: at low loads, guide the path of joint motion; at high loads, restrict exces-
sive motion (displacement) between bones to protect other soft tissue.

2 Biomechanical Properties of Ligaments

2.1 Tensile Properties

The main function of the ligament is to withstand the tensile loads. Therefore, quan-
tification of the mechanical properties of the ligament in response to different load-
ing condition is important for understanding its function as well as the mechanism
of ligament injury healing. The uniaxial tensile test is usually used to measure the
tensile properties of the ligament [1]. Taking the anterior cruciate ligament of New
Zealand rabbits as an example, the general procedure is as follows:
After sacrifice of the subject, the knee joint is taken, including the femur and
tibia. Because subject’s ACL is short and difficult to fix, the “femur-ACL-tibia”
specimen is prepared. The skin, muscle, fat, meniscus, and other ligamentous tis-
sues are carefully removed. In order to facilitate the fixation of the sample, the
proximal femur and the distal tibia are fixed in a standard mold with resin material
(Fig. 3.1). The stiffness of the mold, resin, and bone has been tested to be much
greater than ACL, and thus their deformations could be neglected compared with
the ACL. Since the mechanical properties of ACL are significantly correlated with
water proportion, saline is used to keep ACL moist in both the preparation process
and the subsequent experimental procedures.
The Femur-ACL-Tibia specimen is loaded and measured using a dynamic
mechanical testing machine (Instron E10000, Illinois Tool Works Inc., USA) with a
sensor range of 250 N. ACL is kept coinciding with the load axis. ACL length under
1.0 N loading is measured as the initial length. First, a cycle loading is performed.
A loading magnitude of 1% in the nominal strain and a loading frequency of 1 Hz
are applied for 20 cycles. Second, a tensile test with a strain rate of 0.1%/s is applied.
To calculate the nominal stress, the entire ACL is embedded in paraffin. The average
cross-sectional area is calculated from five positions along the longitudinal axis of
the ligament. The nominal stress is calculated as the ratio of loading to the cross-­
sectional area. The nominal strain is calculated as the change in length per unit of
the original length of the ligament.
The force-displacement curve of ACL is shown in Fig. 3.2. ACL exhibits typical
hyperelasticity under the uniaxial tension. The force-displacement curve can be
divided into toe region, linear region, and yield region. When the load is small, the
3 Biomechanics of Ligaments 79

Fig. 3.1 Femur-ACL-­Tibia specimen Force

Femur

ACL

Tibia

Fixation

Load-Displacement
200
180
160
Toe Region Linear Region
140
120
Load(N)

100
80
F Stif f ness = F/ L
60
40
L
20
0
0 1 2 3 4 5 6 7
Displacement(mm)

Fig. 3.2 Load-displacement curve of ligament under uniaxial tension

fiber bundles in the ligament are not fully stretched, and the ligament is relatively
flexible, which is in the toe region in the figure. The modulus of elasticity in the toe
region increases continuously, but it is at a smaller level than that in linear region.
As the stress increases, all the fiber bundles turn into the tension state, which is in
the linear region in the figure. Linear region is the main functional region of liga-
ment. Compared with the toe region, the modulus of linear region is greater and
nearly constant. As the load continues to increase, some fiber bundles break, and the
80 J. Yao et al.

ligament is damaged. Plastic deformation occurred in the region. With the increase
of the fiber bundles broken, the ligament modulus decreases.
The critical point between the toe region and the linear region is called the toe
region point. The larger the stress in the toe region, the larger the degree of curl-
ing of the fiber bundle in the relaxed state. This is instructive for the setting of
preloading in ligament reconstruction. The normal functional region of the liga-
ment is linear region. Therefore, the elastic modulus of the linear region is an
important parameter of the biomechanical property of the ligament, which is used
to represent the stiffness of different ligaments. In the above experiment, the rab-
bit ACL elastic modulus was about 61.3 MPa. The point between the linear region
and the yield region is called the elastic limit. When the ligament exceeds the
elastic limit, the ligament begins to injury. In the stress-strain curve, the point at
which the stress reaches the maximum value is called the tensile strength. When
the ligament is stretched exceeding its strength, the ligament is completely torn.
Therefore, strength refers to the ability of the ligament to resist damage. The
acute injury to the ligament is mostly due to the load exceeding the strength of the
ligament.
The mechanical properties of the ligament are related to age. Taking the human
ACL as an example, the linear region stiffness and ultimate load will decrease with
age [7]. The cadaveric study indicated that the linear region stiffness of young group
(20–35 years old) (242 ± 28 N/mm) was 10% higher than that of the middle-aged
group (40–50 years old) (220 ± 24 N/mm), and was 34% higher than that of elderly
group (60–97 years old) (180 ± 25 N/mm). The ultimate load of young group
(2160 ± 157 N) was 44% higher than that of the middle-aged group (1503 ± 83 N)
and 228% higher than that of the elderly group (658 ± 129 N). In addition, the
energy absorbed by the ligament injury has the similar tendency as the linear stiff-
ness. Ligaments of young group absorb more energy when destroyed than those of
older groups. In the elderly group, the incidence of collagen ligament destruction in
the middle of the ligament (12/18, 67%) was higher than that in the young group
(5/18, 28%) and the middle-age group (8/18, 44%). In the young group, the skeletal
avulsion at the ligament was the highest (9/18, 50%). Possible causes include: Older
donors’ knee joints have fewer types and amounts of daily activity than younger
donors, resulting in changes in joint geometry and ligament material properties.
In complex in vivo mechanical environments, the loading direction of the joint is
often not parallel to the longitudinal axis of the ligament, and thus also affects the
mechanical response of the ligament. Take the ACL as an example. The stiffness of
the femoral-ACL-tibia specimen parallel to the longitudinal axis of the ACL was
242 ± 28 N/mm, and the stiffness of the specimen parallel to the tibia shaft was
reduced to 218 ± 27 N/mm. The ultimate load of the specimen in the direction of the
longitudinal axis of the ACL is 35% higher than the direction of the tibia shaft. The
experimental results imply that the influence of the tensile direction of the specimen
plays a role in the mechanical properties of the ligament. In fact, the various parts of
the ligament have different lengths. Therefore, the entire ligament is not uniformly
elongated during the stretching. There are also differences in the way the ligaments
yield in different directions of stretching. When the ligament is loaded in the
3 Biomechanics of Ligaments 81

d­ irection of the longitudinal axis, the deformations of elastic fibers are relatively
uniform under the tensile load. The ultimate load in this direction can more accu-
rately reflect the strength of the ligament. Therefore, when testing the mechanical
properties of the ligament, it is necessary to ensure that the longitudinal axis of the
ligament coincides with the loading axis.

2.2 Viscoelastic Properties

The complex interaction of collagen, elastin, proteoglycan, and water in the liga-
ment results in a viscoelastic property of the ligament. This is manifested in the fact
that the mechanical response is related to the rate of loading and exhibits hysteresis,
creep, and stress relaxation. The viscoelastic properties of the ligaments are gener-
ally measured by uniaxial tensile tests at different loading rates. Taking the mea-
surement of ACL of New Zealand rabbits as an example, the general procedure is as
follows:
Femur-ACL-tibia specimens are prepared and fixed in the dynamic mechani-
cal testing machine (Instron E10000, Illinois Tool Works Inc., USA). The liga-
ment is kept in line with the loading direction. In daily joint motion, the ligaments
generally perform a periodic stretching motion at approximate 0.1–1 Hz.
Therefore, a sinusoidal test of 1% strain amplitude is performed at a frequency of
0.1 Hz and 1 Hz, and each frequency was performed for 20 cycles. Each set of
specimens is recovered for 60 min at 0% strain between trials, eliminating the
effects of historical deformation.
In the test, the soft tissue strain was large; therefore the true strain and true stress
were calculated:

ε = ln ( L / L0 ) (3.1)

F L
δ= (3.2)
A0 A0

where L is the measured length, L0 is the initial length, F is the measured tensile
force, and A0 is the cross-sectional area. The data is then fitted to the stress and strain
data of the sinusoidal test:

z = A sin ( 2π ft + ϕ ) + z0 (3.3)

where z is stress or strain, A is amplitude, z0 is the constant parameter, f is frequency,

and φ is phase. The phase difference is defined as the difference between the stress
and the strain phase. The viscosity increased with the phase difference. As a result,
the ligament had a phase difference of 3.22 at 0.1 Hz and a phase difference of 6.20
at 1 Hz, which means that the ligaments exhibit higher viscosity characteristics at
high loading rates.
82 J. Yao et al.

There are several methods of quantifying the viscoelastic properties of the liga-
ment. The parameter “supplementary stress” can also describe this property [8].
Define the “supplementary stress” variable as:

σ y − σ 0.1
Supplementary stress =
σy

where y indicates a different strain rate value. σy indicates the stress at y%/s strain
rate, and σ0.1 indicates the stress at 0.1%/s strain rate. The supplementary stress
represents the percentage of stress at a high strain rate at a strain rate greater than
0.1%/s strain rate at the same strain level. The shape of the stress-strain curve does
not change with increasing strain rate, except that the toe region appears in the lower
strain range. As the strain rate increases, the “supplemental stress” increases signifi-
cantly. When the strain rate is 40%/s, the “supplemental stress” value can reach
70%. This phenomenon of bovine ACL is similar to the conclusion obtained from
the rabbit ACL test.
The viscoelastic effect of the ligament is closely related to its physiological func-
tion. When the joint movement speed is low, the ligament has a low strain rate and
is relatively flexible, then the muscle plays a greater role in stability and restraint of
joint. As the speed of joint motion increases, the stiffness of the ligament increases,
which can compensate the delay of the muscle response.
In addition, the toe region modulus is also one of the methods to reflect visco-
elastic properties [9]. In the uniaxial tensile tests with different loading rates, the
ratio of stress to strain at the critical point between the toe region and the linear
region is defined as the toe region modulus. The viscosity increases with the differ-
ence of the toe modulus at different strain rates. By this method, the change in vis-
cosity of the xenograft porcine superflexor tendon (pSFT) used in ACL reconstruction
before and after decellularization was measured. The natural pSFT has a significant
difference in the toe modulus (29.7, 104.3, 139.8 MPa) under the three different
strain rates (1%/s, 10%/s, 100%/s). However, there is no such difference in the toe
modulus (48.8, 63.1, and 68.1 MPa) after decellularization. This indicates that pSFT
after decellularization results in a decrease in viscosity.

3 Ligament Injury, Treatment, and Rehabilitation

3.1 Injury

There are many factors contributing to the injury of the ligament. Most ligament
injuries are caused by violent, traumatic, non-physiological activities, especially
joint ligaments. For example, medial collateral ligament may tear under violent
knee valgus, and ACL may tear under knee internal rotation. When external factors
cause the ligament to reach the elastic limit and exceed its tolerance, the ligament is
3 Biomechanics of Ligaments 83

injured. The injury may occur in the middle or the attachments of the ligament.
Damage to the joint ligaments can contribute to dislocation, maltracking, and insta-
bility of the joints, and lead to subsequent diseases of other soft tissue and bone,
such as osteoarthritis. In addition, genetic, endocrine, and microbial infections can
lead to ligamentous lesions that gradually damage the ligaments.
The risk of ligament injury is also related to the physiological structure of the
musculoskeletal system and the external environment. Taking ACL injury as an
example, the probability of ACL injury in the subject with narrow intercondylar
notch is greater. Since ACL is located in the joint cavity of the tibiofemoral joint,
and is sandwiched by the medial and lateral femoral condyles, when the knee joint
is subjected to internal and external loads, the two femoral condyles will press the
ACL, causing additional lateral force on the ACL and increasing the chance of ACL
tear [10–12]. In addition, ACL footprints are at the anteromedial aspect of the inter-
condylar area on the tibial plateau and the posteromedial aspect of the lateral femo-
ral condyle. For individuals with an anterior medial aspect of the tibial plateau that
is higher than the posterior lateral aspect, when the knee joint is subjected to a
vertical load, the tibia will be additionally subjected to the forward and medial
loading, thereby causing additional in situ force in ACL, and increasing the prob-
ability of ACL injury. A number of statistical studies have reported the correlation
between this knee anatomical feature and ACL injury [13–15].
Under different sports types and ground conditions, the injury rate of ACL is also
different. Renstrom et al. reported the rate of ACL injury in basketball, ice hockey,
football, and gymnastics. The ACL injury rate of women’s basketball and women’s
gymnastics was the highest, reaching nearly 5%, while the ACL injury rate for
men’s basketball and women’s ice hockey was only 0.7% [16]. At the same time, a
number of statistical studies have analyzed the correlation between ground environ-
ment and ACL injury rate; selecting the appropriate site according to the type of
exercise can reduce the probability of ACL injury [17–20]. In addition, Lambson
et al. found that different sole materials and textures provide different grips (such as
lateral, longitudinal, and torsional resistance) and have an impact on ACL injury [21].

3.2 Treatment

The treatment of ligament injury mainly includes conservative treatment and surgi-
cal treatment. The choice of the treatment methods mainly depends on the type and
severity of the ligament injury. For example, nearly 90% of knee joint ligament
injuries are ACL and MCL injuries [22]. MCL injuries usually heal spontaneous,
although scar tissue will appear between MCL and bones, resulting in nonideal
changes in MCL mechanical properties. However, the clinical treatment is usually
conservative, and the MCL will be repaired by resting. In contrast, ACL tears often
require surgery because ACL has fewer blood vessels and poor healing ability. If
nonsurgical conservative treatment is used, it may lead to subsequent meniscus and
cartilage lesions, resulting in severe instability of the knee joint.
84 J. Yao et al.

ACL reconstruction surgery assisted by arthroscope is the main method to treat

ACL tear in clinic at present. Essentially, the procedure aims to replace the damaged
ACL with an autologous or allogeneic ligament graft and maintain the restraint
function for the knee joint. The success of the operation depends on whether the
knee joint can return to normal motion and mechanical environment after surgery,
or more accurately depends on whether the ligament graft can reconstruct the bio-
mechanical function of normal ACL. The basic steps in ACL reconstruction include:
graft preparation, bone tunnel creation, and graft fixation.
Autologous ligament grafts are commonly used in clinics. Currently used autolo-
gous ligament grafts include patellar tendon, quadriceps tendon, and hamstring ten-
don. Taking the patellar tendon as an example, the surgery cuts the middle third
bundles of the patellar tendon, about 9–10 mm wide. The incision is parallel to the
fiber direction of the patellar ligament and continues to the tibia and patella. The cut
ligament graft with the bones at both ends have a total length of about 95 mm, and
each end contains about 20 mm of wedge-shaped bone. The redundant soft tissue on
the graft is then removed, the wedge-shaped bone is trimmed, and the sutures are
connected on the bones at both ends, which can be used to pull the ligament graft
into the bone tunnel and apply pretension.
After arthroscopic removal of the injured ACL stump, bone tunnels are created
on the tibia and femur for fixation of the ligament graft. To create the tibial bone
tunnel, the ACL tibial footprint is determined on the tibial plateau using an aimer. A
small tunnel is drilled from the medial site of the tibia tuberosity with a 2.4 mm drill
guide pin, and to the center of the ACL tibial footprint. The angle between the guide
pin and the tibial plateau is approximately 55°. The diameter of the bone tunnel is
then expanded to 7–9 mm using a reamer. Then the bone tunnel of the femur is cre-
ated. The knee joint was flexed to approximately 120°, and the ACL femoral foot-
print is determined on the medial side of the lateral femoral condyle. The drilled
guide pin is drilled from the medial site of the patellar tendon and passed through
the ACL femoral footprint, to the lateral femoral cortex. The reamer is then used to
create a bone tunnel about 35 mm deep and 9 mm in diameter along the guide wire
on the femur.
Finally, the implant is fixed in the bone tunnel. The suture of the femoral end of
the ligament graft is used to pull it from the distal end of the tibial bone tunnel into
the joint cavity, and finally the bone blocks at both ends are located in the bone tun-
nel of the tibia and femur. In order to fix the ligament graft at the femoral end, the
knee joint is flexed, and the interface screw is used to fix the bone block of the femo-
ral end of the ligament graft in the bone tunnel. The knee joint is then subjected to
20–30 flexion-extension, and a pretension of about 45 N is applied by using the
suture of the tibial end of the ligament graft. The bone graft of the ligament graft is
fixed in the tibial tunnel at the 30° position of the knee by placing the interface
screw at the distal end of the tibial tunnel.
In addition, allografts are also used in clinical procedures. Xenografts and syn-
thetic grafts have also been used in clinical procedures, but due to their durability
and biocompatibility issues, they are currently used in small quantities. With the
study of the ACL double-bundle anatomy, double-bundle reconstruction is getting
3 Biomechanics of Ligaments 85

increasing attention. Additional tunnels will be created in the double-bundle recon-

struction. Compared to single-bundle reconstruction, double-bundle ACL recon-
struction can better restore knee stability, but at the same time may cause greater
bone volume loss.

3.3 ACL Reconstruction Animal Model

Animal model is often researched for the improvement of ACL reconstruction.

Take rabbit ACL reconstruction as an example (Fig. 3.3). ACL reconstruction is
performed on the left knee joint. After preoperative anesthesia, the right ankle
joint and the left knee joint are shaved and wiped with iodophor and alcohol. Then
the epidermis of the right Achilles tendon is cut open, one-third of the total width
is cut as the graft. Two sutures are connected at both ends of the graft and placed
in physiological saline for use. The left knee joint epidermis and joint cavity are
then dissected, the original ACL is removed. The knee joint is bent to the maxi-
mum knee flexion angle. To create the femoral tunnel, the 1 o’clock position of the
femoral intercondylar notch is used as the pin insertion point. The 2.5-gauge
Kirschner wire is used to drill the tunnel through the anterior and lateral femur. To
create the tibial tunnel, the ACL tibial footprint is used as the pin insertion point.
The tunnel is drilled into the anterior medial aspect of the tibia using a 2.5-gauge

a b

Fig. 3.3 Rabbit ACL reconstruction. (a) Rabbit knee joint before ACL reconstruction. (b) Rabbit
knee joint after ACL reconstruction
86 J. Yao et al.

needle. The sutures at both ends of the graft are respectively passed through the
tunnel, and the graft is pulled into the tunnel. The joint stability is assessed accord-
ing to the tibiofemoral anterior-­posterior translation. Finally, the sutures at both
ends of the graft were tied to the proximal femur and the distal end of the tibia. The
knee joint capsule and the epidermal incision were sutured and placed in the cage
after being injected with antibiotics.

3.4 Rehabilitation

Different ligament injuries have different rehabilitation methods. For example,

patients with ankle ligament injury are not recommended to perform functional
exercise immediately after surgery to avoid delayed or secondary injury. It is gener-
ally recommended to use a fixed shoe or cast gypsum for 6 weeks after the repair of
the proximal deltoid ligament injury. When the medial collateral ligament of the
knee is injured, the knee joint will be fixed by a bracket to reduce the joint motion
and external loading; a 30 days rest is usually suggested.
Rehabilitation after ACL reconstruction is critical to the postoperative outcome.
Passive knee-flexion training within 90° is required within 1 week after surgery, and
ankle and foot training is also required to enhance the calf muscle strength. In the
second week after surgery, appropriate active knee flexion, straight leg elevation,
and hip abduction-adduction training should also be performed. In the third week
after surgery, a protective semi-squat training can be performed appropriately, and
the flexion and extension should be less than 45°.

4 Summary

The biomechanical properties of the ligaments are closely related to their physio-
logical functions. Therefore, the ligaments’ composition, structure, as well as their
biochemical and mechanical interactions with the surrounding tissue are varying in
different locations of the human body. Illustrating the relationship between the bio-
chemical and mechanical characters of ligaments is critical for understanding the
mechanism of ligament injury and improving the treatment strategies. This will
become an important direction for future research and will bring profound signifi-
cance to clinical application.
Statement on the Animal Benefit All animal treatments were approved by the
Animal Care Committee of Beihang University in accordance with the Regulation
of Administration of Affairs Concerning Experimental Animals of State Science
and Technology Commission of China.

Acknowledgement The authors would like to convey their appreciation to Prof. Savio L-Y. Woo
for his precious suggestions.
3 Biomechanics of Ligaments 87

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Chapter 4
Hand and Wrist Biomechanics

Steven Regal, Steven Maschke, and Zong-Ming Li

Abstract The biomechanical function of the human hand and wrist is closely
related to the intricacy of its anatomy. The arrangement of the bones, ligament, and
muscles in the hand allows a complex array of tasks to be performed. This chapter
provides a brief review of the anatomy of the hand and wrist, normal biomechanical
function, and examples of pathomechanics.

Keywords Hand · Wrist · Biomechanics · Pathomechanics

The human hand and wrist are a set of complex anatomic tools that forms a tactile
connection to the world. The intricacies of hand and wrist anatomy permit a multi-
tude of different functions including the ability to grip an object, let go, flex and
extend and to allow the precise movements required for writing, playing sport, and
innumerable other actions. This chapter will briefly review some skeletal and liga-
mentous anatomy of the hand and wrist and then describe the complex biomechan-
ics of the muscles, ligaments, and joints. Lastly, a few examples of pathomechanics
are provided, including arthritic condition of the first carpometacarpal joint, distal
radius fracture, and carpal tunnel syndrome.

S. Regal · S. Maschke
Department of Orthopedic Surgery, Cleveland Clinic, Cleveland, OH, USA
e-mail: regals@ccf.org; maschks@ccf.org
Z.-M. Li (*)
Department of Orthopedic Surgery, Cleveland Clinic, Cleveland, OH, USA
Department of Biomedical Engineering, Cleveland Clinic, Cleveland, OH, USA
Department of Physical Medicine and Rehabilitation, Cleveland Clinic, Cleveland, OH, USA
e-mail: liz4@ccf.org

© Springer Nature Singapore Pte Ltd. 2020 89

C.-K. Cheng, S. L-Y. Woo (eds.), Frontiers in Orthopaedic Biomechanics,
https://doi.org/10.1007/978-981-15-3159-0_4
90 S. Regal et al.

1 Skeletal and Ligamentous Anatomy

The human hand comprises 27 bones (14 phalanges, 5 metacarpals, and 8 carpal bones)
that form the distal portion of the wrist joint. The “wrist joint,” or more accurately “wrist
joint complex,” contains numerous articulations linking the distal forearm to the hand
and consists of the distal radius and ulna articulating with the multi-articular carpal
bones which then articulate with the metacarpals. The carpal bones have been classi-
cally divided into proximal and distal rows based upon their kinematic behavior during
wrist motion. The distal row contains the trapezium, trapezoid, capitate, and hamate
which are tightly bound to each other by stout intercarpal ligaments that allow minimal
motion. The scaphoid, lunate, triquetrum, and pisiform form the proximal carpal row
and is described as an intercalated segment because no tendons insert on them and their
motion is dependent on mechanical forces from their adjacent articulations [1, 2].
Taleisnik [3] divided the carpal ligaments into intrinsic and extrinsic groups deter-
mined by the anatomical origination and insertion of the ligament. The extrinsic liga-
ments of the wrist bridge the carpal bones to the radius, ulna, or metacarpals. The
dorsal extrinsic ligaments consist of the dorsal radiocarpal (radiotriquetral) ligament
and the dorsal intercarpal ligament that form a sideways V. Both ligaments have
attachments to the lunate and are important secondary stabilizers of the scapholunate
joint [1]. The palmar extrinsic ligaments of the wrist have been shown to provide the
most restraint in dorsal/palmar translation of the carpus and include the radioscaph-
oid-capitate, long radiolunate, short radiolunate, ulnotriquetral, ulnolunate, and
ulnocapitate ligaments [4]. The space of Poirier is an area of capsular weakness that
is clinically important in dislocations about the lunate and is located between the
radioscaphocapitate and long radiolunate ligaments (Fig. 4.1). The radioscapholu-
nate ligament is not a true ligament but is a vascular conduit to the lunate [5, 6].

a b

Fig. 4.1 (a, b) Wrist dorsal

4 Hand and Wrist Biomechanics 91

There are nine intrinsic ligaments of the wrist that originate and insert on adja-
cent carpal bones. The two most important intrinsic ligaments are the scapholunate
and lunotriquetral ligaments which can be divided into dorsal, proximal, and palmar
parts. The thickest and strongest part of the scapholunate ligament is the dorsal por-
tion whereas the thickest and strongest part of the lunotriquetral ligament is located
palmarly.

2 Biomechanics

The hand and wrist contain four different types of synovial joints—plane, pivot,
ellipsoidal, and saddle. Plane joints allow simple gliding motion between flat articu-
lar surfaces such as in the intercarpal, intermetacarpal, and carpometacarpal joints
of the second to fourth digits. The interphalangeal joints of the digits are hinge
joints and only allow motion to occur in one plane 90° to the bones to permit flexion
and extension. An ellipsoidal joint formed by oval-shaped condyle and ellipsoidal
cavity allows motion in two planes, flexion/extension and abduction/adduction sec-
ondary to their reciprocal concave/convex articular surfaces like those found in the
radiocarpal and metacarpophalangeal joints. A saddle joint is formed by bones with
concave and convex articular surfaces and only occurs in the carpometacarpal joint
of the thumb, allowing motion in flexion/extension, abduction/adduction, and cir-
cumduction [7].

2.1 Wrist Motion

Normal wrist range of motion in the sagittal plan is about 65° of flexion and 55°
of extension while in the coronal plane there is 15° of radial deviation and 35° of
ulnar deviation. Research on the specifics of carpal motion and wrist kinematics
date back to the nineteenth century and several theories have been proposed. The
eight carpal bones of the wrist are commonly described as containing a proximal
and distal row; however, when discussing carpal kinematics, it is much more com-
plex. Navarro described the columnar theory in 1921 dividing the wrist into three
columns. The lateral column contained the scaphoid, trapezium, and trapezoid; the
central column contained the lunate, capitate, and hamate; and the medial column
contained the triquetrum and pisiform [8]. Taleisnik later modified this theory in
1976 and stated only the scaphoid was in the lateral column while the central col-
umn now consisted of the trapezium, trapezoid, lunate, capitate, and hamate. In
both theories, the central column moved concurrently during flexion/extension
and the medial and lateral columns rotated around the central column in radial/
ulnar deviation [3]. Years later, Craigen and Stanley proposed that carpal motion
is complex and variable and can be accounted for by both the row and columnar
theories [9].
92 S. Regal et al.

The proximal carpal row has no direct tendon attachment and moves passively
when muscle contraction initiates movement at the distal carpal row. In normal
wrists, there is very little motion between the bones in the distal carpal row which
essentially moves as one functional unit. During wrist flexion, the distal carpal row
synchronously flexes accompanied by a small amount of ulnar deviation. Conversely,
during wrist extension the distal row rotates into extension and radial deviation.
During radioulnar deviation, the proximal carpal row moves from a flexed position
in radial deviation to an extended position in ulnar deviation. More recently, studies
of carpal motion have been performed in vivo with computed tomography and mag-
netic resonance imaging. Moojen et al. [10] quantified in vivo carpal kinematics and
compared their results to in vitro studies. Their in vivo results were consistent with
prior studies in that that the majority of wrist flexion and extension occur at the
radiocarpal joint. Their results showed that in 60° of wrist flexion and extension, the
scaphoid contributes to 62% and 87% of the in-plane motion, respectively, while the
lunate contributes 31% and 66%. Kaufmann et al. [11] showed that the midcarpal
joint is responsible for 86% of radial deviation and 66% of ulnar deviation. In radio-
ulnar deviation, the scaphoid flexes and extends, respectively, while in wrist flexion/
extension the scaphoid moves in the same plane of motion. A combination of these
motions, radiodorsal/ulnopalmar, has been described as the dart thrower’s motion
and has been portrayed as the most frequently used motion during activities of daily
living [12–14]. A three-dimensional motion analysis of the carpal bones during the
dart thrower’s motion found that the majority of the motion occurs at the midcarpal
joint and that there is minimal motion between the scaphoid and lunate [13, 15, 16].

2.2 Muscular Biomechanics

Hand and wrist motion is multifaceted and relies not only on the bony articulations
but also on a dynamic balance of muscular forces. The hand is merely a functional
puppet that follows the brain’s desire to perform a specific task; the brain sends
signals to the hand via nerves and activates precise muscles to contract or relax with
instantaneous sensory feedback from visual cues and sensory receptors. This com-
plex, coordinated interaction happens constantly at a subconscious level.
Anatomically and functionally, the wrist is powered by 3 extensors and 3 flexor
muscles while the hand is powered by 9 extrinsic muscles and 17 intrinsic muscles
(Table 4.1). The amount of force a muscle can produce is somewhat proportional to
its cross-sectional area and the mechanical effect on a joint is determined by its
insertion and origin; the flexors insert on the volar aspect of the bone while the
extensors insert dorsally. The muscles of the hand and wrist are in constant harmo-
nious balance of synergism and antagonism. When the wrist is passively extended,
the finger flexor muscles are lengthened and involuntarily finger flexion occurs. In
contrast, passive wrist flexion causes reciprocal finger extension. The combination
of these motions has been termed “the tenodesis effect” and is a clinically useful
4 Hand and Wrist Biomechanics 93

Table 4.1 Muscles of the wrist

Muscle Action
Muscles of the wrist
Wrist flexors
 Flexor carpi radialis Flexion of wrist, radial deviation
 Flexor carpi ulnaris Flexion of wrist, ulnar deviation
 Palmaris longus Flexion of wrist
Wrist extensors
 Extensor carpi radialis longus and Extension of wrist, radial deviation
brevis
 Extensor carpi ulnaris Flexion of wrist, ulnar deviation
Muscles of the hand
Extrinsic muscles
Hand flexors
 Flexor pollicis longus Flexion of MCP and IP joints of thumb
 Flexor digitorum profundus Flexion of MCP, PIP, and DIP joints
 Flexor digitorum superficialis Flexion of MCP and PIP joints
Hand extensors
 Extensor pollicis longus Extension of MCP and IP joint of thumb
 Extensor pollicis brevis Extension of MCP joint of thumb
 Abductor pollicis longus Abduction of thumb
 Extensor indicis proprius Extension of index finger
 Extensor digitorum communis Extension of fingers
 Extensor digiti quinti Extension of small finger
Intrinsic muscles
 Dorsal interossei (4) Abduction of fingers
 Palmar interossei (3) Adduction of fingers
 Lumbricals (4) Flexion of MCP joint and extension of PIP and DIP
joints
 Abductor pollicis brevis Abduction of thumb
 Flexor pollicis brevis Flexion of thumb
 Opponens pollicis Flexion and abduction of thumb
 Abductor digiti quinti Abduction of small finger
 Flexor digiti quinti Flexion of small finger
 Adductor pollicis Adduction of thumb

exam technique when evaluating flexor tendon injuries [17]. Furthermore, position
of the wrist affects the amount of peak force that can be generated by the flexor
tendons [18, 19]. Using electromyography, Volz et al. [20] found that the greatest
grip strength was with the wrist in 20° of extension and weakest in 40° of flexion.
Hazelton et al. [18] found the highest force production at the interphalangeal joints
were greatest with the wrist in ulnar deviation, followed by extension and weakest
with wrist in flexion. Muscular action and joint forces will be further discussed dur-
ing the description of specific joints of the hand and wrist.
94 S. Regal et al.

2.3 Carpometacarpal Joints

There are five carpometacarpal (CMC) joints in the hand that consist of articulations
between the distal carpal row and the bases of the metacarpals. While there are simi-
larities between the joints of the thumb and the joints of the fingers, the thumb is
discussed separately for its function and motion differ significantly. The second
through fourth CMC joints are synovial joints with motion in one plane, flexion and
extension, while the fifth CMC joint is a saddle-like joint with 2 degrees of freedom;
flexion-extension and abduction-adduction. The second and third CMC joint are
immobile while the fifth CMC joint can move as much as 20° due to the bony con-
figuration of the base of the fifth metacarpal and hamate. The immobility of the
second and third CMC joint is a functional adaptation that facilitates the function of
the wrist extensors and radial wrist flexor (extensor carpi radialis longus and brevis,
flexor carpi radialis). These muscles insert on the bases of the second and third
metacarpals and with their rigid attachment to the carpals, the lever arm of the
muscle is increased.
A critical function of the CMC joints of the hand is its contribution to the palmar
arches. The hand consists of a longitudinal and two transverse arches that are essential
in power grip and pinch as well as the ability to cup and flatten the hand (Fig. 4.2). The
intermetacarpal and the deep transverse metacarpal ligaments of the proximal and
distal portions of the metacarpal, respectively, are necessary to maintain these arches
[21, 22]. The longitudinal arch is fixed due to the immobility of the second and third
CMC joints while the transverse arches facilitate conforming the hand to the shape of
an object being held. The proximal transverse arch is maintained by the shape of the
carpal bones as well as their encompassing ligaments, the flexor retinaculum (or
transverse carpal ligament) and the transverse intercarpal ligaments. The bony carpal
arch and the flexor retinaculum comprise what is known as the carpal tunnel. The
carpal tunnel not only allows the palm to increase its contact area with objects, it also
protects the finger flexors and median nerve. When the flexor retinaculum is incised
during a carpal tunnel release, there is widening of the arch but overall transverse
stability is maintained due to the intact transverse intercarpal ligaments [23].

Fig. 4.2 Arches

4 Hand and Wrist Biomechanics 95

2.4 CMC Joint of the Thumb

The first CMC joint is an articulation between the trapezium and the first metacarpal
and has been described as a saddle joint that is concave in the sagittal plane and
convex in the coronal plane (Fig. 4.3). This unique joint allows flexion-extension,
abduction-adduction, and pronation-supination with the net effect of these motions
allowing circumduction or opposition-reposition. Though there is motion in three
anatomic planes, the first CMC joint is commonly considered to have 2 degrees of
freedom. The flexion-extension axis is through the trapezium and the abduction-­
adduction axis run through the metacarpal base; both are constant through a range
of motion. Because these axes are not perpendicular to each other, for any position
of flexion-extension/abduction-adduction, a set degree of pronation-supination
occurs [24, 25]. The bony configuration of the thumb allows for increased range of
motion required for opposition. Opposition is the sequential movements of abduc-
tion, flexion, and adduction of the first metacarpal with concurrent rotation. This
compound movement brings the thumb out of the palm and rotates the metacarpal
to put the thumb into a position to grip an object together with a finger.
Stability of the first CMC joint is provided by seven ligaments, the dorsoradial
ligament, the posterior oblique ligament, the superficial and deep palmar oblique
ligament, the ulnar collateral ligament, the volar and dorsal first metacarpal ulnar
base–second metacarpal radial base intermetacarpal ligaments. The palmar oblique
ligament, also referred to as the beak ligament, originates on the palmar tubercle
of the trapezium and inserts on the ulnar side of the metacarpal base. As a result of
its intracapsular location, it plays a major role in CMC stabilization and resists

Fig. 4.3 (a, b)

Metatarsal joint a b
96 S. Regal et al.

abduction, extension, and pronation forces. Progressive degeneration of the palmar

oblique ligament has been shown to correlate with the stages of osteoarthritis. The
dorsoradial ligament is the thickest and strongest ligament of the CMC joint and is
the primary restraint to dorsal dislocation [26]. Dynamic stability is provided by
three thenar muscles (abductor pollicis brevis, flexor pollicis brevis, and opponens
pollicis) and six extrinsic muscles (flexor pollicis longus, adductor pollicis, abduc-
tor pollicis longus, extensor pollicis brevis, extensor pollicis longus, and the first
dorsal interosseous muscle). The thenar muscles are active in grasping activities
while the extrinsic muscles function mainly to return the thumb to extension from
its position in the palm.

2.5 Metacarpophalangeal Joints

The metacarpophalangeal (MCP) joints have a convex, asymmetric metacarpal head

proximally and a concave proximal phalanx distally. This joint has 3 degrees of
freedom, flexion-extension, abduction-adduction, and slight pronation-supination.
The normal range of motion of the MCP joint is 0–90° of flexion, though some
individuals may have up to 20° of hyperextension. Though the bony joint is incon-
gruent, it achieves stability with its fibrous capsule, thick volar plate, and collateral
ligaments. The radial and ulnar collateral ligaments are dorsal to the center of rota-
tion of the MCP joint and are lax in extension. The volar surface of the metacarpal
head is longer and broader than its dorsal surface, so when the joint is flexed, a cam
effect occurs and the collateral ligaments becomes taut (Fig. 4.4). Movement of the
MCP joint is indirectly through the extrinsic finger flexors and extensors (flexor
digitorum superficialis/profundus, extensor digitorum indicis/proprius/quinti) as
well directly by the intrinsic muscles. The sagittal bands, retinacular tissue that sur-
round the metacarpal head, stabilize the extensor mechanism centrally over the digit
and extend the MCP joint with its insertion onto the volar plate. The lumbricals and
interossei provide MCP flexion, abduction, and adduction through their insertions
into the extensor hood and proximal phalanx [27] (Fig. 4.5).

2.6 Proximal and Distal Interphalangeal Joints

The interphalangeal joints of the hand are ginglymus, or hinge joints, comprised of
two phalanges with congruous articular surfaces that allow up to 10° of hyperexten-
sion and 100° of flexion [28]. The interphalangeal joints achieve stability from the
bony architecture as well as from the volar plate and collateral ligaments. On the
proximal interphalangeal joint, the proper collateral ligament (PCL) originates from
the proximal and dorsal sides of the proximal phalanx and inserts via Sharpey’s
fibers on the middle phalanx. The fibers at the origin are parallel to the phalanx and
the insertional fibers are more oblique, giving the ligament a fan-shaped appearance.
4 Hand and Wrist Biomechanics 97

a b

Fig. 4.4 (a–c) Volar plate

Fig. 4.5 (a, b) Tendon

a

b
98 S. Regal et al.

Fig. 4.6 Pulleys

The accessory collateral ligament (ACL) originates on the volar portion of the PCL
and inserts distally on dorsolateral side of the volar plate on the middle phalanx [29].
A recent three-dimensional computed tomography study of the proximal interpha-
langeal joint found that the dorsal portion of the PCL increased in length as the joint
went from 0° to 90° of flexion and was the most stabilizing structure while the joint
was in flexion. The volar portion of the PCL and distal portion of the ACL provided
joint stability while in extension [30].
Motion of the fingers is a dynamic balance between the extrinsic and intrinsic
muscles of the hand. The extrinsic muscles, those that originate proximal to the
hand, include the flexor digitorum profundus, flexor digitorum superficialis, exten-
sor digitorum communis, extensor indices proprius, and extensor digitorum minimi.
The lumbricals and interossei comprise the intrinsic muscles. The flexor tendons are
held closely to the volar surface of the phalanges by five annular pulleys and three
cruciate pulleys. Not only are these pulleys biomechanically critical to prevent bow-
stringing, they transmit force during finger flexion. The flexor digitorum profundus
inserts on the proximal portion of the distal phalanx; when the muscle belly con-
tracts, force is emitted along the tendon and flexion at the distal interphalangeal joint
follows. Flexion at the joint creates an angled pathway for the profundus tendon as
it exits the A4 pulley which transmits force to the middle phalanx and resultant flex-
ion of the proximal interphalangeal joint. The profundus tendon creates a similar
force as it exits the A2 pulley and causes a flexion moment at the metacarpophalan-
geal joint [7] (Fig. 4.6).

3 Pathological Biomechanics

A thorough understanding of normal hand and wrist biomechanics is helpful in

studying disease etiology and treatment. With daily activities, the hand and wrist are
put through an enumerable amount of complex and coordinated movements that
place mechanical loads on the surrounding muscles, ligaments, and joints. With
injury or overuse, the mechanical loads may be altered and lead to degeneration or
4 Hand and Wrist Biomechanics 99

instability. Pathologic motion ensues which often leads to disability and pain. With
knowledge of normal biomechanics, treatment can be made to manipulate the
mechanical environment or recreate it.

3.1 Arthritis of the Thumb CMC Joint

The thumb CMC joint is the second most common site for osteoarthritis (OA) in the
hand and is the most common joint in the upper extremity to undergo surgical
reconstruction for OA. Arthritis of the thumb CMC joint, also known as basal joint
arthritis or trapeziometacarpal arthritis, can be a debilitating disorder that results in
pain, decreased motion, and reduced strength. Basal joint arthritis affects 1 in 4
women and 1 in 12 men; such a gender factor is thought to be related to ligament
hypermobility secondary to hormonal differences or possibly to subtle differences
in trapezium morphology [26]. The etiology of basal joint arthritis is multifactorial
but it is widely believed to involve the loss of the integrity of the palmar oblique
ligament for multiple cadaveric studies have shown a direct correlation between the
stages of OA and integrity of the ligament [31]. As attenuation or hyperlaxity of the
ligament ensues, increased shear forces are placed on the joint leading to inflamma-
tion (synovitis) and degeneration. With progressive disease, the thumb becomes
adducted and subsequently often be dorsoradially subluxated due to the distal pull
of the adductor pollicus muscle. With the thumb adducted, the hand is at a mechani-
cal disadvantage to grip objects and will often pathologically compensate with fixed
metacarpophalangeal hyperextension, the so-called “Z-deformity” (Fig. 4.7) [32].
Patients with basal joint arthritis often experience pain, at times severe, and diffi-
culty performing daily activities such as hand writing or opening jars. Commonly,
patients complain of functional limitations secondarily to decreased strength and
motion. A recent three-dimensional motion analysis found that patients with OA at
the thumb CMC joint had a 50.6% decrease in the circumduction envelope com-
pared to those without arthritis [33].

Fig. 4.7 Z deformity

100 S. Regal et al.

Nonsurgical treatment for OA of the thumb CMC joint include activity modifi-
cation, nonsteroidal anti-inflammatories, splinting, and corticosteroid injections.
Surgical options include trapeziectomy with/without volar ligament reconstruc-
tion and with/without tendon interposition, metacarpal extension osteotomy,
arthroscopy, resection arthroplasty, implant arthroplasty, and arthrodesis (bone
fusion). The surgical procedure is chosen by extent of disease, age and activity
level of patient, and surgeon preference. For early disease, ligament reconstruction
and metacarpal extension osteotomy are common procedures. Ligament recon-
struction is frequently performed with a strip of the flexor carpi radialis passed
through a drill hole in the first metacarpal and sutured to itself, recreating the volar
oblique and dorsoradial ligaments. Koff et al. [34] performed a cadaveric biome-
chanical study that found ligament reconstruction to reduce laxity in the dorsovo-
lar, radioulnar, and pronosupination directions. Limited evidence is available for
metacarpal extension osteotomy but the biomechanical rationale of its clinical suc-
cess is shifting the joint contact forces to non-arthritic cartilage and reducing joint
laxity [35].
Trapeziectomy with/without volar ligament reconstruction and with/without ten-
don interposition, arthroplasty, and arthrodesis are common surgical options for
more severe disease. All options provide pain relief and improve function though
their biomechanical implications are varied. The native 2 degrees of freedom (DoF)
the trapeziometacarapal joint has is altered with surgical reconstruction. When
arthrodesis is performed, the joint has 0 DoF in contrast to arthroplasty procedures
such as ligament reconstruction tendon interposition (LRTI) and ball and socket
implant have 3 DoF. The change in DoF impacts the joint reaction forces at this
CMC joint. Comparing the above procedures in a biomechanical study, the arthro-
plasty group (3 DoF) had 12 times the joint reaction force than the native joint while
the fusion group (0 DoF) showed the lowest amount of joint forces [24]. Another
biomechanical study found that LRTI had kinematics similar to a native joint though
the pivot point and center of rotation were different. This same study found that the
ball and socket arthroplasty has a fixed axis of rotation which could possibly lead to
a higher rate of wear and loosening [36]. Though the treatment of basal joint arthri-
tis is varied, surgical reconstruction improves pain, increases function, and reliably
produces good to excellent outcomes in 90–95% of cases [32].

3.2 Distal Radius Fracture Malunion

Distal radius fractures account for one-sixth of all emergency visits and up to 46%
of all skeletal fractures seen in a primary care setting. One of the most common
complications after a distal radius fracture is malunion, as high as 24% in those
treated in a cast [37]. A malunion is when a fractured bone heals in an abnormal
position. Numerous studies have evaluated the biomechanical effects and load
mechanics of radial shortening, loss of radial inclination and abnormal volar or
dorsal angulation. In the non-fractured distal radius with neutral ulnar variance,
4 Hand and Wrist Biomechanics 101

79% of the mechanical load of the wrist joint is through the radius and 21% is trans-
mitted across the ulna [38]. Wrists with 2 mm or more of ulnar plus variance showed
69% of the transmitted load through the radius and 31% of the load through the ulna
[37]. Pogue et al. [39] showed that greater than 2 mm of radial shortening resulted
in a significant increase in lunate contact area, and at 6–8 mm of radial shortening,
the ulna was noted to impinge on the triquetrum and/or the ulnar aspect of the
lunate. Palmer and Werner [38] found a 25% increase in load to the ulna with a posi-
tive 1 mm change to the ulnar variance.
Malalignment of distal radius fracture in the sagittal plane cause abnormal wrist
biomechanics and decreased functional results in patients [39, 40]. Fernandez [40]
reported that distal radius fracture malunions with greater than 25° dorsal angula-
tion were more likely to be symptomatic and the scaphoid/lunate fossa had increased
loads and more dorsal contact areas compared to the normal wrist. As the distal
radius articular surface moves from its native 10° volar tilt to 45° of dorsal angula-
tion, load through the ulna increases from 21% to 67% of the total load. Additionally,
it has been reported that malunited distal radius fractures may cause dynamic mid-
carpal instability, increased strain on the triangular fibrocartilage, decreased grip
strength, and median nerve neuropathy [41].
Treatment of distal radius malunions should be reserved for only those who are
symptomatic rather than just treating radiographic findings. Surgical options include
corrective osteotomy, wrist denervation, and wrist fusion. In a study with 195 cor-
rective osteotomies for dorsal malunion of the distal radius, the flexion-extension
arc improved by 49° and there was an increase in prono-supination and increase in
grip strength from 29 to 40 kg [41].

3.3 Carpal Tunnel Syndrome

Carpal tunnel syndrome (CTS) is the most common compressive neuropathy of the
upper extremity with a prevalence of 2.6–5.8% in the general adult population.
There are more than 500,000 surgical procedures performed each year in the United
States with an economic impact exceeding 2 billion dollars. The carpal tunnel is
formed by the carpal bones dorsally and the transverse carpal ligament (TCL)
volarly, with nine flexor tendons and the median nerve passing through the tunnel.
The median nerve is vulnerable to compression due to the unyielding borders of the
tunnel; when the median nerve experiences compression, its blood flow is reduced
and symptoms of pain and paresthesias ensue in the median nerve distribution. Most
cases of CTS are idiopathic or unknown; however some cases have been attributed
to trauma, fluid overload states (pregnancy, renal disease, congestive heart failure),
and space occupying lesions in the carpal tunnel (ganglion cyst, anomalous tendon,
lipoma), all with the common pathway of compression on the median nerve [42].
Surgical release of the TCL is the standard treatment of choice for CTS when
nonoperative measures fail. When the TCL is released open or endoscopically, there
are many known and even more unknown biomechanical consequences. In an endo-
102 S. Regal et al.

scopic carpal tunnel release, the incision is performed from within the carpal tunnel
and only the TCL is incised, whereas in an open release, the skin, fat, and superficial
fascial layer are incised. The intact TCL helps maintain the concavity of the carpal
arch and acts as a pulley for the flexor tendons of the hand. After surgical release of
the TCL, the volume of the carpal tunnel is increased, thus decreasing the compres-
sion on the median nerve. Magnetic resonance imaging (MRI) studies have shown
the contents of the carpal tunnel to be displaced volarly after carpal tunnel release
(CTR). With anterior displacement of the flexor tendons, their moment arm is effec-
tively increased which theoretically may result in decreased grip strength. Several
in vitro biomechanical studies found that flexor tendon excursion was significantly
increased, as much as 26%, after CTR [43, 44]. Some surgeons lengthen and recon-
struct the TCL after a CTR; small clinical studies have shown less volar displace-
ment of carpal tunnel contents as well as earlier improved grip and pinch strength
compared to CTR without reconstruction. These results are perceived to be caused
by the mechanical advantage of the restoring the flexor pulley [45, 46].
Carpal arch flattening and widening of the carpal bones is another known conse-
quence of CTR, though not all authors agree on the extent of widening or its clinical
effects. Kwon et al. [47] compared carpal arch widths with radiographs before and
6 months after open CTR and found the carpal arch widened on average 1.8 mm
after surgery while previous MRI studies found as much as 2.7 mm of carpal arch
widening after release of the TCL. In a finite element study, Guo et al. [48] reported
after TCL release and an axial load was placed, all carpal bones became more radi-
ally deviated and the contact forces at the midcarpal joint were altered, and yet
long-term biomechanics and its clinical effects of dividing the TCL remain unclear.
Recently, Li and colleagues proposed a nonsurgical treatment of carpal tunnel
­syndrome by biomechanically manipulating the carpal arch width as a means to
expand carpal tunnel area and decompress the median nerve [49–51].

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Chapter 5
Biomechanics of the Elbow

Su-Ya Lee and Fong-Chin Su

Abstract This chapter introduces the anatomy, function, and pathomechanics of

the elbow. First, the bone, joints, muscles, tendons, ligaments, and joint capsules in
the elbow are reviewed. The normal functions of the elbow are introduced from
aspects of kinematics, kinetics and joint stability and constraint. The elbow joint
configuration, joint motion, and joint force are integrated to provide joint stability.
The understanding of normal elbow function provides information and applications
in investigation of the pathomechanics of the elbow. The abnormal joint motion and
instability including valgus instability, posterolateral rotatory instability, varus pos-
teromedial rotatory instability, elbow dislocation, elbow fracture, and elbow joint
arthritis are examined. The tendinopathy and cubital tunnel syndrome are also
important to be explained from pathomechanics point of view.

Keywords Elbow · Biomechanics · Anatomy · Function · Kinematics · Kinetics

Stability · Constraint · Pathomechanics

1 Anatomy

1.1 Bone and Joints in the Elbow

The elbow, a complex joint, is composed of the ulna, the radial, and the distal
humerus. The elbow joint is formed by the three articulations, which include ulno-
humeral, radiocapitellar, and proximal radioulnar joint in the elbow (Fig. 5.1a, b).
The distal humerus has several important anatomical landmarks including trochlea,
capitellum, medial epicondyle, lateral epicondyle, coronoid fossa, radial fossa, and
coronoid process in the anterior view (Fig. 5.1c) and coronoid process in the poste-
rior view. These anatomical landmarks in the distal humerus play an important role

S.-Y. Lee · F.-C. Su (*)

Department of Biomedical Engineering, National Cheng Kung University, Tainan, Taiwan
e-mail: fcsu@mail.ncku.edu.tw

© Springer Nature Singapore Pte Ltd. 2020 105

C.-K. Cheng, S. L-Y. Woo (eds.), Frontiers in Orthopaedic Biomechanics,
https://doi.org/10.1007/978-981-15-3159-0_5
106 S.-Y. Lee and F.-C. Su

Lateral epicondyle
Medial epicondyle
Capitellum

Radial head
Trochlea

Coronoid process

Trochlea
Medial epicondyle
Lateral epicondyle
Olecranon
Radial head

Radial fossa Coronoid fossa

Lateral epicondyle Medial epicondyle

Capitellum

Trochlea

Fig. 5.1 (a) Anterior view of elbow joint. (b) Posterior view of elbow joint. (c) Anterior view of
distal humerus
5 Biomechanics of the Elbow 107

to stabilize the elbow joint during the elbow extension and flexion with a wide range
of motion. The coronoid fossa and radial fossa provide the osseous stability and
prevent anterior impingement during flexion of the elbow joint. The olecranon fossa
also provides the osseous stability and prevent posterior impingement during exten-
sion of the elbow joint.
The ulnohumeral joint is formed by the trochlea of the humerus and olecranon of
the ulna (Fig. 5.2a) to stabilize the elbow joint during extension and prevent poste-
rior translation. The function of the ulnohumeral joint, hinge joint, is the movement
of flexion and extension of the arm. The radiohumeral joint, ball-and-socket joint, is
formed by the convex structure of capitellum and concave structure of the radial
head (Fig. 5.2b) to stabilize the elbow joint during flexion and be a valgus stabilizer
of the elbow joint. The proximal radioulnar joint is formed by the lesser sigmoid
notch of ulna and the margin of the radial head. The function of the proximal radio-
ulnar joint and the radiocapitellar joint is the movement of supination and pronation
of the forearm. The radial head is covered with the large area of articular cartilage
which is nearly 270–280° along the proximal radioulnar joint and the radiocapitel-
lar joint.

a Olecranon

Sagittal ridge
Greater sigmoid notch

Sublime tubercle
Lesser sigmoid notch
Coronoid process

b Radial head

Radial neck

Radial tuberosity

Fig. 5.2 (a) Anterior view of ulna. (b) Anterior view of radial
108 S.-Y. Lee and F.-C. Su

Carrying angle, a small degree of cubitus valgus, occurred at the forearm full
extension and supination due to the noncollinearity between the long axis of ulnar
and long axis of humerus. The average carrying angle is 13–16° for women and
11–14° for men. During the movement of elbow joint flexion, the carrying angle
will decrease and disappear due to the colinearity between the long axis of ulnar and
long axis of humerus.

1.2 Muscles, Their Innervation and Tendons

According to movement functions of muscles around the elbow, they can be classi-
fied into the elbow extensor muscles, elbow flexor muscles, wrist flexor muscles,
and wrist extensor muscles. These muscles play an important role in the dynamic
stabilizers to prevent the elbow subluxation and reinforce the osseous stability of the
elbow. These muscles are innervated by the median nerve, radial nerve, ulnar nerve,
and musculocutaneous nerve (C5–C7), respectively.
The elbow extensor muscles are triceps brachii muscles and anconeus muscle.
The triceps brachii muscle is the main elbow flexor muscle and its maximal muscle
is efficient when elbow is flexed at 20–30°. The anconeus muscle has an assistant
elbow extensor role during the elbow extension and a major dynamic stabilizer to
restrain the posterolateral and varus force on the elbow joint. The elbow flexors are
brachialis, brachioradialis, biceps brachii, and pronator teres. The short head of
biceps brachii is a main elbow flexor muscle and a stronger elbow flexor muscle
compared to the brachialis muscle. Brachioradialis has a great mechanical advantage
of any elbow flexor muscles; however, brachialis has a poor mechanical advantage
as it is near the axis of rotation. The common extensor tendon, which is the origin of
the wrist extensor muscles, consists of the extensor carpi radialis brevis, extensor
carpi ulnaris, extensor digitorum communis, and extensor digiti minimi. The wrist
flexor muscles in the medial side of elbow are flexor carpi radialis, flexor carpi ulna-
ris, flexor digitorum superficialis, and flexor digitorum profundus. The common
extensor tendon, which is the major wrist extensor muscles, consists of the flexor
carpi radialis, flexor carpi ulnaris, flexor digitorum superficialis, pronator teres, and
palmaris longus. The wrist extensor muscles in the lateral side of elbow are extensor
carpi radialis longus, extensor carpi radialis brevis, extensor carpi ulnaris, extensor
digitorum communis, extensor digiti minimi, and anconeus. The forearm pronation
muscle is pronator teres and the forearm supination muscles are supinator and long
head of biceps brachii. When the arm is the extreme supination posture, brachiora-
dialis can assist in the pronation of the forearm.
All of wrist flexor and pronator teres are innervated by the median nerve, except
for the flexor carpi ulnaris and little and ring finger flexor digitorum profundus,
which are innervated by the ulnar nerve (Fig. 5.3a). The elbow extensor muscles
include triceps brachii in the lateral and medial heads and anconeus. All of wrist
extensor muscles, brachioradialis and supinator are innervated by the radial nerve
(Fig. 5.3b). Biceps brachii is innerved by the musculocutaneous nerve (C5–C7)
and brachialis is innerved by the musculocutaneous nerve (C5–C6).
5 Biomechanics of the Elbow 109

Ulnar nerve
Medial nerve

Pronator teres

Flexor carpi radialis Flexor carpi ulnaris

b Radial nerve

Brachioradialis muscle

Anconeus Extensor carpi radialis longus

Supinator Extensor carpi radialis brevis

Deep branch radial nerve
Superficial branch radial nerve
Extensor digitorum
Abductor pollicis longus
Extensor carpi ulnaris
Extensor pollicis brevis

Fig. 5.3 (a, b) Motor innervation of wrist flexors

1.3 Ligaments and Joint Capsules in the Elbow

The elbow joint is enclosed by the joint capsule, which is surrounded around the
olecranon, the coronoid fossa, and the radial fossa, except for the humeral epicon-
dyle (Fig. 5.4). The joint capsule, a secondary static stabilizer, has a laxity on the
anterior and posterior side of elbow joint to provide the appropriate movement of
elbow joint during the flexion and extension. The brachialis muscle and triceps bra-
chialis muscles can prevent the joint capsule to pinching in the joint and maintain
the sufficient tension on the capsule during extension and flexion.
The collateral ligaments are fused with the joint capsules and can be divided into
the lateral collateral ligament and medial collateral ligament. The collateral liga-
ments, a primary static stabilizer, cross the articular joints of elbow. The collateral
ligaments have the tension to restrict the varus motion, the valgus motion, and the
axial rotation motion. The function of lateral collateral ligament complex is to
­maintain the stability during the posterolateral force on the elbow joint and hinder
110 S.-Y. Lee and F.-C. Su

varus stress on the elbow joint. The function of medial collateral ligament is to
maintain the stability during the posteromedial force on the elbow joint and hinder
valgus stress on the elbow joint. The lateral collateral ligament complex is com-
posed of lateral ulnar ligament, the radial collateral ligament, and the annular liga-
ment (Fig. 5.5). The annular ligament, one of the lateral collateral ligament complex,

Fig. 5.4 Anterior view of

the joint capsule

Annular ligament

Radial collateral ligament

Lateral ulnar collateral ligament

Fig. 5.5 Lateral collateral ligament complex

5 Biomechanics of the Elbow 111

Anterior bundle

Posterior bundle

Transverse bundle

Fig. 5.6 Medial collateral ligament complex

enclosed the radial head, and the insertion/origin of the annular ligament is located
at the ulna to maintain the stability of forearm rotation.
The medial collateral ligament complex is formed by the anterior bundle, poste-
rior bundle, and transverse ligament (Cooper ligament) (Fig. 5.6). The anterior
bundle of the medial collateral ligament is formed by thick parallel fibers [1], the
posterior bundle of the medial collateral ligament is formed by the fan-shaped cap-
sular fibers [2], and the transverse ligament is formed by the horizontal capsular
fibers [3]. The anterior bundle of the medial collateral ligament is attached to the
antero-inferior aspect of the medial epicondyle and provide the constant tension
during the elbow flexion and extension. The anterior bundle can be further separated
to the anterior band and posterior band. The anterior band of the anterior bundle of
medial collateral ligament shows an isometric strain pattern during the elbow flex-
ion and the posterior band of the anterior bundle of medial collateral ligament has
increased its strain value with the increase of elbow flexion [4]. The difference in
strain pattern between the anterior and posterior bands of the anterior bundle of the
medial collateral ligament is due to the insertion point in the elbow joint [4]. The
posterior bundle of the medial collateral ligament has a tension during the elbow
flexion to restrain the valgus stress [5].

2 Function

2.1 Kinematics of the Elbow

The elbow joint consists of three articulations including ulnohumeral, radiocapitel-

lar, and proximal radioulnar articulations. The ulnohumeral, principal articulation,
allows the motion of flexion-extension in the nearly sagittal plane. The normal range
112 S.-Y. Lee and F.-C. Su

of motion for the elbow joint consists of 0° full extension and 146° extension. The
functional range of motion for the elbow joint consists of 30° flexion and 130° exten-
sion. Recently, researchers have investigated the kinematics of elbow joint by nonin-
vasive three-dimensional technique [6–9]. The instant screw axis of rotation of
elbow flexion-extension is a changeable circular path with the elbow flexion. During
the movement of elbow flexion, the path of axis of rotation showed a counterclock-
wise pattern and a conical shape on the lateral condyle and this path of axis of rota-
tion crossed and converged at the medial facet of the trochlea [6]. The average axis
of elbow flexion-extension is a line from the anterior aspect of the medial epicondyle
to the center of trochlea and the capitellum which has 4–8° valgus relative to the long
axis of the humerus. During the movement of flexion, ulna changes its position with
the anterior glide, lateral shift, and varus rotation relative to the humerus [7, 8]. The
ulna has the internal rotation from the full extension to 90° flexion and external rota-
tion from the 90° flexion to the full flexion relative to the humerus [7, 8]. During the
movement of extension, particularly in the last 5–10°, the ulna has the posterior glide
relative to the humerus. The humerus has significant compression force on the ulna
with the elbow 90° flexion because the greater sigmoid notch has a nearly posterior
30° respective to the axis of the ulna (Fig. 5.7) and the capitellum/trochlea has a near
anterior 30° respective to the axis of the humerus [10, 11].
The proximal radioulnar and radiocapitellar articulations allow motion of fore-
arm pronation and supination in the transverse plane. The normal range of motion
for the forearm pronation-supination consists of 71° pronation and 81° supination.
The axis of forearm rotation is a line from the center of the radial head to the distal
ulna. The forearm pronation-supination plays an important role in the daily activ-
ity which required 50° pronation and 50° supination to perform the functional
movement. Previous studies investigated the motion of radius and ulna during the
movement of forearm pronation-supination via two-dimensional computed tomog-
raphy [12] and three-dimensional computational model [9]. From supination to
pronation, the radius showed a varus rotation, internal rotation, and extension rela-
tive to humerus and ulna showed a valgus rotation [9]. The center of radial head
has anterior, proximal, and lateral translation with the forearm pronation. The con-

30°

Fig. 5.7 Angle between greater sigmoid notch and axis of the ulna
5 Biomechanics of the Elbow 113

tact area of radiocapitellar has a large congruency in the forearm pronation and the
contact area of proximal radioulnar joint has a large congruency in the forearm
supination [9].

2.2 Kinetics of the Elbow

2.2.1 Elbow Joint Forces

The elbow joint plays an important role in the daily activity of the upper extremity.
Understanding the force distribution in the elbow joint is essential to design joint
replacement and investigate the effect of osteotomy. With the 15° elbow flexion with
full pronation and wrist extension, the axial compressive load of 100 N transmitted to
the radiocapitellar joint is approximately 61% loading distribution [13]. With the
increasing weight of axial loading, the axial load distribution through the radiocapitel-
lar joint has decreased to 55% [13]. When the axial compressive load of 160 N is
transmitted to the radiocapitellar, there is nearly 90 mm2 contact area at the radiocapi-
tellar joint at 0° of flexion [14]. The contact area at the ulnohumeral joint increased
from the elbow extension to elbow flexion [15, 16]. The contact area at the radiocapitel-
lar joint increased with the increase of angle of elbow flexion [17]. In general, the peak
contact pressure of radial head does not exceed 5 MPa and the daily activities applied
approximately 100 N force at the radiocapitellar articulation [18]. The contact pressure
of the humeroulnar joint increased from the elbow extension to elbow flexion [15, 16].

2.2.2 Joint Reaction Forces at the Elbow

The free-body diagram is used to estimate the joint reaction force by the equilibrium
equations. The equilibrium equations assume that the sum of forces and sum of
moments acting on the elbow joint are zero. The calculation of elbow joint reaction
force needs to consider the weight of external object, weight of forearm and arm, the
distance between center of mass of forearm/arm and the center of rotation of the joint,
the line of action of muscle, and the angle of forearm and arm in the free-body dia-
gram. The biceps and brachialis muscle was considered as the primary elbow flexors
and the triceps is considered as the primary elbow extensor [10, 19]. Regarding the
dynamic movement that generates the acceleration in the limbs, the joint force and
joint moment at the elbow can be calculated by the inverse Newton-­Euler method.
Recently, most of the studies investigated the joint force and moment at the elbow
joint during performing the daily activities of the upper extremity [20, 21]. The block
to head height generates the flexion moment and external rotation moment of the
elbow joint and the elbow joint force along the humeral longitudinal axis and rotation
axis that is perpendicular to the humeral longitudinal axis than other upper extremity
activities [21]. The reach to head side and back are the high demand of elbow flexion,
forearm pronation, elbow extension moment, and elbow internal rotation moment [21].
114 S.-Y. Lee and F.-C. Su

2.3 Stability and Constraints of the Elbow

A stable joint provides the normal functional activity of the elbow. The dynamic and
static factors contribute to the joint stability by anatomy of the joint, surrounding liga-
ment, joint capsule, and muscles. The bony geometry of elbow joint contributes much
to the joint stability due to its congruous articulation. The radial head and coronoid
process are the major articulation stabilizers to prevent the posterior subluxation or
dislocation. A previous study showed that at least 50% coronoid height is needed to
provide the stability of elbow joint under the valgus force and foramen supination
[22]. The radial head is the minor articulation stabilizer relative to the coronoid pro-
cess [11]. The ligament, joint capsule, and articulation form the static stabilizer of the
elbow joint. The primary static stabilizer consists of ulnohumeral joint and anterior
bundle of medial collateral ligament and the secondary stabilizer consists of radio-
capitellar joint, common flexor tendon, common extensor tendon, and the joint cap-
sule. The anterior joint capsule can be against the joint distraction, joint hyperextension,
valgus stress, and the posterior joint capsule can against the joint hyperflexion and
posterior directed force [19]. Muscles are the dynamic stabilizer across the elbow
joint because muscle contraction can generate the compressive force. The elbow flex-
ors can generate the varus moment to resist the valgus force and elbow extensors can
resist the varus force of elbow joint [23]. The muscles contributing for the valgus
stability are flexor carpi ulnaris and flexor digitorum superficialis muscle [24].
Collateral ligaments are the important soft tissue of the elbow joint to act as the
static stabilizer of elbow joint. In the medial side of elbow joint, the medial collat-
eral ligament is composed of multiple bundles against the valgus force and postero-
medial (internal) rotatory instability. The anterior bundle of the medial collateral
ligament is the strongest bundle of the medial collateral ligament to prevent the
valgus and posteromedial rotatory instability [5, 25]. Additionally, the anterior bun-
dle of the medial collateral ligament is the priority reconstruction of the medial
collateral ligament in clinics because it is the primary restrain and stabilizer [25,
26]. The anterior bundle of medial collateral ligament is composed of the anterior
and posterior bands. The anterior band of anterior bundle of the medial collateral
ligament is the primary restraint to provide the stability in the valgus force [2]. At
120° elbow flexion, the anterior and posterior bands of the anterior bundle of medial
collateral ligament are the co-primary restraints when applying the valgus force [5].
Therefore, the anterior band of anterior bundle of medial collateral ligament may
have isolated injury between 0° and 90° elbow flexion. When the elbow flexion is
greater than 90°, both the anterior and posterior bands of anterior bundle of medial
collateral ligament may be injured at the same time [5]. Recently, the poster bundle
of medial collateral ligament has been considered as a stabilizer, independent of the
integrity of anterior bundle of medial collateral ligament, in the posteromedial
elbow instability. After transection of posterior bundle of medial collateral ligament,
the proximal ulnohumeral joint gapping and torsion angle of ulnohumeral joint
increase as the elbow flexion increases [27] with the intact anterior bundle of medial
collateral ligament.
5 Biomechanics of the Elbow 115

In the lateral side of elbow joint, the lateral ulnar collateral ligament is attached
to the superior crest of the ulna, which is blended with the distal annular ligament at
the proximal of ulna [3]. The lateral ulnar collateral ligament is the primary con-
straint in the lateral collateral ligaments to provide the stability of the ulnohumeral
joint during the varus force and external rotated force [28]. A previous study showed
that one of the distal sections of lateral ulnar collateral ligament or annular ligament
was dissected which generates minor laxity of the elbow joint during the applied
varus and external rotated forces [29]. Both the lateral collateral ligament and lateral
radial collateral ligament were dissected which result in the significant rotatory lax-
ity [29]. The entire transection of the lateral collateral ligament at the insertion or
origin causes the maximal laxity [29]. The maximal external rotatory laxity was
20.6° at the 110° elbow flexion [29]. According to a previous study, the anterior
portion of the lateral collateral ligament causes the significant laxity when applied
the varus and external rotational forces at 80° elbow flexion [30].
To sum up, previous studies showed that articulation is the primary stabilizer
under varus stress and the medial collateral ligament is the primary stabilizer under
valgus stress in elbow flexion [11, 19, 26]. The lateral collateral ligament, capsule,
and osseous structure provide 9%, 13%, and 75%, respectively, for resisting the
varus force in the 90° flexion of elbow joint [31]. The medial collateral ligament,
anterior capsule, and articulation provide 54%, 10%, and 36%, respectively, for
resisting the valgus force in the 90° flexion of elbow joint [31]. The anterior bundle
of medial collateral ligament is the primary stabilizer and the radial head is a sec-
ondary stabilizer of the elbow to resist the valgus force [26]. In the elbow extension,
articulation is the primary stabilizer during the applied varus force of the elbow
joint, and medial collateral ligament, capsule, and articulation have a similar contri-
bution to stabilize the elbow joint during the applied valgus force of the elbow joint
[11, 19, 26]. The medial collateral ligament, anterior capsule, and articulation pro-
vide 31%, 38%, and 31%, respectively, for resisting the valgus force in the full
extension of elbow joint [31]. The lateral collateral ligament, capsule, and osseous
structure provide 14%, 32%, and 55%, respectively, for resisting the varus force in
the full extension of elbow joint [31].

3 Pathomechanics of Elbow

3.1 Abnormal Joint Motion and Instability

3.1.1 Valgus Instability, Posterolateral Rotatory Instability, Varus

Posteromedial Rotatory Instability, and Elbow Dislocation

The valgus and varus loads influence the pattern of contact in the elbow joint, which
is importance for the valgus instability, posterolateral instability, and varus postero-
medial instability in the clinics. Elbow instability pattern is based on the injury
duration, involvement of articulation, the direction of laxity, the extent of laxity, and
116 S.-Y. Lee and F.-C. Su

with or without fracture of elbow joint [32]. The injury of medial collateral liga-
ment, especially anterior bundle, causes the valgus instability after the overuse
injury (chronic injury) [33] or single acute traumatic injury [34]. The disruption of
lateral collateral ligament is the main factor to cause the posterolateral rotatory
instability under an axial load combining valgus load and the forearm supination
after a traumatic injury [33]. The resultant force transmits from the lateral side to
medial side causing the progressive structure injury of the elbow joint. The postero-
lateral rotatory instability is the frequent recurrent instability of the elbow [33]. The
varus posteromedial rotatory instability is associated with the anteromedial facet of
the coronoid fracture, a rupture of the lateral collateral ligament and posterior bun-
dle of the medial collateral ligament under a varus load with the forearm pronation
[35, 36]. Therefore, it is important to understand the contributions of soft tissues and
bony geometry in the stability of elbow joint.
Previous studies have used the cadaver to investigate the extent of valgus laxity
at the specific joint angle by sectioning the different degree of medial collateral liga-
ment and articulation of elbow [2, 26]. Table 5.1 shows the relationship between
valgus laxity and medial collateral ligament, radial head, and muscle force of the
elbow joint. The maximum valgus laxity occurred at the 70–90° elbow flexion with
anterior bundle of medial collateral ligament release and radial head intact [37]. The
entire medial collateral ligament release with the radial head intact causes the 31.2
valgus laxity at the 90° elbow flexion [2]. Additionally, the entire medial collateral
ligament release with radial head removal results in the gross valgus and internal
rotational instability [26].
Posterolateral rotatory instability is a recurrent injury and the most common pat-
tern of elbow instability [32, 38, 39]. Posterolateral rotatory instability commonly
occurs at the tear or disruption from the lateral collateral ligament to the ulnar col-
lateral ligament leading to the elbow dislocation after a traumatic injury [30]. The
tennis elbow or iatrogenic injury from prior lateral elbow surgery may be factors to
cause the posterolateral rotatory instability. Posterolateral rotatory instability is
associated with the posterolateral subluxation or dislocation of the radial head and
proximal ulna away from the humerus due to the laxity of the lateral collateral liga-
ment [40]. Posterolateral rotatory instability can be further divided into three stages
according to the degree of soft tissue disruption and displacement of elbow joint
(Table 5.2).
Posteromedial rotatory instability occurred under the varus load and is associ-
ated with the subluxation and dislocation of the elbow joint [41]. The posteromedial
rotatory instability causes the articular incongruity because the radius and ulnar
rotate posteromedially which is off the articulation of humerus and this injury can
in turn cause the increase of contact pressure in the coronoid surface [41]. The
anteromedial facet fracture [42–44], tear of the lateral ulnar collateral ligament
injury [41], and posterior bundle of the medial collateral ligament injury [27] are
associated with the posteromedial rotatory instability. A previous study indicated
that the isolated sectioning of the posterior bundle of the medial collateral ligament
can cause the increase of 4.5 and 2.7 ulnar rotations at 60° and 90° elbow flexion,
respectively, to generate the posteromedial instability of the elbow joint [27].
5 Biomechanics of the Elbow 117

Table 5.1 The relationship between valgus laxity and medial collateral ligament, radial head, and
muscle force of the elbow joint
UCL intact Radial head Without 5 Normal valgus laxity 10–20° elbow flexion
intact muscle [26]
loading
UCL intact Radial head With 2.6 Valgus laxity [26]
intact muscle
loading
AOL release Radial head • 14 Valgus laxity • 70° elbow flexion [26]
intact • Maximum internal • 60° elbow flexion [2]
rotational laxity
AOL release Radial head 50 Valgus laxity [26]
removal
AB of AOL Radial head • 11.7 Valgus laxity • 30° elbow flexion [2]
release intact • Maximal internal • 40° elbow flexion [2]
rotational laxity
PB of AOL Radial head Little change in valgus [2]
release intact and internal rotation
UCL intact Radial head Little change in valgus
removal and internal rotation
POL release Radial head Little change in valgus [26]
removal or and internal rotation
not
AB Radial head Did not induce more [2]
release + POL intact laxity
release
AOL Radial head • Completely unstable 90° elbow flexion (full
release + POL intact • 31.2 Valgus laxity flexion and full extension
release can confer some stability
with joint surface) [2]
Entire UCL Radial head Gross valgus and • Increase of internal
release removal internal rotational rotational laxity
instability • Increase of elbow
flexion [26]
Entire UCL Radial head Muscle Restore some stability [26]
release removal force (compared to a
UCL-deficient elbow)

Table 5.2 The classification of the PLRS [39]

Stage Soft tissues Elbow joint
1 Posterolateral rotatory 1. Detach or tear lateral collateral Posterolateral
instability ligament subluxation
2 Subluxation 1. Progresses anteriorly and posteriorly Greater
around the elbow to the medial side displacement
2. Detach or tear capsule
3a and Posterior dislocation 1. Involve the medial collateral ligament Fully dislocates
3b and detach
3c Posterior dislocation 1. Detach or tear the common flexor Grossly unstable
pronator origin elbow
118 S.-Y. Lee and F.-C. Su

Besides, the ulnohumeral joint gapping increase with the increase of elbow flexion
after the sectioning of the posterior bundle of the medial collateral ligament.
According to the findings of contact pressure of the coronoid surface, the anterome-
dial fracture with the lesion of lateral collateral ligament which is the involvement
of posteromedial rotatory instability has the high contact pressure value at the edge
of coronoid fracture with lower contact area compared to the intact elbow [41]. The
anteromedial fracture with the posteromedial rotatory instability and tear of lateral
collateral ligament causes a significant subluxation and decreases of elbow flexion
compared to the coronoid fracture with lesion of posterior medial collateral liga-
ment [41]. Therefore, the lateral collateral ligament is an important factor for pre-
venting the subluxation in the posteromedial rotatory instability. According to
previous studies, posterior medial collateral ligament can contribute part of the sta-
bility under the resistance of varus and internal rotational instability (posteromedial
elbow instability) [27, 45].

3.1.2 Elbow Fracture

Elbow is the second dislocated major joint of the upper extremity in adults [46] after
a traumatic injury. Posterior dislocation, a common disorder in the elbow joint,
causes the injury of soft tissues including tear of lateral collateral ligament, the dif-
ferent extent injury of the ulnar collateral ligament and flexor-pronator muscles of
elbow joint [42]. The valgus posterolateral rotatory load is a more common mecha-
nism to cause the elbow dislocation and fracture than varus posteromedial rotatory
load [47]. When the greater sigmoid notch has posterior and inferior subluxation
under a valgus posterolateral rotatory load, a shearing force transmits to the tip of
coronoid to induce the coronoid fracture [48, 49]. The severe valgus posterolateral
rotatory injury eventually results in the terrible triad injury, which causes the elbow
dislocation with radial head and coronoid fractures and ruptures the medial collat-
eral ligament.
Radial head fracture (Fig. 5.8) is associated with the posterior dislocation of the
elbow joint. The 10–15% patients with posterior dislocation have combined with
the radial head fracture or coronoid fracture [50]. Coronoid fracture which is a fre-
quent fracture type of the elbow joint [51] can be divided into three types including
transverse fractures of the tip, fracture involving the anteromedial facet, and frac-
tures at the coronoid base [43] (Fig. 5.9). In the transverse coronoid fracture with tip
subtype II and 50% coronoid height of the elbow joint, the transection of posterior
bundle of the medial collateral ligament causes the significant increase of ulnohu-
meral joint gapping during the elbow flexion [52]. However, the reconstruction of
the posterior bundle of the medial collateral ligament only can decrease the ulnohu-
meral joint gapping and forearm rotation at 90° elbow flexion to restore posterome-
dial stability [52]. It indicated that the intact posterior bundle of the medial collateral
ligament can provide some of the posteromedial stability after coronoid fracture
without fixing [52]. The anteromedial fracture of the coronoid can be further subdi-
vide to three subtypes according to the injury site of the anteromedial coronoid face
5 Biomechanics of the Elbow 119

Fig. 5.8 Type of radial head fracture

Tip

Anteromedial
Radial head

Coronoid process

Basal

Proximal ulna

Fig. 5.9 Type of coronoid fracture

including (1) injury of the anteromedial rim, (2) injury of the anteromedial rim and
tip, (3) injury of the anteromedial rim, tip, and the whole sublime tubercle [43]
(Fig. 5.6). Both the lateral collateral ligament and the posterior bundle of the medial
collateral ligament have tear associated with the anteromedial fractures [43, 44, 53].
The coronoid fracture can increase the forearm rotation angle, which is associated
with the posteromedial instability of the elbow joint [43, 44, 52]. Recently, many
researchers have investigated the effect of extent injury of anteromedial fractures
with lesions of lateral collateral ligament or the posterior bundle of the medial col-
lateral ligament on the posteromedial elbow instability [43, 44].
In clinics, the appropriate reconstruction and fixation can restore the range of
motion and stability of elbow joint, increase the functional outcomes, and reduce
the pain. The valgus posterolateral rotatory injury, terrible triad injury, causes the
elbow dislocation combined with the lateral collateral ligament rupture and radial
head and coronoid process fraction. The management of the valgus posterolateral
rotatory includes fixation of the coronoid, fixation or replacement of the radial
head, repair of the lateral ulnar collateral ligament, possible repair of the medial
120 S.-Y. Lee and F.-C. Su

collateral ligament, and external fixation of elbow as elbow remains unstable. The
coronoid fracture can be repaired by the suture lasso technique for the small frag-
ment of coronoid and by the lag screws with/without mini fragment plate for the
large fragments of the coronoid [49]. The partial radial head fracture can be fixed
with the screws [54, 55] or mini fragment plate [56]. The radial head replacement
can be used to fix the radial head for more than three fragments and the prosthesis
of radial head needs 2 mm distal to the coronoid [57]. In clinics, the lateral collat-
eral ligament was commonly reconstructed by grasping type stitch to restore the
elbow stability and prevent the subluxation under a valgus force [58] because the
valgus posterolateral rotatory injury causes the detachment and avulsion of lateral
collateral ligament from its attachment in the humerus. Recently, some researchers
have indicated that the soft tissue injury may occur initially from the medial side of
elbow joint [47, 59]. According to the MRI findings, posterolateral direction results
in distractive injury to cause the displacement of the soft tissue in the ulnar side
from the insertion point and detachment of soft tissue in the lateral side near the
original point [47]. Therefore, the anterior bundle of medial collateral ligament
may be the initial injury site at some acute injury situation with posterolateral dis-
location [59].
The varus posteromedial rotatory injury causes the avulsion of the lateral col-
lateral ligament and fracture of anteromedial facet of the coronoid. The surgical
fixation was commonly used to repair the anteromedial facet fracture by internal
fixation [44] through buttress plate and screw to fix the anteromedial facet fragment.
There are many surgical approaches including flexor carpi ulnaris-splitting approach,
over-the-top approach [60], posterior incision following the development of a
medial skin flap [61], and the floor of the cubital tunnel approach following trans-
portation of the ulnar nerve to repair the anteromedial facet fracture [62].
Anterior olecranon fracture dislocation is a high-energy injury in a dorsal aspect
of the forearm at the elbow 90° flexion, causing the anterior dislocation of the
radius and ulnar [63] with a large simple coronoid fragment [35]. Posterior
Monteggia fracture is a low-energy injury causing the fracture at the base of the
coronoid process. About 50% patients with posterior Monteggia fracture has com-
bined with radial head fracture and avulsion of the lateral collateral ligament com-
plex [64].

3.1.3 Elbow Joint Arthritis

The osteoarthritic elbow is a degenerative disease that cause osteophytes at the cor-
onoid, olecranon, and radial head, decrease of the joint space of the ulnotrochlear
and radiocapitellar, loose bodies, soft tissue contracture, and synovitis [65, 66]. The
post-traumatic osteoarthritic elbow is in majority of osteoarthritic elbow due to the
elbow dislocation, radial head fracture, and coronoid fracture to cause the cartilage
lesion and post-traumatic deformity [67]. The post-traumatic osteoarthritic elbow
commonly begins from the radiocapitellar joint to ulnohumeral joint with soft tissue
destruction [65, 68, 69]. The osteoarthritic elbow can result in the joint deformity to
5 Biomechanics of the Elbow 121

restrict the joint mobility and elbow stiffness in the advanced stage [66, 68, 69]. The
treatment of osteoarthritic elbow includes the conservative treatment and surgical
treatment. The conservative treatment is the first choice and the surgical treatment
is used when there is failure of nonsurgical treatment [70] and significant impair-
ment of the daily actives (range of motion of elbow less than 30–130°) [68]. The
surgical treatment of osteoarthritic elbow includes arthroscopic approaches [70–72]
and open techniques to restore the joint mobility and relieve the pain. The
arthroscopic debridement focuses on removing the osteophytes, inflamed soft tis-
sue, and loose bodies, releasing the tight capsular, and resecting the radial head [70,
71]. The arthroscopic debridement can restore the functional elbow mobility,
improve the clinical scores, decrease the severity of elbow stiffness, and relieve the
pain for primary and post-traumatic osteoarthritic elbow [71]. According to previ-
ous studies, the early and mild osteoarthritic elbow with the joint congruence can
use the arthroscopy treatment and this treatment can provide the good postoperative
functional and clinical outcomes at follow-up 24 months [70, 71, 73]. The radial
head excision is commonly used in the patients with osteoarthritic elbow involved
in the radiocapitellar arthritis. Patients who underwent radial head excision alone
had a greater return of range of motion and clinical outcomes after mean follow-up
52 months [74]. However, the radial head plays an important role in the valgus sta-
bility. The resection of the radial head decrease valgus instability and increase ulno-
humeral joint pressure under an axial load, eventually leading to the degenerative
changes [13, 75, 76]. The effect of radial head excision has recently been investi-
gated on the progression of ulnohumeral articular surface damage in the arthroscopic
debridement [77]. A previous study showed that the patients with moderate and
severe radiocapitellar chondral loss can improve elbow motion (flexion, extension,
pronation, and supination) and relieve the pain after arthroscopic debridement of
the arthritic elbow without radial head excision [77]. Additionally, a previous study
showed that the shortening osteotomy of proximal radial of 2.5 mm, in the
radiocapitellar osteoarthritis, can preserve the intact radial head to decrease the
radiocapitellar contact pressure under a 250 N axial loading and remain the valgus
stability during the elbow movement [13]. The shortening osteotomy of radial head
might delay the ulnohumeral degeneration [13].
The prosthetic replacement may be considered in patients with severe osteoar-
thritic elbow and joint incongruence or elbow fracture-dislocation. Radiocapitellar
replacement is used as the failure of repairing the radial head by the internal fixa-
tion. The radialcapitellar replacement has the metallic monopolar and bipolar
flexed-neck prosthesis, which have demonstrated good clinical outcomes in repair-
ing the elbow fracture dislocation [78–81]. In regard to the stability of elbow joint,
monopolar implant significantly improves the ulnohumeral laxity and radiocapitel-
lar joint subluxation compared to the bipolar implant in the terrible triad models
[82, 83]. The lateral collateral ligament of elbow is the varus stabilizer; therefore,
the integrity of the lateral collateral is an important factor to affect the elbow stabil-
ity of the radialcapitellar replacement [84]. A previous study indicated that both
monopolar and bipolar prosthesis would improve the stability of the elbow joint in
the coronal plan and axial rotation loading as the adequate lateral collateral liga-
122 S.-Y. Lee and F.-C. Su

ment construction and intact medial collateral ligament [85]. The radiocapitellar
replacement has been used in patients with osteoarthritic elbow who have the asym-
metry elbow joint [86]. The degenerative and inflamed condition of osteoarthritic
elbow commonly involved the lateral side [87]. The radiocapitellar replacement can
restore the joint mobility, improve the clinical outcomes, and relieve the pain in
patients with primary and post-traumatic arthritis after postoperative 22 months
[86]. Although the orientation of the radial head cannot affect the kinematics of
ulnohumeral joint, it can affect the force transmission in the radiocapitellar joint
[88]. Therefore, the design of accurate orientation of radial head is necessary. Total
elbow arthroplasty has been developed from the constrained articulated prosthesis
to the semiconstrained and nonconstrained prostheses to reduce loosing [89]. Total
elbow arthroplasty is indicated in the rheumatoid arthritis patients, patients with
highly comminuted fracture of the distal humerus [90], or primary and post-­
traumatic osteoarthritis with the failure reconstruction [91, 92]. The limitation of
total arthroplasty is the lifting weight restriction (5-lb) during a lifetime to ensure
the durability and ultimate satisfactory function [89]. Additionally, the semicon-
strained total elbow arthroplasty cause the impaired proprioception of elbow joint
[93]. The correct positioning of the prostheses [94], ligament integrity, and prosthe-
sis design remains challenging to improve the stability of elbow joint after total
elbow arthroplasty.

3.2 Repetitive Soft Tissue Injury in the Elbow

3.2.1 Tendinopathy of Elbow

Tendinopathy of elbow can occur on the lateral side and medial side of the elbow.
The lateral tendinopathy of elbow, tennis elbow, causes the tenderness of the origin
of common extensor tendon and pain at the lateral side of the elbow [95]. The
repetitive wrist extension and supination is the major pathomechanics to cause the
degenerative condition of the common extensor tendon [96, 97]. According to previ-
ous studies, the contact pressure between the extensor carpi radialis brevis and capi-
tellum increases with the wrist supination and elbow extension during backhand
strokes [98–100]. Therefore, the repetitive loading of common tendon is a factor to
cause the lateral tendinopathy of elbow. In regard to functional outcomes, patient
with tennis elbow decreases the grip force and isokinetic performances of wrist
extensors [101]. The primary treatment in patients with the tennis elbow is the non-
surgical management by physical therapy, activity modification, nonsteroidal anti-­
inflammatory drugs, and injections for the relief of lateral-sided elbow pain [96,
102, 103]. Surgical management is indicated in patients with tennis elbow when
nonsurgical management fails [104]. Surgical management includes percutaneous,
arthroscopic, and open approaches to release of the affected extensor muscles
5 Biomechanics of the Elbow 123

[104, 105]. Recently, ultrasound has been used to diagnosis tennis elbow [106, 107].
Previous studies found that patients with tennis elbow has not only focal hypoechoic
areas and calcification but also alternation of tendon stiffness by sonoelastography
measurement [108, 109].
The medial tendinopathy of elbow, golfer’s elbow, causes the tenderness of the
origin of common flexor tendon and pain at the medial side of the elbow [110, 111].
The repetitive eccentric loading of the flexor muscles is a main pathomechanism to
cause the golfer’s elbow, especially in the wrist flexion and forearm pronation with
valgus stress at the elbow joint [112]. This long-term repetitive loading cause the
degeneration and microtrauma of tendon to result in the fibrosis and calcification
within the tendon [113]. The sonoelastography has been used to evaluate the com-
mon flexor tendon and sonoelastography is correlated with the histological findings
of the common flexor tendon [113]. As in the tennis elbow, nonsurgical management
is a primary treatment in patients with the golfer’s elbow for the relief of medial-
sided elbow pain [112, 114]. Surgical management is indicated after patients receive
nonsurgical therapy for 4–6 months and remain persistent symptoms [115, 116].

3.2.2 Cubital Tunnel Syndrome

Cubital tunnel syndrome, a compressive neuropathy, causes the impairment of sen-

sation and muscle weakness. Cubital tunnel is composed of (1) the flexor carpi
ulnaris fascia and Osborne’s ligament (roof), (2) posterior and transverse bands of
medial collateral ligament and elbow joint capsule (floor), and (3) medial epicon-
dyle and olecranon (walls). The ulnar nerve is commonly compressed by the soft
tissue, which includes the arcade of Struthers, Osborne ligament, flexor carpi ulna-
ris, and flexor digitorum superficialis. The sensation of ring finger and little finger
has altered. Cubital tunnel syndrome exacerbated its symptoms during the pro-
longed elbow flexion. The pathologic of Osborne ligament results in the decrease of
gliding of ulnar nerve during the elbow flexion and extension [117]. During the
elbow flexion, the ulnar nerve has 2.2 cm excursion and 15% strain within the cubi-
tal tunnel [118]. The intra-neural pressure of the ulnar nerve has the low value at
40–50° elbow flexion and increases the value with the increase of angle [119].
Cubital tunnel syndrome would occur after the elbow dislocation and distal humerus
fracture [120–122] due to the joint deformity, thickening of the cubital tunnel,
swelling, and scarring. Nonsurgical management is indicated in patients with the
mild to moderate cubital tunnel syndrome by using splint to limit elbow flexion to
reduce the compressive and tensile load on the ulnar nerve [123, 124]. Surgical
management is indicated in patients with severe cubital tunnel syndrome, impair-
ment of two-point sensibility, and muscle atrophy by simple decompression [125],
medial epicondylectomy [126], and anterior transposition to release the fascial
structures [127].
124 S.-Y. Lee and F.-C. Su

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Chapter 6
Biomechanics of the Shoulder

Min Zhang and Chih-Hwa Chen

Abstract The glenohumeral (GH) joint is a complex and unstable articulation. The
interaction between various structures of the shoulder caused by mechanical stimuli
and motion provides multiple degrees of shoulder motion. The static stability of the
shoulder is supported by the articulation of the humeral head and the glenoid with
additional GH ligaments, capsule, and labrum. The rotator cuff muscles surrounding
the shoulder joint provide dynamic stability. The combination of these factors forms
the biomechanical system that can respond in accordance with the arm movement.
Different pathological processes and injuries may result in similar clinical manifes-
tations. It is crucial to know the etiology of these different pathological factors from
the viewpoint of the shoulder joint biomechanics to provide the most effective and
curable treatments for patients suffering from shoulder diseases and disorders.

Keywords Shoulder stability · Biomechanics · Rotator cuff · Glenohumeral joint

Shoulder instability

1 Introduction

The shoulder motion is subject to the reaction to the shoulder structure stimuli. Due
to the mismatch between the humeral head and the articular surface of the glenoid,
the stabilization of the shoulder is compensated by static and dynamic stabilizers.

M. Zhang
Beijing Advanced Innovation Center for Biomedical Engineering, Beihang University,
Beijing, China
Key Laboratory for Biomechanics and Mechanobiology of Ministry of Education,
School of Biological Science and Medical Engineering, Beihang University, Beijing, China
C.-H. Chen (*)
Department of Orthopedics, Taipei Medical University—Shuang Ho Hospital, Taipei, Taiwan
School of Medicine, College of Medicine, Taipei Medical University, Taipei, Taiwan
School of Biomedical Engineering, College of Biomedical Engineering, Taipei Medical
University, Taipei, Taiwan
Research Center of Biomedical Devices, Taipei Medical University, Taipei, Taiwan

© Springer Nature Singapore Pte Ltd. 2020 131

C.-K. Cheng, S. L-Y. Woo (eds.), Frontiers in Orthopaedic Biomechanics,
https://doi.org/10.1007/978-981-15-3159-0_6
132 M. Zhang and C.-H. Chen

The static stabilizers include the glenohumeral (GH) ligaments, the labrum, and the
constrained capsule. The dynamic stability is provided by the r­ otator cuff (RC) mus-
cles surrounding the shoulder joint. The combined effect of the stabilizers is to sup-
port the multiple degrees of motion within the GH joint. The scapulothoracic (ST)
joint provides additional mobility and stability to the shoulder.

2 Musculoskeletal and Functional Anatomy of Shoulder

The human shoulder is composed of bones as well as associated muscles, ligaments,

and tendons. It is the connection between the neck and the upper limb.

2.1 Bony Structure of the Shoulder

The skeletal structure of the shoulder includes the humerus, the scapula, and the
clavicle.

2.1.1 Humerus

The humerus is located on the upper limb and is articulated with the glenoid fossa
at the glenohumeral joint. The head of the humerus is elliptical and inclines between
120° and 145° [1] as well as a retroversion within a range of 60° [2]. There are two
bulges on the lateral and anterior sides of the humeral head. They are greater and
lesser tubercles. These two tubercles are separated by intertubercular groove and are
origins to subscapularis, teres minor, infraspinatus, and supraspinatus muscles. The
humerus has two necks: surgical and anatomical necks. The surgical neck is a con-
striction below the tubercles of the greater tubercle and lesser tubercle, and above
the deltoid tuberosity. The anatomical neck is obliquely directed, forming an obtuse
angle with the body. It provides the attachment to the articular capsule.

2.1.2 Scapula

The scapula is located on the posterior chest wall and is in an inverted triangular
shape. It inclines approximately 40° anteriorly to the coronal plane [3]. There is a
broad concavity on the anterior surface of the scapula and it forms the origin of the
subscapularis muscle. The posterior surface of the scapula consists of the infraspi-
natus and supraspinal fossae, which is separated by the scapular spine provide the
origins to the infraspinatus and supraspinatus ­muscles. Further, the scapula is com-
6 Biomechanics of the Shoulder 133

posed of three corners and three sides, namely the lateral, superior, and inferior
angles, and the medial, superior, and lateral borders, respectively. Next to the lateral
angle, the glenoid is a shallow and pear-shape cavity. It inclines 3–5° superiorly [4]
and 2.5–12.5° posteriorly [5].

2.1.3 Clavicle

The clavicle is an elongated bone in an S-shaped and connects the upper limb to the
torso. The lateral and medial end of the clavicle is flat and thick, respectively. The
clavicle transmits forces from the trunk to the upper limb. The articulation between
the clavicle and the manubrium of the sternum is a sternoclavicular (SC) joint. The
articulation between the clavicle and the acromion of the scapula is the acromiocla-
vicular (AC) joint.

2.2 Articulation of the Shoulder

The shoulder joint is composed of four joints (SC joint, AC joint, GH joint, and ST
articulation) with bony and soft-tissue structures. These articulations provide a high
degree of shoulder motion. The arm can reach an elevation angle of 180°, internal
and external rotations of approximately 150°, and flexion and extension of 170° [6].

2.2.1 Sternoclavicular Joint

The articulation between the manubrium sterni and the medial end of the clavicle is
the SC joint. It connects the thorax to the upper limb and allows approximately 35°
of elevation and 50° of axial rotation [6]. The intrinsic bony stability of the SC joint
is mainly supported by the anterior and posterior SC ligaments, the interclavicular
ligament, the costoclavicular ligament, and the articular disc.

2.2.2 Acromioclavicular Joint

The AC joint is composed of the acromion and the clavicle surfaces, which trans-
mits forces from the upper extremity to the chest musculature. The AC articulation
is stabilized by the coracoclavicular and the AC ligaments. The coracoacromial liga-
ment spans between the lateral aspect of the coracoid process and the anterior facet
of the acromion. It is to restraint the superior-inferior migration of the clavicle [7,
8]. The AC ligament is to restrain the anterior-posterior translation of the clavicle [7,
8] and provides scapular and synchronous clavicular rotation [9].
134 M. Zhang and C.-H. Chen

2.2.3 Glenohumeral Joint

The GH joint is a flexible and unstable articulation composed of the scapula glenoid
fossa and humeral head. The glenoid cavity accounts for 25–30% of the humeral
head and can move relatively to the humerus [9]. The glenoid-humerus contact area
varies in degrees during the shoulder motion. Its stability is mainly supported by the
articular capsule, the labrum, and the surrounding muscles [10]. The capsular-liga-
mentous complex includes the superior, the medial, and the inferior GH ligaments.
The superior and the medial GH ligaments are both single-band structures and reach
the lesser tubercle and the humeral neck, respectively. The inferior GH ligament
complex consists of anterior and posterior bands and inserts on the humerus beyond
the lesser tuberosity [11]. The glenoid labrum is a circumferential and fibrocartilagi-
nous ring attaching to the glenoid rim. The glenoid labrum serves as a bumper dur-
ing the shoulder motion and an attachment site of the GH ligaments. The muscles
supplying the stability of the GH joint refers to the RC, which will be described in
Sect. 2.3.

2.2.4 Scapulothoracic Articulation

The ST articulation is composed of the anterior surface of the scapula and the pos-
terior surface of the thoracic [12]. The neurovascular, muscular, and bursal struc-
tures allow smooth motion of the scapula on the thorax. The ST articulation allows
30° of abduction internal rotation, respectively. It increases the shoulder movement
after the initial 120°, which is supplied by the GH joint [12].

2.3 Functional Muscles of the Shoulder

The shoulder muscles supply athletic ability and dynamic stability. The function of
muscles are subjected to its origin and endpoint. The muscles and their functions on
the shoulder complex are described below.
The anterior outer layer muscles on the shoulder complex involve the pectoralis
major and the deltoid muscles. The pectoralis major muscle has two heads (sterno-
costal and clavicular heads) and is located above the anterior chest wall. The sterno-
costal head originates from the anterior sternum surface, the superior six costal
cartilages, and the external oblique muscle aponeurosis. In contrast, the clavicular
head originates from the medial clavicle anterior surface. Both the sternocostal and
clavicular heads insert to the crest of the greater tubercle of the humerus and serve
the elevation and adduction of the arm. The deltoid muscle is composed of the ante-
rior, the intermediate, and the posterior fibers. The anterior fibers originate from the
upper surface and the anterior border of the lateral third of the clavicle and serve the
6 Biomechanics of the Shoulder 135

flexion and internal rotation of the arm. The intermediate fibers originate from the
acromion process and the spine of the scapula and serve the abduction of the arm
after the initial 15° of arm rotation [6]. The posterior section of the deltoid origi-
nates from the spine of the scapula. It serves the external rotation and the extension
of the humerus. All the fibers of the deltoid muscle insert into the deltoid tuberosity
of the humerus.
The inner muscles involve the pectoralis minor, the subclavius, and the subscap-
ularis muscles. The pectoralis minor plays an important stabilizing role on the scap-
ula. The subclavian muscle is located underneath the clavicle and contributes to the
clavicular movement. The subscapularis muscle, which is located in the anterior
scapula, functions as the arm rotator.
The posterior outer layer muscles involve the latissimus dorsi, the trapezius, the
serratus anterior, and the posterior deltoid muscles. The latissimus dorsi muscle
arises from the thoracic vertebrae and inserts into the intertubercular groove of the
humerus. It works in collaboration with the pectoralis major to contribute to the
adduction and medial rotation of the humerus. The trapezius muscle is one of the
broadest back muscles. It arises from the occipital bone, the ligamentum nuchae,
and the spinous processes of T01–T12 and inserts into the third clavicle lateral, as
well as the acromion and scapular spine. The trapezius muscle contributes to the
shoulder elevation and rotation and also acts in head/neck extension [13]. The ser-
ratus anterior muscle arises from the anterior surfaces of the eighth upper ribs and
inserts into the inner medial border of the scapula. The serratus anterior muscle
allows the forward rotation of the arm and to pull the scapula forward and around
the rib cage.
The posterior inner layer muscle below the superficial muscles (the trapezius and
deltoid muscles) includes the supraspinatus, infraspinatus, teres minor, and teres
major muscles. The origin of the supraspinatus muscle is the supraspinatus fossa.
The muscle tracks laterally underneath the acromion and goes on the insertion at the
greater tuberosity [14]. Thus, the supraspinatus muscle assists in the arm abduction
and humerus stabilization [6]. The infraspinatus muscle originates from the infra-
spinous fossa of the scapula and inserts at the greater tuberosity. The origin of the
teres minor muscle is at the lateral margin of the scapula. The muscle inserts at the
most posterior and inferior facet of the greater tuberosity. Both the teres minor and
the infraspinatus muscles assist the stability and rotation of the humerus. The sub-
scapularis muscle is trapezoidal and origins from the anterior scapula aspect and
inserts at the lesser tuberosity [15]. The teres major muscle arises from the inferior
angle of the scapula and passes laterally and superiorly to the bicipital groove. It
contributes to the extension and rotation of the humerus.
The RC is formed by the subscapularis, the infraspinatus, the teres minor, the
supraspinatus muscles, and their associated tendons. The RC muscles contribute to
the abduction and rotation of the humerus and also provide a compressive force to
centralize the humeral head on the glenoid. In the case of a massive rotator cuff tear,
the loss of enough passive muscle tension and dynamic contraction leads to exces-
136 M. Zhang and C.-H. Chen

sive superior translation of the humerus to the glenoid cavity. The translation can
reach 12 mm in some cases [9]. It may result in subacromial impingement and the
erosions of surrounding bone and articulations (i.e., the glenoid, the acromiocla-
vicular joint, and the anterior acromion) (the severe RC tear is described further in
Sect. 4.2.1).

2.4 Summary

The GH joint is an enarthrodial socket-to-ball joint and supports the polyaxial arm
motions. It includes abduction/adduction around the sagittal axis, flexion/extension
around the frontal axis, and external/internal rotation around a longitudinal-­
humeral axis.
GH joint kinematics is not precisely equivalent to enarthrodial kinematics.
Numerous studies have reported the exact determination of the GH joint kinematics
and the founding is controversial. Due to different methodological approaches in
different studies, it is difficult to compare the results. In general, the humeral head
translates approximately 1.1 mm inferiorly during the whole abduction and 2.4 mm
anteriorly before the abduction of 90° and 1.4 mm posteriorly during the abduction
of 90–150° [16].
The GH joint maintains stability in utilizing static and dynamic restraints.
These static stabilizers dynamic restraint involve ligamentous, capsular, cartilagi-
nous, and bony structures, as well as musculature structure of the shoulder,
respectively. The GH ligament stabilizes the GH joint by preventing excessive
movements of the humeral head relative to the glenoid cavity in the extremes of
motion [17]. A competent sealed capsule of appropriate volume, minimal joint
fluid, and an intact congruent glenoid labrum provides the stability of the GH
articulation [18]. Neuromuscular control primarily provides dynamic stability
between the RC muscles and ST musculature. The functional ST musculature
can ideally release the instability of the shoulder joint and the neural feedback
from the GH ligaments and RC muscles, which are used to prevent pathologic
translation of the GH joint.
Dynamic stabilizers may contribute to joint stability by the muscle contraction,
which leads to compression of the articular surfaces, and the passive muscle ten-
sion from the bulk effect of the muscles [17]. The contraction of the RC muscles
compresses the humeral head on the glenoid cavity and the asymmetric contrac-
tion leads to the humeral head rotation during the shoulder motion. The interac-
tion of the RC muscles works in conjunction with other muscles in the shoulder
girdle [19].
The shoulder joint kinematics relies on the ST and deltoid muscles, as well as the
RC muscles interaction. The subscapularis and infraspinatus muscles act as a trans-
verse force couple generating compressive forces. Also, the supraspinatus muscle
plays a significant role in the concavity compression during early abduction [20].
6 Biomechanics of the Shoulder 137

3 Mechanical Properties and Glenoid Architecture

The mechanical parameters of the glenoid relate to bone architecture [21–23]. As

illustrated in Fig. 6.1, the subchondral bone from the sagittal plane view is formed
by the superoinferior, which oriented parallel to the trabeculae in the peripheral
regions and honeycomb-fashion struts in the center of the glenoid [24]. In the trans-
verse view, the trabeculae are plate-like and generally perpendicular to the glenoid
surface (Fig. 6.1b). In the posterior and anterior regions, the thin rods directly con-
nect the semi-circular cortical base to the subchondral plate and present low poros-
ity, while the trabeculae in the middle portion distribute partially and present high
porosity [21, 24].
As a result of the partial distribution of trabeculae in the center of the glenoid and
high alignments of trabeculae in the anterior and posterior portions, the bone in the
center of the glenoid presents a lesser strength, low stiffness, and isotropic charac-
teristic with reference to the bone in the peripheral glenoid [22, 25]. The scapula
bone from the lateral to the medial is orderly the subchondral bone, trabecular bone,
and compact bone. In conformity with the architecture of the scapula, the strength
of the scapula bone reduces significantly beneath the subchondral layer and then
increases to the cortical bone layer [23]. In a regional test, the posterosuperior and
anteroinferior glenoid shows the strongest and weakest bones, respectively [21, 22,
25, 26]. The porous trabecular bone at the center of the glenoid enables the heavy
loads from the articular surface to be absorbed and conveyed, and the dense bone in
the peripheral glenoid enables the compressive stresses generated during the arm
motion to be absorbed [24]. The studies shows the individual glenoid present that
the glenoid trabecular bone Young’s modulus varies between 99 and 264 MPa and

a b

Fig. 6.1 The glenoid bone (a) sagittal view; (b) transverse view. L lateral, M medial, P posterior,
A anterior, I inferior, S superior. (Adapted from Frich et al., 1998)
138 M. Zhang and C.-H. Chen

the strength ranges from 26 to 110 MPa [21, 23, 25]. Young’s modulus and strength
values are related to many factors such as health conditions, gender, and ages [23,
27, 28].

4 Shoulder Joint Arthroplasty

Shoulder joint arthroplasty is a surgical way to alleviate shoulder pain and restore
the shoulder function. This section introduces the shoulder joint replacements from
the following sections: (1) the types of shoulder joint arthroplasty; (2) clinical indi-
cations of shoulder joint arthroplasty; and (3) knowledge-based related to the shoul-
der joint arthroplasty.

4.1 Types of Shoulder Arthroplasty

The artificial shoulder joint arthroplasty can be classified into (1) anatomical and
reverse shoulder arthroplasties, (2) total shoulder arthroplasty (TSA) and prosthetic
humeral hemiarthroplasty (HA), and (3) stemmed and resurfacing shoulder
arthroplasties.

4.1.1 Anatomical and Reverse Shoulder Arthroplasties

The structure of anatomical shoulder arthroplasty is similar to that of a natural shoul-

der joint and composed of a ball replacing the humeral head and a socket replacing
the glenoid fossa. In contrast, the design of reverse shoulder arthroplasty (RSA) is
different. Thus, in prosthesis type, the glenoid fossa is replaced with a ball and the
humeral head is replaced with a socket. Anatomical shoulder arthroplasty is mainly
used for the treatment of the incongruent osseous surface, moderate and severe osteo-
arthritis (OA), and inflammatory arthritis [29]. Primary indications of the reverse
total shoulder arthroplasty (RTSA) are arthritis with massive RC tear. (Detail infor-
mation on the advantages of RSA for severe RC treatment are shown in Sect. 4.2.1.)

4.1.2 Humeral Hemiarthroplasty and Total Shoulder Arthroplasty

In humeral HA (Fig. 6.2a), only the proximal humerus was replaced by an artificial
device, while in the TSA, both the humerus and the glenoid are reconstructed. In the
surgical technique of HA, the entire glenoid can be preserved and the complications
associating with the glenoid component in the TSA can be avoided. HA is used for
patients with intact articular cartilage surfaces. When the cartilage is damaged or the
glenoid erosion is severe, TSA is usually preferred.
6 Biomechanics of the Shoulder 139

a b

Fig. 6.2 (a) Radiograph of a hemiarthroplasty and (b) prosthesis resurfacing

4.1.3 Resurfacing and Stemmed Shoulder Arthroplasties

Prosthesis resurfacing (Fig. 6.2b) refers to the surgical technique in which only the
damaged surface of the humeral head is reconstructed. This technique can preserve
the native inclination and offset of the humerus as well as the head shaft angle.
Prosthesis resurfacing is usually used for the treatments of young and active
patients [30, 31]. The contact between the glenoid bone and the stiff metallic
humeral resurfacing device may lead to late glenoid arthrosis and need a revision
to a TSA [30].

4.2 Clinical Indications of Shoulder Joint Arthroplasty

The indications for shoulder joint replacements involve cuff tear arthropathy (CTA),
primary OA, rheumatoid arthritis, humeral fracture, and the failed shoulder joint
arthroplasty [29].

4.2.1 Cuff Tear Arthropathy

CTA is a common shoulder disease referring to shoulder arthritis with RC tears

[32]. Besides the loss of the shoulder cartilage function, severe CTA also leads to
the dysfunction of RC tendons. This type of shoulder disease is often accompanied
by synovial fluid leakage, GH articular cartilage atrophy, and subchondral osteopo-
rosis on the humeral head [32]. In Sect. 2.3, the RC acts as a dynamic stabilizer.
The dysfunction of these muscles may lead to the migration of the humeral head
140 M. Zhang and C.-H. Chen

Impingement Erosion of the superior glenoid

a b

Fig. 6.3 (a) A radiograph of the RC arthropathy. (Adapted from http://www.djosurgical.com/

patient/rsp/index.htm). (b) Photograph of a patient with CTA

and subacromial impingement. Meanwhile, it may also induce pseudocyesis, pain,

and loss of shoulder function. CTA may be developed after surgical treatments. It
is reported that RC tears were observed in 47% of patients who had TSA from
2004 to 2007 [33] (Fig. 6.3).
CTA is generally treated with RTSA or HA. If the CTA is mild and the shoul-
ders are stable, HA is recommended [34, 35]. Further, if the shoulder is unstable,
RSA treatment is generally used [29]. The application of TSA for CTA treatment
is not an ideal approach [29]. Biomechanical analyses for these reasons are
described below. In the case of severe CTA, the deltoid muscle force may lead to
the superior movement of the humerus and could cause the subacromial impinge-
ment and other indications of CTA (Fig. 6.4a). When the TSA is applied for CTA
treatment (Fig. 6.4b), the GH joint cannot be stabilized, and the humeral head
may still be translated superiorly under the deltoid muscle force. Moreover, it
may lead to eccentric loading on the glenoid socket and finally result in glenoid
loosening. When the RSA is used for the treatment of CTA, the center of rotation
of the humerus is secured on the glenoid and the arm can rotate under the deltoid
muscle force (Fig. 6.4c). RSA is c­ urrently the only recommended treatment for
the elderly adults (≥65 years) with pseudoparalysis and pain, due to the high
long-term implant failure rate [36–38].

4.2.2 Osteoarthritis

OA is a disorder in which the biomechanical properties of the articular cartilage are

gradually degraded. The OA starts from the articular cartilage wearing. When the
wear leads to the direct bone contact of the two parts of the GH joint, OA may cause
osteophytes, subchondral bone thickening, motion restriction, swelling, and pain
6 Biomechanics of the Shoulder 141

a Deltoid muscle Scapula

Humerus

Centre of rotation

b Eccentric loading c Deltoid muscle

RSA

Scapula
Humerus
Glenoid socket Humerus

Scapula Centre of rotation

Fig. 6.4 Schematic diagram of the CTA in (a) the anatomical shoulder; (b) the TSA and
(c) the RSA

[39]. The mild OA is usually treated with a nonsurgical method (i.e., local injec-
tions, medications, and physical therapy [40]). When OA is severe, HA or TSA is
usually recommended [41–43].

4.2.3 Rheumatoid Arthritis

Rheumatoid arthritis is an autoimmune-related disease, which is associated with

the breakdown of articular cartilage, synovial membranes thickening, and inflam-
mation. Thus, patients with rheumatoid arthritis usually suffer from bone ossifi-
cation or fusing and limited motion. The treatment depends on the integrity of
the RC. When the RC is irreparable, RSA is recommended. If the RC is intact,
TSA or resurfacing HA is used, depending on the degree of glenoid erosion [44].

4.2.4 Proximal Humerus Fractures

There are four types of proximal humeral fractures (Fig. 6.5). Type 1 (Fig. 6.5a)
refers to the fracture with collapse or necrosis on the humeral head; Type 2
142 M. Zhang and C.-H. Chen

(Fig. 6.5b) refers to the fracture with irreducible dislocations; Type 3 (Fig. 6.5c)
refers to the facture with completely broken surgical neck; Type 4 (Fig. 6.5d) is
the fracture with severe tuberosity malunions. For Type 1 and Type 2, TSA treat-
ment is recommended. For Types 3 and 4, the treatment depends on the degree of
RC deficiency. HA treatment is recommended for patients with intact RC, and
RSA treatment is used for patients over the age of 65-years-old with massive RC
tear [29].

4.2.5 Revision

The revision of the shoulder arthroplasty is usually recommended for the treatments
of implant problems (i.e., loosening, wearing, improper sizing, and malposition),
osseous problem (i.e., bone loss, glenoid arthrosis), and soft-tissue deficiency. It is
reported that the application of RSA for the failed HA can increase the American
Shoulder and Elbow Surgeons (ASES) score to 30, and improve the forward eleva-
tion from 38.1° to 72.7° [45].

a b

c d

Fig. 6.5 (a) Type 1 proximal humeral fracture; (b) Type 2 proximal humeral fracture; (c) Type 3
proximal humeral fracture; (d) Type 4 proximal humeral fracture
6 Biomechanics of the Shoulder 143

5 Conclusions

The GH joint is an articulation with the compensation of a series of static and

dynamic stabilizers. The static and dynamic stabilizers cooperate with each other to
support the stability of the whole shoulder joint and achieve the shoulder motion.
Once the stabilizing structure is disrupted, it may lead to clinical manifestations of
the shoulder pain or instability. Therefore, treatments to the shoulder diseases and
disorders are subjected to a clear understanding of the etiology of the shoulder prob-
lem and the designs of the shoulder arthroplasties.

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Hedtmann A, Werner A. Shoulder arthroplasty in rheumatoid arthritis. Der Orthopade.
2007;36(11):1050–61.
Levy JC, Virani N, Pupello D, Frankle M. Use of the reverse shoulder prosthesis for the treat-
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ciency. Bone Joint J. 2007;89(2):189–95.
Chapter 7
Biomechanics of Spine

Lizhen Wang, Zhongjun Mo, Yuanjun Zhu, Enze Zhou, and Yubo Fan

Abstract Spinal disease including primary and secondary tumors occurs in various
tissues such as nerve root, blood vessel, spinal cord, and so on. There was about 9.7
patient with spinal tumor in every 1 million. Spine laminectomy has usually been
applied in treating the spinal cord tumor. Spinal instability after spine surgery was
observed with high occurrence rate, due to excision of posterior structures. Total
disc replacement (TDR) is an effective surgical method as well as anterior cervical
discectomy and fusion (ACDF) to decompressing neural elements and restore disc
height. With regard to keeping cervical spine’s normal kinematics, TDR is more
feasible and widely accepted than ACDF for treating degenerative cervical disc dis-
ease. It is important to investigate the biomechanical performances of ligament and
vertebral on the spine stability in repair surgery, which would provide the theoretical

L. Wang · Y. Zhu · E. Zhou

Key Laboratory for Biomechanics and Mechanobiology of Ministry of Education, School of
Biological Science and Medical Engineering, Beihang University, Beijing, China
Beijing Advanced Innovation Center for Biomedical Engineering, Beihang University,
Beijing, China
Z. Mo
Beijing Key Laboratory of Rehabilitation Technical Aids for Old-Age Disability, Key
Laboratory of Technical Aids Analysis and Identification of Ministry of Civil Affairs,
National Research Centre for Rehabilitation Technical Aids, Beijing, China
Y. Fan (*)
Key Laboratory for Biomechanics and Mechanobiology of Ministry of Education, School of
Biological Science and Medical Engineering, Beihang University, Beijing, China
Beijing Advanced Innovation Center for Biomedical Engineering, Beihang University,
Beijing, China
Beijing Key Laboratory of Rehabilitation Technical Aids for Old-Age Disability, Key
Laboratory of Technical Aids Analysis and Identification of Ministry of Civil Affairs,
National Research Centre for Rehabilitation Technical Aids, Beijing, China
e-mail: yubofan@buaa.edu.cn

© Springer Nature Singapore Pte Ltd. 2020 147

C.-K. Cheng, S. L-Y. Woo (eds.), Frontiers in Orthopaedic Biomechanics,
https://doi.org/10.1007/978-981-15-3159-0_7
148 L. Wang et al.

suggestion to disc or cage design. In this chapter, the cervical spine (C2–C7) with
lamina repair surgery was studied at C3–C6 segments. The spinal stability in the
adjacent segments with posterior ligaments excised was worse than the one with
posterior ligament repaired. Repairing or preserving the posterior ligaments in the
lamina repair surgery is benefit to spinal integrity and stability. On the other hand,
the design of disc and the placement location of it were important factors for the
postoperative rehabilitation, especially for the ROM (range of motion) of flexion/
extension and the stress of implant. Therefore, reserving the range of motion and
avoiding adverse problems should be taken into consideration, and more attentions
also should be paid to a proper implant position along the anterior-posterior direc-
tion in ADR surgery.

Keywords Lamina repair · Ligament repair · Replacement · Disc design · Spinal

biomechanics

1 Biomechanical Effect of Posterior Ligament Repair

in Lamina Repair Surgery

Spinal tumors including primary and secondary tumors occurs in various tissues
such as nerve root, blood vessel, spinal cord, and so on. The incidence rate of spinal
tumor was 9.7 in 1 million [1]. Cervical laminectomy has usually been applied in
treating cervical spinal cord tumor [2]. However, the occurrence rate of spinal insta-
bility after laminectomy was reportedly 20% in adults [3] and up to 45% in children
[4], since the posterior structures of vertebrae, including interspinous ligament,
supraspinous ligament, flaval ligament, and spinous process, also was excised with
laminectomy [5]. Excision of posterior structures causes movement of the anterior
vertebrae body, which induces declination and torsion of vertebral body, resulting in
spinal instability [6, 7]. Previous studies reported the increase in ROM after lami-
nectomies, which was likely to result in developing spinal kyphosis or other defor-
mity [8–16]. Spinal deformity following laminectomy would oppress spinal cord or
nerve root, and subsequently result in neurological symptoms as back pain and
radiculopathy.
In order to avoid the complications caused by laminectomy, lamina repairment
was firstly applied in clinics to treat intraspinal lesions in 1976 [17]. Since then,
repairing of the excised lamina simultaneously with excision of the neoplasm was
advocated to maintaining spinal stability and preserving daily activities of the spine
[2, 18]. Good clinical results were found in the follow-up of the patients after lamina
repairment surgery, which can maintain spinal integrity, and prevent postoperative
instability, subluxation, and kyphotic deformities [19–22].
7 Biomechanics of Spine 149

Nowadays, the resected ligamentum flavum (LF) and interspinous ligament

(ISL) have not been repaired during lamina repair surgery. However, the posterior
structures, including the vertebral arch, supraspinous ligament, and interspinal liga-
ment, are believed to play important roles in tethering or tension constraint during
anterior flexion [21]. Hotta [23] demonstrated the importance of ISL in the enhance-
ment of spinal flexion stability. So, Sano [24] and Joson [25] proposed new methods
to conserve ISL during laminectomy. Hirofuji [26] also suggested to reconstruct
ISL by using artificial ligament. However, is there apparent benefits in terms of
biomechanical performance with posterior ligament repairment in lamina repair
surgery than that without posterior ligament repairment? In the present study, a
finite element model of cervical spine (C2–C7) was constructed and used to simu-
late the lamina repairment surgery with and without lamina ligament repairment at
C3–C6 segments, to explore the biomechanical effects of ligament repair on the
cervical spinal stability in lamina repair surgery.

1.1 Construct a Healthy Cervical Model (C2–C7)

To develop the finite element model of the intact cervical spine (C2–C7), computer-
ized tomographies (CT) of a healthy volunteer (male, 28 years, 60 kg, 173 cm) were
achieved by CT scanner (Brilliance iCT, Philips, the Netherlands). The corresponding
ethical committee has approved this research plan (No. IRB00006761-L2010021),
and the participant signed the informed consent form. The CT scan images were
imported into medical image-processing software (Mimics 15.1, Materialise Inc.,
Belgium) to rebuild the vertebrae’s geometry. The intervertebral space was filled with
a solid block as disc, which was divided into nucleus pulposus and annulus ground
substance in a ratio of 4.3:5.7 [27, 28] by CAD software (Solidworks 2012, Dassault
Inc., France). The vertebrae and intervertebral disc were meshed into tetrahedral ele-
ments and hexahedral elements, respectively, by using Hypermesh (12.0, Altair Inc.,
America). Finally, all the meshed vertebrae and discs were imported into finite ele-
ment software (ABAQUS 6.14, Simulia Inc., USA) as separated solid volumes. A
layer of shell with a thickness of 0.4 mm was generated by sharing the common nodes
with the solid vertebrae volume (cancellous bone), and partitioned into cortical shell
and endplate region. A layer of netlike truss elements (annulus fiber) were attached on
the circumferential surface of the ground substance to simulate annulus fibrosus by
sharing the common nodes. Intervertebral ligaments, including anterior longitudinal
ligament (ALL), capsular ligament (CL), posterior longitudinal ligament (PLL), liga-
mentum flavum (LF), and interspinous ligaments (ISL), were simulated using tension-
only nonlinear truss element (Fig. 7.1). In the healthy model of cervical spine, the total
numbers of nodes and elements are 47,068 and 176,373, respectively. The material
properties and mesh type of cervical components [29, 30] are listed in Table 7.1.
150 L. Wang et al.

Fig. 7.1 Finite element

a b
model of C2–7 cervical
spine: (a) anterior view and
(b) sagittal view

Table 7.1 Mesh types and material properties of the cervical spine components
Young modulus Poisson Cross section
Components Element type (MPa) ratio area (mm2)
Cortical bone S3 12,000.0 0.30 –
Cancellous bone C3D4 450.0 0.30 –
Endplate S3 1000.0 0.40 –
Articular cartilage C3D6 10.0 0.30 –
Annulus fiber T3D2 450.0 0.30 –
Annulus ground C3D8 3.4 0.40 –
substance
Nucleus pulposus C3D8 1.0 0.49 –
Mini-plate and screw
C2–C5 ALL T3D2 26.3 0.40 11
PLL T3D2 22.2 0.40 11
FL T3D2 3.1 0.40 46
CL T3D2 3.3 0.40 42
ISL T3D2 4.9 0.40 13
C5–C7 ALL T3D2 28.2 0.40 12
PLL T3D2 23.0 0.40 14
FL T3D2 3.5 0.40 49
CL T3D2 4.8 0.40 50
ISL T3D2 5.0 0.40 13
7 Biomechanics of Spine 151

1.2 Construct the Lamina Repair and Lamina Ligament

Repair Models

Based on the healthy model, all the FL and ISL at C2–C3 and C6–C7 levels were
removed, and both the left and right sides of the laminas at C3–C6 were cut by gaps
with 2 mm width, and then titanium alloy mini-plate is used to fix the lamina and
spinous process to simulate the lamina repairment surgery (Fig. 7.2). The lamina
ligament repair model (LLRM) was based on the lamina repair model (LRM) by
reconstructing the FL and ISL at C2–C3 and C6–C7 segments. The metal compo-
nents in the titanium mini-plate and screw were made of Ti6Al4V with the sizes of
the mini-plate as 10 × 2 × 0.5 mm (length × width × height) and the screw as
4 × 1.6 mm (length × diameter).

1.3 Load and Boundary Conditions

The ligaments were inserted in corresponding position and attached on the adjacent
vertebrae, to which the intervertebral disc was also adhered. The interaction between
the facet joint cartilages was defined as surface-to-surface contact formulation with
0.1 friction coefficient. The bone-implant interface was assigned with a tie con-
straint to simulate thorough osseointegration. All models were immobilized at the

Fig. 7.2 Finite element

model: (a) lamina repair a b
and (b) lamina
ligaments repair
152 L. Wang et al.

C7 inferior endplate with 6 degrees of freedom. A pure moment of 1.5 Nm was

applied at the top of the superior surface of the C2 vertebral body in all six principal
directions to simulate flexion, extension, left and right axial rotation, and left and
right lateral-bending motions in the healthy cervical spine. Subsequently, the pure
moments of 1.5 Nm was also applied to the LRM and LLRM at the top of the supe-
rior surface of the C2 vertebral body.

1.4 ROM and Stress in the Healthy Cervical Spine

The ROM of each motion segment in the healthy model subjected to the pure
moments of 1.5 Nm is shown in Fig. 7.3. The ROM was in agreement with the
in vitro experimental data from the literature [31–33].

1.4.1 ROM in the LRM and LLRM

Compared with the healthy model, in the LRM, the ROM of C2–C3 in flexion, lateral
bending, and axial rotation increased by 113.6%, 23.6%, and 28.5%, while that of
C6–C7 increased by 88.9%, 12.8%, and 20.7%, and change of ROM in other seg-
ments under different conditions was less than 9.2%. The change of ROM at the cor-
responding levels in LLRM was lower than 7.2% compared to the healthy model
(Fig. 7.4).

18
Healthy
16 Moroney (1988)
14 Panjabi (2001)
Finn (2009)
Rotation (degree)

12
10
8
6
4
2
0
C2/C3
C3/C4
C4/C5
C5/C6
C6/C7
C2/C3
C3/C4
C4/C5
C5/C6
C6/C7
C2/C3
C3/C4
C4/C5
C5/C6
C6/C7
C2/C3
C3/C4
C4/C5
C5/C6
C6/C7

Flexion Extension Lateral Bending Axial Rotation

Fig. 7.3 Comparison of ROM in healthy cervical spine and data reported in the literature
 7 Biomechanics of Spine 153

Healthy
12 Lamina repair
Lamina and ligament repair
10
Rotation (degree)

0
C2/C3
C3/C4
C4/C5
C5/C6
C6/C7
C2/C3
C3/C4
C4/C5
C5/C6
C6/C7
C2/C3
C3/C4
C4/C5
C5/C6
C6/C7
C2/C3
C3/C4
C4/C5
C5/C6
C6/C7
Flexion Extension Lateral Bending Axial Rotation

Fig. 7.4 ROM comparison of the healthy cervical spine and surgical models

9
Healthy
8 Lamina repair
Lamina and ligament repair
Facet Joint Contact Stress (MPa)

0
C2-C3(RB) C3-C4(Ex) C4-C5(Ex) C5-C6(RB) C6-C7(LB)

Fig. 7.5 Contact stress in facet joint in the healthy cervical spine and surgical models

1.4.2 Facet Joint Contact Stress

The maximal contact stress in the facet joint in each motion segment is shown in
Fig. 7.5. In the LRM, the facet cartilage at C2–C3 was in a zero-stress state in flex-
ion. Compared to healthy model, the maximal contact stresses of C2–C3 decreased
by 31.0% in right bending. Compared to healthy model, the change of the maximal
contact stresses in the LLRM was less than 3.0% in each motion segment.
 154 L. Wang et al.

0.6
Healthy
Lamina repair
Intervertebral Pressure (Mpa)

0.5 Lamina and ligament repair

0.4

0.3

0.2

0.1

0
Fl Ex LB RB LR RR Fl Ex LB RB LR RR

C2-C3 C6-C7

Fig. 7.6 Intradiscal pressure in the healthy cervical spine and surgical models

1.4.3 Intradiscal Pressure

The intradiscal pressure during different loading conditions in LRM increased by

4.1–73.7% at C2–C3 and 7.8–73.7% at C6–C7 segment compared with the normal
model, and the greatest intervertebral pressure was detected during flexion. In the
LLRM, the change of pressure were less than 11.5% in all loading conditions as
shown in Fig. 7.6.

1.4.4 Stress of Capsular Ligament

In the LRM, the stress of capsular ligament under different loading conditions
increased by 4.5–168.6% at C2–C3 and 9.5–115.6% at C6–C7 compared with the
healthy model. However, in the LLRM, the change of the stresses (C2–C3, C6–C7)
in all conditions was lower than 4.4% as shown in Fig. 7.7.

1.4.5 Stress on Bone-Screw Interface and Screw-Plate System

The stresses on the bone-screw interface and in the screw-plate system of C3–C6
are listed in Table 7.2. In the two kinds of surgical models, the differences of maxi-
mum stresses on screw and bone-screw interface was less than 6 MPa (C4 and C5)
and 106 MPa (C3 and C6), respectively.

1.5 Comparison of with or Without Ligament After Repairment

Since lamina repairment was firstly proposed to treat intraspinal lesions by

Raimondi, it is being gradually used widely. In many postoperative follow-ups, it
was found that lamina repairment can maintain spinal stability and integrity, and
7 Biomechanics of Spine 155

4.5
Healthy
4 Lamina repair
3.5 Lamina and ligament repair

3
Stress (MPa)

2.5
2
1.5
1
0.5
0
Fl Ex LB RB LR RR Fl Ex LB RB LR RR

C2-C3 C6-C7

Fig. 7.7 Stress in the CL in the healthy cervical spine and surgical models

Table 7.2 Maximum Von Mises stress on bone-screw interface and screw-plate system (MPa)
Model C3 C4 C5 C6
Screw LRM 144.6 115.9 130.4 116.2
LLRM 112.9 115.1 133.9 164.8
Titanium plate LRM 259.3 166.5 220.5 257.4
LLRM 153.6 173.8 214.6 359.8
Bone-screw interface LRM 1.458 1.45 2.085 1.844
LLRM 1.69 1.389 2.105 1.654

prevent the development of spinal instability and kyphosis [20–23]. Nong et al. [34]
performed a cadaveric study and proved that the lamina repairment surgery brought
more stability than laminectomy. Healy et al. [35] also performed a cadaveric study
to explore the effect of ISL on the spinal stability, and found that after excision of
the ISL between C2–C3 and C7–T1, the ROM of C2–T1 increased by 7.9%, 2.4%,
and 5.6% in flexion, bending, and rotation, while the ROM of C2–C3 and C7–T1
increased by 36.5% and 25.4% in flexion. Other studies demonstrated the impor-
tance of the ISL in the enhancement of spinal flexion stability, and they proposed
methods to conserve or repair the posterior ligament during laminectomy [23–26].
In the present study, a healthy cervical model (C2–C7), a lamina repair model,
and a lamina ligament repair model were built. The ROM of C2–C3 and C6–C7 in
LRM had an obvious increase which range from 12.8% to 113.6% compared to the
healthy model, whereas the ROM of C2–C3 and C6–C7 in LLRM were close to the
healthy model (<7.2%). The significant difference of ROM in the adjacent segments
(C2–C3 and C6–C7) in LRM and LLRM was due to whether the posterior liga-
ments existing. Since the physiologic role of ISL and FL include a tethering or ten-
sion constraint during anterior flexion [21], without ISL and FL can lead to a
significant increase of the ROM, which was consistent with the experimental results
156 L. Wang et al.

by Healy [35]. However, the changes of ROM at C3–C4, C4–C5, and C5–C6 in
LRM and LLRM were not apparent in comparison with healthy model (<9.2%).
In LRM, the maximal contact stress in facet joint at C2–C3 was 0 MPa in flexion
due to the absence of posterior ligaments, in comparison with healthy model, but the
maximal stress of C2–C3 decreased by 31.0% in right bending. Nevertheless, there’s
no obvious change of maximal facet contact stress at each adjacent segments in the
LLRM (<2.9%).
There is an evident increase of intradiscal pressure at C2–C3 and C6–C7 up to
73.7% in LRM, while the change at the corresponding segments in LLRM was not
obvious (<11.5%). In LRM, the intradiscal pressure at C2–C3 and C6–C7 both
increased by 73.7% in flexion, because the excision of posterior structures causes
movement of the anterior part of vertebrae around the nucleus pulposus [6, 7], and
the posterior ligaments had not been repaired in LRM; therefore, the disks in C2–C3
and C6–C7 have suffered much higher intradiscal pressure in flexion. The increase
in intradiscal pressure is related to adjacent segment degenerations.
Compared to the healthy model, the maximal stresses in capsular ligament at
C2–C3, C6–C7 in LRM increased obviously by up to 168.6%. Exaggerated stresses
do harm to the ligaments and may affect long-term clinical results. However, the
change of stresses at each motion segments in LLRM was small (<4.4%).
In LRM and LLRM, the difference of stresses on bone-screw interface and
screw-plate system in C4, C5 was less than 6 MPa (2.7%), but the difference in C3,
C6 was up to 105.7 MPa (41.8%).
Compared with the healthy model, the ROM, intervertebral pressure, facet joint
contact stress, stresses of capsular ligament at C2–C3, C6–C7 had significant
changes under different loading conditions in LRM. However, those parameters in
LLRM were close to healthy cervical spine. In addition, the stresses on bone-screw
interface and screw-plate system (C3, C6) between LRM and LLRM had great dif-
ferences, because of the integrity of posterior ligaments. Besides, the variation ten-
dency between LRM and LLRM was almost same in terms of ROM, intervertebral
pressure, contact stress in facet joint, stresses in capsular ligament, and stresses on
bone-screw interface and in screw-plate system (C3–C4, C4–C5, C5–C6). It meant
that lamina repairment with posterior structure preserved can maintain stability of
the cervical segments.
The study focused on the effect of with and without posterior ligaments in lamina
repair surgery, and explored the biomechanical properties of cervical spine such as
ROM, intervertebral pressure, facet joint contact stress, stresses of capsular liga-
ment, etc. However, the soft tissues in maintaining the cervical spine stability is
important; therefore, as part of this study to improve the accuracy of the cervical
spine model, a more complete model with soft tissues (muscles) will be built in
future study.
The spinal stability in the adjacent segments with posterior ligaments excised
was worse than the one with posterior ligament repaired. Repairing or preserving
the posterior ligaments in the lamina repair surgery is benefit to spinal integrity and
stability. It is suggested to conserve or reconstruct the posterior ligaments in lamina
repair surgery if the operation technology is realizable.
7 Biomechanics of Spine 157

2 Sensitivity Study on Different ProDisc-C Arthroplasty

Designs After Implanted

Total disc replacement (TDR) is an effective surgical method as well as anterior

cervical discectomy and fusion (ACDF) to decompressing neural elements and
restore disc height. With regard to keeping cervical spine’s normal kinematics, TDR
is more feasible and widely accepted than ACDF for treating degenerative cervical
disc disease [36]. Various prostheses of cervical disc, such as the Bryan cervical
disc, PCM prosthesis, Frenchay artificial cervical joint, Prestige II implant, and the
ProDisc-C, are in commercial application or clinical trials. In 2008, Galbusera et al.
[37] reviewed a number of biomechanical studies about total disc replacement, aim-
ing to figure out the relationship between the geometrical, mechanical, and material
properties of the various cervical disc prostheses. The study suggested that the bio-
mechanics of the implanted spine was affected by the concepts of different design,
which thus influence the clinical outcome.
Among the available devices, “ball-and-socket” shape is commonly employed
for the prosthesis designs [38]. ProDisc-C (Synthes Inc., West Chester, PA, USA) is
one of the typical ball-and-socket disc prostheses. It was composed of a hemispheri-
cal ball and a matched socket, over which the ball can roll. Therefore, the gliding
spherical joint will be critical in the survival and biomechanics of the implanted
spine. Rousseau et al. investigate two types of posterior geometric center simulated
disc models with large radius and small radius and one type of anterior geometric
center simulated disc with large radius to study the biomechanical changes in differ-
ent geometrical parameter designs of a ball-and-socket disc prosthesis [39]. The
result indicated that the ROM of all prostheses is basically same. The mean center
of rotation and the force transmitted through the facet joints was primarily affected
by the position of the geometric center and the radius of curvature, and the lowest
facet forces were observed in the disc prostheses with posterior center and large
radius design. However, the study has some limitations: only two radiuses of curva-
ture (6 and 10 mm) and two positions of disc geometric center (0 or 3 mm posterior
to the center of the endplate), which cannot exclude the accidental factors for lack-
ing gradient variations [40].
Given the importance of the implantation position of the prosthesis on the bio-
mechanics of the cervical spine, Galbusera et al. used the Monte Carlo method to
study the effects of positional changes and generated random input parameters [41].
The results showed that the axial and anteroposterior position of the rotation center
were the important factors affecting the flexibility of the spine, while the effect of
the lateral position was not significant. The authors investigated the biomechanical
effects of shape (oval vs. spherical ball) and location (inferior vs. superior ball) of
various cervical artificial disc replacements. No major kinematic was observed in
the design of the disc, but biomechanically, the oval design with an inferior ball
component appeared to be closest to the intact spine.
Over all, a comprehensive biomechanical evaluation on the disc parameter varia-
tions is still lacking, especially considering the combination of radius of curvature
158 L. Wang et al.

and positions. Therefore, the purpose of our study is to investigate biomechanical

differences by changing the radius of curvature and the inserted position along the
anteroposterior direction and lateral direction.

2.1 Model of Cervical Spine and Different Artificial Discs

2.1.1 Development of FE Model of Cervical Spine and Different

Artificial Discs

The geometry model of the vertebrae was reconstructed based on the computed
tomography (CT) scan images with the slice of 0.625 mm from a healthy male
(32 years, 68 kg, 170 cm) through a commercial software MIMICS (Materialise,
Belgium). Then a 3D nonlinear finite element model of the cervical spine was estab-
lished using software ABAQUS 6.11 (Simulia Inc.). The intact FE model consists of
intervertebral disc, endplate, and five groups of ligaments (anterior longitudinal, pos-
terior longitudinal, capsular, ligamentum flavum, and interspinous ligaments). A
layer of 0.4 mm thick shell was used to model the cortical bone surrounding the
cancellous core. A nonlinear 3D contact was set to the facet joint. The intervertebral
disc consists of the nucleus pulposus and the annulus fibrosus. The nucleus pulposus
accounts for 33% of the total disc volume surrounded by the annulus fibrosus. Three-
node link elements were used to simulate the annulus fibers, which were placed
approximately 30 from the horizontal plane. Truss elements were used to reconstruct
the ligaments and resisted tension only [40]. The detailed information about material
properties and element types used to reconstruct the FE model of the cervical spine
is described below (Table 7.1).
The basic ball-and-socket disc prostheses were constructed in ABAQUS 6.11
(Simulia Inc.). The geometry parameters were obtained from the product called
Prodisc-C (Synthes Inc., West Chester, PA, USA). The Prodisc size M (width
15 mm, depth 12 mm, height 5 mm) with 5 mm radius of curvature was chosen to
fit the specimen properly, and which was named as ProC-R5 [40].
Similarly, ProC-R4 with 4 mm radius of curvature and ProC-R6 with 6 mm
radius of curvature were generated. The heights of the three models are consistent,
and the superior endplate “socket” was altered for fitting the “ball” component with
different radius of curvature (Fig. 7.8). The material properties of the cobalt-­
chromium-­ molybdenum endplates (Alloy of CoCrMo) and polyethylene core
(UHMWPE) were set as linearly elastic materials (E = 220,000 MPa, υ = 0.32;
E = 1000 MPa, υ = 0.49). The spherical joint between the two components was set
as face-to-face contact with no friction to model the kinematical behavior. Then
three FE models of different radiuses of curvature were generated and meshed into
tetrahedron elements [40].
To simulating the anterior arthroplasty, the anterior longitudinal ligaments and
intervertebral disc at C5–6 level were deleted. Each prostheses of intervertebral disc
had 5 implantation sites that vary along the anteroposterior direction and lateral direc-
tion. And then these three types of prostheses were implanted at C5–6 level commonly
7 Biomechanics of Spine 159

Fig. 7.8 The ball

components of (a) a
4mm
ProC-R4, (b) ProC-R5, (c)
ProC-R6 disc design

b
5mm

c
6mm

applied in surgery. As some studies had demonstrated the finite axes of rotation were
sited below the disc and posterior to the endplate center [40, 42]. The center of the
prostheses was set at a position called neutral position, and we named them N4, N5,
N6 (4, 5, 6 for radius of curvature, N for neutral), respectively. The models implanted
2 mm anterior to the neutral position were named A4, A5, A6 (A means anterior). In
the same way, other implanted models were built named P4, P5, P6 (1.2 mm Posterior
to the neutral position; note that, the moving distance was different because the neutral
position wasn’t at central location of endplate), L4, L5, L6 (1 mm Left to the neutral
position), and R4, R5, R6 (1 mm Right to the neutral position). Apart from the anterior
position (15° from the horizontal plane), all prostheses were implanted at an angle of
12° to the horizontal for fitting the super-­inferior endplate of this model well [40].

2.1.2 Loading and Boundary Conditions

For validation of the FE model, we constrained all degrees of freedom of C6 inferior

endplate, and applied 74 N (an axial compression preload) at C5 superior surface’s
center, which was also applied 1.8 Nm (a pure moment) to simulate cervical spine
movement: flexion, extension, bilateral bending, and axial rotation. Under the load-
ing conditions, we calculated the range of motion (ROM) of the C5–C6 (an intact
motion unit) and compared it with previous studies to validate the FE model [43].
Through validation, the intact FE model was established as containing 21,839 nodes
and 112,117 elements.
After the validity of the intact FE model, the same boundary and loading condi-
tions as described above was set to the models implanted with different types of
Prodisc-C prostheses. The range of motion (ROM), the contact force of the facet
joints, the stress of ligament, and the stress on Polyethylene core were recorded
separately under respective loading conditions [40].

2.1.3 Validation of the Intact FE Model

The ROM of the C5–6 intact model in flexion//extension, lateral bending, and axial
rotation was 7.41°, 4.23°, and 5.49°, respectively [40]. Compared with the previous
studies [42], the ROM of the intact model was consistent with the published data
160 L. Wang et al.

above. In addition to the validation, Lee et al. reviewed and summed up the ROM
data from previous FE researches and in vitro experiments, finding that ROM of
C5–6 segment ranged from 7.2° to 9.9° for flexion/extension in sagittal plane, ROM
of C5–6 segment ranged from 3.1° to 15.4° for bilateral bending in coronal plane,
and ROM of C5–6 segment ranged from 2.3° to 13.3° for axial rotation in transverse
plane. Based on the fact that all the ROMs of C5–6 segment were within the range
of results, we considered the motion unit of the 3D finite element model was valid.

2.1.4 Range of Motion After Implanted

7.41°, 4.23°, and 5.49° were observed in the ROM of the intact model in sagittal
plane, coronal plane, and transverse plane, respectively. Compared with the intact
FE model, both the ROM of the FE models implanted with different Prodisc-C
prostheses and positions were all rose under the same external loading conditions.
In flexion/extension load, the ROMs of ProC-R4 and ProC-R5 were approximately
the same (difference <3%), but a remarkable increase was observed in ROM com-
pared with ProC-R4 and ProC-R5 in any position. In lateral bending and axial rota-
tion load, no apparent differences were seen among ProC-R4, ProC-R5, and
ProC-R6 (<2% change). We can also find that there was a trend that the posterior
position caused higher level of ROM to the neutral, middle, left, and right positions
under every loading condition. The closest ROM was observed in N5 (ProC-R5
model with neutral position) compared with intact model. The highest ROM was
observed in P6 model (ProC-R6 with posterior position), which was 25.2% and
23.9% higher than P4 and P5, respectively. The ROM of the intact model and mod-
els implanted with different Prodisc-C prostheses is described in Table 7.3.

2.1.5 Facet Joint Force

In flexion, the force of facet joint was observed in all positions for the prosthesis
with 4 mm radius of curvature (ProC-R4), and second one was ProC-R5, and the
largest force of facet joint occurred in the ProC-R6. In terms of the positions, facet
force was highest in posterior among all positions. P6 model showed the maximum
facet force (47.1 N), increased by 106.9% to the intact model. Compared with the

Table 7.3 The ROM of the intact model and models implanted with different Prodisc-C prostheses
Flexion&Extension (°) Left&Right bending (°) Axial torsion (°)
Intact model 7.41 4.23 5.49
Pro-C-M 9.14 4.58 6.13
Pro-C-A 9.07 4.67 6.54
Pro-C-P 12.44 6.06 8.36
Pro-C-L 11.46 5.73 8.05
Pro-C-R 11.80 5.93 8.20
7 Biomechanics of Spine 161

intact model, an increase was observed in force transmitted through the facet joints
in all cases under extension, left-right lateral bending, and right axial torsion.
Similar facet joint force was also observed in prostheses with different radius size
(4, 5, 6 mm) in all the conditions. However, the changes were significant with the
variation of the positions of implant. In left axial torsion, all models except for the
anterior position showed the decrease of the facet force, with the increase of the A4,
A5, and A6 by 2.69%, 7.23%, and 2.34%, respectively.

2.1.6 Ligament Tensile Stress

In flexion, the stress of the posterior longitudinal ligament (PLL) tensile in the intact
model was 2.577 MPa as shown in Table 7.4. The increased percentage was 10.48%,
20.14%, 34.69%, 25.81%, and 30.77% for the ProC-R4 models with neutral, ante-
rior, posterior, left, and right positions, respectively; 5.63%, 10.48%, 45.67%,
33.14%, and 37.10% for the ProC-R4 models; and 42.18%, 45.36%, 80.05%,79.71%,
and 86.03% for the ProC-R6. The stress of the capsular ligament (CL) was

Table 7.4 Ligaments tensile stress in flexion, extension, left bending, right bending, left torsion,
and right torsion for intact model, ProC-R4, ProC-R5, and ProC-R6
PLL CL FL SL
Flexion Intact model 2.577 2.698 0.4802 0.4288
ProC-R4 2.858 3.003 0.5233 0.4918
ProC-R5 2.722 2.765 0.4792 0.4387
ProC-R6 3.693 3.713 0.6099 0.5681
Extension Intact model 0 0.7841 0 0
ProC-R4 0.5302 1.882 0 0
ProC-R5 0.585 1.987 0 0
ProC-R6 0.5522 1.923 0 0
Left bending Intact model 0.8529 2.297 0.1217 0.07164
ProC-R4 1.133 2.897 0.1438 0.08785
ProC-R5 1.166 2.908 0.1436 0.0894
ProC-R6 1.175 2.914 0.1373 0.0894
Right bending Intact model 0.8197 2.117 0.1761 0.09752
ProC-R4 1.137 2.802 0.1957 0.1143
ProC-R5 1.147 2.659 0.1944 0.1115
ProC-R6 1.206 2.794 0.1838 0.1078
Left torsion Intact model 0.5332 2.928 0.1151 0.03631
ProC-R4 0.8837 3.448 0.1341 0.0475
ProC-R5 0.8977 3.409 0.1313 0.0468
ProC-R6 0.9331 3.466 0.1302 0.051
Right torsion Intact model 0.6196 2.316 0.1768 0.09282
ProC-R4 1.003 3.225 0.1983 0.1106
ProC-R5 1.008 3.014 0.1988 0.107
ProC-R6 1.034 3.213 0.1835 0.1018
162 L. Wang et al.

2.698 MPa in flexion. The increased percentage was 5.74%, 18.35%, 34.40%,
14.53%, and 36.77% for the ProC-R4 models with neutral, anterior, posterior, left,
and right positions, respectively; 2.48%, 7.15%, 43.66%, 19.46%, and 40.96% for
the ProC-R4 models; and 39.66%, 42.18%, 87.88%, 67.27%, and 95.48% for the
ProC-R6.
In extension, the tensile stress of PLL was zero, 0.438, 0.637, 0.987, and
0.874 MPa in the ProC-R4 models in five positions, respectively; 0.585, 0.864,
1.171, 1.008, and 1.334 MPa for the ProC-R5 models; and 0.519, 0.7662, 1.050,
0.969, and 1.292 MPa for the ProC-R6 models. Also, for the tensile stress of CL
apparently increasement was seen in all models, which was up to 114.39–305.31%
compared with the intact model.
In lateral bending and axial rotation, compared with the intact model, increase-
ment was observed in all models for the tensile stress of PLL and CL. However, the
ligament tensile stress of different radiuses and position models were similar, no
marked changes observed.

2.1.7 Stress on the Ball Component

The stresses on the polyethylene (PE) ball component of different designs were
measured under flexion, extension, bilateral bending, and axial rotation conditions,
and the stresses were maximal in flexion compared with other loading conditions.
In flexion, the stress of 93.96, 54.63, 127, 128.6, and 130.7 MPa were seen on poly-
ethylene ball of ProC-R4 models with neutral, anterior, posterior, left, and right
positions, respectively; 75.61, 84.75, 97.66, 87.91, and 111.7 MPa were seen on
polyethylene ball of the ProC-R5 models; and 16.18, 16.77, 15.97, 18.3, and
19.55 MPa were seen on polyethylene ball of the ProC-R6 models, which decreased
markedly. In all positions, the stresses distributions of ProC-R4 and ProC-R5 were
concentrated on the part anterior to the PE ball and the maximum stresses—130.7
and 111.7 MPa—were observed in right position. As for the ProC-R6, the stress was
distributed at the edge of the joint between the hemisphere and plate, and the maxi-
mum stress—19.55 MPa—was also observed in right position as shown in Table 7.5.
In this part, we investigated and quantified the theoretical effects on the spine
biomechanics of the ball-and-socket TDR at the C5–6 level with prostheses of 3
designs and 5 implanted positions. These variations were related to not only design
parameters (radius of curvature) but also surgical procedure (the positioning and
insertion trajectory varied along the anteroposterior direction and lateral direction).

Table 7.5 Stress on the ball component in flexion, extension, left bending, right bending, left
torsion, and right torsion for intact model, ProC-R4, ProC-R5, and ProC-R6
Flexion Extension Left bending Right bending Left torsion Right torsion
ProC-R4 144.2 29.52 16.72 16.93 17.2 16.59
ProC-R5 75.61 18.95 13.96 13.65 14.47 13.95
ProC-R6 12.06 17.39 4.932 5.144 5.661 4.885
7 Biomechanics of Spine 163

We observed the major changes in ROM, stress on polyethylene ball, the force of
the facet joint, and the tensile stress of ligament, which were influenced by the sizes
of implant and the implanted position.
After the implantation of prostheses, the ROM data of C5–C6 finite element
cervical model in this study presented an increase compared with the intact model.
This result was in accordance with the previous study, in which ROM increased
after replacing the disc with the semi-constrained ProDisc-C at the treated segment.
Meanwhile, in flexion/extension there was increasement observed in the ROMs of
ProC-R4, ProC-R5, and ProC-R6 and the increasement was lager in ProC-R6.
However, we do not find the same phenomenon in lateral bending and axial rotation.
These suggested that the influence of different radius of curvature on the ROM was
not obvious apart from flexion/extension. Rousseau et al. [39] verified our results
through the finite element analysis of three types of ball-and-socket designs (PL,
PS, and CL), in which they found that the ROMs increased in flexion/extension but
was consistent with the intact model in axial rotation and bilateral bending.
Most studies found the ROMs can preserve the general motion and similar to the
physiological values, regardless of the various prosthesis designs, which mean pros-
thesis design more strongly related to the quality of motion, than to the quantity
[41]. Some similar researches have indicated that the typical motion quality was the
location of rotation axis [43, 44]. The mean center of rotation (MCR) was analyzed,
finding that the intact model’s MCR was at the posterior one-third of the lower ver-
tebra endplate and varied in a certain area under flexion/extension [39]. With regard
to different types of prostheses, MCR presented a trend to match the prosthesis
center. It is a matter of course that the variation of the position of the implant accom-
panied by that of MCR based on this fact. Therefore, the larger ROM was seen in
posterior position models, the rotation axis of which was adjacent to the actual
center of rotation axis. Take the radius of curvature into account; in order to keep the
height of the disc, the MCR of ProC-R4, ProC-R5, and ProC-R6 would change as
the hemisphere moves up and down. Probabilistic variables were investigated in the
center of rotation (COR). The intervertebral rotation was affected by the anteropos-
terior position of COR only in flexion/extension, but not being affected by the lat-
eral position of the COR. In this part, it is really no apparent difference from left to
right positions, but they all differed greatly from the neutral position. After the pros-
thesis being implanted, the force of the facet joint was observed to be less than that
of ProC-R5 and ProC-R6 in most kinetic situations, and there were significant dis-
tinctions in flexion, with the value of P6 being the largest. It was also found that the
maximum ROM was seen in ProC-R6 model with posterior position (P6) in flexion/
extension. It seemed that the larger force of facet joint was caused by the lager
ROM. Although some researches have pointed out this phenomenon [44], the rele-
vance between ROM and force of facet joint still remained to be figured out.
Womack et al. employed ProDisc-C models varying with 5-, 6-, and 7-mm implant
heights to explore the effects of the size of implant, founding that the size of implant
influenced contact force of facet without influencing the ROM [45]. It was demon-
strated that the force of facet joint was vulnerable to the variation of implanted posi-
tions, but no tendency was observed.
164 L. Wang et al.

The capsular ligament (CL) was associated with the force of facet joint and the
related pain, so it was paid main attention in preview studies. In the part, increased
tensile stress of CL was observed in all cases after implantation. And the ligament
tensile stress of larger radius model with posterior position is the largest, while cap-
sular ligament tension of model with neutral and anterior positions slightly reduced.
The overmuch tensile stress companied by the force of facet joint may cause fatigue
damage, and partially affected the adjacent ligament, finally had a bad impact on the
long-term clinical results [40].
For each prosthesis implanted, the stress distribution on the core of PE is
approximately similar, no matter how the position of implant varied, and the max-
imum value of stress was witnessed in flexion. The stress of ProC-R4 and ProC-R5
concentrated on the part anterior to the PE ball. In contrast, the pressure of
ProC-R6 was lower and spread over the joint edge between plate and hemisphere.
In view of this point, ProC-R6, a prosthesis having a larger curvature, seemingly
could lower the stress of implant and avoid the concentration of stress. In the long
run, this (large curvature) design may delay spherical bearing wear on surfaces,
thereby avoiding the inflammatory reactions caused which wear debris led to.
Speaking of wear debris, most studies primarily focused on osseointegration and
biological response (to wear debris) at the interface between prosthesis and bone.
A caprine model was used to assess the biomechanical characteristic. No evi-
dence of wear particles or loosening implant (subluxation) was found, while it
was reported that one patient implanted the PCM disc had a large amount of wear
debris [40, 46].
Based on the observation, the ROM, force of facet joint and tension of capsule
ligament were affected by the radius of implanted prosthesis, while the position
had an influence on all these aspects under all loading conditions. These aspects
(the ROM, force of facet joint and tension of capsule ligament) are sensitive to the
position in anteroposterior direction. The disc having larger curvature has less
stress on the polyethylene, which can avoid stress concentration, but bring adverse
outcomes such as increased force of facet joint and tension of ligament. Therefore,
the design of disc prosthesis should be considered retaining the range of motion as
well as avoiding the adverse problems, so as not to affect the long-term clinical
results [40].
In summary, surgical procedure such as repairing or preserving the posterior
ligaments in the lamina repair surgery and better implant design are important fac-
tors for the postoperative rehabilitation, especially the range of motion (ROM) of
flexion/extension and implant stress, and spinal integrity and stability. Thus, a
proper implant design should consider reserving the range of motion as well as
avoiding adverse problems, and a proper surgical procedure and implant position
along the anterior-posterior direction ought to be paid more attentions in spine
biomechanics.

Acknowledgement This work was supported by Beijing Municipal Science and Technology
Project (No. 161100001016013).
7 Biomechanics of Spine 165

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Chapter 8
Biomechanics of the Hip

Bolun Liu, Jia Hua, and Cheng-Kung Cheng

Abstract The hip joint is a crucial support structure for the human body structure,
second only to the knee in the terms of weight-bearing forces placed upon it, and is
an essential joint for walking. A solid understanding of the anatomy and biome-
chanics of the hip joint is necessary for improving treatments for hip disorders and
for the design of hip prostheses. In this chapter, the anatomy of the hip joint is intro-
duced and is then followed by a more in-depth analysis of the kinetic and kinematic
movements of the joint.

Keywords Hip joint · Anatomy · Biomechanics · Kinematics · Kinetics

1 Anatomy of the Hip

The femoral head and acetabulum form a ball-and-socket joint (Fig. 8.1), which is
surrounded and protected by powerful muscles, tendons, and a ligamentous capsule.
Both the femoral head and acetabulum are covered with articular cartilage and sepa-
rated by a small volume of synovial fluid which is produced by the synovial mem-
brane. The synovial fluid keeps the cartilage nourished and provides lubrication for
the joint. The bones, muscles, tendons, ligaments, and synovial fluid work together
to make the hip joint flexible, stable, and strong.

B. Liu
School of Biological Science and Medical Engineering, Beihang University, Beijing, China
J. Hua
Department of Nature Science, Faculty of Science and Technology, Middlesex University,
London, UK
C.-K. Cheng (*)
School of Biomedical Engineering, Shanghai Jiao Tong University, Shanghai, China
e-mail: ckcheng2020@sjtu.edu.cn

© Springer Nature Singapore Pte Ltd. 2020 169

C.-K. Cheng, S. L-Y. Woo (eds.), Frontiers in Orthopaedic Biomechanics,
https://doi.org/10.1007/978-981-15-3159-0_8
170 B. Liu et al.

Fig. 8.1 Anatomy of the Pelvis

hip joint

Femoral Acetabulum
head

Labrum
Femoral
neck

Capsule
Femur

1.1 Bony Structure

1.1.1 Acetabulum

The acetabulum resembles a concave hemisphere and is closely matched to the

shapes of the femoral head.
The cup-shaped acetabulum is located at the intersection of three pelvic bones—
the ilium (40% area of acetabulum), ischium (40%), and pubis (20%) [1]. These
three bones are connected by cartilage by the time a person reaches the age of 14.
The cartilage begins to ossify at around the age of 14–16 and ends at the age
of 23 [2].
The acetabulum is oriented inferiorly, laterally, and anteriorly. The angle between
the open plane of the acetabulum and the sagittal plane can be used to describe the
level of anteversion of the acetabulum, which is critical for flexion stability of the
hip joint. On a radiograph, the anteversion angle of the acetabulum is determined as
the angle between a line drawn through the anterior and posterior edge of acetabu-
lum and a line perpendicular to a line connecting the posterior pelvic margins at the
level of the sciatic notch (Fig. 8.2). The anteversion angle of the acetabular (AV.A)
is an index to measure the coverage of the femoral head by the acetabulum in the
horizontal plane. The mean acetabular anteversion is about 23°. The acetabular
anteversion increases slightly with age and the value in men is about 2.7° lower than
that in women [3]. Excessive AV.A have been linked to greater joint instability and
a greater prevalence of anterior dislocation of femoral head.
8 Biomechanics of the Hip 171

Fig. 8.2 Measurement of

the anteversion angle of the
acetabulum

Fig. 8.3 Measurement of

Sharp’s angle, the
acetabular roof angle (AA),
and the acetabular
depth-width ratio (ADR)
[4] (Reprinted with
permission from ‘Skeletal
Radiology’. License AA
Number: 4567410923053) ADR=(A/B)*1000 A
B

Sharp’s
angle
teardrop line

The morphology of acetabulum is a primary factor cause of developmental dys-

plasia of the hip (DDH) and femoroacetabular impingement (FAI). Therefore, cor-
rectly evaluating the morphology of acetabulum is necessary for the clinical
diagnosis of DDH and FAI. The indices, namely Sharp’s angle, acetabular roof
angle, acetabular depth-to-width ratio, center-edge angle, and femoral head extru-
sion index, are often used for describing the acetabular morphology and diagnosing
DDH [4, 5].
The Sharp’s angle, which is measured between the acetabular margin line and
teardrop line on the coronal plane, is an index for reflecting lateral coverage of the
femoral head (Fig. 8.3). The normal range of the Sharp’s angle is between 33° and
38°, and an angle of greater than 42° is considered as dysplastic [6].
Tönnis detailed a method of using the acetabular roof angle to measure the incli-
nation of the acetabular load-bearing surface on anterior-posterior radiographs of
the hip [7]. The load-bearing surface of the acetabulum, also known as the acetabu-
lar sourcil, is an area of dense bone on the acetabular roof. The acetabular roof angle
172 B. Liu et al.

is formed between a line connecting the medial sourcil and lateral rim of the acetab-
ulum and a horizontal line between the lowest points of two teardrops (Fig. 8.3).
The acetabular roof angle typically ranges from 0° to 10°, while greater than 10°
can be considered as hip dysplasia. A larger angle generally means a more unstable
hip joint, while an angle of less than 0° indicates that the acetabulum tends to over-
cover the femoral head [7].
The acetabular development can be evaluated by the acetabular depth-to-width
ratio (ADR) [8], which is calculated by depth/width × 1000. The width of the ace-
tabulum is measured as the distance between the tip of the inferior teardrop to the
lateral rim of the acetabulum on the coronal plane (Fig. 8.3). The depth is the dis-
tance between the deepest point of the acetabulum to a line connecting the medial
and lateral rim of the acetabulum [9]. A depth-to-width ratio of less than 250 is
considered hip dysplasia [10].
The bony coverage of the femoral head by the acetabulum provides inherent
stability for the hip joint. The center-edge angle (CE angle) was first proposed by
Wiberg [11] to describe the relationship between the femoral head and acetabulum.
The CE angle is formed by the intersection of a line through the center of femoral
head and superolateral rim of acetabulum and a vertical line passing through the
center of the femoral head (Fig. 8.4a). A CE angle of over 25° is normal in adults,
lower than 20° is associated with DDH [11, 12], and an angle greater than 39° is
considered as acetabular over-coverage, which often causes impingement.
Another index for measuring the bony coverage of the femoral head by the
acetabulum is the femoral head extrusion index (FHEI). This index is calculated as
the percentage of the uncovered portion of the femoral head to the width of the
femoral head (Fig. 8.4b) and is useful in assessing developmental dysplasia as well
as femoroacetabular impingement. Values between 17 and 27% are considered
within the normal range. An FHEI of greater than 27% may be categorized as
developmental dysplasia, while values lower than 17% can be considered as over-
coverage [13].

a CE Angle b

FHEI=A/(A+B)

A B

Fig. 8.4 Measurement of center-edge (CE) angle (a) and femoral head extrusion index (FHEI) (b)
8 Biomechanics of the Hip 173

1.1.2 The Acetabular Labrum

The acetabular labrum is a circular fibrocartilage structure with a triangular cross

section which attaches directly to the bony edge of the acetabulum (Fig. 8.1). The
labrum joins the transverse ligament at the lower rim of the acetabulum to form a
continuous and complete sealing ring. An adult labrum has an average circumfer-
ence of around 16 cm for males and 14 cm for females [14] and an average thickness
is 2–3 mm [15].
It is one of the most important structures in the hip joint cavity [16]. The labrum
forms a seal around the joint cavity to prevent leakage of the lubricant film that lies
between the femoral head and the acetabular cartilage, ultimately reducing the
occurrence of cartilage damage and osteoarthritis. This seal also has a suctioning
effect on the joint through negative intra-articular pressure, which maintains the
stability of the joint and makes it more difficult to dislocate [16].
The labrum also increases the contact area between the acetabulum and femoral
head by 22% and increases the depth of the acetabulum. This increases the stability
of the hip joint [17]. Studies have shown that a normal labrum shares 1–2% of the
load on the hip joint, whereas the labrum of DDH patients bears 4–11% of the joint
load [18, 19].

1.1.3 Femoral Head

The femoral head, consisting of a dense trabecular bone structure, is located at the
proximal end of the femur and is supported by the femoral neck (Fig. 8.1). The
femoral head is crucial for supporting the body as well as transmitting and absorb-
ing loads generated during daily activities. The diameter of the femoral head is
generally larger in men than in women [20].
The femoral head is approximately spherical with a smooth surface, and about
60–70% of the femoral head is covered by articular cartilage [21]. There is a small
rough depression called the fovea capitis on the posterior and inferior part of the
femoral head which acts as an attachment point for the ligamentum teres femoris. The
strength and stiffness of the femoral head vary from region to region depending on
the thickness of the surface cartilage. The cartilage is thickest around the area anterior
to the zenith region [22]. Since the articular cartilage is viscoelastic, the load-bearing
area of the femoral head changes in accordance with the magnitude of the load. As
the load increases, the load-bearing area changes from the periphery of the femoral
head to the center of the lunate surface and the anterior and posterior horns [23].

1.1.4 Femoral Neck

The femoral neck, projecting in a superior and medial direction, is a cylindrical

bone which connects the femoral head to the long femoral shaft (Fig. 8.1). The main
functions of the neck are to support the femoral head and to maintain the hip at the
correct angle.
174 B. Liu et al.

The femoral Neck-Shaft Angle (NSA) is the angle formed by the long axis of the
femoral neck and the longitudinal axis of the femoral shaft. During infancy, the
NSA has an angle of inclination of about 140–150°, and this decreases progres-
sively as children get older to reach a value of about 125° at puberty (average
125 ± 5°). The NSA does not typically change again after this. When the angle
exceeds 130° after growth has stopped, this condition is known as a coxa valgus
deformity. In cases where the angle is less than 120°, this is known as a coxa varus
deformity. Coxa valga is more likely to be found in patients with hip dysplasia [24,
25]. In contrast, coxa vara is more commonly associated with femoroacetabular
impingement (FAI) [26].
Femoral neck anteversion (FNA) is the angle between the projection of the femo-
ral head-neck axis on the transverse plane and on the coronal plane. If the head-neck
axis is inclined forwards towards the transcondylar plane, then it is termed antever-
sion, and if the same is directed downwards and posterior, it is termed as retrover-
sion. Anteversion reduces the coverage of the femoral head by the acetabulum, and
thus the leg tends to rotate internally to prevent the femoral head from dislocating,
whereas retroversion has the opposite effect. Femoral neck anteversion ranges from
30° to 40° in infancy and decreases progressively as the body grows. For adults, a
normal anteversion angle ranges from 15° to 20°, with males having slightly less
femoral anteversion than females [27]. Abnormal femoral neck anteversion and
structural deformities cause lead to FAI, which is considered a precursor to osteoar-
thritis [28].

1.1.5 Femoral Calcar

The femoral calcar is an important component of the internal weight-bearing struc-

ture of the proximal femur located at the posteromedial conjunction of the femoral
neck and shaft, and runs along the posterointernal margin of the femoral neck from
the diaphysis towards the femoral head [29]. This ridge of dense bone is a result of
the stress distributions in the proximal femur under physiological loading, which is
a combination of compression, tension, and shear. The complex loading pattern is
caused by the large bending moments and torsion around the femoral head. The
femoral neck is equivalent to a cantilever beam, and the femoral calcar is located at
the base of the cantilever beam, thus shortening the arm of force and reducing the
bending moment of the femoral neck-shaft connection. The femoral calcar influ-
ences how load is transferred through the femur, reduces the load on the posterior
and medial cortical bone [30], increases the load on the anterior and lateral cortical
bone, and distributes the stress more evenly in the proximal femur. Due to high
compressive loads placed on the region of the femoral calcar, the trabecular bone
in this area is almost as hard and strong as the cortical bone. This is useful for THA
as the dense bone acts to support the implant, thereby reducing loosening and
subsidence.
8 Biomechanics of the Hip 175

1.2 Muscles and Ligaments

1.2.1 Muscles

The muscles of the hip, working together to provide force for movement and stabil-
ity, are crucial for the normal functioning of the hip joint. By contracting various
muscles, the hip joint is capable of moving through 6 degrees of freedom based on
the femoral head center: flexion and extension around a transverse axis, abduction
and adduction around a sagittal axis, external rotation and internal rotation around a
longitudinal axis (Fig. 8.5).
The most powerful flexor of the hip joint is the iliopsoas, which is composed of
the psoas major, iliacus, and psoas minor muscles. The psoas major (superficial
layer) originates at the T12-L4 vertebrae and the iliacus originates at the iliac fossa.
At the other end, both muscles have an insertion point on the lesser trochanter. Only
about half of the population have a psoas minor muscle (deep layer), which origi-
nates from the costal processes of the L1 to L5 vertebrae and inserts at the iliopec-
tineal arch. The rectus femoris, sartorius, and tensor fasciae latae are other flexors
which assist the iliopsoas.
The gluteus maximus, as the largest muscle in the body, acts as the main extensor
of the hip joint. The gluteus maximus mainly arises from the dorsal surface of the
sacrum and gluteal surface of the ilium and then branches out as two fibers. The
upper and lower fibers insert on the iliotibial tract and gluteal tuberosity, respec-
tively. The force of the gluteus maximus also contributes when rotating the hip
externally as well as maintaining the body’s upright posture. Other main extensors
of hip include the biceps femoris, semimembranosus, and semitendinosus.

Fig. 8.5 Axis of rotation Z Z

around the hip joint center
and movements produced
by the hip joint [31]
(Reprinted with permission
from ‘Orthopaedics and Y X
Trauma’. License Number:
4570520375663)
X Y
Abduction Adduction

Extension Flexion

External Rotation Internal Rotation

176 B. Liu et al.

The gluteus medius, gluteus minimus, and tensor fascia latae form the major
abductors of the hip joint, assisted by the piriformis and sartorius. The gluteus
medius and gluteus minimus originate at the gluteal surface of the ilium and insert
at the lateral and anterolateral surface of the greater trochanter, respectively. The
tensor fasciae latae originates from the anterior superior iliac spine and inserts at the
iliotibial tract. The piriformis is located in the middle of the gluteal region; it arises
from the surface of the sacrum and inserts at the greater trochanter.
Hip adduction is primarily accomplished by the adductor longus, brevis, and
magnus muscles with assistance from the gracilis and pectineus muscles. The
adductor longus, brevis, and gracilis also play roles in flexing the hip, whereas the
adductor magnus and pectineus contribute to hip external rotation.
The primarily external rotators of the hip are obturator externus, quadratus femo-
ris, and gemelli with assistance from the gluteus maximus, sartorius, and piriformis.
The obturator externus originates from the external surface of the obturator mem-
brane and the surrounding bony surface and inserts at the intertrochanteric fossa
through the posterior part of the femoral neck. This muscle also plays a role as an
adductor of the hip joint. The quadratus femoris arises from the lateral side of the
ischial tuberosity and ends at the intertrochanteric crest of the femur.
Internal rotation of the hip joint is mainly accomplished by the actions of the
tensor fascia latae, anterior fibers of the gluteus medius, and minimus muscles.

1.2.2 Capsule and Ligaments

The hip capsule helps maintain the stability of the hip joint. The capsule is com-
posed of a strong and dense fibrous cylindrical sleeve originating from the acetabu-
lar margin 5–6 mm beyond the acetabular labrum and attaching anteriorly at the
intertrochanteric line [32]. The femoral head and most of the femoral neck are
enclosed in the joint capsule, whereas the lateral half of the femoral neck as well as
the great trochanter and lesser trochanter are not enclosed in capsule. Because of the
need to bear greater loads, the anterosuperior part of the hip joint capsule is thicker,
whereas the posteroinferior part is thinner and looser. On the inside, a synovial
membrane lines the inner surface of the capsule and produces synovial fluid to
lubricate the articular surface and provide nutrition to the articular cartilage.
The stability of hip joint is strengthened by four ligaments, three extracapsular
ligaments (iliofemoral ligament, ischiofemoral ligament, and pubofemoral liga-
ment) and one intracapsular ligament (ligamentum teres femoris).
The iliofemoral ligament (also called Y-ligament) lies on the anterior side of the
hip joint and resembles an inverted “Y.” The ligament originates on the lower part
of the AIIS (Anterior inferior iliac spine) and then divides into two branches which
subsequently attach at the distal and proximal part of the intertrochanteric line,
respectively. The iliofemoral ligament is the strongest ligament in the body with a
tensile strength exceeding 350 N [1]. Its lateral branch limits excessive abduction
and adduction of the hip joint. It also limits internal and external rotation when the
hip joint is in extension and limits external rotation when the hip joint is in flexion.
8 Biomechanics of the Hip 177

The medial fibers of the iliofemoral ligament limit abduction and external rotation
of the hip [1, 32].
The ischiofemoral ligament is located on the posterior superior side of the hip
joint. It originates at the ischial portion of the acetabulum and then crosses the
hip capsule as two fibers. The central fibers (superior ischiofemoral ligament)
spiral superiorly around the neck of the femur from the posterior surface of the
ischium to the medial surface of the greater trochanter of the femur. The lateral
and medial inferior ischiofemoral ligaments attach to the neck of the femur and
reinforce the posterior aspect of the joint capsule. The ischiofemoral ligament
contributes over 60% of the restraining force required to limit excessive internal
rotation in flexion and extension [33]. It is helpful for maintaining stability as
well as reducing the amount of muscle energy required to maintain a standing
position.
The pubofemoral ligament (also called pubocapsular ligament), located at the
anterior inferior aspect of the hip joint, plays a role in supporting the joint capsule
and maintaining the anterior and inferior stability of the hip joint. It originates at the
iliopubic eminence, the pubic portion of the acetabular rim, superior aspect of the
pubic ramus and the obturator crest, and inserts at the inferior surface of the femoral
neck. The pubofemoral ligament restricts internal rotation once the hip is flexed
beyond 30°, as well as restricting excessive abduction [34].
The ligamentum teres femoris (also called femoral head ligament) is a flat trian-
gular fibrous band in the hip capsule. The base attaches to both sides of the trans-
verse acetabular ligament and the edges of the acetabular notch, and the tip connects
to the fovea capitis on the head of the femur. The femoral head ligament is covered
by synovium with blood vessels passing through it. It is generally believed that this
ligament has no restrictive effect on the motion of the hip joint [35].

2 Biomechanics of the Hip

2.1 Kinematics of the Hip Joint

Kinematics is the evaluation of motion and positioning, but does not consider the
physical properties of the object itself or the forces imposed on it. In human motion
analysis, joint angular displacement is the most common method for describing the
relative motion between limbs. A comprehensive understanding of joint kinematics
is important for the diagnosis and treatment of joint diseases.
Because of the congruency of the surface of the hip, almost all movement
between the femoral head and the acetabulum is rotational, without detectable
­translation [36]. Usually, hip motion is described by the movement of the femur
relative to the pelvis around the hip joint center. The hip joint can move through 3
degrees of freedom: flexion and extension in the sagittal plane, abduction and
adduction in the frontal plane, and internal and external rotation in the transverse
plane (Fig. 8.5).
178 B. Liu et al.

Hip joint motion is achieved through the action of a series of muscles and con-
nected tendons, and is limited by the bony structure of a hip joint, the acetabular
labrum, and surrounding ligaments. The largest movement occurs in the sagittal plane,
where the flexion angle ranges from 0° to 140° and the extension angle ranges from
0° to 20°. In the frontal plane, the range of abduction is from 0° to 50° and adduction
is from 0° to 30° with the hip joint extended. When the hip joint is flexed to 90°, the
abduction limit increases to 80° whereas the adduction limit decreases to 20°. In the
transverse plane, the limits of external and internal rotation are 50° and 40°, respec-
tively, with the hip flexed to 90°. When in the prone position with the hip extended, the
external rotation limit decreases to 30° because of the restrictive actions of the soft
tissues [37]. The ranges detailed above show the largest angles that the hip joint can
safely reach, but the joint seldom reaches such extremes during daily activities.
Typical joint ranges of motion in daily activities can be used to evaluate a
patient’s functional movement in clinical settings. Common daily activities that
require a large range of motion include trying shoes on the floor, sitting down on a
chair or rising from it, and ascending or descending stairs. A study by Johnston and
Smidt [38] measured the range of motion for 33 males performing these sample
activities. It was found that the greatest motion in the sagittal plane occurred when
squatting on the floor to tie shoes. In the frontal and transverse planes, the two great-
est motions occurred when squatting to tie a shoe on the opposite foot across the
thigh. These values indicate that for carrying out daily activities a flexion angle of
at least 120° and an external rotation angle of at least 20° is necessary.
Walking is one of the most repetitive activities for the hip joint. Understanding
the movement of the hip joint during walking is helpful for further understanding
hip joint function. Compared with other joints, the hip has a larger range of motion
in the frontal and transverse planes during level gait [39]. One single gait cycle is
typically composed of an initial heel strike (0%) through to the second contact of
the same foot (100%) and can be divided into two phases: stance phase and swing
phase (Fig. 8.6). The stance phase refers to the period when the foot contacts with

STANCE SWING

0% Mid-Stance 60% 100 %

Heel Strike Toe off Heel Strike

Fig. 8.6 Period of one gait cycle [31] (Reprinted with permission from ‘Orthopaedics and
Trauma’. License Number: 4567661288157)
8 Biomechanics of the Hip 179

a b c
40 15 20

Hip Internal / External Rotation (Deg)

Hip Adduction / Abduction (Deg)
30
Hip Flexion / Extension (Deg)

10
10
20
5
10
0
0 0
-10 HLTHY
-10
-5 MOA
-20
SOA
-30 -10 -20
0 50 100 0 50 100 0 50 100
Percent of Gait Cycle Percent of Gait Cycle Percent of Gait Cycle

Fig. 8.7 Hip movements in the (a) sagittal, (b) frontal, and (c) transverse plane for nonexistent
(solid), moderate (dotted), and severe hip osteoarthritis (dashed) groups. Flexion, adduction, and
internal rotation are represented as positive angles. The shaded region represents 1SD above and
below the healthy/non-OA group waveform and the vertical line represents the toe off period of the
gait cycle [40] (Reprinted with permission from ‘Journal of Electromyography and Kinesiology’.
License Number: 4567410168348)

ground and accounts for about 60% of the gait cycle. The swing phase is the period
when the limb is swinging forward and accounts for about 40% of the gait cycle.
The motions of the hip joint during gait are illustrated in Fig. 8.7 [40]. At heel
strike (0% of gait cycle), the hip is flexed to 30–35° in the sagittal plane, before
extending to a neutral position at midstance [39, 40]. The end of the stance phase is
gauged by the “toe off” period at about 60% of the gait cycle, at which point the hip
is extended to 10–15°. In the frontal plane, the hip joint is in an adducted position
during the stance phase, and the maximum adduction angle occurs at about 20% of
the whole gait. In the swing phase, the hip joint reverts to an abducted position,
which continues until the middle of the swing phase. In the transverse plane, the hip
is externally rotated in the stance phase and converts to internal rotation around the
middle of the swing phase. The hip joint remains internally rotated until late in the
following stance phase, at which point it rotates externally again.
Hip joint diseases such as osteoarthritis (OA) often have an influence on the range of
motion of the hip joint. Moderate OA results in a considerable decrease in hip range of
motion in the sagittal plane, but there is only a significant decrease in the range of
motion in the frontal and transverse planes in patients with severe OA [40] (Fig. 8.7).
Total hip arthroplasty (THA) involves replacing a diseased or damaged hip joint
with a prosthesis. THA is often performed in cases of severe joint pain, OA,
­avascular necrosis (AVN), and femoral neck fracture. However, numerous studies
found that the range of motion of the hip in the sagittal plane was reduced after THA
[41–44]. The achievable limit of hip extension is reduced after THA [41, 44–46],
but it has been reported that the limit of hip flexion is not significantly impacted by
THA [42, 47]. But, in contrast, Beaulieu et al. did find a reduction in peak flexion
angle after THA [41]. The decrease in the extension limit may be related to the
increased passive resistance of the flexors (i.e., a flexion contracture) [48].
180 B. Liu et al.

2.2 Kinetics of the Hip Joint

Kinetic analysis of the hip joint focuses on the forces acting on the hip that cause
motion. Hip motion is the result of the interaction between internal forces (muscles,
joints, tendons, ligaments, and joint contact forces [49]) and external forces acting
on the system (gravity, ground reaction forces, and inertia [49]). Such kinetic infor-
mation is useful for evaluating hip motion and diseases, as well as developing treat-
ment methods and designing hip prostheses.

2.2.1 Static Loading

The human body is an elaborate structure in which bones and soft tissues interact
under static or dynamic conditions to maintain balance and generate motion. Static
analysis of the hip joint is useful for evaluating changes in the anatomical structure
or different treatment modalities on the hip joint reaction forces. Free-body dia-
grams, as shown in Figs. 8.8 and 8.9, can be used to illustrate contact forces during
various loading conditions, such as single leg stance, double leg stance, and carry-
ing external loads.

Single-Leg Stance

In a single leg stance, the human body can be considered as a lever-like structure
with the femoral head acting as the fulcrum. A simplified free-body diagram can be
used to calculate and illustrate the joint reaction force indirectly (Fig. 8.8). Since the
weight of the non-supporting leg is included in the load acting on the load-bearing
hip, the effective center of gravity of the body moves close to the non-supporting leg.

Fig. 8.8 Joint reaction

force on the hip joint M R
during single leg stance
illustrated using a
simplified free-­ My Ry
body diagram

A B

W
8 Biomechanics of the Hip 181

Fig. 8.9 Anterior view of

the pelvis in erect double
leg stance. DR = moment
arm for the right hip,
DL = moment arm for the
left hip, WR = upper body
weight act on right hip,
WL = upper body weight
act on left hip

As the lower extremities account for 1/3 of the full body weight, the non-­supporting
limb accounts for half of that, or 1/6 of the full body weight. Therefore, the gravita-
tional force (W) acting on the load-bearing hip is 5/6 body weight (BW). This down-
ward force will create a moment around the center of the femoral head, with the
gravitational moment arm (B) being the distance between the center of the femoral
head and the center of gravity of the body. To maintain balance, this moment is off-
set by a counteracting moment generated by the combined abductor muscle force
(M) acting over a lever arm measured as the distance between the center of the femo-
ral head and the insertion site of the abduct muscles on the greater trochanter.
To calculate the joint reaction force (R) in single leg stance, the sum of all
moments acting on the joint equals zero:

( A × My ) − ( B × 5 / 6W ) = 0.
Usually the ratio between B and A (B:A) is about 2.5.
Thus, My = 2.5W,

Ry = My + W = 2.5W + W = 3.5W

R = Ry / ( cos30° ) = 3.5W / ( cos30° ) ≈ 4W

When the hip joint succumbs to disease or trauma, loading the joint can be
extremely painful [21]. Reducing the hip joint reaction force can offer immediate
pain relief. According to the above calculations, the joint reaction force can be
reduced in two ways. One way is to reduce the moment generated by body weight.
Since the moment is calculated as the force multiplied by the moment arm, the
moment can be reduced by either reducing body weight or the length of the moment
arm. For example, tilting the trunk towards the diseased hip will shift the center of
gravity closer to the hip joint (this results in Trendelenburg gait), thereby reducing
the body weight moment arm. Another way is to reduce the required hip abductor
force. This can be achieved by increasing the moment arm of the abductor muscle
182 B. Liu et al.

force. For example, in THA a femoral implant with a greater offset may be chosen
or the acetabular component may be positioned medially. The effectiveness of off-
setting the hip is illustrated by the fact that the reaction force on the hip in patients
with coxa vara is 25% lower than the average hip joint, while the reaction force in
patients with coxa valgus is 25% higher than the average hip joint [50]. This is due
to the moment arm of the abductors decreasing; thus, more abductor muscle force is
need to balance the body weight.
Using a cane in the hand contralateral to the diseased hip is also a way to lower
the joint reaction force by reducing the body weight passing through the affected
hip. The cane effectively creates a moment that counteracts the moments gener-
ated by body weight. Therefore, lower abductor muscle force is required and so
the joint reaction force is reduced, which in turn alleviates pain in the affected
hip. Since the force arm produced by cane is much larger than that of abductor
muscles, even small forces on the cane can generate moments that are large
enough to significantly reduce the force of abductors. It has been shown that
applying about 15% of body weight to a cane can cut the joint reaction force by
50% [50].

Double-Leg Stance

In double leg stance, the upper body weight is distributed equally between the
two femoral heads (WR = WL) with equivalent gravitational moment arms
(DR = DL) (Fig. 8.9). The moment acting on each hip joint is equal in magni-
tude and opposite in direction. The pelvis is in balance in the coronal plane
with negligible assistance from surrounding musculature. Therefore, if abduc-
tor muscles are not required to maintain balance in frontal plane and sagittal
plane, there would be an equal force of 1/2 superimposed body weight (W).
This force will be increased if the abductor muscle acts to maintain balance and
stability.

Trabecular Bone System

As mentioned above, in standing or upright weight-bearing activities, over half of

the weight of the HAT (superimposed body weight; head-arms-trunk) passes down
through the pelvis to the femoral head. Correspondingly, the ground produces an
opposing ground reaction force (GRF) acting on the femoral shaft. These two nearly
parallel and opposite forces create a bending moment with a moment arm (MA) that
is dependent on the angle and length of the femoral neck. Due to this bending
moment, tensile and compressive stresses appear on the lateral and medial aspect of
the femoral neck, respectively (Fig. 8.10).
Long-term load-bearing affects the micro-structure of bones. The trabecular
structure of cancellous bone is arranged according to the trajectories of the principal
8 Biomechanics of the Hip 183

Fig. 8.10 The weight-­

bearing line of the head,
arms, and trunk (HAT)

stresses in the bone [51]. This nonuniform arrangement increases the resistance to
mechanical stress. The primary pathway of force transmission in the proximal
femur is reflected by the appearance of the trabecular system.

2.2.2 Dynamic Loading

As detailed previously, free-body diagrams are a simple method for indirectly esti-
mating hip contact forces. Knowing the real-time hip contact forces during daily
dynamic activities (walking, running, squatting, etc.) is also necessary for better
understanding the relevant muscle function and strength and the wear and stability
of the hip joint. Dynamic hip contact forces (HCFs) may be measured using direct
and indirect means. Direct measurements are carried in vivo using instrumented
telemetric prostheses [52, 53]. This method is considered as the gold standard for
measuring loading on the hip [54] and can be used to verify indirect measurement
models. Indirect measurements may be performed using musculoskeletal models
and inverse static optimization techniques to calculate muscle forces and hence joint
loading [55, 56]. Some studies have claimed that results calculated using this indi-
rect method are comparable to experimental data [53, 57–60].
Numerous studies have measured HCFs during dynamic activities [53, 54, 61–
63], of which walking and running are the most two common activities. It has been
shown that the typical peak force (BW) in gait ranges from 1.6 to 5.7 times body
weight, but is influenced by physiological differences, gender, age, and walking
184 B. Liu et al.

Fig. 8.11 Typical hip 3

contact force (HCF) in

Hip Contact Force/BW

healthy individuals during 2.5
one gait cycle [52]
2

1.5

0.5

0
0 20 40 60 80 100
Gait Cycle (%)

speed. Figure 8.11 details the typical HCF during one gait cycle, showing two peaks
for hip contact force. The initial peak occurs during heel-strike and early midstance,
and the second peak occurs just before toe-off.
The contact force is related to the walking speed, whereby increased speed
results in an increased HCF [53, 54, 64]. A study [54] on musculoskeletal models
calculated the HCFs for 20 young healthy adults and found that the peak HCF
increased from 4.22 body weight to 5.41 body weight when the walking speed
increased from 3 to 6 km/h. The greater force is because (1) the increased dynamic
variation of ground reaction force with the walking speed in the heel-strike stage
[65], and (2) the increased stride length corresponds to the increased velocity, which
generates a greater offset of the ground reaction force from the joint axis and mobi-
lizes more muscle activity to maintain balance. The HCF is also linearly and posi-
tively correlated with BMI, meaning that obese people generate a greater HCF
during most of the stance period [57].
During running, there is only one peak HCF, which happens in the stance phase
at 0–30% of the gait cycle [54]. As with walking, the HCF is positively correlated
with speed.
Bergmann et al. has measured hip contact forces using instrumented total hip
implants [52]. The results of his study are illustrated in Fig. 8.12. The graph demon-
strates that the greatest contact force was measured during jogging, reaching about
4.1 times body weight, and walking down stairs generated the second greatest force.
The lowest joint contact force was produced during cycling.
There are also other unpredictable loads placed on the joints that can generate
substantial force, such as the peak HCF during stumbling being recorded at 7.2–8.7
times body weight [61, 66]. Therefore, it should be emphasized that after THA
patients should pay attention not only to daily activities that generate relatively low
HCFs, but also to unexpected events such as stumbling or unstable periods when
standing on one leg which may produce a resultant force in excess of 8 times
body weight.
Furthermore, it should also be noted that direct measurements using instru-
mented telemetric prostheses can only be performed in patients who need THA. Such
methods cannot evaluate the physiological condition of healthy joints.
8 Biomechanics of the Hip 185

4.5
4.1
4.0

3.5
Hip Contact Force/BW

3.0 3.1
3.0
2.6
2.5 2.3
2.1
2.0 1.8

1.5
1.0
1.0

0.5

0.0
Walking Jogging Stand up Sit Stairs Stairs Knee Cycling
Down Up Down Bend
Daily Activities

Fig. 8.12 Hip contact force (resultant forces) during different activities [52]

3 Summary

The mechanical conditions of the hip joint are determined and reflected by its ana-
tomical features. This chapter provides essential information on a normal hip joint
based on an evaluation of its bony structure and surrounding muscles and ligaments,
in addition to their roles in hip functionality and related static and dynamic condi-
tions of the hip joint. However, when the hip joint undergoes pathological changes
such as osteoarthritis or trauma, these mechanical conditions of the hip may be
altered. This needs to be taken into consideration when considering a suitable clini-
cal treatment such as total hip replacement or other surgery.

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Chapter 9
Biomechanics of the Knee

Huizhi Wang, Bolun Liu, Xinzheng Qi, Savio L-Y. Woo,

and Cheng-Kung Cheng

Abstract Composed of tibiofemoral and patellofemoral joints, the knee is a com-

plex synovial joint in the human body, both in terms of anatomy and biomechanics.
Common knee injuries include torn ligaments and tendons as well as menisci that
could lead to cartilage degeneration and osteoarthritis. Therefore, a thorough under-
standing of the anatomy and biomechanical function of the knee is important for
diagnosing any knee disorders, developing appropriate clinical treatments, and
improving the design of joint replacement prostheses. In this chapter, the functional
anatomy of the knee and the biomechanics and kinematics of both the tibiofemroal
and patellofemoral joints will be reviewed. Then, the knee pathomechanics and cor-
responding clinical treatments will be presented and discussed.

Keywords Knee joint · Biomechanics · Implant

1 Functional Anatomy of the Knee Joint

The tibiofemoral joint and patellofemoral joint are the two articulating surfaces that
constitute the knee joint and both are diarthrodial joints that consist of bones, hya-
line cartilage, ligaments, tendons, as well as the musculature (Fig. 9.1). The tibio-
femoral joint also has medial and lateral menisci between its surface to distribute

H. Wang · B. Liu · X. Qi
School of Biological Science and Medical Engineering, Beihang University, Beijing, China
S. L-Y. Woo
Musculoskeletal Research Center, University of Pittsburgh, Pittsburgh, PA, USA
C.-K. Cheng (*)
School of Biomedical Engineering, Shanghai Jiao Tong University, Shanghai, China
e-mail: ckcheng2020@sjtu.edu.cn

© Springer Nature Singapore Pte Ltd. 2020 189

C.-K. Cheng, S. L-Y. Woo (eds.), Frontiers in Orthopaedic Biomechanics,
https://doi.org/10.1007/978-981-15-3159-0_9
190 H. Wang et al.

patella
femur medial collateral
ligament
cartilage
posterior cruciate
lateral collateral
ligament
ligament

lateral
meniscus

tibia

anterior cruciate medial

ligament meniscus
Front view Back view

Fig. 9.1 Anatomy of the knee

the loads as well as to absorb impact forces on the joint. All these soft tissues work
in synergy to stabilize the knee while the muscles power its motion.
Using the principles of biomechanics, the mechanical behavior and the function
of the biological system, in this case the knee joint, can be analyzed and understood.
The motion between two bony structures in a joint is known as kinematics. Normal
kinematics of the knee is maintained by biomechanical functions of each joint com-
ponent. Changing of any one of these components secondary to injury or diseases
could alter the normal balance and synergy of the knee joint and introduce abnormal
kinematics that could cause increased loading of other soft tissue structures and
induce additional damages.
In this section, the anatomy and function of the knee components, as well as the
joint kinematics, are presented.

1.1 Bones

As the femoral condyles are round while the tibial plateau is relatively flat, the con-
formity is reinforced by the menisci lying between them. In the sagittal view, the
anterior section of the tibia is generally higher than its posterior section. Hashemi
et al. [1] demonstrated that the posterior slope of the tibia ranged from −3° to 14°,
and was steeper in females than the males. Also, in the coronal view, the tibial pla-
teau is oriented upward in a medial-to-lateral direction. The coronal tibial slope
ranged from −1° to 6° and was less steep in females. Besides, there is typically a
valgus angle of 7–10° between the tibia and femur. The medial condyle of the distal
femur projects more distally than the lateral condyle [2].
9 Biomechanics of the Knee 191

The patella is a sesamoid bone and has the appearance of an inverted triangle.
The cartilage of the patella is also the thickest in the human body [3].

1.2 Hyaline Cartilage

The hyaline cartilage in the knee joint is a layer of elastic tissue which covers the
contact surfaces of the bones along which the joint moves. Hyaline cartilage is
mainly composed of a matrix of proteoglycans and collagen traversed with intersti-
tial water. This cartilage layer serves numerous functions, including providing a
smooth surface for joint movement, buffering compressive loads, and protecting the
underlying bone. With a thickness of between 1.69 and 2.55 mm, the hyaline carti-
lage in the knee is significantly thicker than in the hip (1.35–2.00 mm) and ankle
joints (1.00–1.62 mm) [4].
The micro-structure of hyaline cartilage has low permeability, which acts to trap
water within the matrix during loading. This pressurizes the cartilage and increases
the stiffness by up to ten times that of the intrinsic modulus of the solid matrix [5].
The increased stiffness of the matrix means there is very little deformation, and the
cartilage can take up to 90 min to recover after loading [6]. It has been shown that
the thickest regions of the knee cartilage on the femur and tibia are aligned at full
knee extension, suggesting an adaption of the cartilage to high loading such as dur-
ing the heel strike phase of gait [7]. In contrast, under conditions of reduced loading,
such as immobilization following surgery, the hyaline cartilage suffers atrophy.
However, a sudden change in the loading pattern on the knee (for example, a knee
with a ruptured ACL could cause a redistribution of loading on the articular surface)
does not produce a significant increase in cartilage thickness, but may in fact initiate
degeneration of the cartilage [7]. It has been reported that regular cyclic loading
enhances the synthesis of proteoglycans which makes the cartilage stiffer, but con-
tinuous compressive loading hinders the synthesis of proteoglycans, which causes
damage to the cartilage through necrosis [5].

1.3 Menisci

The crescent-shaped menisci are fibrocartilaginous structures lying between the

contact surfaces of the tibiofemoral joint, plugging the gap between the femur and
the tibia. To conform to the shape of the femoral condyle and the tibial plateau, the
menisci are wedge-shaped in the coronal view, and have a concave upper surface
that allows them to “hold” or stabilize the convex femoral condyles. The medial
meniscus has a longer span in the A-P direction, while the lateral meniscus has a
more rounded shape (Fig. 9.2). The menisci are connected to the tibia primarily by
ligaments located at the four horns of the menisci, which restrict their movement
relative to the tibial plateau but do allow some limited movement.
192 H. Wang et al.

Fig. 9.2 Anatomy of Tibial tuberosity

the menisci

Lateral meniscus

Medial meniscus

As the knee moves, the menisci deform to share and buffer forces in the joint and
indirectly increase the articular contact area, thus stabilizing the knee and decreas-
ing stresses on the hyaline cartilage of the tibia and femur. Studies have demon-
strated that up to 70% of the loading on the lateral compartment of the knee is
carried by the lateral meniscus while 50% of the loading on the medial compartment
is borne by the medial meniscus [8].
The menisci also work with the hyaline cartilage to lubricate the knee joint and
allow smooth motion between the articular contact surfaces. McCann et al. con-
ducted cadaveric testing on bovine knees and demonstrated that removal of the
menisci resulted in an increased friction coefficient on the joint [9].
Undue femoral gliding on the tibia plateau is also restrained by the menisci, mak-
ing them particularly important for a knee with ACL deficiency. Previous studies
have shown greater loading on the menisci following resection of the ACL [10].

1.4 Ligaments

Four major ligaments in the tibiofemoral joint are: the anterior and posterior cruci-
ate ligaments (ACL and PCL), and the medial and lateral collateral ligaments (MCL
and LCL). The ACL and PCL are intra-articular ligaments while the MCL and LCL
are extra-articular (Fig. 9.1).
The bone insertions of the ACL are located at the medial posterior side of the
lateral femoral condyle and the anterior side of the tibial plateau. Both insertion
sites have a considerably larger cross section than the midsubstance of the ligament
[11]. For biomechanical purposes, some researchers [11] have proposed dividing
the ACL into two bundles according to the anatomical location of its tibial insertion:
the anteromedial (AM) and posterolateral (PL) bundles. Length of the AM bundle is
relatively constant through joint flexion angles from 0° to 90°, while the PL bundle
is more stretched in extension [12]. However, pursuing this approach even further,
other studies [13] have proposed dividing the ACL into three bundles (the anterome-
dial, intermediate, and posterolateral bundles).
9 Biomechanics of the Knee 193

The ACL plays an important role in constraining anterior tibial translation, thus
preventing the femur from posterior luxation, while also helping to avoid excessive
internal and valgus rotations of the tibia [14–16]. As the knee flexes, the femur ini-
tially rolls back along the tibial plateau during early flexion, before converting to
anterior sliding due to the drag force from the ACL. Besides, previous studies [17]
also showed an increased ACL force under a combined loading of axial compressive
force and anterior tibial load, comparing with using an anterior tibial load alone,
indicating a biomechanical role of ACL in resisting compressive joint impact.
The PCL inserts at the lateral posterior side of the medial condyle of the femur
and stretches to the inferior posterior side of the tibial plateau. As with the ACL, the
PCL may also be divided into two functional bundles, which are named according
to the location of their femoral attachments [12]. Both the AL bundle and the PM
bundle have increased lengths with flexion [12].
In contrast to the ACL, the PCL prevents the tibia from undue posterior transla-
tion, which decreases the risk of anterior luxation of the femur [18]. During knee
extension, the PCL forces the femur to slide back along the tibial surface as it rolls
forward. Besides, the PCL has been reported to prevent excessive external tibial
rotation, especially for the joint flexion angles beyond 60° [19].
The MCL and LCL are located at the medial and lateral side of the knee, respec-
tively. The LCL inserts at the lateral femoral condyle and the lateral superior side of
the fibular head, while the MCL attaches to the medial femoral condyle and the
inferior medial side of the tibial plateau.
The MCL and LCL function together to constrain the knee joint from excessive
internal-external and varus-valgus rotations. The MCL cooperates with the ACL in
constraining anterior tibial translation. This partnership is clearly evident in cases of
ACL injury, which often result in a decrease in joint stability and an increase in the
MCL force, subsequently placing the MCL at a greater risk of injury [20].

1.5 Muscle System

There are two major muscle groups primarily responsible for the extension and
flexion of the knee: the quadriceps muscles, located at the front of the femur, which
contract to extend the knee; and the hamstring muscles, located the back of the
femur, which contract for knee flexion.
The quadriceps muscles consist of the vastus lateralis, rectus femoris, vastus
intermedius, and vastus medialis muscles, all of which are controlled by the femoral
nerve [21]. The rectus femoris muscle inserts at the hip bone and the tibia, while the
other three muscles insert at the femur and connect to the quadriceps tendon.
The quadriceps muscles, mainly serving as a knee extensor, form a large fleshy
mass which covers the front and sides of the femur. The rectus femoris muscle also
acts as a flexor of the hip due to its attachment to the ilium [22]. As the knee exten-
sor, the quadriceps muscles are crucial for most daily activities (walking, running,
jumping, etc.) and serve to stabilize the knee. Weak quadriceps muscles are reported
194 H. Wang et al.

to compromise knee stability [23]. The lever arm of the quadriceps muscle is
increased by the presence of the patella, which is discussed in more detail in
Sect. 1.7.
The hamstring muscles consist of the semimembranosus, biceps femoris mus-
cles, and semitendinosus, all of which are controlled by the sciatic nerve. The short
head of the biceps femoris inserts at the trochanter of the femur and the lateral side
of the fibular head, while the long head originates at the sciatic tuberosities and has
the same fibular insertion point as the short head. The semitendinosus and semi-
membranosus muscles both originate from the sciatic tuberosities and insert at the
medial side of the tibia.
The hamstring muscles act to flex the knee, while also function to extend the hip
except for the short head of the biceps femoris [24]. The short head of the biceps
femoris crosses only the knee joint and is therefore not involved in hip extension.
The biceps femoris is an external rotator of the tibia, while the semitendinosus and
semimembranosus muscles function to rotate the tibia internally [25]. As an antago-
nist to the quadriceps muscles, the hamstring muscles also function to control the
joint motion during daily activities.

1.6 Biomechanics of the Tibiofemoral Joint

Motion and biomechanics of the tibiofemoral joint are greatly influenced by the
morphology of the articular surfaces, and of course the integrity of all the joint
structures [16]. The posterior tibial slope is considered an important characteristic
for producing anterior shear forces on the tibia. Wang et al. suggested that in knee
arthroplasty surgery, the posterior tibial slope has a significant effect on postopera-
tive kinematics of the joint and thus the slope angle should be highly scrutinized
intraoperatively [26]. Woo et al. found that increasing the posterior tibial slope
caused an increased anterior tibial translation which could stabilize the knee with a
deficient PCL. In contrast, decreasing the posterior slope may be considered for a
knee with ACL deficiency [27]. Females have a deeper posterior tibial slope than
males, resulting in a greater anterior tibial force, especially when in the posture of
weight-­bearing, placing females at greater risk of ACL rupture than males [1, 28].
Conversely, the lateral section of the tibial plateau is generally located higher (more
proximal) than the medial section, forming a slope which is larger in males than in
females, but the effect of this coronal slope on joint mechanics is not yet clear [1].
However, while the link between slop angle and knee mechanics has been widely
studied, large differences between individuals means there is a large degree of varia-
tion across the general population [1]. Thus, understanding this variation could be
beneficial for developing more accurate subject-specific implants that could better
replicate normal knee biomechanics.
The tibiofemoral joint has 6 degrees of freedom (DOFs) of motion: three (anterior-­
posterior, proximal-distal, and medial-lateral) translations, as well as three (flexion-
extension, varus-valgus, and internal-external) rotations (Fig. 9.3). Because the femoral
9 Biomechanics of the Knee 195

Fig. 9.3 Joint motions in 6

degrees of freedom
I-E rotation

A-P translation

M-L translation

F-E rotation

V-V rotation

P-D transalation

condyles have a circular shape and the tibial plateau is relatively flat, the tibiofemoral
joint has good rotational flexibility in terms of flexion-extension (0–165°) [29].
The flexion movement of the knee joint can be divided into three functional
phases, comprising the screw-home arc, the functional active arc, and the passive
flexion arc [30]. The first phase is defined to represent joint activity through joint
flexions from 0° to 20°, during which the joint motions are mainly determined by
the morphology of the tibial plateau and the femoral condyles. Because of the asym-
metry between the distal regions of the lateral and medial femoral condyles, the
tibia undergoes internal rotation during this phase. The second phase represents
joint activity from 20° to 120° of flexion, during which there is little axial rotation
of the tibia. The final phase is defined as joint flexion over 120°. During this phase,
the medial femoral condyle moves proximally because of its contact with the poste-
rior section of the medial meniscus; this might explain why the posterior horn of the
medial meniscus is typically ruptured during deep joint flexion [31]. Meanwhile,
the lateral femoral condyle continues to move posteriorly during the passive flexion
arc, resulting in a subluxation at the end of this phase.
During normal gait, the knee has a flexion angle of 0–10° at heel strike, then
flexes to 15–20° at 15–20% of the gait cycle, followed by an extension during
20–40% of the gait cycle, and then flexes to around 60° in the swing phase [32].
Meanwhile, the knee undergoes internal-external rotation of up to 5° and varus-­
valgus rotation of up to 4°, combined with medial-lateral translation of up to 12 mm,
proximal-distal translation of up to 14 mm, and anterior-posterior tibial translation
of up to 7 mm [33]. As the knee is flexed, the medial condyle of the femur has little
anterior-posterior movement but the lateral condyle rolls backward on the tibia,
resulting in a coupled internal tibial rotation [34].
196 H. Wang et al.

During normal gait, axial compression on the articular contact surface of the
knee ranges from 0 to 3.2 times body weight (BW) [35]. The greatest axial
­compression occurs at around 50% of the gait cycle, just before the toe-off phase,
and most of the joint forces are distributed on the medial tibial plateau. Loading in
the A-P and M-L directions is much lower than the axial loading, ranging from 0 to
0.28 BW and 0 to 0.14 BW, respectively. Internal-external moments range from 0 to
0.02 Nm per BW.

1.7 Biomechanics of the Patellofemoral (PF) Joint

As the name suggests, the PF joint mainly consists of the patella and the femur. The
quadriceps tendon inserts at proximal patella which connects the patella to quadri-
ceps femoris muscle. On the distal side, the patellar tendon attaches directly to the
tibial bone. As a gliding joint, the patella slides along the femoral trochlea during
knee flexion/extension. The primary function of the PF joint is to increase the lever
arm of the quadriceps muscles and thus to enhance the efficiency of extending the
knee [36].
During flexion, the patella moves posteriorly and distally with respect to the
femur condyles, following a “C”–shaped pattern (Fig. 9.4). Movement of the patella
outside the sagittal plane is minor by comparison, tilting and twisting by less than
15° [37]. The lateral facet of the patella has been reported to bear greater contact
forces than the medial facet during knee flexion [37]. Contact between the articular
surfaces of the PF joint reach a peak when the joint flexes to 90°. Past 90°, the
patella starts to rotate laterally and contacts the femur at the medial side. During
deep flexion (around 140°), the patella falls into the femoral notch and the contact
area is greatly reduced (termed the “odd facet”), resulting in high localized stresses.
Therefore, patellar chondromalacia and patellofemoral pain syndrome are often
experienced during this “odd facet” stage [38].
To have a better understanding on the biomechanics of the PF joint, the quadri-
ceps angle (Q angle) needs to be introduced first. As shown in Fig. 9.5, the Q angle

Fig. 9.4 Movement track

of the patella during 20º
knee flexion femur
60º

Lateral Medial
epicondyle epicondyle
90º

135º
9 Biomechanics of the Knee 197

Fig. 9.5 Quadriceps angle

superior anterior iliac

Q angle

center of the patella

tibial tuberosity

is the angle between a line that connects the center of the patella and the superior
anterior iliac and another line that goes through the center of the patella and the
tuberosity of the tibia. However, there is a significant difference in Q angle between
males and females. For males, the Q angle at full knee extension ranges from 0° to
19°, while that for females is larger, ranging from 6° to 27° [39]. This is mainly due
to the larger pelvis in females. Changes in the Q angle can help with understanding
the mechanics of knee motions and patellar traction. During knee extension, the
tibia gradually rotates externally and as a result the Q angle increases. Inversely, the
Q angle decreases during knee flexion when the patella is pulled into the trochlea of
the femur by a traction of horizontal forces from the oblique muscle. Thus, stability
of the patella is largely dependent on the value of the Q angle and strength of the
oblique muscle. Loss of stability may result in the patella tilting externally, resulting
in wearing of the lateral patellar cartilage. The size of the Q angle can be affected
198 H. Wang et al.

by some factors, such as the size of the pelvic bone and connection between joint
structures [40]. Abnormal joint structure such as excessive anterior tilt of the ­femoral
head, excessive knee abduction, and other irregular rotations of the tibiofemoral
joint could all result in an increased Q angle.

2 Pathomechanics of the Knee Joint and Clinical Treatment

2.1 ACL Injury and Clinical Treatments

2.1.1 ACL Injury

The ACL is frequently injured because of its critical role in constraining joint
motion [41]. Most ACL injuries occurred in the absence of physical contact, and
frequently during sport activities such as skiing, football, and basketball [41–43].
Females also have a higher incidence of injury than males [28]. Serious damage to
the ACL can have a considerable impact on absence from work and the life quality.
Long-term complications of ACL injury include secondary injuries to other knee
structures such as meniscal tear, MCL injury that could induce degenerative changes
to the cartilage both without and with surgical reconstruction [44, 45].
More than 75% of ACL tears are a complete rupture of the ligament, while the
remaining 25% are partial tears [46]. Generally speaking, 1/3 of the patients had
ACL reconstruction surgery, while a second 1/3 had delayed surgery. The remaining
1/3 would not require surgery. For the latter group, the ACL healed and the knee
functions as well as those following surgery.

2.1.2 Conservative Treatment

Conservative treatments for ACL injury include plaster fixation, cryotherapy, mus-
cle training, and strengthening of coordination [47]. With limited ACL function,
anterior translation of the tibia may be restricted if there is adequate proprioception
to contract the hamstring muscles [47]. However, although such conservative treat-
ments are noninvasive and less stressful for the patient, the clinical outcome is rela-
tively unpredictable and remains controversial. In a clinical report at 10–13 years
after surgery, the ACL reconstruction group was reported to perform significantly
better than the nonoperative group (conservative treatments) in maintaining involve-
ment in sports [48]. In contrast, other studies have shown good patient satisfaction
after 20 years following conservative treatments, though the objective measures
indicated increasing knee degeneration [47]. When treated by conservative means
alone, Noyes [49] reported that tears across one-quarter of the ACL body did not
usually progress further, while one-half tears progressed in 50% of people and
three-quarter tears progressed in 86% of people, eventually becoming a complete
deficiency 7 years after treatment. Thus, the initial size of the ACL tear might be
important for evaluating the expected clinical outcome of conservative treatment.
9 Biomechanics of the Knee 199

2.1.3 ACL Repair

The first attempts at repairing ruptured ACLs involved reconnecting the ligament
remnants by sutures (termed a primary repair) to facilitate healing. However, in a
5-year clinical follow-up study on ACL primary repair, 53% of the patients had a
reinjury, 94% suffered instability, and 71% had pain [50]. It was generally con-
cluded that the poor results of primary repair could be attributed to the poor healing
capacity of the ACL [51, 52].
Functional tissue engineering was introduced in the 1980s as a novel method to
“grow tissues or organs from a single cell taken from an individual” [53]. With
developments in functional tissue engineering, biological scaffolds such as extracel-
lular matrix (ECM) have been used to reinforce ACL healing [54, 55]. ECM bioscaf-
folds serve to bridge the gap between the ACL remnants to facilitate the migration
and proliferation of the cells and formation of the blood vessels, as well as the
transportation of wastes, and thus consequently accelerate tissue formation and
improve the healing of the ACL. Woo et al. [55] used ECM in sheet and gel forms
to repair a transected goat ACL. The results showed continuous formation of neo-­
tissue in the ECM group while there was limited tissue growth in the control group
(suture only). Also, the stiffness of the femur-ACL-tibia complex for the group
using ECM was 2–3 times that of the group using suture repair alone.
Mechanical augmentation for ACL repair has also shown positive results for
improving ACL healing. Fleming et al. introduced a form of suture augmentation
where the sutures were fixed directly to the bone to reinforce the repaired ACL and
reduce anterior laxity of the joint [56]. Fisher et al. [10] showed that, in comparison
to traditional suture repair, mechanical augmentation of ruptured ACLs with sutures
resulted in improved joint stability, higher load in the repaired ACL, and lower load
in the medial meniscus, demonstrating the effectiveness of suture augmentation for
restoring joint stability and protecting the medial meniscus. The subsequent intro-
duction of biodegradable ACL grafts allowed for early reinforcement of the repaired
ACL and gradual transferring of loading to the ACL as it heals, along with the con-
current dissolution of the graft [57]. Similarly, a degradable magnesium ring device
was designed and used by Farraro et al. as mechanical reinforcement which was
combined with biological reinforcement (ECM scaffold) for ACL repair to restore
joint stability and to load the femoral insertion site to prevent disuse atrophy
throughout the ligament healing [58].

2.1.4 ACL Reconstruction

Because of the bad capacity of healing of the ACL and the unsatisfying clinical
outcomes of conservative treatments and repair surgeries, ACL reconstruction has
remained the gold standard for treating ACL ruptures [59]. This involves replace-
ment of the original ACL with a graft that is fixed into femoral and tibial tunnels to
restore joint stability. There are a variety of sources for the graft, with the choice of
using an allograft, autograft, or artificial graft. The bone-patellar tendon-bone
­complex (BPTB) and four-strand hamstring tendon (HS) have become the two most
200 H. Wang et al.

commonly used autografts, and the LARS artificial graft (LARS Company, France)
is the most popular synthetic graft, with a market history of over 20 years [60, 61].
Satisfactory outcomes have been reported in the short term following ACL
reconstruction. Previous study displayed no loss in range of motion of the knee
2 years after the surgery and limited postsurgical complications [62]. Another recent
study [63] reported that 1 year following ACL reconstruction, the rate of graft fail-
ure was 6.5% for HS and 2.1% for BPTB, while the rate of returning to sports was
71% when using a HS graft and 78% when using a BPTB graft.
However, although ACL reconstruction shows positive results in the short term,
long-term complications have been reported. First, the complex anatomy of the
ACL insertions cannot be restored, and thus the rotational joint stability cannot be
totally restored. Tashman et al. [64] measured knee kinematics during downhill run-
ning 4–12 months following ACL reconstruction and found that the anterior tibial
translation for the reconstructed knee had no significant difference with the unin-
jured knee, but the reconstructed knee had larger external rotation (3.8° larger on
average) and varus rotation (2.8° larger on average). Second, there could be donor
site morbidity when using autografts. In a study by Salmon et al. [65], donor site
related complications were reported to appear in 42% of the patients 13 years after
ACL reconstruction, while 45% of patients suffered pain when kneeling. Third,
there have been reports of enlargement of the bone tunnels and rupture of the grafts,
which have an incidence of up to 72% and 22%, respectively [66, 67]. Bone tunnel
enlargement can cause graft loosening, fixation failure, knee instability, and osteo-
arthritis, while a graft rupture directly calls for follow-up surgery. Other potential
complications include loss of proprioception, graft wear, graft laxity [68], extension
loss, and long-term osteoarthritis [69, 70]. A recent study reported an incidence of
knee osteoarthritis of nearly 20% at 12 years following ACL reconstruction [45].

2.2 Meniscal Tear and Clinical Treatments

2.2.1 Meniscal Tear

A tear in the meniscus is a relatively common soft-tissue injury. A meniscal tear can
cause pain, swelling, and joint instability, and long term could induce knee osteoar-
thritis due to increased stresses on the hyaline cartilage. Englund et al. [71] assessed
the integrity of the menisci in 991 subjects using a 1.5 T MRI and found that 19%
of females and 56% of males had some level of tearing, and over 60% of subjects
with osteoarthritis had a meniscal tear. Among the subjects without any symptoms
of knee pain, aching, or stiffness, 60% were found to have a meniscal tear.
There are a variety of types of meniscal tear which may be characterized based
on the location and appearance: horizontal tear, flap tear, radial tear, root tear, verti-
cal tear, oblique tear, and complex tear.
Horizontal tears are defined as occurring parallel to the tibial plateau in the
region that divides the meniscus into superior and inferior halves. A flap tear occurs
9 Biomechanics of the Knee 201

where there are displacements of torn fragments toward the articular space. A radial
tear is vertical to the tibial plateau and transects the longitudinal collagen bundle.
This type of meniscal tear impairs the axial strength of meniscus and might increase
the risk of meniscal extrusion [72]. A meniscal root tear is defined when a radial tear
happens within 1 cm of the bony tibial attachment. A vertical tear runs parallel to
the longitudinal collagen bundle and divides the meniscus into peripheral and cen-
tral portions. Oblique tears are oriented oblique to the longitudinal collagen fibers.
Complex tears are defined as a combination of two or more types of tears occurring
simultaneously. According to Englund et al. [71], among 308 subjects with menis-
cal tear, 40% were horizontal tears, 37% were complex tears, 15% were radial tears,
12% were oblique tears, 7% were longitudinal (vertical) tears, and 1% were
root tears.

2.2.2 Meniscal Repair

Where appropriate, repairing the meniscus with sutures is often a good option for
restoring normal mechanical function while maintaining proprioception and vascu-
larity. In a 2-year follow-up study on 280 meniscal repairs [73], successful results
were obtained in 252 knees, with a total failure rate of 10%. Of those patients that
were deemed successful, there was an absence of any tenderness of the joint line,
blocking or swelling. However, whether to perform a meniscal repair could be
largely dependent on the tear type and the surgeon’s individual ability and experi-
ence. Vascularity is only provided at the periphery of the menisci (up to 25% of the
width, termed the red-red zone) (Fig. 9.6) as well as at its horn attachments [74], and
thus the capacity of healing of the meniscus is rather poor in the middle portion
(termed the white-white zone) (Fig. 9.6). Previous studies demonstrated how tears
on the posterior root of the medial meniscus could be repaired to restore the normal
joint loading profile [75]. If a vertical tear is located peripherally, meniscal repair
using sutures is usually the preferred treatment [76]. Other types of meniscal tears,
particularly radial tears, are more difficult to repair and heal. For these difficult

Fig. 9.6 Illustration of the red-red-zone

red-red and white-white red-red-zone
zones of the menisci

white-white zone
202 H. Wang et al.

tears, meniscectomy or meniscal replacement may be a more suitable option. It was

reported that around 25% of meniscal tears could be repaired in patients younger
than 40 years old [77].

2.2.3 Meniscectomy

Meniscectomy is a surgical procedure to partially or completely remove a damaged

meniscus. A clinical follow-up study by Roos showed that undergoing meniscec-
tomy increased the risk of tibiofemoral osteoarthritis by 14 times at 21 years after
the surgery [78]. Ihn et al. performed cadaveric testing using pressure films [79] and
found that following meniscectomy, the peak contact stress in the knee joint
increased because of the reduced contact area.
Compared with partial meniscectomy, total meniscectomy could result in a
smaller articular contact area, which may speed the development of osteoarthritis.
Meniscectomy could also have a considerable effect on the ligaments, with one
study [65] reporting a sixfold increase in graft rupture 13 years after undergoing
meniscectomy and ACL reconstruction. Conversely, forces in the meniscus could be
doubled after transecting the ACL [80].
In comparison to medial meniscectomy, lateral meniscectomy is reported to have
more postoperative complications [81]. As mentioned previously, the lateral menis-
cus shares more load for the knee compartments. Thus, removal of the lateral menis-
cus could be expected to have a more pronounced effect on stress distribution in the
joint. Also, the lateral tibial plateau is convex in contrary to the concave medial
plateau; therefore, removal of the lateral meniscus would cause more point contacts
and increase the peak articular contact stress. A clinical study [82] on meniscectomy
reported good results in 80% of the patients following medial meniscectomy while
only 47% of patients who underwent lateral meniscectomy reported similar results.

2.2.4 Meniscal Replacement

If a patient develops complications such as joint pain from early degeneration after
meniscectomy, they may be considered as a candidate for meniscal replacement.

Allograft

Meniscal allografts are obtained from donors and should contain no living cells
[77]. If donor cellular material remains in the graft, a dense cartilage matrix would
be used to lock the materials so that the allograft does not elicit any immune
response.
Meniscal replacement was first introduced in the 1980s [83]. A previous study
[84] reported a total failure rate of 29% for allograft transplants 13 years after the
replacement surgery, while the overall Lysholm score improved from 36 to 61
9 Biomechanics of the Knee 203

comparing with the preoperative situation, showing a promising potential for

relieving pain and postponing the need for knee arthroplasty in younger patients
[85]. Similar results have been reported by other researchers [86], whereby menis-
cal replacement has been shown to prevent further narrowing of the joint space,
reduce knee pain, and halt further degeneration of the cartilage.

Meniscal Bioscaffold

The red-red zone of the meniscus has a vascular supply while the middle section
(white-white zone) does not. In a partial meniscectomy, if the red-red zone is well
preserved, an artificial scaffold can be sutured to replace the missing tissue and
restore the mechanical function of the meniscus.
The Menaflex Collagen Meniscal Scaffold (Regen Biologics Inc., New Jersey,
USA) and the Actifit Scaffold (Orteq, London, UK) are two of the most commonly
used meniscal scaffolds on the market. The former is made of Achilles tendon of
bovine that is pressure heat molded into the shape of a meniscus. A clinical follow-
­up study demonstrated significantly increased tissue formation with the use of this
scaffold over a partial meniscectomy [87], and more activity was regained postop-
eratively in the scaffold group than the meniscectomy group. The Actifit scaffold is
a porous biodegradable scaffold made of polyurethane that allows neo-tissue to
gradually replace the scaffold material over time. A 1-year biopsy study showed
viable “meniscus-like” tissue replacing the scaffold material and a considerable
reduction in patient pain [77].

2.3 Knee Osteoarthritis and Treatment Options

2.3.1 Knee Osteoarthritis

Knee osteoarthritis is a common disease in middle-aged and older people, present-

ing as progressive degeneration of the joint cartilage, including osteophytes forma-
tion, cartilage loss, sclerosis of subchondral bone, degeneration of menisci, laxity of
ligaments and alterations in the synovium and fat pad [23]. There are numerous
factors that may lead a person to develop osteoarthritis, to name a few, cumulative
high weight-bearing, poor posture during gait, muscle weakness, and sudden tem-
perature changes [88–90]. With knee osteoarthritis, people suffer from stiffness,
pain, and loss of knee function.
For patients in the early stages of arthritis, basic and conservative treatments are
often used, such as nonsteroidal anti-inflammatory medication, localized corticoste-
roid injections, and weight loss [91]. As the osteoarthritis progresses, destruction of
the matrix occurs and the external loads exceed the physiological limit of the carti-
lage, resulting in asymmetric wearing of the cartilage and subsequent bone loss.
Generally, once the pain reaches a certain level, the patient and physician may opt
204 H. Wang et al.

for surgical knee osteotomy. This may be a high tibial osteotomy or fibular osteot-
omy. However, under severe loss of cartilage and/or bone and consequent intolera-
ble pain and dysfunction of the knee joint, the only viable option is to undergo knee
arthroplasty, during which the joint surfaces are replaced by prosthetic components.
The ultimate goal of knee arthroplasty is to replace the problematic knee joint with
a prosthetic knee in order to restore the joint functionality and relieve the pain.

2.3.2 High Tibial Osteotomy (HTO)

Although osteoarthritis can present in any of the knee compartments, a large portion
of the cases reported occur in the medial compartment of the tibiofemoral joint [92],
with fewer cases being reported for the lateral side or the patellofemoral joint [93].
When osteoarthritis appears in the medial side, the medial joint space is usually nar-
rowed because of the loss of cartilage and bone, resulting in abnormal force trans-
mission along the lower limb.
For patients who are younger and more active, high tibial osteotomy (HTO) is
often chosen for early and moderate osteoarthritis. In this case, part of the tibial
bone is removed to relocate the joint surface and to restore joint alignment. For
medial arthritis, more bone would be removed at the medial side, changing the joint
alignment from varus to be slightly valgus, thus decreasing medial joint pressure
and slowing down the degeneration of the medial cartilage. This may postpone or
avoid the necessity for knee arthroplasty. Previous studies comparing clinical results
of HTO and unicompartmental knee arthroplasty (UKA) concluded that UKA pres-
ents lower revision rates, less postoperative complications, and less postoperative
pain. However, HTO allowed for a better range of motion, which could be more
satisfactory for highly active patients [94].

2.3.3 Fibular Osteotomy

The fibula bone is generally considered to be less critical for joint functionality than
the other long bones of the lower limb. The fibula provides an origin for several
muscles of the knee joint and carries axial weight-bearing loads ranging from 6.4%
[95] to 16.7% [96]. It has been freely used as a source for grafts and as a vascular-
ized transplant to bridge large bony defects for conditions such as congenital pseud-
arthrosis of the tibia [97], tumor resection [98], nonunion [99] and grafting
operations in case of femoral head necrosis [100].
Proximal fibulectomy (fibular osteotomy) has been demonstrated by several
studies to improve the restoration of joint functionality and reduce pain in
patients with OA. It is a simple but effective procedure, with the number of
patients with a fibulectomy in China surpassing 1000 in 2015 [101]. To perform
a fibular ­osteotomy, the proximal part of the fibula is first exposed, followed by
an osteotomy with a length of 2–4 cm at 7–8 cm from the proximal fibula head.
In a follow-up study on 110 patients over a 2-year period, Yang et al. [102]
9 Biomechanics of the Knee 205

a b

Fig. 9.7 Preoperative radiographs; anteroposterior (a) and lateral (b)

reported significant improvement in alignment (Figs. 9.7 and 9.8) and function
of the knee, as well as relief of pain following the fibular osteotomy. Zou et al.
[103] investigated 92 patients with varus knee OA treated by either fibular oste-
otomy or HTO and found that the outcomes of fibular osteotomy were superior
to HTO in either short term or long term. Nie et al. [104] reported on 16 patients
with knee OA in the medial compartment who underwent proximal fibulectomy
and found that there were significant improvement in VAS pain and HSS score 1
day and 6 months after surgery. In addition, the hip-knee-angle (HKA) improved
and remained stable for 3 months and there was an inverse relationship between
the overall peak knee adduction moment (KAM) and HKA. Yazdi et al. [105]
evaluated the effect of partial fibulectomy on the articular contact pressure in
cadaver knees and it was demonstrated that partial fibulectomy decreased the
medial articular pressure and increased that in the lateral compartment. Although
the procedure is relatively simple and there are good clinical results, it may
206 H. Wang et al.

a b

Fig. 9.8 Immediately postoperative radiographs; anteroposterior (a) and lateral (b)

cause adjacent peroneal nerve injury. Sandoval et al. [106] followed up 116
patients with proximal fibulectomy for 2 years and reported that only 9.4% suf-
fered complications, mainly for neuropraxia of the peroneal nerve, hematoma of
the wound and infection. While fibulectomy has generally been shown to be
effective, it is not clear exactly how the procedure relieves knee pain. Zhang
et al. [107] stated that nonuniform settlement and bilateral degeneration of the
plateau leads to varus knee, while with an osteotomy of the fibula can modify
this situation. Weakened support from the lateral fibula results in a correction of
the varus deformity, and consequently shifted the loading from the medial com-
partment to the lateral, which eventually leads to relieved pain and restored joint
functionality.
Qi et al. [108] hypothesized that a reduction in lateral muscle contraction after
fibulectomy may cause a rebalance in the resultant joint moment, making the con-
tact forces in the medial compartment shift laterally and decrease in magnitude.
According to Qi [108], the balance of joint forces in the coronal plane of a varus
knee may be gauged by the following equations (Fig. 9.9):
FLM + FB + FMM = FJL + FJM, where FJM is the medial joint contact force, FJL is the
lateral joint contact force, FLM is the lateral resultant muscle force, FB is body weight
due to the gravity, FMM is the medial resultant muscle force, and FJM can be ignored
due to varus knee.
9 Biomechanics of the Knee 207

Fig. 9.9 Before operation

F
B FJM FJL

FLM

FMM

dB dLM

dLM × FLM = dB × FB + dMM × FMM, where dLM is the moment arm of lateral resul-
tant muscle force to knee joint center, dB is the moment arm of body weight to the
knee joint center, and dMM is the moment arm of medial resultant muscle force to the
knee joint.
′
After removing a portion of the fibula (Fig. 9.10), the lateral muscle ( FLM ) is
′
released which decreases the valgus moment ( d LM × FLM < d B × FB ). To compen-
sate, the varus resultant moment is reduced by shifting the body weight laterally
which subsequently decreases the moment arm of body weight ( d B′ < d B ).
′
Meanwhile due to the decrease in the lateral muscle force ( FLM ), the overall knee
′ ′ ′
joint forces also decrease ( FLM + FB = FJL + FJM ).
In summary, proximal fibulectomy is an innovative procedure to treat medial
knee OA without the need for resecting the knee joint. Studies performed to date
lack sufficient quantitative biomechanical evidence to recommend using this proce-
dure as standard practice. Further clinical follow-up studies and comparative analy-
ses to other common treatment methods are required.
208 H. Wang et al.

Fig. 9.10 After fibular

osteotomy

FB

F′JM F′JL
F′LM
FMM

d′B dLM

2.3.4 Knee Arthroplasty

Knee arthroplasty is often considered when conservative treatments and less inva-
sive bone osteotomies are either unsuccessful or are not considered a viable option
because the natural cartilage has reached an irreparable state. Knee arthroplasty can
offer pain relief and help regain normal joint function. The knee prosthesis gener-
ally consists of the femoral, tibial, and patellar components. The tibial component
usually contains a polyethylene liner inserted into a metal baseplate.
Knee arthroplasty may be performed as a unicompartmental knee arthroplasty
(UKA) or a total knee arthroplasty (TKA). For TKA, there are generally two types
of knee prosthesis in clinical use: cruciate-retaining type (CR type) and posterior-­
stabilized type (PS type).

Unicompartmental Knee Arthroplasty (UKA)

UKA is an operation used to relieve arthritis by replacing the articular surface of

either the medial or lateral condyle without sacrificing the cruciate ligaments and
the patella, as opposed to total knee arthroplasty (TKA) which replaces both knee
9 Biomechanics of the Knee 209

compartments at the same time. In theory, because UKA retains more soft tissues, it
can better restore knee functionality and stability than TKA and would allow the
patient to retain a better ontological feel. In the early years following the introduc-
tion of unicompartmental procedures, the failure rate was quite high due to poor
surgical techniques and poorly designed components. The average revision rate of
UKA at 2 and 6 years has been reported at 20% and 28%, respectively, in 1970s
[109, 110]. With successive improvements in the design of components, mature
clinical techniques using minimally invasive surgery have significantly improved
the clinical success rate with appropriate patient selection [111]. The survival rate
of UKA at 2 and 5 year is 98.7% and 95.5%, respectively, and the knee function
score remains satisfactory [112]. However, the long-term survival rate is signifi-
cantly lower than that of TKA [113]. Failure rates of UKA vary across literature and
for different regions [114–117]; 27% (10 years) in Finland, 12.1% (8 years) in UK,
and 4.6% (10 years) in Japan. The success of UKA is dependent on many factors,
including the age and activity of the patient, surgeon’s experience, and the type of
implant used.
UKA has been used in clinic for over 60 years. In the early 1950s, McKeever
[118] inserted metal plates into a patient to replace the damaged articular cartilage
surface, becoming one of the first documented cases of UKA. By the 1960s the
procedure had reached mainstream practice thanks to improved designs and the use
of alternative materials. Gunston [119] developed the first unilateral metal-on-PE
bearing, which is still the most common material combination in use today. The
1970s saw the introduction of non-constrained prostheses that increased the activity
of the joint and could achieve a greater joint range of motion than TKA prostheses
[120]. In the 1980s, Goodfellow introduced the idea of an Oxford active platform
into the design of single condyle prostheses (Oxford unicompartmental knee
replacement, OUKR) which increased the articular contact area and reduced the
contact stress [121]. In recent years, custom-made UKA prostheses (for example,
iUni by ConforMIS Inc.) developed from CT scans and manufactured by 3D recon-
struction and printing have been introduced. As the shape of the prosthesis is
designed according to the individual anatomy of the femoral condyles, custom pros-
theses can provide better alignment and more natural movement. However, given
that custom implants are a recent development, the long-term outcome is relatively
unknown. According to the American Joint Replacement Registry [122], UKA
accounted for about 3.2% of primary knee replacement procedures from 2012 to
2017, and there was a downward trend year on year. This same trend has also been
observed in Australia [123] and Sweden [124], with the former showing a decrease
in UKA from 14.5% in 2003 to 5.1% in 2016. However, since 2017 the trend has
reversed and there has been a slight uptake in UKA procedures in Australia [123],
Sweden [124], and Britain [125].
There are a number of potential causes of failure of unilateral knee prostheses,
including degeneration of the adjacent tibiofemoral joint and patellofemoral joint,
implant loosening, mechanical injury, malposition, and infection. Among them,
aseptic loosening and joint disease (including contralateral arthritis) are the most
common causes of failure [123–125]. Typical factors leading to loosening of the
210 H. Wang et al.

prosthesis are malalignment of the components, undercorrection of a preexisting

deformity, deficiency of the ACL, improper tibial slope, and dislocation of the bear-
ing in mobile designs. Each of these factors may cause asymmetrical loading on the
prosthesis and therefore produce more wear particles, leading to further osteolysis.
Joint diseases after UKA, such as the progressing of OA in the other knee compart-
ments, can be caused by overcorrection of the mechanical axis or impingement due
to an oversized femoral component [126].
At present, biomechanical studies of unicondylar knee prostheses typically focus
on the effect of the mechanical axis of the knee joint on the medial or lateral articular
stress. If the stress of the articular surface is not evenly distributed, it may accelerate
implant failure [127]. In general, the stability of ligaments and the amount of angular
deformation must be carefully assessed preoperatively. Medial arthritis often first
appears in the anteromedial region of the knee joint, and then gradually extends to
the femoral condyles and intercondylar fossa. Inflammation of the knee caused by
cartilage degeneration and the presence of intercondylar fossa osteophytes alters the
biochemical and mechanical environment of the ACL. Degeneration of the ACL sub-
sequently changes the kinematics of the knee joint, leading to further degeneration
of the posteromedial region. In the early stages of medial knee arthritis, if the ACL
does not display functional deficiencies, UKA can be chosen to slow down regres-
sion of the ACL and the contralateral compartment. However, if the functionality of
the ACL is impaired, for example, through rupture or resection, then the stability of
the knee joint may be affected. In such situations UKA is not a viable option.

Total Knee Arthroplasty (TKA)

In the operation of TKA, all of the articular surfaces in the knee are replaced with
prosthetic components. The two most common types of total knee prostheses in
clinical use today are cruciate-retaining (CR) and posterior-stabilized (PS). Both
types require the removing of the ACL, but with CR prostheses the posterior cruci-
ate ligament (PCL) is retained, while PS prostheses also require a resection of the
PCL. With the PS knee, a femoral cam and a tibial post interact as a functional
replacement for the PCL. When the femoral component slides anteriorly, the cam
contacts the tibial post, forcing the femoral component to roll back along the tibia.
This mechanism is designed to prevent excessive anterior femoral translation and
help to maintain joint stability.
The anterior region of the tibial liner in TKA is often designed to be higher than
the posterior part in order to avoid excessive anterior femoral translation and
increase the contact area of the tibiofemoral joint. This stabilizes the knee and
decreases contact stress on the components [128].
The polyethylene liner in the tibial component may be anatomically shaped
(“anatomical design”) (Fig. 9.11b) or be a simpler nonanatomical design (Fig. 9.11a).
For the nonanatomical design, the medial and lateral part of the polyethylene liner
are often symmetrical, concave, and have the same curvature radius [128]. In this
case, the curvature of the femoral component may be also designed to conform to
9 Biomechanics of the Knee 211

a b
proximal

distal

Fig. 9.11 Different designs of the polyethylene liner (a) nonanatomical design and (b) anatomical
design [129] (Reprinted with permission from Elsevier, license number: 4687410127428)

the tibial liner in order to maintain the knee stability and prevent component dislo-
cation [128]. However, the normal knee shape is asymmetrical and this nonanatomi-
cal design could induce abnormal knee kinematics such as inadequate rollback of
the femur and insufficient internal rotation of the tibia. Thus, anatomical prosthesis
designs aim to mimic the morphology of the intact knee to restore the kinematics of
the knee. Liu et al. found that [129] changing the posterolateral region of the tibial
liner to be convex could better restore the posterior translation of the lateral femoral
condyle and the internal rotation of the tibia through joint flexion from 0° to 140°.
A study by Moonot et al. [130] demonstrated that asymmetrical tibial liners with a
highly conforming medial aspect and a moderately conforming lateral aspect could
adequately restore the internal tibial rotation and reduce excessive anterior move-
ment of the lateral femoral condyle, thus reducing wear on the liner and increasing
implant longevity.
When considering the type of TKA implant to be used, it is still controversial
whether the PCL needs to be retained for proper knee functionality [131]. CR knees
require an intact and functioning PCL, and so this must be carefully evaluated
beforehand. Otherwise, if the PCL is compromised then joint stability could be at
risk. In this case a PS knee is more desirable. However, when using a PS design,
joint stability is greatly affected by the design of the tibial post and the femoral cam,
and this would also have a considerable effect on joint kinematics and kinetics.
If the cartilage on the patella is degraded and may compromise knee functional-
ity, then there is the option of replacing the cartilage with a smooth p­ olymer surface
(patellar replacement). However, Cadambi et al. reported that replacing the patellar
surface reduces the success rate of TKA [132]. Huang et al. also showed that tensile
stress on the patellar bone increased after the surface was replaced [133]. Rand
[134] stated that introduction of the patellar component could alleviate anterior
knee pain of the patients. However, the revision rate of TKA is still relatively high
because of the patellar component related complications, such as infection, fracture,
212 H. Wang et al.

subluxation, wear, and loosening of the patellar component [135, 136]. Obese
patients are also not recommended to undergo patellar arthroplasty because the
higher loading could increase the risk of loosening and fracture [137].

3 Summary

In this chapter, the basic anatomy and functionality of bony structures, menisci,
cartilage, tendons, and muscles in a normal knee joint were presented, accompanied
by a discussion of the biomechanics of the patellofemoral and tibiofemoral joints.
Pathological changes to the structures of the knee could alter the joint kinematics,
which in long term could induce secondary injuries to the other surrounding tissues.
Clinical treatments should be carefully chosen to best rebuild the normal biome-
chanics and functionality of the knee.

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Chapter 10
Biomechanics of Foot and Ankle

Duo Wai-Chi Wong, Ming Ni, Yan Wang, and Ming Zhang

Abstract The human foot-and-ankle is a highly developed, biomechanically

complex structure which sustains the weight of the body and facilitates forces
transmission during propulsion. Apart from 28 bones, the foot is composed of
more than 30 joints surrounded by more than a hundred of muscles, tendons,
and ligaments. The geometry of the foot and the balance-controlling mechanism
of the body enabled us on a variety of motions, including walking, running, and
jumping.
However, the high and complicated load on the foot impose risk of the foot
injury, trauma, and other problems. Common foot disorders include hallux valgus,
bunion, flatfoot, plantar fasciitis, heel pain, and Achilles tendonitis. Ankle fracture
in elderly people is a major burden in developed countries with an aging popula-
tion. There was a threefold increase in the incidence of ankle fractures in elderly
people in the last century. Aging and overweight also contribute to the chance of
foot problems. Besides, calcaneal fracture is common for young and physically
active population and may turn into degenerative or traumatic arthritis after serious
injuries.

D. W.-C. Wong · Y. Wang · M. Zhang (*)

Department of Biomedical Engineering, The Hong Kong Polytechnic University,
Hong Kong, China
Hong Kong Polytechnic University Shenzhen Research Institute, Shenzhen, China
e-mail: ming.zhang@polyu.edu.hk
M. Ni
Department of Biomedical Engineering, The Hong Kong Polytechnic University,
Hong Kong, China
Tongji Hospital, Tongji University School of Medicine, Shanghai, China
Pudong New Area People’s Hospital, Shanghai, China

© Springer Nature Singapore Pte Ltd. 2020 219

C.-K. Cheng, S. L-Y. Woo (eds.), Frontiers in Orthopaedic Biomechanics,
https://doi.org/10.1007/978-981-15-3159-0_10
220 D. W.-C. Wong et al.

Both surgical and conservative methods have been adopted to treat foot problems
and diseases. Most of the interventions targeted the treatment on the problem site
but the effect of the foot problems could extend beyond the site to adjacent regions
or the entire foot. Assessment and evaluation of the biomechanical environment and
the variations before and after the intervention could help intervention design, plan-
ning and thus minimizes complications.
Experimental methodologies, such as motion capture analysis, pedobarogra-
phy, and cadaveric experiments have been developed to quantify foot biomechan-
ics. However, the internal biomechanics of the foot, such as the stress distributions
within bones and soft tissues is not easy to measure by experiments. Computational
methods or platforms such as the finite element (FE) analysis are useful tools to
investigate biomechanics of the musculoskeletal structures. This evaluation
method has been used to study injury mechanism, improve prosthetic and orthotic
designs, and predict surgery outcome, in addition to promoting fundamental
understanding of foot biomechanics. In this chapter, four common foot problems
and interventions of the foot and ankle were analyzed by FE models including
hallux valgus, ankle arthroplasty, tarsometatarsal joint fusion, and calcaneal
fractures.

Keywords Hallux valgus · Ankle arthrodesis · Tarsometatarsal joint fusion

Calcaneal fracture · Finite element method · Foot and ankle

1 Biomechanics of First Ray Hypermobility

and Hallux Valgus

Summary
Hallux valgus (or hallux abducto valgus) has been one of the most common foot
problems and associated with functional disability. Clinical studies were conducted
that featured the pathoanatomy and pathomechanics of hallux valgus. However, the
effectiveness of current treatments remains unsatisfactory, while complications and
recurrence rates are undeniable. It is pragmatically demanding to further understand
the biomechanics of hallux valgus to improve intervention. This study constructed
a three-dimensional foot model of the subject and simulated with hypermobility.
Besides, partial models consisted of isolated first ray and were constructed and
compared among the normal participant and hallux valgus scenario. The model par-
ticipant was invited to participate in a gait analysis session to acquire the boundary
and loading condition for the simulation of walking stance. The finite element (FE)
analysis outcome suggested that the hypermobility case generated higher joint force
at the metatarsocuneiform and metatarsophalangeal joint. In the medial-lateral
direction, the metatarsocuneiform joint force switched sharply that could indicate a
potential risk of metatarsus primus varus.
10 Biomechanics of Foot and Ankle 221

1.1 Background

Hallux valgus (or hallux abducto valgus) is represented by a lateral and medial
deviation deformity of the hallux and the first metatarsal, respectively. The enlarged
and swollen medial projected eminence is also a characteristics of hallux valgus and
thus it is also known as the bunion. Hallux valgus imposes significant public health
burden as supported by the incident rate of related foot surgery. There could also be
secondary problems such as poor gait patterns and impaired coordination and stabil-
ity that may lead to falling risks to the elderly population [1–5].
The prevalence of hallux valgus was found strongly associated with family his-
tory, while gender is also suggested to be a contributing factor [6]. The shape of the
foot bones, arch height, and the level of hypermobility may be affected by heredity
[7]. In fact, the incidence of hallux valgus on women is more than two times higher
than that of men [8]. Similarly, the different sex presents different bone morphology
and alignment, in addition to the level of hypermobility or laxity [9–11]. Other
influencing factors included footwear, body weight, habit, and occupation [12].
In fact, hallux valgus ranks high in the list of common foot complaint. More than
one-quarter of adults in the United Kingdom suffered from the problem [8], while
nearly 15% of students reported hallux valgus as reported by Owoeye et al. [13].
The same study reported that 9% of the students with hallux valgus showed pain
and 14% demonstrated difficulty in prolong walking. Survey on the elderly popula-
tion reported even higher prevalence [14] which results in economic burden on
hospitalization and society. More than 50 k surgeries were taken to treat hallux
valgus which accounted for more than one-quarter of all forefoot surgeries [15].
More than 2 absent days are incurred by relevant surgery, resulting in more than
AUS$3800 productivity loss and AUS$3700 hospitalization cost in Australia in
2008 [16–19].
Despite that surgical correction for hallux valgus are not few, the outcome
remains unsatisfactory with failures, complications, and recurrence. The complica-
tion rates and recurrence rates can be up to 55% and 16%, respectively [20, 21],
contributed by over-correction, avascular necrosis, etc. [22]. Surgery using soft tis-
sue correction procedure produces even higher failure rates [22].

1.2 Biomechanical Study of Hallux Valgus

Biomechanical studies on hallux valgus and its intervention have been conducted to
better understand the pathogenesis of the disease and improve treatment outcomes.
The hypermobility of the first ray was first introduced by Morton and Lapidus which
attracted debates on the appropriate interventions [23, 24]. Arthrodesis procedure
was proposed aiming to address the problem of stability. The evaluation of stability
was also included in other studies on the outcome of osteotomy of hallux valgus
222 D. W.-C. Wong et al.

[25]. Currently, mobility and stability are assessed by manual dorsal excursion [26],
load-bearing radiographs [12], or custom-made mechanical devices [27]. Yet the
quantification of hypermobility has been believed to be subjective and confined to
static measurement [23].
Foot types and deformities are often classified using plantar pressure measure-
ment [28]. Hallux valgus was found to impair the loading at the hallux region. The
peak pressure of the forefoot was found shifting laterally [29], as evidenced by the
heightened peak pressure and pressure time-integral at the central forefoot [30].
Conversely, some study discovered that the plantar pressure pattern moved medially
[31, 32]. There could be other factors, including secondary deformities, that may
influence the pressure pattern on the medial metatarsal region [33]. Hallux valgus
patients shall have a persistent reduction in hallux loading compensated by the cen-
tral metatarsal area [33].
Pedobarographic assessment has been used as a biomechanical tool to evaluate
surgical interventions of hallux valgus. By expanding the contact area under hal-
lux, Mittal et al. [34] suggested that McBride procedure could restore some of the
hallux functions. Another operation carried out by Saro et al. [35] suggested that
the operation did not produce positive biomechanical effect as indicated by the
significant reduction in peak pressure under the hallux and heel region. Some stud-
ies compared different osteotomy procedures (Mitchell and Scarf) using plantar
pressure distribution [36].
Since consensus was not reached on the interpretation of plantar pressure distribu-
tion towards clinical outcome of the surgeries, researchers endeavored to investigate
how hallux valgus attenuates the biomechanical environment of the foot by means of
manual examination and further plantar pressure studies. This approach has been
achieved by the finite element (FE) simulations that could investigate the internal
stress or strain pattern as well as the load transfer characteristics noninvasively [37].
A major extrinsic factor of hallux valgus, the wearing of high-heeled shoes, was
considered in the study of Yu et al. [38] using FE model. In addition, a simplified first
ray model was used to understand the linkage between first ray hypermobility and
hallux valgus [39]. Meanwhile, we have constructed a FE model to imitate hallux
valgus and simulated the walking stance. Five instants were extracted from the simu-
lation findings and the outcome on stress, strain, and joint loading were used to
evaluate the changes of kinematics and stability induced by hallux valgus.

1.3 Finite Element Model Development

1.3.1 Clinical Image Acquisition and Geometry Reconstruction

The model geometry of the normal foot and hallux valgus foot (asymptomatic) was
reconstructed from magnetic resonance (MR) images of two female subjects. They
were both aged 28, 165 cm tall, while the body weights were 54 kg and 56 kg,
respectively, for the normal and hallux valgus foot participants. Both participants
10 Biomechanics of Foot and Ankle 223

reported no other musculoskeletal pathology, pain, or lower limb trauma or surgery

within the past 6 months. Segmentation software were used to segment and process
the MR images (Mimics v 10, Materalise, Leuven, Belgium and Rapidform XOR2,
3D INUS Technology Inc., Seoul, Korea). We constructed the encapsulated soft tis-
sue and bony structures, including 30 bones and two sesamoids, using 3D solid,
while the ligaments were modelled as 3D surfaces and muscles were modelled as
1D connectors.

1.3.2 Material Properties

The elastic modulus of the bone was 7300 MPa with the Poisson’s ratio of 0.3
[40], and was assumed isotropic and homogeneous. The material of the encapsu-
lated soft tissue was hyperelastic with data experimented by Lemmon et al. [41].
The supporting ground was bilayers. The bottom layer was rigid, while the upper
layer was deformable (40 GPa), representing concrete ground. The elastic modu-
lus of all ligaments was 264.8 MPa, which was the reported average elasticity of
rearfoot ligaments [42]. The thickness of ligaments was 1.5 mm as reported by
Milz et al. [43].

1.3.3 Load and Boundary Conditions

Ground reaction force (GRF) and tibial inclination from the gait experiment of the
model subject was input as the loading and boundary conditions to simulate stance
phase in five consecutive static steps named: heel strike (0% stance), GRF first peak
(27% stance), GRF valley, (45% stance), initial push-off (60%), and GF second
peak (75%). The magnitude of muscle forces was adopted from literature [44–46]
based on the level of muscle activation and maximum capacity.
Frictionless contact was assigned at all joint facets. The coefficient of friction
between the ground and tissue contact was 0.6 [47]. The constructed geometrical
of the bony components were illustrated in Fig. 10.1, demonstrating a predicted
metatarsophalangeal (MTP) dorsiflexion angle of 27.3° at 75% stance. The axial
direction was defined as the longitudinal axis along the tibia and fibula segment.
Both the direction of the metatarsocuneiform (MC) joint force and the MTP joint
force were defined as acting from the proximal side to the distal side.

1.4 Study Design

The study was divided into two parts. The first part involved with the reconstruction
of the entire foot and ankle model for the normal subject while comparing to that of
the hypermobile foot. By weakening the deep transverse metatarsal ligament
(DTML) between the first and second metatarsals, the hypermobility of the first ray
224 D. W.-C. Wong et al.

Axial Direction

AP Direction

Resultant
MC Joint Force

Resultant
MTP Joint Force

Fig. 10.1 Illustration of the joint forces and defined axes directions. (Reprinted from Medical
Engineering & Physics, 36, Wong et al., Biomechanics of first ray hypermobility: An investigation
on the joint force during walking using finite element analysis, 1388–1393, Copyright (2014), with
permission from Elsevier)

was resembled on the normal foot [48]. The MC and MTP joint forces were output
from the simulation. The second part of the study involved with the building of
partial foot model (the first ray) for the normal and hallux valgus participant. The
bone alignment and displacement were extracted for analysis.

1.5 Implications of the Finite Element Model

1.5.1 Model Validation

Model validation was performed by comparing the measured and predicted plantar
pressure. The participant was asked to walk at their self-comfortable speed. An in-­
sole plantar pressure measurement system (F-Scan, Tekscan, USA) was utilized to
assess the plantar pressure distribution. Figure 10.2 shows the comparison of pre-
diction and measurement at the instant of GRF first peak and second peak. During
GRF first peak, the predicted maximum peak pressure was 0.49 MPa, locating at the
heel while the measurement value was 0.46 MPa. On the other hand, the plantar
pressure was concentrated at the hallux, toes, and metatarsals at GRF second peak.
The predicted and measured maximum peak pressures at the hallux region were
0.52 MPa and 0.46 MPa, respectively, which was generally agreeable.
10 Biomechanics of Foot and Ankle 225

Heelstrike GRF First Peak GRF Valley Initial Push-off GRF Second
% Stance
Peak

0% 27% 45% 60% 75%

Finite Element Prediction
Plantar Pressure Measurement

0.00 0.04 0.07 0.11 0.14 0.18 0.22 0.25 0.29 0.33 0.36 0.40 0.43 MPa

Fig. 10.2 Comparison of FE predicted and experimental result on plantar pressure distribution.
(Reprinted from Medical Engineering & Physics, 36, Wong et al., Biomechanics of first ray hyper-
mobility: An investigation on the joint force during walking using finite element analysis,
1388–1393, Copyright (2014), with permission from Elsevier)

1.5.2 Load Transfer Across the First Ray

The MC joint forces of the normal and the hypermobile foot in AP, axial, and medio-
lateral (ML) directions during stance are shown in Fig. 10.3. Before the instant of
GRF first peak, joint forces in all directions were quite small, but increased
­apparently after the instant of GRF valley. On the other hand, the force in both axial
and AP directions increased consistently until terminal stance, while that in medial-­
lateral direction switched laterally during late stance.
The deviation of MC joint force became prominent during late stance. There
were about one-tenth leverage in the medial direction and one-fifth leverage in the
axial and AP direction joint forces upon hypermobility during initial push-off. The
increase was more than 25% at GRF second-peak instant in axial and AP directions,
and skyrocketed to 200% in the medial direction.
226 D. W.-C. Wong et al.

MC Joint Force (N) MTP Joint Force (N)

10 10
Normal
5 0
Hypermobile 0 20 40 60 80
–10
0 Normal
0 20 40 60 80 –20 Hypermobile
–5
–30
–10 –40

–15 –50
% Stance % Stance
0 10
0 20 40 60 80
Normal
–50 Normal 5
Hypermobile
Hypermobile 0
–100 0 20 40 60 80
–5
–150
–10
–200 –15

–250 –20
% Stance % Stance
500 250
Normal Normal
400 Hypermobile 200
Hypermobile
300 150

200 100

100 50

0 0
0 20 40 60 80 0 20 40 60 80
–50

Fig. 10.3 Metatarsocuneiform (MC) and metatarsophalangeal (MTP) joint force comparing nor-
mal foot and foot with hypermobile first ray. ML direction (+ Medial), axial direction (+ Inferior),
AP direction (+ Anterior). The dotted lines were interpolated from the results of the five instants
for illustration. (Reprinted from Medical Engineering & Physics, 36, Wong et al., Biomechanics of
first ray hypermobility: An investigation on the joint force during walking using finite element
analysis, 1388–1393, Copyright (2014), with permission from Elsevier)

The MTP joint force demonstrated comparable trend as that of the MC joint
force. Joint forces along the ML and AP directions advanced with time (percentage
stance phase) and the deviation became obvious after the GRF valley instant.
Notwithstanding, the joint force in the axial direction turned from superior to infe-
rior at 75% stance. In fact, the MTP joint force differences among the normal and
10 Biomechanics of Foot and Ankle 227

hypermobile foot were generally less than that of the MC joint force, while the larg-
est difference between the normal and hypermobile foot occurred in the axial
direction.
MTP and MC joint force increase with hypermobility which could be due to the
reduction in shock attenuation capacity of the arch. To maintain the stability and
integrity of the foot, the load on the first ray may be increased. However, joint prob-
lems could be occurred with the burden of heavy joint force. The sharp change of
the MC joint force direction could result in joint instability and may consequently
lead to the malalignment of the first metatarsal. Since the attenuation of joint force
primarily happened at the MC joint rather than the MTP joint, it was suggested that
hallux abducto valgus deformity could be secondary to the metatarsus primus varus.

1.5.3 Bone Alignment and Displacement

The intermetatarsal angle (IMA) and the hallux valgus angle (HVA) were used to
quantify bone alignment. The former parameter represents the angulation between
the first and second metatarsal, while the latter was calculated by the intersection of
the first metatarsal and phalanx axes. To estimate the alignment angles, we esti-
mated the longitudinal axis of the bone shaft by means of regression algorithm and
assumed that the bones were cylindrical. For normal condition, HVA and IMA were
9.1° and 15.0°, respectively. However, imposing a hallux valgus condition elevated
these parameters to 10.4° and 25.7°, respectively. The angles advanced with increas-
ing forefoot loading. Hallux valgus patients demonstrated higher deterioration of
IMA, which was 20% higher than that of normal foot. The finding also supported
the fact that hallux abducto valgus deformity could be secondary to the metatarsus
primus varus.

1.6 Conclusion

The outcome on MC and MTP joint force provides insights on the development of
hallux valgus upon the laxity effect constituted by first ray hypermobility. The
increased joint loading may contribute to the risk of joint problems, whereas the
abrupt change on the loading direction at the MC joint may indicate potential devel-
opment of metatarsus primus varus.

2 Biomechanical Study of Ankle Arthrodesis

Summary
Ankle arthrodesis is considered as the standard treatment for some ankle problems,
including degenerative deformity, traumatic arthritis. However, many complications
228 D. W.-C. Wong et al.

have been observed after ankle arthrodesis. An investigation on the biomechanical

influence of ankle arthrodesis on the entire foot helps provide a baseline for the
surgical plan. This study constructed a finite element (FE) model of the foot and
ankle, and the biomechanical performances of a normal foot and a foot with ankle
arthrodesis were compared. The results showed that ankle arthrodesis increased the
peak plantar pressure and anterior movement of the center of pressure. The talona-
vicular joint and joints of the first to third rays also increased after ankle arthrodesis.
The findings suggested that the subtalar joint contact force and pressure did not
increase after arthrodesis that may indicate that the arthritic joint may not be result
from the surgery and may be due to the ongoing degeneration. This study provides
additional insights on the assessment of surgery outcome.

2.1 Background

Ankle arthritis is a common foot and ankle problem, while osteoarthritis (OA) sec-
ondary to fracture and trauma was highly prevalent. Survey indicated that about
15% of the people was affected by the disabling conditions and pain ascribed to OA
and approximately 6% have OA of the ankle [49]. Another survey in the United
Kingdom estimated that the number of ankle OA patients requiring hospitalization
or clinical care was 47.7 per 100,000 [50].
Ankle arthritis is a prevalent disabling condition that impair one’s physical func-
tion and quality of living. Glazebrook et al. [51] reported that patients with end-­
stage ankle arthritis scored significantly lower in the evaluation of function and
quality of living. Further, the consequence with respect to mental and physical dis-
ability could be as severe as that of the end-stage hip arthrosis [52]. Ankle arthrod-
esis, firstly performed in 1879, was considered as the salvage procedure for end-stage
ankle arthritis. Despite significant relief of pain and retaining plantigrade foot func-
tion, ankle arthrodesis is known to cause gait alterations as well as arthritic changes
in the subtalar and other distal foot joints [53–56]. Existing retrospective clinical
studies revealed that there was a high incidence rate of ipsilateral hind- and mid-foot
arthritis associated with the deterioration [56, 57].

2.2 Biomechanical Research on Ankle Arthrodesis

The complication of ankle arthrodesis can be partly contributed to the changes of

biomechanical behavior of the foot after the operation. A postoperative patient with
an ankle arthrodesis may walk comparatively slower than a normal participant while
the percentage duration of the stance phase may remain unchanged [56, 58–60].
Recognizing the influence of the ankle arthrodesis by considering the whole foot
segment and the ankle joint is imperative to head for the optimization of the proce-
dure and design.
10 Biomechanics of Foot and Ankle 229

Finite element (FE) approach aims to explore information of biomechanical

environment of the human musculoskeletal system which provides valuable infor-
mation such as contact pressure of articular joints, soft tissue deformation, and
stresses of the bony structures. Nevertheless, relevant studies on ankle arthrodesis
confined to the use of simplified FE models, such as that with partial geometries or
two-dimensional models [61, 62]. A more precise representation using three-­
dimensional anatomically detailed FE models could further our understandings on
the complex interactions among foot segments [63].
In the present study, a three-dimensional FE model with more precise anatomical
structures will be reconstructed. We investigate the biomechanical responses of both
the whole foot segment and the ankle joint upon arthrodesis which could be benefi-
cial to identify risks and improve surgical protocols.

2.3 Computational Analysis

2.3.1 Geometry Construction

A normal adult (height 164 cm and body weight 54 kg) was recruited in the study.
The MR images of her right foot were extracted under a setting of 0.625 mm pixel
resolution and 2 mm slice interval. The three-dimensional FE model was recon-
structed featuring the foot-and-ankle complex with 28 bony components, encapsu-
lated soft tissue, 103 ligaments, plantar fascia, and major muscles [63, 64]
(Fig. 10.4). The reconstruction process was carried out in the segmentation soft-
ware, Mimics (Materialise, Leuven, Belgium), and meshed in the finite element
package, Abaqus (Dassault Systèms Simulia Corp., Providence, RI, USA).
We resembled the ligaments and plantar fascia using wires that connected the
insertions points on the bony structures and meshed them with tension-only truss
elements. Nine major muscle groups were assumed by axial connectors. The bilayer
ground plate consisted of an upper layer with high elastic modulus and a rigid lower
layer. The coefficient of friction between the foot plantar surface and the ground
support surface was set to 0.6 [47].

2.3.2 Material Property

Most of the components were assumed to be isotropic, linearly elastic, and homo-
geneous, including the osseous structure and soft tissue, and the Young’s modulus
and Poisson’s ratio of these components were adopted from existing literature
[42, 65–67]. The bulk soft tissue and skin were assigned as hyperelastic material
with nonlinear properties. Most of the three-dimensional components were
meshed as linear tetrahedral elements, while that of the plantar fascia and liga-
ments were meshed as truss. The mesh and material properties are shown in
Table 10.1.
230 D. W.-C. Wong et al.

Fixed surfaces
Achilles
Tendon
a
Muscle Forces

x
y
Fascia
Plantar z

f=0.6

ctio n
d Rea
Groun rces
Fo
a

Fig. 10.4 The three-dimensional finite element model of the foot and ankle and application of
boundary and loading conditions. (Reprinted from PlosOne, Wang et al., Effects of Ankle
Arthrodesis on Biomechanical Performance of the Entire Foot, e0134340 (2015), under CC-BY)

Table 10.1 Material property and mesh element type for the foot model components
Element Young’s modulus E Poisson’s Cross-section area
Component type (MPa) ratio v (mm2)
Bone C3D4 7300 0.3 –
Encapsulated soft C3D4 and Hyperelastic – –
tissue S3
Cartilage C3D4 1 0.4
Ligaments T3D2 260 – 18.4
Plantar fascia T3D2 350 – 58.6
Ground C3D8R 17,000 0.1 –

2.3.3 Boundary and Loading Conditions

The model participant was invited to conduct a gait analysis using the motion cap-
ture system (Vicon, Oxford Metrics, Oxford, UK) to obtain the boundary and load-
ing conditions for the input of the FE analysis. We targeted on seven body segments
with 16 retroreflective markers attached on the lower extremity of the participant.
The participant stood on the force platform (AMTI, Watertown, MA, USA) to con-
duct the static calibration for the motion capture system. The orientation of the
shank was defined by the three-dimensional angulation between the shank segment
and the global system, denoted as α in Fig. 10.4 with the time series in Fig. 10.5.
The force plate would detect the ground reaction force in the vertical, anterior-­
posterior, and medial-lateral directions. In Fig. 10.5, we extracted the first-peak,
midstance, and second-peak instants of the ground reaction force curve in the verti-
cal direction for further analysis.
10 Biomechanics of Foot and Ankle 231

The proximal side of the FE model was fixed, including the superior surfaces
of the tibial, fibula, and the encapsulated soft tissue (Fig. 10.4). The ground reac-
tion force was applied on the rigid ground plate to mimic the setting of the force
platform. The foot-shank angle was applied through the rotational degree of free-
dom of the ground plate whereas the translational degree of freedom was not fixed.
The muscle forces were approximated by the cross-sectional area, the normalized
electromyography, and the muscle gain of the muscles during walking stance [46,
68, 69], and later adjusted based on another study [45].

Ground Reaction Forces

750
AP-GRF
650
ML-GRF
550 Vert-GRF

450
Force (N)

350

250

150

50

–50 0 10 20 30 40 50 60 70 80 90 100

–150

80 Ground-Shank Angle

60
Angle (º)

40

20

0
0
–20 10 20 30 40 50 60 70 80 90 100
% Stance Phase

First Peak Mid-stance Second Peak

Fig. 10.5 Ground reaction forces and ground-shank angle recorded in the gait analysis and the
three instants, first peak, midstance, and second peak, for simulation. The three instants were
marked in the curves. (Reprinted from PlosOne, Wang et al., Effects of Ankle Arthrodesis on
Biomechanical Performance of the Entire Foot, e0134340 (2015), under CC-BY)
232 D. W.-C. Wong et al.

2.4 Effects of Ankle Arthrodesis on Foot Biomechanics

2.4.1 Model Validation

Plantar pressure during balanced standing and walking stance was assessed and
compared between the experiments and predictions from the FE model. Model
validation was completed by comparing these findings. As shown in Fig. 10.6, the
pressure pattern was generally agreeable with the peak pressure located at the
heel region.

2.4.2 Plantar Pressure

Figure 10.7 shows the plantar pressure distribution of the intact foot and the foot
after arthrodesis at the three stance instants (first peak, midstance, and second peak).
At the first-peak instant, there was a slight difference in peak plantar pressure
between the conditions, which was 0.33 MPa and 0.36 MPa for the intact foot and
arthrodesis foot, respectively. The peak plantar pressures for the intact foot between
the midstance and second-peak instant were both 0.68 MPa. However, that of the
arthrodesis foot was higher and increased chronologically. The peak plantar pres-
sure was 0.78 MPa and 0.93 MPa, respectively, for the midstance and second-peak
condition for the arthrodesis foot. Compared to the intact condition, the center of
pressure after arthrodesis has shifted slightly towards the medial side and appeared
beneath the third metatarsal bone.

2.4.3 Joint Contact Pressure

Figure 10.8 summarizes the maximum contact pressure of the articular joints
between the intact and arthrodesis condition at the first-peak, midstance, and
second-­peak instants. There were observable increases of maximum pressure at the
talonavicular and intertarsal joints after the ankle arthrodesis procedure. In consid-
eration of the average of the maximum contact pressure across the time instants, the
talonavicular joint remained highest and was increased from 0.80 to 1.21 MPa; 1.14
to 1.59 MPa; and 2.00 to 2.14 MPa after surgery at the three instants.
The medial cuneonavicular joints carried higher maximum contact pressure
compared with the other cuneonavicular joints. The maximum contact pressure of
the joint increased from 0.60 to 0.79 MPa; from 0.97 to 1.20 MPa; and from 1.90 to
1.97 MPa after ankle arthrodesis, respectively, for the first-peak, midstance, and
second-peak instants. However, the highest magnitude of the change due to the
surgical procedure was evident at the lateral cuneonavicular joint. The percentage
changes were 80.3%, 64.7%, and 11.6%, respectively, at the first-peak, midstance,
and second-peak instants.
Distally, considering the tarsometatarsal joints, the second tarsometatarsal
joint sustained the highest maximum contact pressure compared with the other
10 Biomechanics of Foot and Ankle 233

a
CPRESS (MPa)
(KPa)
0.191
0.150 > = 150
0.138
0.125 138
0.113 225mm2 232mm2 125
0.100 0.051MPa
0.088 0.058MPa 113
0.075 100
0.063 88
0.050
0.038 75
0.025 63
0.013
0.000 50
38
25
13
>=0

150mm2 155mm2
0.168MPa 0.157MPa

b CPRESS (MPa)
(KPa)
0.332
0.300 > = 300
0.275
0.250 275
0.225
0.200 250
0.175 225
0.150
0.125 200
0.100 175
0.075
0.050 150
0.025 125
0.000
100
75
50
25
>=0

150mm2 155mm2
0.300MPa 0.307MPa

c CPRESS (MPa) (KPa)

0.683 > = 300
0.300
0.275 275
0.250 250
0.225 1000mm2 1032mm2
0.200 225
0.175 0.227MPa 0.223MPa 200
0.150
0.125 175
0.100
0.075 150
0.050 125
0.025
0.000 100
75
50
25
>=0

Computational Prediction Experimental Measurement

Fig. 10.6 Comparison of the plantar pressure between computational prediction and experimental
measurement in (a) balanced standing position, (b) the first-peak instant, and (c) the second-peak
instant for validation. (Reprinted from PlosOne, Wang et al., Effects of Ankle Arthrodesis on
Biomechanical Performance of the Entire Foot, e0134340 (2015), under CC-BY)
234 D. W.-C. Wong et al.

Normal Ankle Arthrodesis

CPRESS (MPa) CPRESS (MPa)
0.332 0.362
0.300 0.300
0.275 0.275
0.250
0.225 0.250
0.200 Max 0.225
0.175 0.200
0.150 0.362 0.175
First Peak

0.125 0.150
0.100 0.125
0.075 15 mm 0.100
0.050 0.075
0.025 0.050
0.000 0.025
0.000

Max: 0.332

CPRESS (MPa)
CPRESS (MPa)
0.683 0.779
0.300 Max: 0.683 0.300
0.275 0.275
0.250 16 mm 0.250
0.225 0.225
0.200 0.200
0.175 0.175
0.150
Mid-stance

0.125 0.150
0.100 0.125
0.075 0.100
Max: 0.779 0.075
0.050
0.025 0.050
0.000 0.025
0.000

CPRESS (MPa) CPRESS (MPa)

0.683 0.930
0.300 0.300
0.275 5 mm 0.275
0.250 0.250
0.225 0.225
0.200 0.200
0.175
Max 0.175
Second Peak

0.150 0.150
0.125 0.930 0.125
0.100
0.100
0.075 Max 0.075
0.050
0.025 0.683 0.050
0.000 0.025
0.000

Fig. 10.7 Comparison of the plantar pressure distribution between normal foot model and ankle
arthrodesis foot model at the three instants. (Reprinted from PlosOne, Wang et al., Effects of Ankle
Arthrodesis on Biomechanical Performance of the Entire Foot, e0134340 (2015), under CC-BY)
 10

2.5 Comparison of Joint Contact Pressure

Normal
Arthrodesis
2.0

1.5

1.0
Biomechanics of Foot and Ankle

0.5

Joint Contact Pressure (MPa)

0.0

First Peak
First Peak
First Peak
First Peak
First Peak
First Peak
First Peak
First Peak
First Peak

Midstance
Midstance
Midstance
Midstance
Midstance
Midstance
Midstance
Midstance
Midstance

Second Peak
Second Peak
Second Peak
Second Peak
Second Peak
Second Peak
Second Peak
Second Peak
Second Peak

Subtalar Talonavicular Calcaneoc- Medial Intermediate Lateral First Second Third

uboid Cuneonavi- Cuneonavi- Cuneonavi- Tarsometat- Tarsometat- Tarsometat-
cular cular cular arsal arsal arsal

Fig. 10.8 Comparison of the contact pressure at nine joints in the hind- and mid-foot between the normal foot model and the ankle arthrodesis foot model at
the first-peak, midstance, and second-peak instants. (Reprinted from PlosOne, Wang et al., Effects of Ankle Arthrodesis on Biomechanical Performance of the
Entire Foot, e0134340 (2015), under CC-BY)
235
236 D. W.-C. Wong et al.

tarsometatarsal joints. The maximum contact pressure was increased from 0.60 to
0.90 MPa; from 0.91 to 1.19 MPa; and from 1.72 to 1.88 MPa after the ankle
arthrodesis procedure, respectively, for the three stance instants. In fact, the surgi-
cal procedure imposed the largest influence of the third tarsometatarsal joint
accounting for the percentage changes of 62.8%, 51.4%, and 2.0% at the three
stance instants. The fourth and fifth tarsometatarsal joints did not demonstrate
consistent trend throughout the stance instants. The former showed a maximum
contact pressure reduction after surgery at the first peak and midstance, whereas
the latter presented a reduction at the midstance and second-peak instant.
Ankle arthrodesis reduced the maximum contact pressure of the subtalar and cal-
caneocuboid joints. The maximum contact pressure of the calcaneocuboid joint was
decreased from 0.32 to 0.24 MPa; from 0.48 to 0.39 MPa; and from 0.51 to 0.49 MPa
after surgery at the three stance instants, respectively. Furthermore, the maximum
contact pressure of the subtalar joint was decreased from 0.39 to 0.37 MPa; from
0.54 to 0.51 MPa; and from 0.78 to 0.70 MPa after surgery, respectively, at the three
instants. The reduction of maximum contact pressure of the hindfoot joints may sug-
gest that subtalar arthritis may not be a consequence of ankle arthrodesis. We specu-
lated that the progression could be attributed to the pre-­existing degenerative changes.

2.4.4 Joint Contact Force

Figure 10.9 compares the joint contact forces among the intact and surgery condi-
tions at the selected instants of walking stance. The contact force elevated chrono-
logically (first-peak, midstance, and then second-peak instants) for the talonavicular,
cuneonavicular, and the first and second tarsometatarsal joints. Apparent change
appeared at the first-peak instance whereas most of the joint presented their highest
value at the second-peak instant.
The talonavicular joint acted as the highest load-bearing bone in the foot and
ankle complex. The joint forces were 181 N, 259 N, and 514 N, respectively, at the
first-peak, midstance, and second-peak instants. The forces were increased more
than half for the first peak and midstance and reached to 578 N at the second peak
which was slightly higher than the applied vertical ground reaction force (540 N).
Conversely, the load transfer towards the calcaneocuboid declined after arthrodesis
by 31%, 17%, and 8%, and reached to 33 N, 55 N, and 74 N, respectively, for the
three instants of walking stance.
In general, the first ray sustained a higher contact force compared to that of the
second and third ray. They experienced greater contact force at the second-peak
instants. The medial cuneonavicular and first tarsometatarsal joints of the first ray
increased by 31% and 75%, respectively, at the first-peak instant, while the interme-
diate cuneonavicular and second tarsometatarsal joints of the second ray increased
by 52% and 79%, in addition to the 74% and 71% increase at the lateral cuneona-
vicular and third tarsometatarsal joints of the third ray.
Figure 10.10 demonstrates the differences in load transfer between the intact and
arthrodesis model at the first-peak instant, which was more prominent compared to
that of the other two instants. Approximately one-third of the body weight was
 10

700
600 Normal
Comparison of Joint Contact Force
500 Arthrodesis
400
300
200
Biomechanics of Foot and Ankle

100

Joint Contact Force (N)

First Peak
First Peak
First Peak
First Peak
First Peak
First Peak
First Peak
First Peak
First Peak
First Peak

Midstance
Midstance
Midstance
Midstance
Midstance
Midstance
Midstance
Midstance
Midstance
Midstance

Second Peak
Second Peak
Second Peak
Second Peak
Second Peak
Second Peak
Second Peak
Second Peak
Second Peak
Second Peak

Talonavicular Calcaneoc- Medial Intermediate Lateral First Second Third Forth Fifth
uboid Cuneonavi- Cuneonavi- Cuneonavi- Tarsometat- Tarsometat- Tarsometat- Tarsometat- Tarsometat-
cular cular cular arsal arsal arsal arsal arsal

Fig. 10.9 Comparison of the contact forces at ten joints in the hind- and mid-foot between the normal foot model and ankle arthrodesis model at the first-peak,
midstance, and second-peak instants. (Reprinted from PlosOne, Wang et al., Effects of Ankle Arthrodesis on Biomechanical Performance of the Entire Foot,
e0134340 (2015), under CC-BY)
237
238 D. W.-C. Wong et al.

For Normal Foot

For Ankle Arthrodesis Foot

0.07 0.06
0.11
0.0
9
0.34
0.58
0.23 0.33

Fig. 10.10 Load transfer (times of body weight) in the normal and ankle arthrodesis foot model at
the first-peak instant. (Reprinted from PlosOne, Wang et al., Effects of Ankle Arthrodesis on
Biomechanical Performance of the Entire Foot, e0134340 (2015), under CC-BY)

transferred through the talonavicular joint to the medial joints while less than 10%
of the body weight was transmitted through the calcaneocuboid joint to the fourth
and fifth rays. From mid-foot to forefoot, 23% of the body weight was conveyed
medially and 11% laterally. The ankle arthrodesis imposed additional burden on
load transferred which was increased to 58% at the talonavicular joint and reduced
that of the calcaneocuboid joint. Similarly, the midfoot-to-forefoot transfer increased
to 34% in the medial three rays and decreased to 7% in the lateral two rays. The
change in load transfer pattern may induce risk of foot pain the medial columns
which may constitute to foot deformity in long term. Orthotic intervention such as
wedge insole may help revise the load transfer pattern after surgery.

2.4.5 Bone Stress

As shown in Fig. 10.11, ankle arthrodesis increased the von Mises stress of the bone
in general. At the first-peak instant, the von Mises stress increased apparently by
19% and 52%, respectively, in the first and third metatarsal bone, while the lateral
metatarsal only processed small slight changes. However, all the metatarsal showed
an obvious elevation in stress at the midstance and second-peak instants. The sec-
ond metatarsal represented the part with the highest stress which was 42 MPa and
52 MPa, respectively, for the normal and arthrodesis condition. The third metatarsal
comes after the second metatarsal. The stress was 20 MPa at midstance and increased
to 34 MPa at the second-peak instant.

2.4.6 Foot Deformation at the Second-Peak Instant

As shown in Fig. 10.12, the predicted results showed different joint position and foot
deformation between the intact and surgery conditions, particularly at the second-­
peak instant. The foot-shank angle for both conditions were 30°. However, the ori-
entation angle was 28° for the intact foot and 44° for the arthrodesis foot, respectively,
between the horizontal plane and the first ray axis at the second-peak instant.
10 Biomechanics of Foot and Ankle 239

Normal Ankle Arthrodesis

S, Mises S, Mises
(Avg: 75%) (Avg: 75%)
20.000 21.062
18.337 20.000
16.673 18.337
First Peak

15.010 16.675
13.346 15.012
11.683 13.350
10.019 11.687
8.356 10.025
6.692 8.362
5.029 6.700
3.365 5.037
1.702 3.375
0.039 1.712
0.050

S, Mises S, Mises
(Avg: 75%) (Avg: 75%)
25.505 31.439
20.000 20.000
18.340 18.340
16.679 16.679
Mid-stance

15.019 15.019
13.358 13.359
11.698 11.698
10.037 10.038
8.377 8.377
6.716 6.717
5.056 5.057
3.395 3.396
1.735 1.736
0.074 0.076

S, Mises S, Mises
(Avg: 75%) (Avg: 75%)
42.133 51.911
20.000 20.000
18.341 18.344
Second Peak

16.682 16.689
15.023 15.033
13.364 13.378
11.706 11.722
10.047 10.067
8.388 8.411
6.729 6.756
5.070 5.100
3.411 3.445
1.752 1.789
0.093 0.134

Fig. 10.11 Comparison of von Mises stress in five metatarsal bones in normal foot model and ankle
arthrodesis foot model at three instants. (Reprinted from PlosOne, Wang et al., Effects of Ankle
Arthrodesis on Biomechanical Performance of the Entire Foot, e0134340 (2015), under CC-BY)

2.4.7 Limitations

The FE model in this study inherited some simplifications and assumptions. The
ankle arthrodesis was realized by constraining the contact at the ankle articulation
rather than reconstructing and installing the models of the screws or pins. It would
be better to reconstruct the screws to examine its behavior and influences. Besides,
the suggested Young’s modulus and Poisson’s ratio was not relatively accurate [40].
It was derived from a weighted average elasticity of the cortical and trabecular
based on their volumetric contribution [66]. Further model refinement shall be made
to advance a more accurate model or material representation.
240 D. W.-C. Wong et al.

Normal Ankle Arthrodesis

30 º

30 º

Y X
X Y

GRFx 28 º 44 º
GRFx

Fig. 10.12 Angular positions of normal foot and ankle arthrodesis foot at a second-peak instant in
the sagittal plane. (Reprinted from PlosOne, Wang et al., Effects of Ankle Arthrodesis on
Biomechanical Performance of the Entire Foot, e0134340 (2015), under CC-BY)

We anticipated that the influence of the simplifications and assumptions pro-

duced similar offset errors to the models of the two conditions. Therefore, due to the
self-compare study design, we believe that the outcome in terms of trend or differ-
ences between the conditions were less affected by these limitations. On the other
hand, another limitation of this study was that we assumed the gait pattern (bound-
ary and loading conditions) between the normal and ankle arthrodesis conditions
was similar. There are claims that the arthrodesis may not change the input bound-
ary and loading conditions, despite that some patients may demonstrate change in
spatiotemporal parameters.

2.5 Conclusions

Ankle arthrodesis is a common surgical procedure that aims at pain relief and func-
tion improvement for patients with ankle degeneration. However, the fusion and
constraints on the ankle joint, which is the major foot joint, corrupt the normal
biomechanics of both the ankle joint and the entire foot, leading to potential postop-
erative complications.
The biomechanical consequences of ankle arthrodesis are indicated by the
differences in biomechanical parameters, including plantar pressure, contact
10 Biomechanics of Foot and Ankle 241

force, stresses, and deformation, which could explain the mechanism of some
clinical findings. The high load on the medial rays may result in pain and dete-
riorate the arthritic condition, while the large stress on the second and third
metatarsals could impose risk of bone fractures. There was a decrease in subtalar
joint loading after ankle arthrodesis such that we believe the postoperative
arthritis of the subtalar joint may not be a consequence of the ankle arthrodesis
procedure.
The model used in this study was regarded as a representation of the normal
physique and may be regarded as a baseline reference from a biomechanical point
perspective. Foot in valgus position may lateralize the loading. In addition,
orthotic intervention may help to relieve the negative effects of ankle arthrodesis.
Further evaluations are required to decide the effectiveness of these
interventions.

3 Biomechanical Study of Tarsometatarsal Joint Fusion

Summary
The Lisfranc joint complex is also named as the tarsometatarsal joint (TMT) and
is recognized as a crucial connection that facilitates stability of the midfoot and
forefoot. The joint comprises sophisticated osseous and capsuloligamentous
structure such that the injury of the TMT joint may lead to disabling osteoarthritis
(OA) requiring surgery. Acknowledging the effectiveness of surgical intervention
and minimizing risk of complication are imperative in surgical design. Determining
the internal biomechanical environment, such as plantar pressure distribution,
stress of the bone, and deformation of soft tissue, attenuated by surgical interven-
tion facilitates evaluation. In this study, we aimed to evaluate the influence of
TMT joint fusion biomechanically using a finite element model of the foot and
ankle complex, which consisted of 28 bony structures, 72 ligaments, plantar pres-
sure, and an encapsulated bulk tissue. Our finite element prediction suggested that
TMT joint fusion elevated the plantar pressure by 0.42, 19, and 37% in three
featured time instants compared to the intact foot. In particular, the load transfer
across the cuneonavicular and the fifth cuboideometatarsal joints were increased
by 27% and 40%, respectively, at the second-peak instant that may impose risk of
joint arthritis. On the other hand, the maximum stress of the second metatarsal
bone was increased by more than 20% that may lead to vulnerability to stress
fracture.

3.1 Background

The tarsometatarsal (TMT) joint, or the Lisfranc joint, is named after a French sur-
geon, Jacques Lisfranc (1790–1847), who served in the Napoleon’s [70]. The TMT
joint plays an important role in bridging the midfoot and the forefoot. In addition,
242 D. W.-C. Wong et al.

the arrangement of the five metatarsals on the distal side and the four midfoot bones
(three cuneiforms and cuboid) facilitates structural support for the transverse arch
along with the attaching ligamentous structures. The TMT joint is often divided into
three columns along the anterior-posterior direction by the articulation of the sec-
ond and third TMT joints. The TMT joint can have little sagittal plane motion with
a range of 0.6 mm, 3.5 mm, and 13 mm, respectively, for the central, medial, and
lateral columns [70, 71].
In the United States, fractures of the TMT joint accounted for 0.2% of all frac-
tures, in which there was one fracture in every 55,000 persons each year [72]. The
treatment to TMT joint injuries, however, remains no consensus. Nonoperative
intervention could be indicated for nondisplaced fracture. Surgical methods using
either closed or open reduction would be used to treat displaced fracture assisted
with different implants, such as Kirschner wires, screws, plates, or suture-button
devices. Correct reduction and alignment with sufficient stability is the key to satis-
factory clinical outcome [73].
While joint fusion procedure aims to restore some normal foot functions, it
may produce some undesirable biomechanical effects. The constraints on the
joint may induce additional stress onto the bony structures leading to irritation,
loosening of implants, and breakage. A mid-term follow-up on TMT joint fixa-
tion patients reported that more than 10% of them developed posttraumatic
arthritis and nearly 3% developed subluxation [74]. In addition, approximately
7% of them developed flatfoot or severe symptoms that required a secondary
surgery [74].

3.2 Biomechanical Study of Tarsometatarsal Joint Injury

It is imperative to evaluate the biomechanical performance and thus the effective-

ness of the surgery to minimize potential complications. TMT joint plays an impor-
tant role in load transfer from hindfoot to the forefoot that facilitates foot propulsion
and body movement. TMT joint modulates load transfer by two different mecha-
nisms depending on the magnitude of load. For small loads, TMT adjusts the joint
contact area to regulate the contact area and contact pressure. For large loads, the
group of joints in the TMT would be rearranged and redistribute the load among the
group of joints [75].
Ankle joint and other foot joints work interdependently and synergistically to
maintain balance and bring about ambulation. Therefore, a localized joint prob-
lem is likely to affect adjacent joints and subsequently impair the function of the
foot and ankle complex. The internal stress and strain distribution could be an
indicator reflecting the changes resulted from interventions yet difficult to be mea-
sured by physical experiment approach. Computer simulation via a FE approach
represents a feasible alternative to explore the internal biomechanical environ-
ment of the foot and ankle. The strength of the approach is the capability in man-
aging complex geometries, material properties, boundary, and loading conditions
10 Biomechanics of Foot and Ankle 243

that offer additional insights to the problem. In this study, we simulated a TMT
joint fusion procedure on a comprehensive 3D FE foot and ankle model to evalu-
ate the biomechanical performance of the intervention.

3.3 Finite Element Simulation of Tarsometatarsal Joint Fusion

3.3.1 Finite Element Model and Simulation of Joint Fusion

The FE model was reconstructed from the right foot of a female (54 kg, 1.64 m).
The model consisted of a volume of encapsulated soft tissue embracing 28 body
segments and other soft tissues [63, 64]. The first and second tarsometatarsal joint
fusion procedure was realized in the simulation platform [76]. Clinically, the
affected joint is linked by screws whereas the process was simplified in the simula-
tion by fusing the articular contact interface among the medial and intermediate
cuneiform, and the first and second metatarsal bones (Fig. 10.13).

a b

Fig. 10.13 Surgery of first and second tarsometatarsal joint fusion (a), and four tied bones in the
model for simulation (b). Articular surfaces among the first and second metatarsal bones and
medial and intermediate cuneiforms were tied together to simulate the fixed joints. (Reprinted from
Medical Engineering & Physics, 36, Wang et al., Biomechanical study of tarsometatarsal joint
fusion using finite element analysis, 1394–1400, Copyright (2014), with permission from Elsevier)
244 D. W.-C. Wong et al.

3.4 Boundary and Loading Conditions

The model subject was recruited to perform locomotion analysis using the motion
capture system, as well as the force platform and electromyography. Reflective mark-
ers were attached to the interested body segments whereas the kinematic and kinetic
information during gait were extracted. As shown in Fig. 10.14, the GRFs with time
were obtained featuring the first-peak, midstance, and the second-peak instants.
The first peak of the vertical GRF happened at 25% stance phase while that of the
second peak occurred at 70%. The midstance was defined as the valley of the curve
and occurred between the first- and second-peak instants. Extrinsic muscle forces
were estimated and applied according to the linear EMG-force assumption, mea-
sured EMG and suggested cross-sectional area of the muscles [68, 69]. The input of
the boundary and loading conditions in the four simulated time instants are sum-
marized in Table 10.2.
The muscles in the simulation were modelled as connectors jointing the relevant
attachment points. Tendon Achilles were assumed by five axial connectors and
forces were applied onto these connectors equally. Figure 10.15 illustrates the other

Fig. 10.14 The vertical

ground reaction force and
the three investigated gait
instants

Table 10.2 Boundary conditions of the four simulated instants: balanced standing, first peak,
midstance, and the second peak
Loadings Balanced standing First peak Midstance Second peak
GRF (N) 270 578.6 519.3 600
Ankle-shank angle (rad) 0 0.113 0.216 0.485
Tibialis anterior (N) – 0 0 0
Tibialis posterior (N) – 34 42.5 0
Achilles tendon (N) 135 500 900 1100
Extensor digitorum longus (N) 0 0 0 0
Flexor digitorum longus (N) 0 40 20 96
Flexor hallucis longus (N) 0 30 0 284
Peroneus longus (N) 0 0 41.25 0
Peroneus brevis (N) 0 20 22 91.8
10 Biomechanics of Foot and Ankle 245

Fixed Surfaces
Achilles Tendon
Force

Muscle Forces

Z
GRF
Y

Fig. 10.15 Boundary and loading conditions for the simulation of gait instants. The superior sur-
faces of soft tissue, tibia and talus bones were fixed. Ground reaction forces of anteroposterior and
vertical directions were applied. Muscle forces were applied to muscle representatives. (Reprinted
from Medical Engineering & Physics, 36, Wang et al., Biomechanical study of tarsometatarsal joint
fusion using finite element analysis, 1394–1400, Copyright (2014), with permission from Elsevier)

muscle construction represented by the red dotted lines. The proximal end of the
encapsulated soft tissue, tibia, and fibula were fixed along with GRFs applied beneath
the rigid ground plate. The ground plate was also rotated according to the foot-shank
orientation profile sourced from the locomotion analysis. Besides, balanced walking
was also mimicked with half body weight (270 N). It was also assumed that only
Achilles tendon was activated and other muscle forces were negligible.

3.5 Biomechanical Effects of Tarsometatarsal Joint Fusion

Plantar pressure distribution, contact pressure of the articular joint at the midfoot and
hindfoot, as well as the maximum von Mises stress of the metatarsal bones would be
compared between the intact and the surgical conditions. In addition, model validation
was carried out by comparing the plantar pressure and joint contact pressure between
FE prediction and physical experiment which demonstrated a reasonable agreement.

3.5.1 Plantar Pressure Distribution

Figure 10.16 demonstrated that the plantar pressure distribution between the intact
and surgical conditions were similar but the surgical model showed a larger peak
pressure value. The peak plantar pressure was increased by 0.42%, 19%, and 37%
after surgery, respectively, at the first-peak, midstance, and second-peak instants,
which was more prominent during later stance. The corresponding peak pressure
values from intact to surgical conditions were: from 0.50 to 0.51 MPa; from 0.60 to
0.72 MPa; and from 0.64 to 0.88 MPa.
246 D. W.-C. Wong et al.

First Peak Mid-stance Second Peak

CPRESS (MPa) CPRESS (MPa)
CPRESS (MPa) 0.603 0.643
0.506 0.300 0.300
0.300 0.275 0.275
0.275 0.250 0.250
0.250 0.225 0.225
Normal

0.225 0.200 0.200

0.200 0.175 0.175
0.175 0.150 0.150
0.150 0.125 0.125
0.125 0.100 0.100
0.100 0.075 0.075
0.075 0.050 0.050
0.050 0.025 0.025
0.025 0.000 0.000
0.000

CPRESS (MPa) CPRESS (MPa)

CPRESS (MPa) 0.717 0.878
0.508 0.300 0.300
0.300 0.275 0.275
0.275 0.250 0.250
0.250 0.225 0.225
0.225 0.200 0.200
0.200 0.175 0.175
Fusion

0.175 0.150 0.150

0.150 0.125 0.125
0.125 0.100 0.100
0.100 0.075 0.075
0.075 0.050
0.050 0.025 0.050
0.025 0.000 0.025
0.000 0.000

Fig. 10.16 Plantar pressure distributions in the normal and fused tarsometatarsal joint models in
three instants. (Reprinted from Medical Engineering & Physics, 36, Wang et al., Biomechanical
study of tarsometatarsal joint fusion using finite element analysis, 1394–1400, Copyright (2014),
with permission from Elsevier)

Arch height stiffness and contact area are also determinants to contact pressure.
The arch height stiffness was reflected by its flexibility which was quantified by the
change in arch height during balanced standing (measured from the dorsal peak of
intermediate cuneiform to the tuberosity of the calcaneus bone). Our study showed
that the surgery reduced about a quarter flexibility compared to that of the intact foot.

3.5.2 Contact Pressure of Plantar Foot and Joints

The joint fusion surgery elevated the maximum contact pressure of the ankle, talo-
navicular, intermediate cuneonavicular, cuboideonavicular, and the fifth cuboideo-
metatarsal joints. Figure 10.17 illustrates the maximum joint contact pressure
normalized to that of the ankle joint during the first-peak instant.
10 Biomechanics of Foot and Ankle 247

Comparison of Contact Pressures

4

3.5
Ratio of Contact Pressure (100%)

2.5

1.5

0.5

0
1st Peak

Midstance

2nd Peak

1st Peak

Midstance

2nd Peak

1st Peak

Midstance

2nd Peak

1st Peak

Midstance

2nd Peak

1st Peak

Midstance

2nd Peak
Ankle Talonavicular NavicoICune Navicocuboid Meta5Cuboid

Normal Fusion

Fig. 10.17 Comparison of normalized contact pressure at five joints between normal foot and foot
with two tarsometatarsal joint fusion. These five joints showed increased contact pressure after the
joints fusion. All contact pressures were divided by that of the ankle joint during the first-peak
instant. (Reprinted from Medical Engineering & Physics, 36, Wang et al., Biomechanical study of
tarsometatarsal joint fusion using finite element analysis, 1394–1400, Copyright (2014), with per-
mission from Elsevier)

Figure 10.17 shows that the maximum contact pressure progressed chronologi-
cally along the stance phase, particularly dominated by the ankle joint. The fusion
surgery did not produce considerable change at the ankle joint with a percentage
increase of 12%, 14%, and 0.58%, respectively, for the three stance instants. The
joint between the navicular and cuboid bone presented the largest percentage change
during midstance despite relatively small magnitude.

3.5.3 von Mises Stress in the Five Metatarsal Bones

Figure 10.18 illustrates the von Mises stress plot during midstance. While metatar-
sal bones were relatively more susceptible to fracture due to its long and thin shape
with large load transfer, von Mises stress was believed to be one of the key predic-
tors for stress fracture [77].
The maximum stress was located at the second metatarsal bone at midstance.
The magnitude increased from 26 MPa under normal condition to 31 MPa under the
fusion condition. Similarly, the stress was also elevated by 16% and 14%, respec-
tively, during first peak and second peak. Besides, the maximum von Mises stress of
the fifth metatarsal bone was increased by 5.1% and 9.5% after fusion, respectively,
248 D. W.-C. Wong et al.

Fig. 10.18 Von Mises a S, Mises

stress in the five metatarsal (MPa)
bones (a) in normal foot 25.505
model and (b) model with 10.000
9.173
the first and second 8.346
tarsometatarsal joint fusion 7.519
6.691
in midstance. The second 5.864
metatarsal showed the 5.037
4.210
maximum change during 3.383
2.556
midstance instant. 1.729
(Reprinted from Medical 0.901
0.074
Engineering & Physics,
36, Wang et al.,
Biomechanical study of
tarsometatarsal joint
fusion using finite element
analysis, 1394–1400,
Copyright (2014), with
permission from Elsevier) b S, Mises
(MPa)
31.058
10.000
9.175
8.349
7.524
6.699
5.873
5.048
4.223
3.397
2.572
1.747
0.921
0.096

during the first-peak and midstance instants. On the other hand, there were no sub-
stantial change of the maximum stress for the first and fourth metatarsal bone com-
paring the normal and the fusion conditions.
Stress fractures are more prevalent at the second and third metatarsals which was
reported as one of the major complications after foot surgeries [78, 79]. With approxi-
mately one-fifth of stress increase, our prediction supported the fact that TMT joint
fusion between the first and second rays induce risk of second metatarsal bone fracture.

3.6 Conclusions

TMT joint fusion could be a salvage procedure to repair severe flatfoot. The stiffen-
ing created by the fusion attenuated the internal stress and strain of bones and soft
tissue, as well as the plantar pressure distribution. The peak plantar pressure increased
in all simulated instants whereas the largest increase happened during push-off.
10 Biomechanics of Foot and Ankle 249

The surgical procedure produced relatively pronounced raise in the peak contact
pressure between the navicular and cuboid joint, whereas increases in contact pres-
sure were also predicted in other joints, including the ankle, talonavicular joint, the
fifth cuboideometatarsal, and intermediate cuneonavicular joints. Based on the find-
ings, we believed that the cuboideonavicular and the ankle joints were more suscep-
tible to arthritis due to the large contact pressure. Likewise, the large von Mises
stress on the second metatarsal induced by the procedure could probably increase
the risk of stress fracture which in line with the higher complication rates of second
metatarsal stress fracture in clinical findings.
Effective interventions are expected to remedy the pain, impaired functions, and
quality of life because of the disease or problems, even though surgery may inter-
fere natural anatomy and physiology resulting in complications and other negative
outcomes. Biomechanical information provides additional information for physi-
cians to understand the limitations or potential consequences of an intervention and
support their decision-making process.

4 Biomechanical Study of Calcaneal Fracture Mechanism

Summary
Calcaneus fracture comprises 1–2% of all fractures and about 60% of those affect-
ing the foot, with approximately 75% as intra-articular fractures. Fractures of the
calcaneus are typically produced by axial compressive force yet relevant research
using cadavers demonstrated variations in experimental design and outcome.
Biomechanical tolerance of calcaneus towards axial collision impact also remains
unclear. Finite element (FE) analysis provides a versatile platform to estimate the
internal features of the calcaneus in a controlled environment. In this study, a com-
prehensive FE analysis was adopted to evaluate the influence of axial impact on the
risk of calcaneal fractures. An impact at 5.0 m/s induced a maximum stress (von
Mises) of 3.21 MPa and 2.41 MPa, respectively, for the calcaneus and talus trabecu-
lar, in addition to maximum shear stress (Tresca) of 3.46 and 2.55 MPa.
Approximately one-fifth of the volume surpassed the yielding point of compressive
stress and more than 80% exceeded that of the shear stress. These volumes were
centered at the talocalcaneal articulation and the inferior calcaneal tuberosity that
resembled common sites of fracture. This study can provide insights into injury
prevention and fracture management for high energy trauma.

4.1 Background

Calcaneus plays an important role in the foot by its unique morphology and its vari-
ous connections to other soft tissue attachment. It sustains the pulling force of the
plantar fascia, tendon, and ligaments during weight-bearing and forming a tenseg-
rity structure to facilitate the stability of the longitudinal arch and lateral column of
250 D. W.-C. Wong et al.

the foot [80]. Besides, calcaneus transmits majority of the body weight to the ground
and acts as a strong lever for the greatest plantarflexor of the foot during propulsion.
Calcaneus is the most common fracture site of the hindfoot, and the consequence
could be devastating. Calcaneal fractures occur during the high-energy events, such
as a car crash or a fall from height. The annual incidence was 11.5 in every 100,000
population and males had a 2.4 times higher occurrence than females [81]. In males,
the annual incidence was 16.5 in every 100,000 population, with a peak incidence
of 21.6 in the age group 20–29. In females, the overall incidence was 6.26, with a
more evenly distributed rate across the age cohorts and showing a gradual increase
towards the post-menopause.
Calcaneal fracture is difficult to treat and requires a lengthy recovery period.
Treatment involves both conservative and surgical interventions to reconstruct the
normal anatomy of the heel and restore mobility so that patients can return to nor-
mal activity [82]. But even with appropriate treatment, some fractures may result in
long-term complications, such as pain, swelling, loss of motion, and arthritis. Many
complications can be prevented and treated with the considerations of biomechanics
during surgical planning.

4.2 Biomechanical Research of Calcaneal Fractures

The ankle joint that encompassed the calcaneus and talus stands close to the load
line. Therefore, the calcaneus is more vulnerable to high axial compressive force
that leads to calcaneal fracture [83, 84]. From the biomechanical point of perspec-
tive, it is worth knowing the detailed mechanism of the fracture, while relevant
studies examined the influence of collision impact during an accident and the toler-
ance of the foot and ankle [83]. The fracture was induced to cadaveric specimens
with a prescribed impact velocity or energy [85], while some mimicked a pedal
impact using different pre-dorsiflexed ankle position, as well as different impact
forces and velocities [86–89].
Among hindfoot fracture, calcaneus was one of the most frequent sites of injury,
followed by talus and ankle fracture [84]. Despite, cadaveric studies in support to
this fact reported mixed results probably due to the variation in research protocols.
One study envisaged an extremely high impact velocity at 12 m/s to simulate a
pedal impact upon a landmine explosion on the vehicle [87]. Different loading
profiles were also considered in quasi-static scenarios [88]. Even though within a
single study, the reports of fracturing load on different specimens can range from
3.7 to 8.3 kN [84].
Computational simulation provides an alternative to evaluate the potential of cal-
caneal fracture upon impact otherwise difficult to be conducted ethically using
physical experiments [90]. The advantage of the finite element (FE) method included
the assessment of internal biomechanical environment of complex structures in
well-controlled conditions which support different designs and clinical applications
[91–94]. Previous studies had also utilized dynamic analyses in applications such as
10 Biomechanics of Foot and Ankle 251

car crash, landing, and running [2, 3, 95]. A pedal impact on the forefoot was also
simulated using a foot-shank model complex by Shin et al. and his colleagues [96].
The aim of this research was to study how different impact velocity attenuate the
stress of the heel and thus the risk of fracture by means of FE analysis. Prior to the
dynamic simulation, we constructed an anatomically detailed FE model of the foot
and ankle complex and performed a validation. The outcome measure of the simula-
tion included the reaction forces and the volume fraction of the yielding bone upon
different impact velocities.

4.3 Mechanism of Calcaneal Fracture

4.3.1 Model Reconstruction

We recruited a healthy female (age 28; height 165 cm; body mass 54 kg) to partici-
pate in the study. She did not reported any musculoskeletal pain, disorder or previ-
ous foot surgeries. The coronal magnetic resonance (MR) images of the right foot
was scanned using A 3.0-T scanner (TrioTim, Siemens Medical Solutions, Erlangen,
Germany) at neutral position and under no weight-bearing. The clinical images
were processed in an image segmentation software (Mimics 10, Materialise, Leuven,
Belgium) where 30 bones and the encapsulated tissue were segmented and further
optimized in another software (Rapidfrom XOR2, INUS technology Ltd., Seoul,
Korea). The calcaneus and talus bones were further segmented into the cortical
layer and the trabecular core according to the settings of Sabry et al. [97]. Since the
cartilage was difficult to identify in the clinical images, we simplified the layer
geometry into a nonlinear contact stiffness [65] along with a frictionless behavior
[98]. The ligaments, tendons, and fascia were constructed using trusses, surfaces,
and connectors jointing the insertion points on the constructed osseous geometry
which was further confirmed by anatomy expert. The model was an extension to our
previous work in which the validation process using both plantar pressure measure-
ment and cadavers, and the mesh convergence test were conducted [99]. The recon-
structed finite element model of the foot and ankle complex is shown in Fig. 10.19.

4.3.2 Material Properties

The material properties of the model parts were all sourced from literature as
shown. The calcaneus and talus were segmented into trabecular and cortical core
and assumed linearly elastic with a Young’s modulus of 0.4 MPa and 17 GPa, and
the Poisson’s ratio of 0.3 [100] while that of the other bones without segmentation
were assigned 7.3 GPa [40]. Hyperelastic material property was assigned to the
encapsulated soft tissue and skin using the constitutive equation of the second
order polynomial strain energy potential and first-order Ogden model, respectively
[41, 101]. The suggested average elasticity of rearfoot ligament from literature
252 D. W.-C. Wong et al.

Side view

Trabecular Core
Cortical Layer Fixed end

Achilles tendon
force
Plantar Fascia
Retinaculum

Encapsulated
soft tissue

Foam plate

Rigid plate

Impactor

Top view

Fig. 10.19 Finite element model of the foot and ankle complex. Finite element model of the foot
and ankle complex showing the top and side view of the parts geometry and demonstrating the
boundary and load conditions used in the simulation. (Reprinted from PlosOne, Wong et al., Finite
Element Analysis of Foot and Ankle Impact Injury: Risk Evaluation of Calcaneus and Talus
Fracture, e0154435 (2016), under CC-BY)

was assigned to our model with a value of 264.8 MPa [42, 102]. The forefoot liga-
ments were assumed as truss and assigned with a cross-sectional area of 18.4 mm2
[63], while the other ligaments modelled with shell surface have a thickness of
1.5 mm [43, 98]. The footplate was regarded as a 19-mm thick foam padding with
a higher elastic modulus (15 MPa) sticking on top of another plate with rigid defi-
nition [84].

4.3.3 Boundary and Loading Conditions

The simulation was carried out using commercially available finite element package
(Abaqus 6.11, Dassault Systèmes, RI, USA). The coefficient of friction bounded by
the encapsulated soft tissue and the ground plate was set to 0.6 [47] and the bones
were tied to the encapsulated soft tissue.
Firstly, two sets of simulations were conducted for model validation which
attempted to resemble the two sets of conditions in a cadaveric study [84].
According to the study protocol. The encapsulated bulk tissue and the proximal end
of tibial and fibular were encastré. As shown in Fig. 10.22, a foot pedal was driven
by an impact plate striking at 5.0 m/s such that the pedal would eventually meet the
10 Biomechanics of Foot and Ankle 253

plantar foot surface [84]. The mass of the impactor was assigned 7 kg while that of
the foot pedal was 4.5 kg and comprised one deformable and one rigid layer [86].
On the other hand, a vertical ground reaction force resembling half body weight of
a 54 kg person was applied on the pedal in superior direction once the foot came
into contact. The second load case for validation presented the same settings as the
first load case, except that the Achilles tendon would be loaded 1940 N. Immediately
after the simulation for validation, a parametric analysis with different impact
velocities from 2.0 to 7.0 m/s would be conducted based on the aforementioned
boundary and loading conditions for validation.

4.3.4 Data Analysis

Ground reaction force (GRF; as computed by the contact between the plantar foot
and pedal) and tibial reaction force (TRF) would be evaluated on the two scenarios
(i.e., with and without Achilles tendon load). TRF is the predicted reaction force to
maintain the fixture of the proximal tibial end.
By varying the impact velocity at 1.0 m/s interval from 2.0 to 7.0 m/s, we inves-
tigated the influence on GRF, TRF, as well as the maximum von Mises stress and
shear (Tresca) stress of the calcaneal and talar trabecular core. The volume fraction
of bone exceeding yield in compression and shear would be regarded as the risk
indicator for bone fracture. The compressive and shear yield was 1.8 MPa and
0.79 MPa, respectively [103, 104].

4.4 Biomechanical Evaluation of Impact Injury

on the Calcaneus
4.4.1 Model Validation

Figure 10.20 illustrates the GRF and TRF under impact with and without Achilles
tendon load and compared the outcome between our FE predictions and existing
study [84]. Regarding GRF, the differences between prediction and experiment find-
ings were approximately 10% under both the conditions with and without Achilles
tendon load. FE analysis found that the GRFs were 7400 and 6000 N with and without
Achilles tendon load conditions. Besides, the differences of TRF between simulation
and experiment were relatively prominent (27.5%) under the condition with Achilles
tendon, while the difference (600 N) was less without the Achilles tendon load.

4.4.2 Ground Reaction Force and the Tibial Reaction Force

Figure 10.21 suggests that an increase in impact velocity resulted in increases in

both GRF and TRF, while the slope of increase for GRF was larger. The GRF was
nearly two times than TRF in baseline, and they reached 11.53 kN and 7.78 kN,
254 D. W.-C. Wong et al.

Finite Element Prediction Experiment Result from Funk et al., 2002

12

10

8
Force (kN)

2
n=6 n=6 n=7 n=7
0
GRF TRF GRF TRF
Impact with
Pure Impact Achilles Tendon Loaded

Fig. 10.20 Validation of finite element model by comparing the prediction results to existing lit-
erature. Comparison of finite element prediction and cadaveric experiment results from Funk et al.
[84] on the ground reaction force (GRF) and tibial reaction force (TRF) under pure impact and
impact with Achilles tendon loading. (Reprinted from PlosOne, Wong et al., Finite Element
Analysis of Foot and Ankle Impact Injury: Risk Evaluation of Calcaneus and Talus Fracture,
e0154435 (2016), under CC-BY)

14

12

10
Force (kN)

0
2.0 3.0 4.0 5.0 6.0 7.0
Impact Velocity (m/s)

GRF TRF

Fig. 10.21 Ground reaction force (GRF) and tibial reaction force (TRF) under different impact
velocity (2.0–7.0 m/s). (Reprinted from PlosOne, Wong et al., Finite Element Analysis of Foot and
Ankle Impact Injury: Risk Evaluation of Calcaneus and Talus Fracture, e0154435 (2016),
under CC-BY)
10 Biomechanics of Foot and Ankle 255

a b
Cortical layer

Fig. 10.22 Von Mises stress of calcaneus and talus. (a) Cross section view of von Mises stress of
the calcaneus and talus at 5.0 m/s impact velocity. Orange arrows indicate compressive stress.
Cyan arrows indicate tensile stress. (b) X-ray of a typical patient with a compressive fracture of the
calcaneus. Arrows indicate regions of fractures. (Reprinted from PlosOne, Wong et al., Finite
Element Analysis of Foot and Ankle Impact Injury: Risk Evaluation of Calcaneus and Talus
Fracture, e0154435 (2016), under CC-BY)

respectively, at the highest impact velocity. Their differences ranged from 33% to
47% in the study range of impact velocities.

4.4.3 Stress and Tresca

Figure 10.22a displays the von Mises stress of the calcaneus and talus. In addition,
as shown in Figure 10.22b, the fracture sites of one typical patient presented similar
pattern to that of the location of the peak stress. Figures 10.24 and 10.25 suggested
that the increase of impact velocity resulted in the increase of both the maximum
von Mises stress and Tresca stress. The Tresca stress was 7% higher than the maxi-
mum von Mises stress at 2.0 m/s impact and the difference was enlarged with
increasing impact velocity. At 7.0 m/s impact velocity, the maximum von Mises
stress was 5.06 MPa compared to 5.47 MPa of Tresca stress.
Figures 10.23 and 10.24 illustrates the volume fraction of the trabecular bone of
calcaneus that was higher than the yielding point. Interestingly, the yielding was dom-
inant by shear stress. Nearly 80% of the bone experienced yielding at 4.0 m/s and
nearly total fraction exceeded shear yield at 7.0 m/s. The trabecular bone experienced
less yield and only two-third of the volume exceeded compressive yield at 7.0 m/s.
The volume of trabecular calcaneus that exceeded yield is presented in Fig. 10.24.
The trabecular calcaneus underwent shear yielding predominantly compared to
compressive yield. The volume of bone with shear yielding increased considerably
256 D. W.-C. Wong et al.

a Calcaneus Trabecular Impact Velocity (m/s)

Von Mises stress

2.0 3.0 4.0 5.0 6.0 7.0

Tresca stress

(MPa)
0.00 0.25 0.50 0.75 1.00 1.25 1.50 1.75 2.00 2.25 2.50 2.75 3.00
b Talus Trabecular
Von Mises stress
Tresca stress

(MPa)
0.00 0.25 0.50 0.75 1.00 1.25 1.50 1.75 2.00 2.25 2.50 2.75 3.00

Fig. 10.23 Von Mises and Tresca stresses of the (a) calcaneus trabecular and (b) talus trabecular
at different impact velocities. (Reprinted from PlosOne, Wong et al., Finite Element Analysis of
Foot and Ankle Impact Injury: Risk Evaluation of Calcaneus and Talus Fracture, e0154435 (2016),
under CC-BY)

from 36.2% at 3.0 m/s impact to 79.7% at 4.0 m/s. Nearly all trabecular bone of the
calcaneus exceeded the yielding point of shear at 7.0 m/s impact. The trabecular
bone that exceeded the compressive strength was relatively mild. About one-fifth
and two-thirds of the volume reached the compressive yield at 5.0 m/s and 7.0 m/s
impact, respectively (Fig. 10.24).
The maximum stress and Tresca of trabecular talus are demonstrated in
Figs. 10.23 and 10.25. The line of shear stress was consistently larger than that of
the von Mises stress, while both parameters increased with increasing impact veloc-
ity. The stresses were 0.48 and 0.55 MPa for the maximum von Mises and Tresca at
2.0 m/s impact and were increased to 3.68 and 3.90 MPa, respectively, at 7.0 m/s.
Nearly one-fifth of the bone volume experienced a compressive yield which was
then increased to half from 5.0 to 7.0 m/s.
Figure 10.23 shows that both the peak of von Mises stress and shear (Tresca)
were located at the inferior calcaneal tuberosity and talus articulation, which was
generally agreeable with the findings of cadaveric study and common fracture sites
[84, 87]. The stress concentration at the posterior talocalcaneal articulation, as
well as the superior side of the talar trochlea suggested that talus was also suscep-
tible to fracture during compressive impact [87]. Lateral malleolar articulation and
10 Biomechanics of Foot and Ankle 257

6 100.0%
90.0%

% Volume of trabecular bone

5
80.0%
70.0%
4
Stress (MPa)

60.0%
3 50.0%
40.0%
2
30.0%
20.0%
1
10.0%
0 0.0%
2 3 4 5 6 7
Impact velocity (m/s)

Volume of trabecular bone exceeded compressive yielding stress

Volume of trabecular bone exceeded shear yielding stress
Maximum von Mises stress
Maximum Tresca stress

Fig. 10.24 Maximum von Mises and Tresca stress with yielding volume of trabecular calcaneus
against impact velocity. (Reprinted from PlosOne, Wong et al., Finite Element Analysis of Foot and
Ankle Impact Injury: Risk Evaluation of Calcaneus and Talus Fracture, e0154435 (2016), under CC-BY)

6 100.0%
90.0%
% Volume of trabecular bone
5
80.0%
70.0%
Stress (MPa)

4
60.0%
3 50.0%
40.0%
2
30.0%
20.0%
1
10.0%
0 0.0%
2 3 4 5 6 7
Impact velocity (m/s)

Volume of trabecular bone exceeded compressive yielding stress

Volume of trabecular bone exceeded shear yielding stress
Maximum von Mises stress
Maximum Tresca stress

Fig. 10.25 Maximum von Mises and Tresca stress with yielding volume of trabecular talus against
impact velocity. (Reprinted from PlosOne, Wong et al., Finite Element Analysis of Foot and Ankle
Impact Injury: Risk Evaluation of Calcaneus and Talus Fracture, e0154435 (2016), under CC-BY)
258 D. W.-C. Wong et al.

talocalcaneal articulation fracture could be followed by the calcaneal fracture and

displaced talus. The volume of yielding trabecular bone of the calcaneus and talus
was similar in both compression and shear, despite that the maximum stress of the
talus was smaller. The material was assumed linearly elastic in the simulation.
Therefore, the prediction may overestimate the risk of fracture. It shall be improved
with elasto-plastic behavior [105].

4.5 Conclusion

An axial compressive impact (5.0 m/s) induced yielding to the trabecular bone of
the heel which predisposes potential fracture. Our prediction showed that the frac-
ture could be dominant by shear failure and compounded by compression. Future
study shall consider the sensitivity of different loading patterns on fracture which
could provide additional insights to design measures for injury prevention and inter-
vention for fracture management.
In the future, this computational platform can investigate the relationship between
different loading modes and fracture pattern/mechanism that could support design
for the prevention of injury, as well as management of the fracture.

Acknowledgments The work of this chapter was supported by the Key R&D Program granted by
the Ministry of Science and Technology of China (2018YFB1107000), NSFC granted by the
National Natural Science Foundation of China (11732015), and General Research Fund granted by
the Hong Kong Research Grant Council (PolyU152065/17E).

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Chapter 11
Biomechanics of Human Motion

Rongshan Cheng, Zhongzheng Wang, Cong Wang, Fuping Li,

Yifei Yao, Yan Yu, and Tsung-Yuan Tsai

Abstract In contemporary orthopedics, biomechanics of human motion has come

to reflect the investigation of the joint’s mechanical properties throughout joint
motion. This involves the stresses in the joint throughout motion, the limits of and
to motion, and the interaction between these two during joint function. This chapter
will discuss these properties with regard to each joint. As such, an appreciation and
understanding of joint kinematics, including the native joint, the diseased joint, and
the replaced joint is critical for the next stage of improvements in joint arthroplasty.
This chapter will outline and discuss the current understanding of how joint kine-
matics change throughout common pathologies as well as following joint
arthroplasty.

Keywords Hip joint · Knee joint · Spine joint · Kinematic · Common pathologies
Joint arthroplasty

1 Biomechanics of Hip Joint Motion

Studies on the hip biomechanics about hip movement or structure can be valuable
to underpin the understanding of joint function, etiology, and treatment of hip-
related diseases. Although ongoing endeavors to improve arthroplasty materials are
of value in increasing longevity of implants, component positioning and dynamic

R. Cheng · Z. Wang · C. Wang · Y. Yao · T.-Y. Tsai (*)

Clinical Translational R&D Center of 3D Printing Technology,
Department of Orthopaedic Surgery, Shanghai Ninth People’s Hospital,
Shanghai Jiao Tong University School of Medicine, School of Biomedical
Engineering, Shanghai Jiao Tong University, Shanghai, China
e-mail: tytsai@sjtu.edu.cn
F. Li · Y. Yu
Department of Spine Surgery, Tongji Hospital, Tongji University School of Medicine,
Shanghai, China

© Springer Nature Singapore Pte Ltd. 2020 265

C.-K. Cheng, S. L-Y. Woo (eds.), Frontiers in Orthopaedic Biomechanics,
https://doi.org/10.1007/978-981-15-3159-0_11
266 R. Cheng et al.

function have gained attention as significant factors affecting joint mobility, stabil-
ity, and survivorship after total hip arthroplasty. Thus, it is critical to understand and
appreciate hip kinematics on the normal hip, the diseased hip, and the replaced hip
for the improvement of hip disease treatment in orthopedics. The following sections
will discuss the structural factors contributing to the balance between hip stability
and mobility throughout the healthy status, common pathologies, as well as hip
arthroplasty follow-ups.

1.1 Fundamentals of Hip Joint Motion

The hip joint connects the femur and acetabulum of the pelvis. The hip joint plays
an important role to dynamically sustain and transmit the rotational moment, the
gravitational force of the body, and the ground reaction force of the lower extremi-
ties throughout an extensive range of motion. The hip joint has to maintain balance
and stability of the body in an erect position during standing. While moving, a com-
bination of both static and dynamic stabilizers helps to prevent joint dislocation and
to maintain mechanical efficiency.

1.1.1 Stability

The acetabulum results from the triradiate cartilage growth center of the pelvic
innominate bone at the union of the ilium, ischium, and pubic bones. Though the
acetabular cup appears to have a hemispherical shape, it is spherical only in the
upper 1/3rd or in the dome, allowing the required maximal distribution of force in
areas for weight-bearing during upright stance. As mentioned above, the inclined
acetabulum gives an acetabular index (slope of the acetabulum on an anterior-pos-
terior (AP) radiograph) an average of 38° in males and 40° in females allowing for
increased abduction but decreased adduction (Fig. 11.1a) [1]. The osseous structure
on the femoral side of the joint also contributes to joint stability during static or
dynamic loading. The femoral head is semispherical in shape, ranging from hemi-
spherical to 2/3rds of a full sphere. The head quickly tapers into the femoral neck
that connects to the body of the femur. The distance between the center of the femo-
ral head and the anatomic axis of the femur represents the “head-neck offset” and is
directly associated with the moment arm and efficiency of the hip abductors. Similar
to the anteversion of the acetabulum, the femoral head/neck is anteverted relative to
the anatomic axis by approximately 10–20° in adults (Fig. 11.1b).
Though the spherical acetabular design imparts a high degree of stability and
additional ligamentous support to the hip joint, acting as checkrein to all 6 degrees
of freedom during hip motion, the extra-articular ligaments consist of band-like
thickenings of the capsule that allow for hip motion within a certain range of arc.
Cadaveric studies have demonstrated some variability and controversy regarding
the exact nature and discrete nomenclature of these bands [1]. However, it is gener-
11 Biomechanics of Human Motion 267

a b

Femoral anteversion
angle

Anterior/posterior axis
Inclination
Planar anteversion
True anteversion

Fig. 11.1 Pelvic and femoral version. (a) True acetabular anteversion is the angle between the
anterior/posterior axis and the interception line of transverse plane and the cup opening plane.
Planar anteversion is the complement to the angle between the normal axis of the cup opening
plane and the anterior/posterior axis. Inclination is the angle of the cup rotating along the anterior/
posterior axis with respect to the medial/lateral axis. The anterior/posterior axis is perpendicular to
the frontal pelvic plane formed by two ASIS and pubic symphysis. (b) Femoral anteversion is the
inclination of the femoral neck axis with reference to the retrocondylar line. With the long axis
determined by the best-fit cylinder of the femoral shaft, the neck axis is defined as the centerline of
the femoral head and neck model. The retrocondylar line is determined from the postfemoral con-
dyles (Reprinted with permission from Wolters Kluwer Health)

ally described that the capsule has four extra-capsular ligaments consisting of lon-
gitudinal fibers of the iliofemoral, the ischiofemoral, the pubofemoral ligaments as
well as the annular fibers of the zona orbicularis. These ligaments play a crucial role
in different joint positions during hip motion, which is supported by the change in
motion after removal of the ligaments.
Dynamic stabilizers of the hip joint include flexors, extensors, internal and exter-
nal rotators, abductors, and adductors. Similar to the rotator cuff stabilizing shoul-
der, antagonist function from dynamic stabilizers help to maintain the femoral head
within the acetabulum. However, the interactions among muscle groups in the hip
are much less well understood compared to that among the muscles of the rotator
cup. Conceptually, it is assumed that antagonistic muscle groups help to counter
each other’s motion to lead to a hip rotation with minimal translation, as mentioned
above. For example, with gluteus minimus and medius function during hip abduc-
tion, the adductor complex eccentrically contracts to help translate the femoral head
back into the center of the acetabulum, thereby maintaining concentric and primar-
ily rotatory motion. However, since the insertion points on hip abductors and
the abductor complex are not directly located opposite on the femur, the resulting
268 R. Cheng et al.

difference in lever arms and moments results in a more complex intermuscular rela-
tionship than, say, that of the subscapularis and infraspinatus. Moreover, additional
dynamic stabilizers also participate in direct stabilization of the hip joint, acting as
physical blocks to femoral head escape. In particular, muscles that pass directly over
or even attach to the hip capsule may physically confine the translation of the femo-
ral head with applied loads.

1.1.2 Mobility

Motions of the lower extremities mostly require a combination of both translational

and rotational changes in the hip joint. The rotation is the primary biomechanical
degree of freedom in the hip motion, while the exception is flexion/extension in
neutral abduction and external rotation. In this position and within this arc of
motion, the centers of the femoral head and acetabulum are maintained in an over-
lapping position by balanced forces from hip flexors and adductors. Outside of this
arc of motion, an associated translation due to rotation of the femoral head must be
countered by opposing static or dynamic stabilizers to maintain a stable joint [2].
Experimental results for the normal range of motion of the native hip are pro-
vided in Table 11.1. The range of motion in the hip during life’s activities has large
variance between patients. Nevertheless, a minimum range of motion is required for
daily activities such as sitting, standing, climbing stairs or walking. Thus, the evalu-
ation of the range of motion can improve the assessment of functional limitations.
In general, Heller et al. demonstrated that the hip requires a smaller arc of motion
with a flexion/extension arc of 40°, abduction/adduction arc of 10°, and 10° rota-
tional arc during walking without assistance on level ground, compared to other
activities such as uneven surface ambulation, running, or raising from a chair which
require a much greater range of motion [3]. It is the osseous structures that deter-
mine the absolute limits of the joint motion while the soft tissue components deter-
mine the in vivo range of motion during activities.
The hip joint is constrained by the mechanical boundaries of the bones compos-
ing the joint so that there is osseous impingement at the motion extremes. The osse-
ous anatomy may change in pathological situations (i.e., osteoarthritis, trauma,
osteonecrosis), while it is the soft tissues (ligaments, muscles, labrum, etc.) that
determine the in vivo range of motion. Soft tissues either restrain or block a motion
by interposition and impingement. Turley et al. [5] investigated this phenomenon by
comparing the ranges of motion in the hips of subjects through a series of daily liv-
ing activities. They found a significantly decreased range of functional motion as
Table 11.1 Normal motion ranges for the adult native hip at rest and observed during level
surface gait
Normal range Level surface gait range
Adduction/abduction (x-axis) 25°/50° 5°/5°
Internal/external rotation (y-axis) 90°/70° 5°/5°
Flexion/extension (z-axis) 140°/30° 30°/10°
Data from Heller et al. [3, 4]
11 Biomechanics of Human Motion 269

compared to the osseous range of motion particularly in extension and flexion with
adduction (Fig. 11.2). Conversely, Turley et al. [5] found that osseous impingement
occurred in vivo at the extremes of adduction in an upright stance as well as abduc-
tion at 90 degrees of flexion corresponding to impingement of the lesser trochanter

Healthy range of motion benchmark 150 Flexion (degrees)

CT patient range of motion

Impinged motion

100

50

90 50 50 90
Abduction (degrees) Abduction (degrees)

50

Extension (degrees)

Fig. 11.2 The difference in the hip range of motion is presented between the predicted and real-
ized motions. Flexion/extension and abduction/adduction motion differences between predicted
models of motion based on osseous factors versus motion observed from the in vivo measure-
ments. The yellow area corresponds to a range of motion observed in vivo from patients during a
series of motions involved in activities of daily living. Purple areas correspond to the predicted
range of hip motion based on osseous factors alone. Red areas correspond to in vivo hip motions
where osseous impingement limits further motion (Reprinted with permission from Springer Nature)
270 R. Cheng et al.

on the pubis and the greater trochanter on the lateral acetabular rim. This is particu-
larly salient with regard to total hip replacement because an implant or osseous
impingement versus soft tissue impingement presumably puts the patient at higher
risk of dislocation and earlier wear/failure.

1.1.3 ROM and Gait

The human gait cycle has long been studied using high-speed cameras. Observational
studies on gait analysis were conducted, particularly in injured or weakened patients.
We will discuss the hip functions in the gait cycle. The human gait comprises two
main phases, stance phase corresponding to 60% of gait and swing phase, making
up the rest 40%. The simplification of the stride pattern observed in humans serves
as a blueprint for analyzing the position of the hip and the points at which static and
dynamic factors are involved throughout the gait cycle.
The main role of the hip is to support the weight of the body, transferring this
weight force through the pelvis and into the lower extremities throughout the gait
cycle. However, the hip must transfer force through a dynamic range, depending on
the combination of static and dynamic stabilizers not only to maintain concentric
alignment of the joint but also to facilitate the transition in the gait cycle and locomo-
tion. At the beginning of the gait cycle, the hip is flexed, slightly externally rotated,
and in neutral adduction centering the femoral head in the acetabulum, which allows
for a large degree of the femoral head coverage. After heel strike, the hip extends
when the gait progresses towards toe-off. Just before toe-off, the hip begins to flex
and abduct to allow for the leg to swing through during the swing phase and clear the
ground. This meets with internal rotation through the acceleration phase followed
again by external rotation at the end of swing phase to maintain a centered femoral
head as the leg passes from the behind the body to the front of the body.
At any given point of the gait cycle, the forces on the hip are the sum of both
moment forces produced by hip musculature and loading forces distributed from the
head, arms, and thorax. The net sum of these forces is the total amount of force
across the joint, also known as joint reactive force. The direction and magnitude of
the hip joint reactive force vector change through the gait cycle, ranging from 3.5 to
5 times the subject’s total body weight [6]. It is the interplay between concentrically
contracting muscles and dynamic and static stabilizers that are dramatically altered
in some pathologic conditions of the hip and following the surgical solutions.

1.2 In Vivo Hip Kinematics

Imaging modalities and diagnostic criteria of hip pathology nowadays are frequently
based on static findings (i.e., radiographs, lab values). Still, it is important to note
that all pathologies of the hip involve dynamic scenarios and that disease develop-
ment cannot occur without eventual effects on motion. Moreover, past and current
innovations for THA have only focused on improving fixation methods and bearing
11 Biomechanics of Human Motion 271

surfaces, so that the current challenges with the contemporary THA involve in vivo
dynamic phenomena such as edge loading, impingement, and dislocation. Thus, a
kinematic understanding of the hip is critical for evaluating the etiology of hip
pathology as well as improving the restoration of hip function through arthroplasty.

1.2.1 Local Coordinate System

The hip is a synarthrodial spheroidal joint comprising a near-spherical femoral head

and a complementary acetabular cup resulting in a soild and stable multiaxial ball-
and-socket synovial joint. In the discussion of the kinematics and biomechanics of the
hip joint, it is important to establish the planes of motion in which the joint moves.
The hip has motion with 6 degrees of freedom, which means it can rotate and translate
along three axes perpendicular to each other. The rotational axes are described in
terms of abduction/adduction or rotation along the anterior/posterior axis (x-axis),
internal/external rotation or rotation along the cephalad/caudal axis (y-axis), and flex-
ion/extension or rotation along the medial/lateral axis (z-axis) (Fig. 11.3) [7].

Fig. 11.3 The 3D image Sag

ittal
demonstrates anatomic plan
e
planes and the axes of
motion about the hip.
Rotation about the x-axis is l plane
Fronta
shown in red. It
corresponds to abduction/
adduction, rotation about Transverse
the y-axis is shown in plane
green and corresponds to
internal/external rotation,
and rotation about the
z-axis is shown in blue,
corresponding to flexion/
extension. The red, green,
and blue femurs of the
right hip show examples of
abduction, internal
rotation, and flexion,
respectively (Reprinted
with permission from
Wolters Kluwer Health)
272 R. Cheng et al.

Similarly, translational motion is described in terms of translation along each of

these axes (i.e., anterior translation, lateral translation). Though the motion of the
hip occurs largely as the rotation of the femoral head within the acetabulum, it rep-
resents the combination of both rotational motions and balanced translations.
Consequently, throughout the hip’s arc of motion, the main rotational components
with slight translational motions are all coupled through a series of static and
dynamic stabilizers.
With regard to the constraints of motion and anatomy of the pelvis, the acetabu-
lar cup has both inclination and anteversion, meaning that the cup of the right hip is
both negatively rotated about the x-axis (abducted) and positively rotated, or ante-
verted, about the z-axis (flexed). The degree of inclination and anteversion has clas-
sically been determined with regard to the body’s axis and ranging between 35–45°
of inclination and 15–25° of anteversion (flexion) during upright stance. However,
it is important to note that the orientation of the pelvis changes with various posi-
tions and throughout the gait cycle [8]. As a result, depending on the pelvic tilt, the
acetabulum may appear to be more or less anteverted or inclined. To address this,
the International Society of Biomechanics recommended a standardized pelvic
coordinate system [7].

1.2.2 Kinematic Measurement Methods

Over the past decade, the development and implementation of 2D/3D registration
techniques have been employed to address the growing need for higher accuracy in
human kinematic and implant wear measurements. These techniques evaluate a
single fluoroscopic image of the hip using a stored 3D model of the same prosthetic
implant to match the orientation of components to the silhouette on fluoroscopy.
The position of the components can be reconstructed by doing so. Through evaluat-
ing a series of sequential images, the implant motions and relationship between
implants and bones can be evaluated. These methods have provided initial advance-
ments to our current understanding of THA motion in vivo, particularly with regard
to femoral head/cup separation during gait and abduction activities, intraoperative
stability assessment, and position during extremes of motion [9–12]. However, the
accuracy of such methods has been significantly inferior to other methods of mea-
surement, namely RSA, thus limiting the use for further kinematic evaluation, par-
ticularly during motion [12].
Most recently, methods that employ the combination of orthogonal fluoroscopic
images, as well as 2D/3D registration techniques, have been developed, known as
dual fluoroscopic imaging system (DFIS) [13]. This technique involves an initial
CT image of the patient’s hip that is subsequently used to generate a 3D adaptive
global surface model of the femur, pelvis, and any implanted components [14, 15].
As a result, a patient-specific model of osseous geometry is generated and allows
for more accurate measurements than previous techniques that relied on general-
ized implant models (Fig. 11.4). Patients are then imaged at a rate of 30 Hz through-
11 Biomechanics of Human Motion 273

a b

X-ray Source A X-ray Source B

Fig. 11.4 Dual fluoroscopic imaging system imaging registration. (a) Experimental setup of mea-
surement of a subject walking on a treadmill using DFIS. (b) An example of a total hip arthroplasty
registered to images in the computer-simulated dual fluoroscopic imaging system (DFIS).
(Redrawn from Tsai, T.-Y., J.-S. Li, et al. A novel dual fluoroscopic imaging method for determina-
tion of THA kinematics: in-vitro and in-vivo study. Journal of biomechanics, 2013. 46(7):
1300–1304)

out the activity of interest, for example, gait, with two fluoroscopic images
positioned orthogonally to one another (Fig. 11.4a). The fluoroscopes obtain
images synchronously, producing a tandem view of the hip from orthogonal posi-
tions and reducing the artifacts from parallax and beam scatter otherwise experi-
enced by single beam methods [13]. These images are then processed in conjunction
with the 3D CT images, which virtually position the 3D models to match the exact
positions of the patient’s pelvis, femur, and implants observed in the orthogonal
X-ray images (Fig. 11.4b). All images in the series from fluoroscopy are analyzed
in the way mentioned above to generate a series of 3D images that depict the exact
motion of the patient’s pelvis, femur, and implants during gait. This provides solid
information about the hip motion in all 6 degrees of freedom as well as allows for
predictions of angular momentum, force, and even wear characteristics. DFIS has
provided the exciting potential for more accurately measuring small perturbations
in components separation and also in vivo motion trajectory without the need for
invasive markers as in RSA [16]. The accuracy of DFIS is comparable to RSA and
able to measure translational and rotational changes with a measurement error of
0.2 ± 0.3 mm and 0.2 ± 0.8°, respectively [17]. However, although DFIS is a non-
invasive tool, it does inherently increase radiation exposure beyond prior 2D/3D
registration or RSA techniques but remains on the order of 5–6 mSv with current
methods [16].
274 R. Cheng et al.

1.3 Hip Kinematics in Common Pathologies

The hip geometry and its kinematics represent the summation of complex interac-
tions between the static and dynamic stabilizers. The most common changes to this
function can be attributed to alterations in anatomy originating with the acetabular
shape and position (i.e., pincer lesion, DDH) or changes in the femoral head and
neck shapes (i.e., cam lesion, Perthes, SCFE, altered femoral version). Frequently
these changes are reciprocal, and both femoral and acetabular effects must be evalu-
ated, respectively. Though many of these changes originate in infancy or childhood,
the effects of these changes can often go unrecognized or even undiagnosed well
into adulthood. Consequently, the adult hip can represent the response to a lifetime’s
worth of altered hip kinematics that must be recognized and accounted for by the
arthroplasty surgeon.

1.3.1 Femoroacetabular Impingement and Labral Injury

The most common anatomic changes affecting native hip kinematics are cam and
pincer lesions. Cam lesions represent additional bony contours to the femoral head,
typically over the superior lateral base of the femoral head. The resulting loss in
overall head sphericity results in a functional decrease in the head-neck offset of the
hip [18]. As previously mentioned, this offset is critical for the hip range of motion
and results in a contracted arc of abduction. At the extremes of motion (i.e., flexion
and abduction), the flattened head-neck junction impinges on the acetabular labrum
and eventually osseous rim [19]. Known as femoroacetabular impingement (FAI),
the constant cycling of the labrum between the misshapen femoral head and acetab-
ulum results in accelerated wear and deterioration of the labrum. This cyclical dam-
age also results in consequent changes, including cysts, sclerosis, and microfracture,
in the underlying bone. Similarly, the pincer lesion represents an overgrowth of the
acetabular rim, particularly in the anterosuperior quadrant. The resulting functional
overcovering of the femoral head again can lead to a contracted arc of motion due
to impingement.
Regardless of the etiology of labral pathology, the loss of labral integrity results
in a breakdown of the articular seal and significantly increases the joint reactive
forces. Among other actions, the labrum acts as a gasket to seal the hip joint through-
out the motion. Upon loading, articular cartilage extrudes synovial fluid at a rate
determined by the adhesive and cohesive properties of the fluid and cartilage, the
pressure in the system, and the rate of loading [20]. The intact labrum allows the
pressure in the articular system to increase through a hydraulic effect providing a
transfer and dispersion of the applied force to the entire joint and joint fluid.
Consequently, loss of the labral seal results in a leak of the synovial fluid leading to
a significant decrease in the fluid pressure and causing increase in cartilage loading
rates, creep rates (i.e., extrusion of synovial fluid), and overall joint reactive forces
[21, 22]. Biomechanical modelings predict that the loss of labral integrity increases
11 Biomechanics of Human Motion 275

the contact stresses on the weight-bearing articular cartilage of the hip by up to 90%
[21]. Moreover, the loss of the hydraulic effect with labral pathology shifts the peak
pressures of the system laterally, resulting in an increase in overall joint reactive
force primarily over the lateral acetabular edge [21].

1.3.2 Total Hip Arthroplasty

As we continue to elicit more details about the kinematics of the native hip, how
arthroplasty or resurfacing alters the mechanics of the hip remains largely unknown
and controversial. Current arthroplasty techniques require not only substitution of
the natural hip mechanics for those interjected by artificial implants but also altera-
tions in much other static and even dynamic stabilizers of the hip. Dramatic changes
in both dynamic and static stabilizers result from the surgical approach for
THA. However, many of the same factors that can affect native hip function also
plague the total arthroplasty function. Factors such as femoral neck offset to prevent
impingement, over- and under-coverage of the femoral head by the acetabular com-
ponent to prevent escape and dislocation, and also soft tissue balancing to prevent
translation and edge loading are all even more critical factors regarding to total hip
arthroplasty.
The hip is critical for some parameters of the gait cycle and is important in deter-
mining stride length, leg progression, and single-leg stance stability. Previous inves-
tigations utilizing external skin markers to evaluate primarily gait efficiency and
cadence demonstrated significantly reduced gait velocities as well as stride lengths
following THA. Kyriazis and Rigas [23] demonstrated that among 20 females with
severe hip OA, gait velocity and stride lengths were significantly lower than healthy
age-matched controls both before and after THA using external markers and force
plate analysis. However, they not only found a significant improvement in these
metrics in patients post THA compared to pre THA, but there was continued
improvement such that at 8–10 years follow-up, gait velocity and stride length
approached but did not reach that of healthy controls. In a similar vein, Wykman
et al. [24] reported a significant improvement of overall gait velocity, stride length,
and duration of single-leg stance of the affected hip following THA compared to
preoperation. They made the further distinction that this improvement was most
pronounced in patients with bilateral hip involvement though this benefit was most
notably observed after the second hip was replaced. Together, these studies suggest
that after THA, the affected hip has a significantly increased range of motion lead-
ing to the overall increase in the duration of the gait cycle and overall mechanical
efficiency. However, after THA, the significant improvement providing more effi-
cient hip mechanics and lower energy expenditures perhaps never quite reaches that
of the age-matched native hip [25, 26].
Though these studies provide intriguing information about the gait alterations
following THA, they are limited in part by the methods of obtained data; namely
surface mounted markers. More recently, Tsai et al. [16] describe THA kinematics
with the use of DFIS, directly evaluating implant position throughout the gait cycle.
276 R. Cheng et al.

Initial findings demonstrate similar increases in maximum hip extension as well as

increases in overall hip abduction after THA [16]. Meanwhile, Tsai et al. [27] inves-
tigated the in vivo 3D kinematics of the hip in unilateral THA patients during gait.
Initial results demonstrated that there was 3D motion asymmetry of the hip and
pelvis in unilateral THA patients during gait (Fig. 11.5). Regardless, these studies
offer exciting new steps towards a better and more accurate depiction of how the
arthroplasty hip functions and how small changes in implant positioning or muscle
tensioning can affect wear and prosthetic life span.
As previously mentioned, the hip capsule and labral tissues play a critical role in
stabilizing the native hip throughout its arc of motion, namely with regard to transla-
tion as well as rotation by shear and compressive forces. Replacement causes inter-
ruption of the capsular components leading to the need for considerations of capsular
repair and postoperative motion restrictions. Perhaps one of the most dramatic proce-
dures is the resection of the hip labrum in order to ensure appropriate sizing and seat-
ing of the acetabular component. This excision also helps to prevent the interposition
of the labral and associated capsular tissues behind the prosthetic components or
during motion of the replaced hip. However, the lack of labral function eliminates the
gasket and hydraulic effects on the joint itself, thereby increasing joint reactive forces
and even increasing the translation of the components throughout motion. Though
dynamic stabilizers help to retain the femoral head particularly during gait, other
activities of daily living and hip motions can result in dramatic translation of the
femoral head and even put the joint at risk of dislocation. In vivo imaging studies have
demonstrated the separation of the femoral head component of THAs by as much as
0.5–1 mm particularly during activities that require extensive internal or external rota-
tion such as pivoting and shoe tying in asymptomatic patients [28]. Further investiga-
tions into this phenomenon have suggested that this translation results in increased
loading as the head returns from its displaced position in addition to increased soft
tissue stretch and risk for dislocation events at the extremes of displacement [10].
The orientation of hip arthroplasty components including the acetabular cup,
femoral neck length, femoral neck ankle head sizes, etc., also dramatically affect the
kinematics of the hip. With regard to kinematics, the placement and orientation of
implants help to determine the range of motion and overall stability of the joint. Soft
tissue impingement, restriction, and laxity as well as osseous impingement affect
the total range of motion and stability of the native hip. Similarly, these factors also
affect the hip motion following THA. Femoral head size is a critical component of
hip stability and motion following arthroplasty. Several comparisons of head size
and dislocation rate following THA have globally demonstrated that the larger the
femoral head, the greater the jump distance and the lower the risk of dislocation [29,
30]. Of course, hip motion requires static and dynamic stabilizers, and while femo-
ral head size is important, the role of soft tissue stabilizers cannot be underesti-
mated. Another critical component to THA motion is the orientation and position of
the acetabular components. Experimental modelings demonstrate that cup antever-
sion and inclination (abduction) relationship, as well as femoral anteversion, play an
interrelated balance between the range of motion and stability. D’Lima et al. [31]
demonstrated that in general 45–55° of acetabular abduction provides the optimal
 Hip Rotations Hip Translations Pelvic Rotations

1 10
Non-operated side
0
Operated side 0.5
0
-20 0
-10
-0.5

←ER/IR→ (º)
←M/L→ (mm)
←A/P→ Tilt (º)
-40 a d g
-1 -20
0 20 40 60 80 100 0 20 40 60 80 100 0 20 40 60 80 100
1 10
20
0.5 5
11 Biomechanics of Human Motion

10 0 0

-0.5 -5

←ER/IR→ (º)

←AB/AD→ (º)
0 b e h
-1 -10

←In/Out of Cup→ (mm)

0 20 40 60 80 100 0 20 40 60 80 100 0 20 40 60 80 100
60 1 10

40 0.5 5

0 0
20
-0.5 -5

←P/A→ (mm)

←EXT/FLEX→ (º)
←Lift/Drop→ (º)

0 c f i
-1 -10
0 20 40 60 80 100 0 20 40 60 80 100 0 20 40 60 80 100

Gait Cycle(%) Gait Cycle(%) Gait Cycle(%)

Fig. 11.5 Average and standard deviation of hip kinematics for the operated and nonoperated hips in unilateral THA patients during gait. Significant differ-
ences in hip rotations, hip translations, and pelvic A/P tilt were observed. (Redrawn from Tsai, T.-Y., J.-S. Li, et al. Does component alignment affect gait
symmetry in unilateral total hip arthroplasty patients? Clinical Biomechanics, 2015. 30(8): 802–807)
277
278 R. Cheng et al.

situation of the maximal range of motion with maximal stability. Tsai et al. [32]
demonstrated that an average 5.1° increase in the internal rotation was observed in
the implanted hip than the contralateral non-implanted hip and internal rotation was
significantly correlated with a linear combination of the increase of cup anteversion,
medial cup translation, and leg-lengthening.

2 Biomechanics of Knee Joint Motion

The knee joint comprises two distinctly separate joints/articulations, the tibiofemo-
ral (TF) joint and the patellofemoral (PF) joint. The main functions of the knee joint
are (1) to allow locomotion with (a) minimum energy requirements from the mus-
cles and (b) stability, accommodating for different terrains, and (2) to transmit,
absorb, and redistribute forces caused during the activities of daily life [33].

2.1 Fundamentals of Knee Joint Motion

2.1.1 The Tibiofemoral Joint Motion

The tibiofemoral joint motion is movement with 6 degrees of freedom (DOF), three
in rotation, and three in translation. The three degrees of freedom in rotation are
flexion–extension (F–E) in the sagittal plane (primary), varus–valgus (V–V) (or
adduction–abduction) in the frontal plane and internal–external (I–E) rotation in the
horizontal plane. The three degrees of freedom in translation are anterior–posterior
(A–P) movement, mediolateral (M–L) translation, and compression. The 6 DOF
movement could be described in a clinical joint coordinate system (Fig. 11.6) [34].
Full extension (i.e., zero-degree flexion) is usually defined when the long axis of the
tibia and femur are aligned in the sagittal plane [33].

Flexion–Extension

The F–E axis has a different definition from many researchers. Morrison assumed
that a fixed axis of rotation was coincident with the axis of rotation of the knee joint
in the position of full extension [35]. The line through the center of medial and lat-
eral femoral condyles are defined as the F–E axis. Some surgeons used the transepi-
condylar axis (TEA) as the F–E rotation axis in total knee arthroplasty (TKA).
Berger defined surgical TEA as a line connecting the sulcus of the medial epicon-
dyle and the lateral epicondylar prominence [36]. The angle between the surgical
TEA and the posterior condylar line is defined as the posterior condylar angle.
Another TEA definition is called clinical TEA. It is defined as a line connecting the
medial and lateral epicondylar prominence by Yoshioka [37].
11 Biomechanics of Human Motion 279

Joint
distraction
F-E

A-P
V-V

M-L

I-E

Fig. 11.6 The six DOF of TF joint motion expressed in a clinical joint coordinate system. M–L
translation and F–E occur along and about an epicondylar femoral axis. Joint distraction and (I–E)
rotation occur along and about a tibial long axis. A–P translation and V–V rotation occur along and
about a floating axis, which is perpendicular to both femoral epicondylar and tibial long axes
(Reprinted with permission from Elsevier: Masouros, S., A. Bull, and A. Amis, (i) Biomechanics
of the knee joint. Orthopaedics Trauma, 2010. 24(2):84–91)

Internal–External Rotation

Many studies have shown that the I–E rotation axis is located near the center of the
medial tibial plateau. Wang et al. used human knee joint specimens to study the
effect of flexion and rotation on the length patterns of the ligaments of the knee.
Their results showed that the I–E rotation axis was located slightly posterior to the
center of the medial plateau for mid-flexion angles (30°, 60°, 90°), but at 0 and 120°
flexion, this axis passed through the mid-point of the medial spine of tibial emi-
nence [38]. These results were in line with Shaw and Murray’s research experimen-
tally showing that the I-E rotation axis passes through the medial spine of the
intercondylar eminence [39].
280 R. Cheng et al.

Varus–Valgus

Varus–valgus occurs at about the center of the femoral condyles. Crowninshield

et al. found that abduction occurs at about the lateral condyle while adduction
occurs at about the medial condyle [40]. Based on their results, Pennock and Clark
chose the V–V axis which intersects the transepicondylar line at the mid-point
between the epicondyles and so that it bisects the angle between the projection of
the femoral condyles on the transverse plane [41].

2.1.2 The Patellofemoral Joint Motion

Patella is the largest sesamoid bone in the human body. It is embedded in quadriceps
tendon and its function is to increase the mechanical leverage of the quadriceps. At
full knee extension, the patella contacts femur at the distal end of the patella
(Fig. 11.7a). As the flexion angle increases, the patella engages into the femoral
trochlear groove and the contact area spreads across the width of the patella and
moves proximally (Fig. 11.7b) [34]. The increase of PF contact area with knee flex-
ion is a clever mechanism that controls the magnitude of stresses by spreading the
increasing PF joint load with knee flexion over a larger area.

a PF b
Q PF
PT
Q
PT
Q

Q
PF

PF PT

PT

Fig. 11.7 PF joint force at (a) extension and (b) 90° flexion, showing geometrically the increase
of PF joint force with flexion. (PT patellar tendon, Q quadriceps muscles, PF patellofemoral, TF
tibiofemoral) (Reprinted with permission from Elsevier: Masouros, S., A. Bull, and A. Amis, (i)
Biomechanics of the knee joint. Orthopaedics Trauma, 2010. 24(2): 84–91)
11 Biomechanics of Human Motion 281

2.1.3 Soft Tissue Balance

The soft tissues in the knee joint provide dynamic stability. The muscles stabilize
the joint according to the movement and provide stability of the joint. Ligaments
and meniscus provide passive stability. The ligament elongates as a response to
external force, and thus maintain the joint stability.
Two cruciate ligaments, anterior cruciate ligament (ACL) and posterior cruciate
ligament (PCL) are arranged in a crossed formation in the knee joint. The primary
function of ACL is to prevent excessive tibial anterior translation. The primal func-
tion of PCL is to restrain posterior tibial translation. Two cruciate ligaments act
together to control the A-P rolling and sliding of TF joint during F–E [42].
In the M–L direction, the two collateral ligaments stabilize the knee joint by
restraining the V–V and I–E rotation [34]. The medial collateral ligament (MCL) is
the primary restraint to valgus and internal tibial rotation [43]. The lateral collateral
ligament (LCL) is the primary restraint to varus angulation but slackens with knee
joint flexion, which reduces its restraining capability [44].
The main ligament in PFJ is medial patellofemoral ligament (MPFL). It acts as
the primary passive restraint to lateral patellar displacements and assists in control-
ling patellar motion, especially guiding the patella into the trochlear groove in early
knee flexion.

2.2 In Vivo Healthy Knee Kinematics

Gait analysis is based on an optical motion tracking system and is widely used in
investigating in vivo joint kinematics and kinetics. Gait cycle could be divided into
two phases, stance phase and swing phase. The stance phase is defined as the period
between heel strike and toe off. Swing phase is defined as the period between toe off
and next heel strike. In gait analysis, healthy knee joint motion features a large sag-
ittal plane range of motion (ROM), small rotation in the horizontal plane and frontal
plane. The knee joint kinematics of healthy adults is shown in Fig. 11.8 [45].
For F–E angles, there are two peaks in one gait cycle. The first peak is smaller
and in the mid-stance phase, which has a value of 20° flexion. The second peak is
larger and in the early stage of the stance phase, which has a value of 60° flexion.
In the frontal plane, knee joint movements involve both abduction and adduction.
During the stance phase, the knee joint undergoes abduction. After the start of the
swing phase, the knee joint transform to adduction. At the end of the swing phase,
the knee joint turns back to the abduction. Overall, the abduction/adduction angle is
small during the gait cycle.
In the horizontal plane, at the beginning of the stance phase, tibia has a slight
external rotation according to the femur. After heel strike, both femur and tibia
undergo internal rotation. The tibia has a faster speed of internal rotation. As a
result, the knee joint has an internal rotation in the stance phase. After the middle-­
stance phase, both femur and tibia undergo external rotation and keep external rotat-
ing until the middle-swing phase.
282 R. Cheng et al.

60

40
flexion/extension. deg.

f6

f5
20
f4
f3

f2

0
f1

–20

10

5
q1 q2
rotation.deg. abd/add. deg.

–5

10

Y2
0
Y1

–5
0 20 40 60 80 100
% of gait cycle

stance swing

Fig. 11.8 Chao et al. evaluated 148 subjects’ lower limb gait. All the subjects were allowed to
walk at their preferred speed and wore shoes [45] (Reprinted with permission from Elsevier: Chao,
E., R. Laughman, et al. Normative data of knee joint motion and ground reaction forces in adult
level walking. 1983. 16(3): 219–233)
11 Biomechanics of Human Motion 283

2.3 Knee Kinematics in Common Pathologies

2.3.1 Osteoarthritis and Total Knee Arthroplasty

Knee Osteoarthritis

Osteoarthritis (OA) is one of the most common sources of locomotor disability and
musculoskeletal pain worldwide, and the prevalence is as high as over 40% in older
adults [46]. Factors that may increase the risk of osteoarthritis include older age,
sex, obesity, joint injuries, and deformities. Accepted by most surgeons, knee OA
patients are classified into two categories: (1) idiopathic: those with no presently
known prior event or disease related to the OA; and (2) secondary: those with known
events or disease associated with OA. The knee OA patients can be further divided
into five stages: (1) stage 0: no radiographical signs or pain; (2) stage 1: minor bone
spur growth in X-rays of knee joints; (3) stage 2: greater bone spur growth and
healthy size of cartilage; (4) stage 3: damaged cartilage and minor narrow space
between bones; and (5) stage 4: the cartilage is completely gone and the joint space
between bones is dramatically reduced. Osteoarthritis symptoms often develop
slowly and worsen over time. Knee OA patients always have signs of tenderness,
loss of flexibility, grating sensation, stiffness, and pain. The biomechanical behavior
of knee OA joints is correspondingly changed compared to normal knees, especially
in end-stage knee OA patients. Kinematics and kinetics parameters are crucial for
the evaluation of osteoarthritis severity and treatment outcomes.

Kinematics Characteristic of KNEE OA Patients

Kinematics analysis mainly studies the variation of spatiotemporal parameters of

knee joints. The range of motion, walking speed, stride length, and the gait cycle
period of knee OA patients all show abnormal changes compared to that of normal
knees. Moreover, one explanation of that is individuals with severe knee osteoarthri-
tis and great pain are hypothesized to adopt neuromuscular strategies to increase
knee joint stiffness, decrease joint movement, and alter movement patterns to shift
or reduce tissue loads and thus limit pain [47]. Previous studies reported that end-­
stage knee OA patients walked at a lower speed than healthy subjects and the knee
flexion angle reduced before heel strike. Reduced range of motion, slower stride
cadence, and shorter stance phase were reported in the knee OA patients [48–51],
which is called an antalgic type of gait. Taking analgesic may relief severe joint pain
and increase the stride velocity, but the anomalous gait will aggravate osteoarthritis
[50]. Knee OA patients at different stages showed different gait characteristics and
kinematics parameters, which should be taken into consideration when rehabilita-
tion and treatment programs were designed accordingly.
Knee kinematics of different stage of knee OA patients have been investi-
gated in the past decades. All the patients showed a reduction of flexion at the
early stage of stance phase, and extension insufficiency develops with the pro-
284 R. Cheng et al.

gression of osteoarthritis. The decreases of hip internal rotation and ankle dor-
siflexion angle from late stance to early swing were also found in the progression
of knee OA [52].

Kinetics Characteristic of KNEE OA Patients

The change of joint loading has a crucial effect on articular cartilage. Native joint stress
should be homogeneously distributed under proper lubrication. The increase of joint
loading and repeated impact of joint are considered to induce joint wear and decide the
severity of knee OA. Uneven stress distribution may cause the damage and loss of
articular cartilage and the secondary degeneration of knee osteoarthritis. External knee
adduction moment, especially the mid-stance knee adduction moment, is a key param-
eter, which is closely associated with joint loading. Two knee adduction moment peaks
showed in the early and late stance phase. The first knee adduction moment peak is of
great clinical significance because it is correlated with cartilage thickness and joint
loading [53]. In the past decade, the mid-stance knee adduction moment attracted more
and more attention, which is not dependent on the stride velocity and is taken as an
ideal indication for knee OA diagnosis. Expect for the operative management; gait
retraining is an effective treatment for correct knee adduction moment. So far, several
gait patterns were reported to reduce the adduction moment, such as toe-out gait, slow
velocity, stride length reduction, side swing, and so on [54–56].

Total Knee Arthroplasty

Through the progression of knee OA, conservative treatment would have few effects
on the patients with tremendous pain, deformities, and disabilities. Total knee
arthroplasty (TKA) is the most effective surgical interventions for pain relief and
functional recovery in patients with advanced degenerative arthritis or rheumatoid
arthritis [57]. Aging of the society has led to increase in the prevalence of arthritis
and the incidence of TKA for end-stage arthritis. With the development of TKA
techniques and design, the demand for TKA increased in the past 20 years, and over
1300,000 patients took TKA procedures annually [58]. TKA has three components:
femoral components, tibial components, and patellar components. Following differ-
ent criteria, TKA prosthesis can be classified as (1) cruciate retaining, and posterior
stabilized prosthesis; (2) mobile-bearing and fixed bearing prosthesis; (3) cemented
and uncemented prosthesis. The knee prosthesis can be further divided into medial
pivot, single radius, and multi-radius based on geometric design.
Although total knee arthroplasty has been developed for many years, complica-
tion rates are still high after primary TKA procedure [59]. John Insall proposed that
total knee arthroplasty should meet the following requirements: (1) correct align-
ment axes; (2) equivalent joint gap during flexion and extension; (3) balanced col-
lateral ligament tension; (4) –3° to 130° of knee flexion; (5) 3 mm changes of joint
line; and (6) balanced patellar trajectories. These biomechanical factors should be
taken into consideration to avoid secondary complication like polyethylene wear,
11 Biomechanics of Human Motion 285

periprosthetic fractures, loss of flexion, joint instability, and infection. Different

choices of prosthesis play an important role in postoperative kinematics behavior. In
this section, two major types of TKA prosthesis, cruciate retaining (CR) and poste-
rior stabilized (PS) prosthesis, will be discussed in the following literature. With or
without the posterior cruciate ligament (PCL) retaining, different in-vivo kinemat-
ics and kinetics characteristics were investigated by researchers.

Cruciate Retaining Prosthesis

With the retaining of the PCL, CR prosthesis is considered to restore normal knee
biomechanical function compared to PS prosthesis. PCL retention in total knee
replacement has the advantages of enhanced inherent stability, a greater range of
motion, improved proprioception, and increased rollback associated with the native
PCL retention and joint line. Tsai et al. investigated the articular cartilage contact
kinematics of the knee before and after a cruciate retaining arthroplasty. In their
study, the distances between medial and lateral contact locations in TKA knees
were significantly larger than those of the OA knees (Fig. 11.9) [60]. Further, the

50%
Native
40% Knee

30% TKA
Anterior

Contact Center Liner

20%
OA TKA
TKA
10% OA

0%

-10%
OA
Posterior

-20%
TKA
-30%

-40%

-50%
-50% -40% -30% -20% -10% 0% 10% 20% 30% 40% 50%
Medial Lateral

Fig. 11.9 Average medial and lateral articular contact locations and the center points between
medial and lateral contacts of the knees before and after TKA operations were depicted. The solid
and dotted lines represent the distances between medial and lateral contact locations at full exten-
sion and maximal flexion, respectively (Reprinted with permission from John Wiley and Sons: Li,
C., A. Hosseini, T.Y. Tsai, et al. Articular contact kinematics of the knee before and after a cruciate
retaining total knee arthroplasty. J Orthop Res, 2015. 33(3):349–358)
286 R. Cheng et al.

contact points on the medial and lateral compartments were more laterally located
than those of the OA knees. The centers of medial and lateral contact locations have
shifted from the medial side of the tibial plateau of the OA knees to the lateral side
of the TKA knees. The bearing surface design of polyethylene liner has been recog-
nized as a major factor that could affect the postoperative kinematics and contact
patterns of the knee. Failure of polyethylene liner has been reported to account for
approximately 50% of CR-TKA revision procedures. The small contact locations in
the TKA knees found in postoperative patients imply that the contact forces induced
by repeated sliding and rolling during knee motion were localized in these small
medial and lateral contact areas, which may induce unfavorable surface fatigue wear.
In the normal knees, the medial and lateral femoral condyles roll backward to
assist further knee flexion as the degree of flexion increases. However, CR prosthe-
sis was reported to show evidence of the paradoxical anterior femoral movement
during mid-flexion [61]. Improved CR prosthesis with femoral component oversiz-
ing and reducing femoral radius can control the paradoxical anterior femoral
­movement efficiently [62]. The survivorship of improved CR prosthesis was up to
94% after 10 years follow-ups [63].

Posterior Stabilized Prosthesis

For the patients with injured/contracted/degenerated PCL, over 20° of flexion con-
tracture. Without the cruciate ligament retaining, the PS total knee arthroplasty is
more applicable in advanced stage patients. Due to the reduction in the difficulty of
surgery, the PS prosthesis is widely used in the clinical field. The PCL substituted
with a post-cam device, which constrains the posterior femoral offset at 70° of knee
flexion and helps the knee joint to roll back during flexion. The PS prosthesis is
easier to realize gap balance and allow minor changes of joint line, for which the
prosthesis wear can be reduced. Tsai et al. compared the in vivo kinematics of the
knee after a posterior cruciate-substituting total knee arthroplasty between Caucasian
and South Korean patients. Paradoxical anterior translation of contact points was
observed from 45° to 90° of flexion in the Caucasian patients, whereas contact
points of the South Korean patients moved posteriorly from full extension to 60° of
flexion and then remained relatively constant until 90° of flexion. South Korean
TKA patients had more anterior contact points on the medial compartment, more
lateral contact points on the lateral compartment, and bicondylar femoral posterior
translation rather than medial pivot pattern compared to the Caucasian TKA patients.
Different tibiofemoral articular contact kinematics should be considered for the
design of bearing articular surface in Asian patients (Fig. 11.10).

2.3.2 Ligament Deficiency and Reconstruction

Four important ligaments stabilize the knee joint, including the anterior cruciate
ligament (ACL), posterior cruciate ligament (PCL), medial collateral ligament
(MCL), and lateral collateral ligament (LCL). Each separate ligament prevents
11 Biomechanics of Human Motion 287

a Femoral condyle motions

b
Tibiofemoral contact points
Medial compartment Lateral compartment Medial compartment Lateral compartment
Caucasian TKA South Korean TKA Caucasian TKA South Korean TKA
0 0 *
15 15
30
Flexion angles (º)

30

Flexion angles (º)

45 45
60 60
75 75
90 90
105 105
Maximal Maximal
flexion flexion
50 40 30 20 10 0 –10 –20 –30 –40 –50 50 40 30 20 10 0 –10 –20 –30 –40 –50
% %
Medial Lateral Medial Lateral

Fig. 11.10 Contact kinematics of Caucasian and South Korean total knee arthroplasty (TKA)
knees in a mediolateral translation. (a) Normalized femoral condylar motions. (b) Normalized
tibiofemoral contact kinematics. Positive values mean medial translation. ∗p < 0.05 (Reprinted
with permission from The Knee Surgery and Related Research: Bae, J. H., et al. In vivo Kinematics
of the Knee after a Posterior Cruciate-Substituting Total Knee Arthroplasty: A Comparison
between Caucasian and South Korean Patients. Knee surgery & related research, 2016. 28(2):
110–117)

excessive motion of the knee. When some of the ligament was damaged, the knee
would become unstable in the direction that the injured ligament stabilized. Different
types of physical tests in clinical practice (anterior drawer test, posterior drawer test,
etc.) are based on the abnormal behavior of knee after ligament injuries. The most
common injured ligaments in the clinical field are ACL and PCL. This section will
focus on the kinematics and kinetics characteristics after ACL/PCL injury and
reconstruction.

ACL Deficiency and Reconstruction

ACL is one of the major knee stabilizers, which constrains not only the anterior
tibial translation but also the internal-external rotation stability. Zhao et al. investi-
gated the kinematics of ACL-deficient patients and healthy subject in the Chinese
population. In their study, individuals with ACL deficiency exhibit greater knee
internal rotation during higher demand activities, such as ascending and descending
steps or jogging. Compared to Caucasian population, Asian patients showed smaller
tibial varus [64]. An anomalous tibial rotation will change the loading distribution
on the meniscus and cause secondary meniscal damage. Zhang et al. reported that
ACL deficiency with meniscal injury would alter the kinematics when compared to
isolated ACL injury [65].
Previous studies showed that after ACL tear more than 50% of individuals
showed radiographic evidence of osteoarthritis 10–12 years post-injury [66, 67]. An
ACL reconstruction is one of the standard treatments for ACL injury. Operative
treatment showed superior outcomes for knee symptoms and function, and in knee-­
specific and health-related quality of life, compared to patients who chose nonsurgi-
 288 R. Cheng et al.

a MEDIAL PLATEAU b LATERAL PLATEAU

5.0 0.0
Posterior (mm) Anterior

Posterior (mm) Anterior

-5.0
0.0
-10.0

-5.0 -15.0
0.0 20.0 40.0 60.0 80.0 100.0 0.0 20.0 40.0 60.0 80.0 100.0
% of step-up % of step-up
c d
-15.0 20.0
Medial (mm) Lateral

Medial (mm) Lateral

-20.0 15.0

-25.0 10.0
0.0 20.0 40.0 60.0 80.0 100.0 0.0 20.0 40.0 60.0 80.0 100.0
% of step-up % of step-up
Intact Pre-op 6M Post-op 36m Post-op

Fig. 11.11 Cartilage contact locations after ACL reconstruction during the step-up motion.
Anterior-posterior translation of cartilage contact locations on the (a) medial and (b) lateral tibial
plateau; Medial-lateral translation of the cartilage contact locations on (c) medial and (d) lateral
tibial plateau (Reprinted with permission from Elsevier: Lin, L., J.-S. Li, W.A. Kernkamp,
A. Hosseini, C. Kim, P. Yin, L. Wang, T.-Y. Tsai, et al. Postoperative time-dependent tibiofemoral
articular cartilage contact kinematics during step-up after ACL reconstruction. Journal of biome-
chanics, 2016. 49(14): 3509–3515)

cal treatment [68]. Tsai et al. measured the articular cartilage contact kinematics
after ACL reconstruction (Fig. 11.11) [69]. This study showed that the tibiofemoral
cartilage contact locations of the knee changes with time after ACL reconstruction.
Li also measured the tibiofemoral cartilage contact biomechanics in patients after
ACL reconstruction. These research revealed that the abnormal posterior and lateral
shift of cartilage contact location to smaller regions of thinner cartilage seen in
ACL-deficient knees persisted in the ACL-reconstructed knees around 0° and 15°,
resulting in a persistent increase of cartilage contact deformation at those flexion
angles [70]. Kernkamp WA et al. predicted the isometry and strain for ACL recon-
struction, and an area of least anisometry was found in the proximal-distal direction
just posterior to the intercondylar notch (Fig. 11.12). Moving the femoral socket
positions in the anterior-posterior direction affected the theoretical ACL strains
­significantly. Posterior femoral attachments resulted in decreased lengths with
increasing flexion angles, whereas anterior-distal grafts increased in length with
increasing flexion angles.
11 Biomechanics of Human Motion 289

a >18
16
14
12

Strain (%)
10
8
6
4
2
0
Anteromedial Central Posterolateral

b >18
16
14
12

Strain (%)
10
8
6
4
2

Anteromedial Central Posterolateral 0

Fig. 11.12 Medial view of a 3D femur model in 90° of flexion. The “heat map” illustrates the
isometry distribution (mean maximum strain-minimum strain) over the medial aspect of the lateral
femoral condyle for single point-to-point curves when connected to the anteromedial, central, or
posterolateral tibial attachment during the dynamic step-up (a) and sit-to-stand motion (b). The
darkest blue area on the femur represents the most isometric attachment area, whereas the red areas
highlight those with a high degree of anisometry. Specifically, the circle represents the most iso-
metric attachment. The black cross (×) on the femur shows the “over the top” position as would be
achieved by transtibial drilling; the black dot shows the center of the ACL footprint as described
by Parkar et al. (Reprinted with permission from Elsevier: Kernkamp, W.A., A.J.T. Jens,
N.H. Varady, E.R.A. van Arkel, et al. Anatomic is better than isometric posterior cruciate ligament
tunnel placement based upon in vivo simulation. Knee Surg Sports Traumatol Arthrosc, 2018)

PCL Deficient and Reconstruction

PCL injuries occupy up to 44% of all acute knee injuries, but the prevalence of
isolated PCL injuries (PCL injuries in which no other ligamentous injuries
require repair and reconstruction) was reported as little as 3.5% [71, 72]. In vivo
and in vitro drawer tests reported that PCL is the primary restraint to the poste-
rior translation of the knee [73, 74]. Li performed an in vivo kinematics study on
PCL-deficient knees compared with contralateral knees, data of which demon-
strated that PCL injuries caused an increase of about 5 mm posterior tibial trans-
lation through all the flexion angle and an increase of about 1 mm lateral tibial
translation at 90° of knee flexion [75]. Anatomic studies showed that PCL orien-
tated anteromedially on femur through the whole range of knee flexion. This
structure implies that PCL injury is not only a loss of posterior stabilizer but also
290 R. Cheng et al.

a medial-lateral stabilizer. The abnormal contact pattern along with the ACL-
deficient kinematics characteristics will yield secondary joint degeneration when
treated nonoperatively.
Isolated PCL injuries have been treated nonoperatively and often have good
functional results, but the 5-year incidence of osteoarthritis in nonsurgically treated
PCL-deficient knees has been reported to be up to 80% and 50% on the medial
femoral condyle and patella, respectively [76–78]. Tunnel selection is a crucial
parameter for PCL reconstruction to restore native PCL function. Kernkamp et al.
simulated the PCL elongation with in vivo kinematics and found that too proximal
(i.e., nonanatomical) femoral attachments are unable to replicate anatomical graft
length changes [79]. However, recent studies reported that isolated PCL reconstruc-
tion could not restore either anteroposterior or rotational stability compared to the
healthy knee. A supplemental surgical technique is required to overcome residual
external rotation instabilities, varus laxity [80].

3 Biomechanics of Spine Motion

3.1 Fundamentals of Spine Joint Motion

The spine is made up of the vertebrae and the intervertebral discs, facet joints, and
ligaments, forming the central axis of the human body, and transmitting the load as
well as protecting the spinal cord. The spine provides motion functions for trunk
such as three-dimensional physiological activities.

3.1.1 Vertebral Body

The vertebral body is mainly composed of cancellous bone, and the surface is a
thin layer of cortical bone [81, 82]. It presents as a short cylinder with a slightly
thin central portion and a large expansion at both ends. The upper and lower sides
are rough and can be divided into two areas: the central part is concave and porous,
filled by the cartilage onto the edge; the edge part bulges and is cortical bone,
firmly attached to the intervertebral disc. The vertebral body is a complicated struc-
ture composed of cartilage endplates, cancellous bones, and cortical bones. The
function of these different ingredients contributes to their unique biomechanical
properties. Vertebrae rely on their natural structure to resist various stresses.
Mainly, the vertebrae are almost composed of cancellous bone (net structure)
entirely, but a hard shell covers the outer part. Since the axial stress of the vertebra
presents the largest, the trabecular bone along the vertical direction exhibits the
hardest. The trabecular bones are arranged along the direction of the normal stress
(axial force) to exert their biological function as much as possible. The horizontal
trabecular bone acts as a lateral bracket to prevent vertical deformation of the tra-
becular bone.
11 Biomechanics of Human Motion 291

The vertebral body primarily sustains compressive forces. As the weight of the
vertebral body increases from top to bottom, the vertebral body also becomes larger
from top to bottom. For example, the shape of the lumbar vertebral body is thicker
and broader than that of the thoracic and the cervical vertebrae and is sustained by
a larger load. The mechanical properties of the vertebral body are related to the
anatomical features and bone masses.

3.1.2 Intervertebral Disc

The intervertebral disc is located between adjacent vertebral bodies, and the adjacent
vertebral bodies are firmly connected aiming to maintain the arrangement of the
vertebral canals [81, 83]. The thickness of the intervertebral disc is about one-­fourth
of the total length of the spine above the sacrum. Intervertebral disc is a kind of solid
viscoelastic material, which has the characteristics of creep, relaxation, and hyster-
esis, and can absorb the energy of vibration. Under a slight load, the deformation
disappears after unloading. If the load is too excessive, the irreversible deformation
will occur. The intervertebral disc consists of three parts: nucleus pulposus, fibrous
annulus, and cartilage endplate. The nucleus pulposus is a liquid mass located in the
center of the intervertebral disc. The lower lumbar vertebra is more backward. It
contains a large amount of hydrophilic glucosamine and present as gelatinous tissue.
Its water content varies greatly with age and load. When young, the water content is
up to 90%, but with the aging of people, the water content decreases gradually.
Under compression load, water in nucleus pulposus seeps through the endplate, and
the volume of nucleus pulposus decreases. When the load decreases, water returns
and the volume of nucleus pulposus recovers. A fibrous annulus is composed of
fibrocartilage tissue. There are many intersecting collagen bundles in fibrocartilage.
The unique alignment of annular fibers helps the intervertebral disc maintain a cer-
tain degree of torsion resistance. The posterior part of the fibrous ring is woven by
the posterior longitudinal ligament (PLL). The cartilage endplate between the verte-
bral body and the intervertebral disc is composed of hyaline cartilage.
It is an essential biomechanical function of an intervertebral disc that it can bear
and distribute the loads and restrict excessive activity. Compression load acts on
nucleus pulposus and annulus fibrosus through the end plate. Hydraulic pressure
generated inside the nucleus pulposus causes annulus fibrosus to expand outward.
The outer annulus fibrosus bears the maximum tensile stress. The inner annulus
fibrosus bears less tensile stress than the outer one, but it bears a part of compres-
sive stress.

3.1.3 Pedicle and Facet Joint

The type of the spinal segment motion depends on the direction of the articular
surface of the intervertebral joint, and the direction of the articular surface varies
among the whole spinal vertebrae [81, 83]. The joint plane of the lower cervical
292 R. Cheng et al.

spine is parallel to the coronal plane and 45° to the horizontal plane. It allows the
cervical spine to flex forward, extend backward, bend laterally, rotate, and extend to
a certain extent. The articular surface of the lumbar spine is perpendicular to the
horizontal plane and 45° to the coronal plane, allowing flexion, extension, and lat-
eral bending, but limiting rotation.
In addition to guiding segmental motion, the facet joints also bear different kinds
of loads, such as compressive force, tensile force, shear force, and torsion force. The
amount of loads they bear vary with the different movements of the spine. The load
on the facets of the joints is the greatest at extension, accounting for 30% of the total
load (another 70% of the load from the intervertebral disc). The load on the facet
joint is also higher when flexion and rotation occur. The tensile loading of facet joints
mainly occurs as the lumbar forward bending. When the lumbar forward bending
reaches the maximum limitation, 39% of the tension load is borne by facet joints.

3.1.4 Ligament

The main components of the ligament are collagen fibers and elastic fibers [81]. The
collagen fibers give the ligaments a certain strength and rigidity, and the elastic fibers
give the ligaments the ability to extend under the loading. Most of the fibers of the liga-
ment are nearly parallel [83, 84], so their functions are more specific and often only
bear the loading along a single direction. The function of the spinal ligaments is to
provide a proper physiological activity for adjacent spines, as well as maintain the
stability of the spine. The specimen of the spine in vitro still maintains a certain inter-
vertebral disc pressure under the traction load. The prestress is derived from the tension
of the ligament and is most prominent in the ligament flavum. All ligaments possess the
ability to resist tension, but they are fatigued quickly under compressive forces. The
ligament strength is closely related to the cross-sectional area of ​​the ligament.
The ligaments of the spine bear most of the distraction loads of the spine. They
act like rubber bands. When the load direction is consistent with the fiber direction,
the ligaments have the strongest bearing capacity. When the spinal motion segments
are applied by different forces and moments, the corresponding ligaments are
stretched and stabilized for the motion segments.
It is generally believed that the anterior longitudinal ligament (ALL) is the tough-
est, and together with the PLL, can prevent the spine from excessive flexion and
extension, but the effect of limiting axial rotation and lateral flexion is not obvious.
The facet joint capsule ligament plays a key role in resisting torsion and lateral flex-
ion. The main function of the interspinous ligament is to stabilize the spine by limit-
ing the ability to flex.

3.1.5 Muscle

The dynamic stability of the spine is correlated with the function of the complete
paraspinal muscle during activities. The muscles associated with the spinal activity
can be divided into the front and back groups according to their locations [85]. The
11 Biomechanics of Human Motion 293

muscles located behind the lumbar vertebrae can be further categorized into three
groups: the deep layer, the middle layer, and the superficial layer [81, 83, 84]. The
deep muscles include the interspinous muscles that end at the adjacent spinous pro-
cesses, the intertransverse muscles that start at the adjacent transverse processes,
and the rotator muscles that start and end at the transverse processes and spinous
processes. The middle layer muscles mainly refer to the multifidus muscles of the
transverse process and the spinous process of the upper vertebral body. The superfi-
cial muscles can be divided into three groups: iliocostalis, longissimus, and spinalis.

3.2 In Vivo Spine Kinematics

In vitro biomechanical studies can describe the displacement patterns of spinal

motion under different loads. However, it is not possible to establish normal spinal
motion because the load generated in the body muscle cannot be simulated in vitro
studies. Therefore, some methods have been developed to quantitatively study the
movement of the spine in the body.
In the past, flexion/extension dynamic X-ray films have been widely used to
measure the abnormal motion of the spine. X-ray films suggest signs of instability
of the segments including narrowing of the intervertebral space, formation of osteo-
phyte, and spondylolisthesis. However, these can only provide two-dimensional
images. Because the true spine motion is three-dimensional and unstable, X-ray
films do not reflect accurate spine motion.
In 1974, in order to avoid the error caused by the bony landmark, Aronson built
a biocompatible metal mark into the bone of the subject and performed X-ray ste-
reoscopic imaging [86]. The measurement accuracy can reach 0.1–0.2 mm. This
method becomes the gold standard for assessing bone image measurements.
However, this method is invasive and cannot be a routine clinical examination.
Later, based on this technology, the dual plane fluorescence imaging technique
(DFIS) combined with the computed tomography imaging technique for bone mod-
eling, after the later registration, can accurately simulate the three-dimensional
motion data [87].
A large number of spine-related in vivo studies have been carried out based on
DFIS combined CT (Fig. 11.13). In studies of the normal cervical spine in vivo, the
anterior portion of the intervertebral disc experienced large changes in traction/
compression deformation and shear deformation between functional maximum
flexion and neck extension [88]. Higher level discs experience a higher range of disc
deformation. No significant differences were found in the deformation range of the
posterior areas of all the discs. The range of disc deformation depends on the level
of the disc, and in addition to the C6/7 intervertebral disc, the deformation of the
anterior region is greater than the central and posterior regions. The position of
center of rotation (COR) during dynamic extension-flexion-extension (EFE) motion
and axial left-right-left (LRL) rotation is shown as segment-specific and neck
motion-related. The intervertebral segments CORs of C45 and C56 are closer to the
geometric center than C34 and C67 are. The ROM is larger during EFE exercise
294 R. Cheng et al.

a b

Fig. 11.13 (a) Experimental set-up of dynamic in vivo imaging using the DFIS. (b) Virtual DFIS
used to recreate intervertebral kinematics throughout the dynamic motion (Reprinted with permis-
sion from Elsevier: Zhong, W., S.J. Driscoll, T.Y. Tsai, et al. In vivo dynamic changes of dimen-
sions in the lumbar intervertebral foramen. Spine J, 2015. 15(7): 1653–9)

than during the LRL rotation at each intervertebral level. During LRL rotation, the
later COR corresponds to a smaller ROM. The data obtained from this study can
provide insight into the improvement of motor-preserving prosthesis design and
surgical implantation techniques designed to restore normal neck function and pre-
vent adjacent segmental degenerative cervical surgery.
In vivo studies of the lumbar spine showed that during weightlifting, L4-5 and
L5-S1 of lower lumbar segments showed larger anterior-posterior (AP) and
proximal-­distal (PD) translations than higher vertebral segments, respectively [89,
90]. Body and lumbar foramen size showed segmental characteristics during
dynamic weightlifting. Also, the movement behavior of the upper lumbar facet
joints (L2-L3 and L3-L4) was similar but different from that of the lower lumbar
joints (L4-L5).

3.3 Spine Kinematics in Common Pathologies

3.3.1 Herniated Disc Symptoms and Spondylolisthesis

Spinal degenerative diseases are most common among all spinal diseases, and disc
herniation caused by degenerative disc disease is the most common cause of pain in
the lower back and neck [91, 92].
Degenerative disc disease’s symptom is usually lower back or neck pain caused
by aging and wear of the disc. When the herniated disc tissue compresses the spinal
nerves or the spinal cord, it can also cause weakness in the arms or legs, numbness
and burning shot pain (radicular pain) [93, 94]. Cervical and lumbar vertebrae
undergo maximum exercise and pressure and are most susceptible to disc degenera-
tion, so there is a high probability of painful disc degeneration. Disc degeneration is
not a disease and usually does not cause long-term disability, and most cases can be
11 Biomechanics of Human Motion 295

treated with nonsurgical approach. Degenerative disc disease varies in nature and
severity. Degenerative discs do not always cause pain or other symptoms. Because
the intervertebral disc itself is short of innervation, it causes or accelerates the onset
of other spinal disorders when the degenerated disc affects other structures in the
spine, such as muscles, joints, or nerve roots.
Discogenic pain usually results from two main factors: One is inflammation.
When the disc is degraded, inflammatory factors from the interior of the disc may
leak, causing swelling of the surrounding spine. Therefore, inflammation causes
muscle tension, muscle spasm, and tenderness in the back or neck. Pain and numb-
ness may radiate to the arms and shoulders (the symptom of cervical radiculopathy),
or into the buttocks or legs (the symptom of lumbar disc herniation), due to inflamed
nerve roots.
The other is unstable micro-motion. When the outer layer (fibrous ring) of the
disc degrade, the cushioning and support of the intervertebral disc usually reduce,
resulting in small, unnatural movements between the vertebrae. Unstable spinal seg-
ments can induce micro-motions and cause tension and irritation in the surrounding
muscles, joints, and nerve roots, leading to recurrent severe pain episodes. In most
cases, however, the disc herniation itself is not painful, but the tissue leaking from
the intervertebral disc, inflaming or stimulating nearby nerves, causes nerve root
pain. Leg pain from sensitive nerves is often referred to as sciatica.
Spondylolisthesis is a forward translation of a vertebral segment below which a
vertebral segment is located. Typical symptoms are an activity-related history of
low back pain and painful spinal activity and hamstring tension without radiculopa-
thy sign and imaging. Plain films, computed tomography, and single photon emis-
sion computed tomography are useful in determining the diagnosis. The best way to
treat the symptomatic stress response of the spinal joint or adjacent vertebral struc-
tures is to immobilize the spine and activity restriction.

3.3.2 Spinal Fusion

The spinal surgery usually applies a rigid internal fixation device to secure the spine,
aiming to correct deformities, relieve pain, stabilize the spine, and protect the nerves
[95, 96]. Spinal fusion surgery includes a variety of surgical procedures: for example,
lumbar fusion, cervical fusion, and OLF [91]. Although each surgery is different, they
are all designed to help relieve pain or neurological symptoms caused by the interver-
tebral joints, depending on whether the patient is undergoing surgery for degenerative
disc disease, lumbar spondylolisthesis, or other diseases. During spinal fusion sur-
gery, two adjacent vertebrae are combined to eliminate the underlying mechanism of
pain. Fusion of joints eliminate instability of the spinal segments and reduce pain
caused by micro-motion, muscle tension, and inflammation. Moreover, the most
important thing is that fusion can solve the nerve compression problem completely.
Fusion surgery establishes a mechanism of bone growth that occurs months after
surgery. For this reason, the complete recovery process for fusion surgery can last up
to a year, although most patients return to normal activity within 6 weeks.
296 R. Cheng et al.

It is recommended to use a back or neck brace to keep the spine stable and to
minimize painful movements that may disrupt the healing process after surgery.
Also, rehabilitation (physical therapy for example) is often recommended to modu-
late the muscles to support the spine better and to provide painkillers to control
postoperative pain when necessary [97].

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Chapter 12
Biomechanics of the Fracture Fixation

Yingze Zhang, Hongde Wang, Tianrui Wang, Wei Chen, and Yanbin Zhu

Abstract Biomechanical factors is an important aspect that affects bone healing

directly. Although some biologic etiologies of fixation failure can be directly affected
by the physician, there are only minimally under the surgeon’s control. The surgeon
should do their best to preserve soft tissue, vessel, and the zone of injury. Skillful surgi-
cal technique, tight wound closure, and appropriate antibiotic therapy could decrease
the risk of infection and reduce the risk of fixation failure. If failure occurs suddenly or
prior to the expected time when fracture healing would occur, a mechanical issue is
usually the primary cause. Biomechanics study the role of force and energy in biologi-
cal systems. The fracture fixation should follow the principle of biomechanics.
Excessive stress concentration and fatigue, leading to increased pressure load and
bending load, results in internal fixation failure. Understanding the biomechanical
principles underlying stable fixation and failure fixation could help the surgeon deter-
mine the appropriate investigation and intervention. Appropriate biomechanical fixa-
tion technology will promote fracture healing, accelerate rehabilitation of patients, and
reduce nonunion of fracture. Biomechanical study can help the design of the internal
fixation and also plays an important role on the improved clinical effects; furthermore,
it will help clinicians to choose reasonable diagnosis and treatment strategies.

Keywords Biomechanics · Innovation · Orthopedics trauma · Fixation principle

Fixation devices

Y. Zhang (*)
Department of Orthopaedic Surgery, The Third Hospital, Hebei Medical University,
Shijiazhuang, Hebei, People’s Republic of China
Key Laboratory of Biomechanics of Hebei Province,
Shijiazhuang, Hebei, People’s Republic of China
Chinese Academy of Engineering, Beijing, People’s Republic of China
H. Wang · T. Wang · W. Chen · Y. Zhu
Department of Orthopaedic Surgery, The Third Hospital, Hebei Medical University,
Shijiazhuang, Hebei, People’s Republic of China
Key Laboratory of Biomechanics of Hebei Province,
Shijiazhuang, Hebei, People’s Republic of China

© Springer Nature Singapore Pte Ltd. 2020 301

C.-K. Cheng, S. L-Y. Woo (eds.), Frontiers in Orthopaedic Biomechanics,
https://doi.org/10.1007/978-981-15-3159-0_12
302 Y. Zhang et al.

1 Introduction

Biologic and mechanical problems are the two underlying problems, when fracture
implants fail prior to fracture union [1–3]. Patient’s systemic biology as biologic
factors including chronic diseases, smoking, medications, and many other causes
may cause delayed union and fixation failure [4–6]. Many biologic etiologies of
fixation failure can be treated by the physician, but there are still many biologic
etiologies beyond the surgeon’s control [7, 8]. Therefore, surgeons should make
many efforts to preserve soft tissue and vascularity, and respect the zone of injury
[9]. Meticulous surgical technique, wound closure, and appropriate perioperative
antibiotic therapy can all reduce the risk of infection and treatment failure.
Mechanical problems are usually the main cause, when failure occurs acutely or
prior to the expected time that fracture healing [10–13]. To determine the appropri-
ate investigation and intervention, surgeons should understand biomechanical prin-
ciples underlying the stable fixation and fixation failure.

2 Pin and Wire Fixation

There are some biomechanical differences among pins, rods, and nails used for
fracture fixation. Pins only resist alignment changes, rods resist deviations in align-
ment and translation, and nails resist changes in alignment, translation, and rotation.
Kirschner wires and Steinmann pins are often used for both provisional and defini-
tive fracture fixation. Due to its poor bending resistance, it should be used in con-
junction with bracing or casting. They are usually inserted as final fixation with
limited open reduction or percutaneously. They should be inserted slowly and stop
drilling frequently. To prevent thermal damage to bone and soft tissues. To make
their removal easier after fracture healing, we recommend using smooth wires.
Threaded wires can better fix the fractures compared with temporary fixation,
but the fracture fragments must be fixed together when insertion wire to avoid dis-
traction. If the cortical bone is hard, there is a risk of pin breakage. For small frag-
ments in metaphyseal and epiphyseal regions, especially in the fracture of distal
foot, forearm, and hand, such as Colles fracture, and in displaced metacarpal and
phalangeal fracture after closed reduction, pin or wire fixation is usually sufficient
[14, 15]. In most cases, pins are inserted under the control of an image intensifier.
This can protect the soft tissues from further damage, theoretically allowing for
maximum bone regeneration; however, it must be noted that nerves and tendons are
not wound around the pin during insertion. Wire fixation is used alone or in combi-
nation with other implants for definitive fixation of some metaphyseal fractures,
such as in the cervical spine, proximal humerus, and patella [16]. The wire should
not be notched as it may reduce the fatigue life of the implant. It is rare touse wire
alone to provide adequate stability for functional rehabilitation of the extremity [17].
For some intra-articular fractures, simple rigid fixation using screws or plates for
a long time might result in some complications such as articular degeneration,
12 Biomechanics of the Fracture Fixation 303

a b c

Fig. 12.1 (a) Components of the elastic bionic fixation; (b) Assembly of the fixation device; (c)
Post-operative X ray film of the fixation device

arthritis, and the limited articular mobility. Given that, our research team used the
biomechanical principle to invent an elastic fixation device for treatment of ankle
fracture combined with distal tibiofibular syndesmosis (DTS). As presented, the
elastic bionic fixation device included elastic cable, a bolt, and a button (Fig. 12.1),
which could provide both rigid and elastic fixation, and therefore reduce the possi-
ble intra-articular issues, compared to the traditional rigid fixation. With this device,
we treated 17 cases of ankle fracture combined with DTS, and at the final follow-up
all of them obtained excellent and good outcomes according to the AOFAS score.

3 Screw Fixation

Screws are made up of four parts: head, shaft, thread, and tip. The head of a screw
acts as an attachment for the screwdriver and can be hexagonal, cruciate, slotted, or
Phillips. The head also acts as a reaction, and the pressure generated by the screw
acts on the bone. The shaft or shank is the smooth portion of the screw between the
304 Y. Zhang et al.

head and the threaded portion. The thread is defined by its root (or core) diameter,
its thread (or outside) diameter, its pitch (or distance between adjacent threads), and
its lead (or distance it advances into the bone with each complete turn). The root
area determines the resistance of the screw to pullout forces and relates to the area
of the bone at the thread interface and the root area of the tapped thread. The cross-­
sectional design usually is a buttress (ASIF screws) or V-thread (usually used in
machine screws). The tip of the screw is either round (require spretapping) or self-­
tapping (fluted or trocar). Clinically, if it is necessary to consider pulling out from
the screw because of soft bone, it is more inclined to use a larger thread diameter,
and if the bone is stronger and more fatigue is needed, the screw with a wider root
diameter has a higher anti-fatigue failure ability. Screws also usually are divided
into machine-type screws and ASIF screw.
The use of screws to convert torque forces into compressive forces through a
fracture is a valuable technique. Its success requires the application of a screw in
such a way that the proximal portion of the screw is allowed to slide in the near bone
and the thread is formed in the opposite cortex so that the head of the screw can
exert load and forces the fracture to heal. Careful selection of the angle of the screw
corresponding to the fracture is necessary to prevent the fracture fragments from
slipping when compressed.
Screw Breakage by Shearing During Insertion
A screw is a mechanical device that is used to convert rotary load (torque) into com-
pression between a plate and a bone or between bone fragments. The basic compo-
nents of a screw are shown in Fig. 12.2. As shown in Fig. 12.3, when the thread of
the screw is released from the shaft, it is actually a slope or a slope, and the lower
bone is pulled toward the fixing plate, causing compression between the bone and
the bone. In order to achieve this effect, the screw head and shaft should rotate
freely within the steel plate; otherwise, the compressive force generated may be
limited. The locking screw passes through the plate hole; although this fixed inter-
face is beneficial in some clinical situations, it prevents compression between the
plate and the bone.
In the cortical bone, a tap is necessary so that the torque applied by the surgeon
translates into compression rather than cutting the thread, thereby overcoming the
friction between the screw thread and the bone (Fig. 12.3) that it is being driven into
(Fig. 12.4). In some cases such as inserting screw into a dense bone or inserting a
smaller diameter screw, using a separate tap and then inserting the screw, the screw
can be pushed into the bone. Most modem screw designs have self-tapping screw
tips that cuts the path of the thread when the screw is inserted. Screws with multiple
cutting flutes at the up of the screw appear to be the easiest to insert and have a
greater grip. Tapping in cancellous bone is less advantageous because tapping
reduces the pullout strength of the screw. In some cases, it may beneficial to tap the
cancellous bone. A clinical example is when treating a femoral neck fracture with a
physiologically older patient versus a younger patient; you may need to use a tap to
make a thread in the denser bone of a younger patient. The reason for using tap in
the dense bone is to prevent the frictional force from causing femoral head to rotate
12 Biomechanics of the Fracture Fixation 305

Major diameter

Pitch diameter

Root
diameter Single depth

Thread Thickness of thread

angle 60º

Helix angle

Pitch

Root

Fig. 12.2 Nomenclature of screws. The root diameter is the inner diameter of the screw and the
pitch defines the distance between threads

during the insertion of screw resulting malreduction. In particularly hard bones the
frictional forces become so great that it becomes difficult to advance the screw [18].
One problem with the placement of the screw is that the shear failure of the
screw, the head twisting off usually, making it difficult to remove the shaft from the
bone. This can occur especially if the tap is not used before insertion, or when a
smaller (less than 4-mm diameter) screw is inserted into the dense bone. The stiff-
ness and strength of the screw are related to the fourth power of its radius (the effect
of moment of inertia for screws of the same material). The 6-mm diameter screw is
306 Y. Zhang et al.

Fig. 12.3 A screw is a

mechanical device that
converts torque into
compression between
objects. The screw thread
is actually an inclined
plane that slowly pulls the
objects it is embedded into
together (Fn normal or Fz
compressive force acting Fn
against the screw head; Ft
tangential or frictional
force acting along the
screw thread; Fz resultant
of the two forces; α angle
of the screw thread. The
smaller the angle α [finer
thread] the lower the
frictional force)
Ft

Ft

Fn
Fz

about five times stiffer than a 3-mm diameter screw and 16 times more resistant to
shear damage than a 3 mm diameter screw. The junction of the screw head and
threaded portion of the screw is the transition point of shape and size. Therefore, it
acts as a stress concentrator, usually where the screw breaks.
12 Biomechanics of the Fracture Fixation 307

Fig. 12.4 Schematic

diagram showing the
approximate distribution of
torque acting on a screw
placed into cortical bone.
With a pre-tapped hole,
about 65% of the applied
torque goes to produce
compression and 35% to
overcome the friction
associated with driving the
screw. When the hole is not
tapped, only about 5% of
the torque is used to
produce compression, the
rest going to overcome
friction and to cut threads in
bone. These observations do
not apply in cancellous bone

Fig. 12.5 The factors that

Out diameter
determine the pullout
strength of a screw are its
outer diameter and length Bone
of engagement (this defines
the dimensions of a
cylinder of bone that is Length Inner
carried in the threads and of thread diameter Pitch
is sheared out as the screw in bone
is pulled out of the bone)
and the shear strength of
bone at the screw-bone
interface, which is directly
related to its density. A
finer pitch screw produces
a small gain in purchase

Screw Pullout
Especially, in cancellous bone, the maximum force that a screw can withstand along
its axis. The pullout force depends on the size of the screw and the density of the
bone placed. As shown in Fig. 12.5, when the force acting on the screw exceeds its
pullout strength, the screw will be pulled out or “stripped” out of the hole, and the
sheared bone will be placed in thread, greatly reducing the nail holding force and
fixing force. The larger the diameter of the screw, the larger the number of threads
per unit length, and the longer the insertion length of the screw shaft, the greater the
pulling force. And a greater density of the bone it is placed into. The diameter and
length of the embedded screw can be considered to define the outer surface of a
cylinder along that screw shears. Given a maximum stress that bone of a particular
308 Y. Zhang et al.

density can withstand, increasing the surface area of the screw cylinder increases
the pullout force (because force = stress multiplied by the area over which it acts).
In order to enhance screw purchase, it is conceivable to insert the screw of largest
diameter into the bone of the highest density with the length of the implant as long
as possible. However, placing screws of as large a diameter as possible has disad-
vantages. Larger screws occupy a larger volume in small fracture fragments, limit-
ing the number of possible fixation sites and propagating adjacent fracture lines.
In cancellous bone, the extraction of the screw becomes a more important prob-
lem because the porosity of cancellous bone reduces its density and thus the shear
strength. Drilling preparation, especially drilling, rather than tapping, can increase
the pullout strength of cancellous bone (such as pedicle screws in the vertebral
body). The reason why the cancellous bone is knocked down is that the tap is
removed from the hole or placed in the hole, which can effectively increase the
diameter of the hole and reduce the amount of bone material that interacts with the
thread. When the bone density is reduced, the tapping is more harmful, and the
pullout strength can be reduced from 8 to 27%. The pullout strength can also be
related to the time after insertion. As the bone heals, it can remodel around the
screw, possibly doubling its initial pullout strength [19].
Recent research has focused on whether pullout strength is an appropriate mea-
sure of screw performance in cancellous bone. In nonlocking steel and screw con-
structions, the stability of most structures comes from the friction created by
compression between the plate and the bone. When the screw is inserted into the
bone, if it is able to generate high values of insertional torque, the compression of
the steel plate to the bone is increased, and the stability is increased. As the maxi-
mum insertional torque is reached and then exceeded, the screw will then “strip out”
and lose its supporting force in the bone. Although there is a relationship between
maximum insertional torque, screw pitch, and compression forces, it has been found
that the pullout strength has no correlation with either the maximum insertional
torque or screw pitch. Therefore, this may be a better way to measure screw perfor-
mance and optimize screw characteristics.
Screw Breakage by Cyclic Loading
Once screw is successfully inserted and the construction is completed, the screw
will be subjected to cyclic bending forces as the patient begins to mobilize
(Fig. 12.6). Ideally, a nonlocking screw initially tightens the plate to achieve the
maximal torque, which is translated into the maximum compression between the
plate and the bone (Fig. 12.4). The screw on the bone portion is in frictional contact,
depending on the friction generated between the plate and the bone. The frictional
force is directly dependent on the compressive force generated by the screws. If a
slip occurs between the plate and the bone, the bending load will be transferred from
the screw head into the plate, at which point the screw comes into contact with the
plate. The bending load perpendicular to the axis of the screw, coupled with possible
stress corrosion and fretting corrosion, may cause the screw to fail rapidly in fatigue.
Zand et al.’s research shows that when the screw is fastened to the steel plate, it is
subjected to a maximum load of less than 1000 loading cycles due to bending
12 Biomechanics of the Fracture Fixation 309

Fig. 12.6 A mechanism

Applied load
for rapid failure of screws Transfer of load
in cyclic bending occurs to plate by
when the screw has not bone-plate
been tightened sufficiently friction
to keep the plate from
sliding along the bone
surface (the plate-bone gap
shown here is exaggerated
for clarity). The results is
that bending loads are
applied transverse to the Transfer of
long axis of the screw, load to screw
which in combination with
fretting corrosion caused
by the screws rubbing Direct
against the plate results in compression
early failure of the screw between
components

fatigue, compared to a fully fastened screw capable of withstanding more than 2.5
million loading cycles. The load is less than 10–15% of the maximum load. This
emphasizes the clinical importance of ensuring screw tightness during the fixation
of the plate.
Locking the screws on the board can reduce the problem, since the problem is
less subjective when the screw head is fully fastened to the plate hole. Small-­
fragment screws (3.5- to 4-mm outer diameter) can fatigue because of their small
core diameters. Although the use of locking screws with a larger core diameter and
shallower thread can reduce the possibility of fatigue failure, a smaller core d­ iameter
and deeper thread can increase purchase strength in the bone. Screws with smaller
core diameters are more likely to fatigue than larger ones. The fatigue strength of
the screw must be weighed against the purchasing power of the screw and the size
of the screw associated with the size of the bone fragment. The surgeon sometimes
must make a decision between a screw with a large core diameter with shallower
thread, which maximizes fatigue strength, and a smaller core diameter screw with
deeper threads, which maximizes purchase power.
Cannulated screws are used for fixation when the insertion of a guide wire is
helpful to guide the future path of the screw. However, as the bone density increases
and the diameter of the guide wire increases, the drilling accuracy of the guide wire
decreases. Cannulated screws follow the same mechanical principles as solid
screws, but material must be removed from the center of the screw to accommodate
the passage of the guidewire. Manufacturers commonly increase the diameter of the
screw at the base of the thread to fit the loss of this central material. The same size
310 Y. Zhang et al.

Fig. 12.7 Using a fully

threaded lag screw causes
the threads to engage in
bone on both sides of the
fracture. This inhibits the
screw from compressing
the bone fragments
together

of cannulated screws usually has less thread depth than solid screws. The result
depends on the size of screw, rather than pullout strength. For screws with a diam-
eter of 4 mm, the tensile strength of the cannulated screws of the same outer diam-
eter is about 16% lower. Alternatively, to maintain the same thread depth, the outer
diameter of the screw may be increased. Another consideration is that the cannu-
lated screw is much more expensive than the solid screw [20].
Fully Threaded Lag Screws
The lag screw is a very effective device which can produce amount of pressure
across fracture fragments and the fracture site. The head of the screw and upper por-
tion of the shaft must be allowed to glide in the near broken pieces to pull the far
broken fragments toward it, thereby creating compression on the fracture surface.
As shown in Fig. 12.7, a fully threaded lag screw can prevent the gliding action
between the two fracture fragments. The fully and partly threaded lag screws were
used to compare the compressive forces across the fracture site. The results showed
that the average compressive force at the opposite cortex (i.e., the force in the screw
itself) was about 50% greater when a partly threaded screw was used.

3.1 Machine Screws

The machine screws are threaded throughout the length and can be self-tapping or
threaded before insertion. Most are self-tapping; there is a cutting flute that cuts the
screw threads as the screw is inserted. Machine screws are mainly used to fix the hip
compression screw on the femoral shaft. The size of the machine screw holes is
critical. A hole that is too large can cause the thread to be unsafe, and a hole that is
too small can cause the screw to be inserted or fractured during insertion. The drill
bit selected should be slightly smaller than the screw after the screw minus the
12 Biomechanics of the Fracture Fixation 311

thread. For a self-tapping screw, the drill point is used to drill holes in soft bone. The
size of the screw and drill tip should be checked before surgery.

3.2 Asif Screws

Screws developed by the Swiss ASIF Group for bone fixation techniques and prin-
ciples are widely used. The threads are more horizontal than the machine screws,
and these screws rarely seldom self-tapping; the drill must be tapped with a cutting
tapper before inserting the screws. ASIF screws are available in cortical, cancellous,
and malleolar designs. Mini screws for fixation of small fragments and small bones,
and the standard cancellous and cortical screws, come in multiple lengths and diam-
eters. Standard cancellous and cortical screw heads have a hexagonal recess for a
special screwdriver, while the smaller screws have a Phillips head.

3.2.1 Cortical Screws

The full length thread of the cortical ASIF screw is available in a variety of diame-
ters (4.5, 3.5, 2.7, 2.0, and 1.5 mm). If the hole in the near cortex is drilled too deep,
the cortical screws can be used as a positional or lag screws for inter-fragmentary
compression.

3.2.2 Cancellous Screws

These screws have larger threads that provide more support for soft cancellous
bone, making them more suitable for use on the metaphyseal areas. The cancellous
screws are available in 6.5- and 4.0-mm diameters with thread lengths of 16 and
32 mm, respectively. Regardless of the lengths of the screw, both lengths are
threaded. The malleolar 4.5-mm screw is also included in this group, but it is unique
in that it has a self-tapping thread. Choosing the right drill size and tapping the hole
is the key to a safe purchase. Plastic and metal washers are commonly used with
these types of screws to reattach ligament tears or to increase compression between
the fragments by providing a larger cortical surface area for screw head.

3.2.3 Self-Tapping, Self-Drilling Screws

The self-tapping screws are the same sizes as cortical screws. A small portion of the
ends of these screws are used to remove bone fragments. Self-tapping screws have
a lower pullout strength due to their structure. These screws are preferably used for
external fixation pins [21].
312 Y. Zhang et al.

3.2.4 Locking Screws

The locking screw is a self-tapping screw with a locking screw at the head. These
screws require accurate predrilling so that the locking plate is tightly attached to the
locking plate and requires a special screw drivers for implantation.

4 Plate and Screw Fixation

Pauwels et al. firstly defined and applied the tension band principle to fix fractures
and nonunion. This engineering principle applies to the transformation of the tensile
force into a compressive force on the convex side of an eccentrically loaded bone.
This is accomplished by placing a tension band (bone plate) across the fracture on
the tension (or convex) side of the bone. The tension is counteracted by the tension
band at this position and converted into a compressive force. If the plate is applied
to the compression (or concave) side of the bone, it is likely to bend, fatigue, and fail
[22]. Therefore, a basic principle of tension band plating is that it must be applied to
the tension, and the bone itself will get a compressive force, so the tension band
device does not require a heavy and rigid tension band principle and is also used for
some olecranon and patellar fractures. Tension bands and axial compression are
often combined when using plates and screws [23–25].
We have found that almost all plate hole breaks occur at the plate hole near frac-
ture area [26]. Therefore, the hole area seems to be the weakest part of the board,
and naturally it is a place for improvement. We only widened the locking compres-
sion plate (LCP) in the hole area to make it a gourd-shaped LCP to increase the
strength of the plate and reduce the plate breakage (Fig. 12.8) [27, 28]. After a series
of axial loading single cycle to failure test, torsion single cycle to failure test, four-

Fig. 12.8 Gourd-shaped a

LCP designed to enhance
the plate strength in order
to reduce plate breakage.
(a) The Gourd-shaped LCP
(up) and LCP (down)
viewed from above; (b)
Gourd-shaped LCP (up)
and LCP (down) viewed
from below b
12 Biomechanics of the Fracture Fixation 313

point bending single cycle to failure test, and dynamic four-point bending test, it is
concluded that the gourd-shaped LCP structure has greater stiffness, strength, and
longer fatigue life than LCP. This may be a more reasonable LCP that can reduce
the rate of clinical breaks [29].
Our team used a new anatomical plate and compression bolt fixation technique,
combined with a small incision of the posterior foot, to treat intra-articular calcaneal
fractures and achieved good or excellent clinical results, and had fewer soft-tissue
problems (Fig. 12.9) [30]. Compared to the conventional plate and cancellous
screws technique, our fixation technique requires higher loads to cause structural
failure, which may be related to the design of the implant. According to the mea-
surement of the calcaneus specimen and the data of the three-dimensional CT image
of the calcaneus, the anatomical steel plate and the compression bolt were designed.
The use of conventional anatomical plates and cancellous screws to fix a calcaneal
fracture is characterized by compression of the plate to the lateral wall of the calca-
neus. The actual stability lies in the friction between the plate and the bone, which

Fig. 12.9 (a) components

of the calcaneal
a
fracturefixation system; (b)
the anatomical steel plate
viewed from up; (c)
post-operative lateral and
posteroanterior radiograph;
(d) post-operative
CT images

b
314 Y. Zhang et al.

Fig. 12.9 (continued)

can easily be achieved by our anatomic plate and compression bolts. Putting the
compression bolts together can be seen as another piece of plate that is compressed
onto the inner side wall of the bone specimen to provide higher friction and restore
the width of the calcaneus.
Another example was the application of compression bolt in the treatment of
Schatzker type II–VI tibial plateau fractures (Fig. 12.10), in which joint surface
widening and collapse are commonly accompanied [31, 32]. The traditional metal
plates and screw fixation of fractures of such types are commonly associated with a
high rate of postoperative reduction loss, which likely result in the development of
traumatic arthritis. Our preliminary reports of using this compression bolt presented
the favorable results, both in biomechanics and clinical effectiveness.
12 Biomechanics of the Fracture Fixation 315

Fig. 12.10 Application of

compression bolt in the
treatment of Schatzker type
II–VI tibial plateau
fractures

compression bolt

4.1 Locking Plates

Locking plates are a combination of steel plate technology and percutaneous bridge
plating technology using locking screws as fixed angle devices [33]. Locking steel
plates provide a stronger, longer lasting fix than nonlocking steel plates [34]. They
have been proven to allow for greater loads bearing than regular plates. The Less
Invasive Stabilization System (LISS) (Synthes, Inc., West Chester, PA) uses unicor-
tical locking screws that allow for greater elastic deformation than conventional
plating systems. The locking plate can also be used in combination with locking and
unlocking screws, mechanically similar to a pure locking structure. The locking
plate works best on osteoporotic bones, where pulling out the steel plate is problem-
atic. They also provide sufficient load-bearing strength to avoid the distal femur,
proximal humerus, and medial and lateral plates of the tibial plateau. However, the
locking plate structure also has an inherent that inhibits the movement of the frac-
ture site, making it insufficient to stimulate callus formation. Therefore, the locking
plate of the distal femoral fracture can result in insufficient and asymmetrical ankle
formation, with minimal deposits in the proximal cortex. A recent study of locking
plates for distal femoral fractures confirmed this and showed a nonhealing rate of
10–23% and a reoperation rate of open fractures of 31%.

5 Intramedullary Nail Fixation

Satisfactory stable intramedullary fixation of the fracture is possible under the fol-
lowing conditions:
316 Y. Zhang et al.

1. When a non-comminuted fracture occurs in the narrowest part of the medullary

canal, it can be considered to unlock the intramedullary nail; not only the lateral
force and shear force are eliminated, but also the rotational force is controlled. If
the medullary canal of one fragment is much larger than the other, it often results
in poor control of the rotational force; in these cases, interlocking techniques are
required. In general, the interlocking screws should be placed at least 2 cm from
the fracture to provide sufficient stability for postoperative functional activity.
Axially unstable fractures are best treated with static or double-locked nails.
2. The curvature of the bone must be taken into consideration when selecting the
type of staple and determining the degree of reaming necessary. Biomechanically,
unlocked nails achieves stability by a curvature mismatch in curvature between
the bone and the nail, resulting in a longitudinal interference fit. If curvature
mismatch is large, more reaming will be required. The entry portal is critical for
all nails and should be in areas where the insertion force is minimized. In the
femur, this is a straight nail that conforms to the medullary canal in the piriform
fossa, or a nail that is curved at the proximal trochanter with a slightly lateral
proximal bend. For the tibia and humerus, the offset between the entrance and
the alignment of the tube create a powerful force on the posterior and medial
cortex, respectively. The humeral head of the nail begins to reduce the insertion
of the force into the tibia.
3. Sufficient diameter and continuity of the medullary canal are prerequisites for
intramedullary nail techniques. Excessive reaming should be avoided as it sig-
nificantly weakens the bone and increases the risk of thermal necrosis. We rec-
ommend reaming until the cortical “chatter” is encountered, i.e., “reaming to
accommodate,” but never insert a nail larger than the diameter of the tube. In
general, we use nails 0.5 or 1.0 mm smaller than the largest reamer.
4. The locking intramedullary nailing technique should allow the fracture to be
nailed into the joint 2–4 cm. These techniques require the use of locking screws
or tightening screws. These techniques require the use of blocking screws or
“Poller” screws. A new design of an intramedullary nail with an oblique distal
locking screw and a screw that can be locked into the incision to form a fixed
angle can increase the stability of these metaphyseal fractures.
A perfect intramedullary nail has not yet been designed. Different bone contours
make this nail impossible, but improvements in the design of the intramedullary nail
continue. Special nails may be designed for each bone, all types of fractures, frac-
tures or the same bones in different areas. The intramedullary nails should meet the
following requirements:
1. It should be strong enough to provide sufficient stability to maintain alignment
and position, including preventing rotation; it should include the necessary inter-
locking screws only.
2. It should be constructed so that contact-compression forces can impact the frac-
ture surfaces, an ideal physiological stimulus.
3. It should be easy to remove when placed; accessories are provided for easy
movement.
12 Biomechanics of the Fracture Fixation 317

Before selecting this technique, surgeons should be aware that intramedullary

fixation, like other internal fixations, may present complications. This is not a tech-
nique that can be used at will. We recommend the following considerations:
1. Adequate preoperative planning must ensure that the fracture can be fully stabi-
lized within the working area.
2. The patient should be able to tolerate a major surgical procedure. Patients with
severe pulmonary injury should be taken special consideration, because the
added fat emboli from the procedure may intensify pulmonary problems.
3. The proper length and diameter of the nail must be available before the [35–37]
surgery is determined.
4. Appropriate equipment, well-trained assistants, and optimal hospital conditions
are necessary for successful insertion of an intramedullary nail.
5. A metal nail is not a substitute for the union and if subjected to excessive will
also bend or break the strain during the recovery period.
6. Closure nailing techniques should be used whenever possible, using these tech-
niques to improve healing rates and reduce infection; [38–41] however, surgeons
must be familiar with both open and closed techniques. As more experience is
gained with closed techniques, fewer and fewer fractures are needed for open reduc-
tion [42, 43]. However, limited open reduction is better than accepting a poor closed
­reduction. This situation most frequently occurs in high-energy subtrochanteric
femoral fractures, traction does not adequately correct flexion and abduction.

5.1 Types of Intramedullay Nails

Just as plate, intramedullary nail has an anatomic and functional name. The central
body nail is inserted into the bone in a straight line with the medullary canal. It
interferes longitudinally with the bone through multiple points of contact [44–49].
They rely on restoring bone contact and stability to avoid axial deformation of the
fracture during rotation [50, 51]. The classic Küntscher cloverleaf and Sampson
nails are examples of centromedullary nails. The condylocephalic nails enter the
bone of the condyles of the metaphysis and usually enter the opposite metaphyseal-
epiphyseal area. They are usually inserted into groups to increase rotational stabil-
ity. Ender and Hackenthall pins are examples of condylocephalic nails.
Cephalomedullary nails have a centromedullary portion but it is also allowed to be
fixed to the femoral head. The Küntscher Y-nail and Zickel subtrochanteric nail are
examples of this type [52, 53].
Interlocking techniques further improves these classics by adding interlocking
centromedullary and interlocking cephalomedullary nails [54–56]. Interlocking
nails allow longer working length of the interlocking nail screw axial and rotational
deformation resistance of fracture. Modney first designed the first interlocking nail.
Küntscher also designed an interlocking nail (the detensor nail), which was modi-
fied by Klemm and Scheilman and later modified by Kempf et al. These pioneers
318 Y. Zhang et al.

developed techniques and implants that form the basis of some designs and
­techniques used today. Cephalomedullary interlocking nails, designed to treat com-
plex fractures and the proximal femur, were axially and rotationally unstable, such
as complex subtrochanteric fractures, pathologic fractures, and ipsilateral hip and
shaft fractures. These nails can be secured with bolts, nails, and special lag screws
such as Russell-Taylor reconstruction nails, Williams y nails, and Uniflex nails [57].
The current intramedullary nails for femoral fixation design reflect regional internal
fixation nails. Antegrade femoral nails can be performed through the piriformis or
trochanteric inlet. The retrograde femoral nail passes through the entrance between
the femoral condyles [58, 59].
Interlocking fixation is defined as a dynamic, static, and double lock. Dynamic
fixation controls bending and rotational deformation but allows axial load transfer
of the bone. Axial stable fractures and partial nonunion can be fixed by power. Static
fixation controls the rotation, bending, and axial load, so that the implant has more
bearing potential and reduce the fatigue life of the equipment. It is particularly use-
ful in crushing, nonisthmal fractures of the femur and tibia. The double-locked
mode controls bending, rotational forces, and some axial deformation, but some
shortening occurs due to the ability of the screw to translate axially within the nail.
This type of fixation is often used for humerus fracture with delayed union and not
healing.
The dynamics of the interlocking nails were originally designed to avoid fracture
healing, [60] as it is theoretically believed that static interlocking will stop the repair
of the fracture. This technique involves conversion of the static mode to a dynamic
mode by removing the screws from the longest fragment. Dynamization increases the
fatigue life of the nail by reducing the load-carrying capacity of the nail while increas-
ing the compressive force at the break point; however, if there is insufficient cortical
stability or bone regeneration before exercise, shrinkage may occur [45, 61, 62].

5.2 Reamed Versus Unreamed Intramedullary Nailing

For patients with multiple fractured long bone fractures, the need for reaming for
intramedullary nailing has been controversial [63]. Physicians who support non-
reamed nails emphasize the lack of physiological effects of reaming, such as fat
embolism in the lungs [64, 65]. Experimental evidence suggests that reaming has an
adverse effect on lung function. This adverse effect does not appear to be apparent
in most clinical patients; however, some authors believe that the development of
pulmonary complications may be related to the severity of the associated chest
injury, rather than to the reaming of the medullary cavity. Studies supporting the
reaming nail showed no statistically significant difference in the incidence of pul-
monary complications in patients with and without reaming [66]. Due to various
factors leading to the development of adult lung failure syndrome, it is difficult to
determine which patients’ lung expansion may be harmful. Whether the long bone
12 Biomechanics of the Fracture Fixation 319

reaming nail increases the frequency of infection is another controversial area.

Current clinical data show no significant difference in infection rates between
reamed and non-reamed intramedullary nail.

6 External Fixation

External fixation is accepted in trauma management, ranging from damage control

to final treatment. External fixation requires more careful clinical and radiographic
monitoring than internal fixation, but the general application and management prin-
ciples are absolutely straightforward, [67, 68] and its versatility allows it to be used
in a variety of fractures [69, 70]. However, external fixation is not suitable for all
fractures; [71–73] when other forms of fixation, such as screws, plates, or nails, are
more suitable, it should not be used [74].
External fixator should be used when the other methods of fracture fixation are
not applicable, although the external fixation will cause inconvenience to the patient
and is highly likely to cause surface needle infection, it fills the clinical vacancy
[75–77]. After high energy trauma with open injuries, plates and intramedullary
nails are sometimes considered an unacceptable risk of deep infection. Although the
degree of comminution and the extent of involvement sometimes lead to inherent
­instability of the fracture morphology, the external fixator can even better mechani-
cally control the fracture through the joint. Unlike plates and most intramedullary
nails, external fixator provides an opportunity for postoperative correction. The
adjustability of the external fixator has been unique until recently, partly explaining
why they continue to play an important role in musculoskeletal wound care. External
fixation has become the preferred method for treating some of the most challenging
bone pathological diseases encountered in the clinic [78]. Although there are alter-
native treatments, it is still an important factor in limb salvage in early and late bone
remodeling of severe limb injuries [79]. This is currently the only system that allows
surgeons to control fixation flexibility during bone healing. External fixtures have
undergone tremendous changes, from the most primitive combination of wood ply-
wood design to the modern design of widely used metals and composites. The
development of these devices has brought many complications and it has become a
more technically demanding process. Despite these factors, many surgeons around
the world continue to use external fixators to treat complex fractures, segmental
defects, and congenital malformations. The work of many clinicians, researchers,
and engineers around the world is responsible for the current external fixture design
[80]. For example, the dispersion and compression mechanisms of modern equip-
ment are attributed to Lambret in 1911. In 1931, Pitkin and Black field first pro-
posed a double cortical pins to connect two external fixation clips as a bilateral
frame to promote fracture healing. Anderson et al. published a series of papers from
1933 to 1945, outlining the application of half-pins and transfixation pins in various
long bone fractures, arthrodesis, and limb lengthening surgery [81]. These incre-
320 Y. Zhang et al.

mental improvements have resulted in currently available designs, providing three

main configurations of external fixtures [82].
Professor Gavril A. Ilizarov’s contribution to the modern design of unilateral
and circular external fixes should be recognized [83–85]. He also invented meth-
ods for limb salvage and bone extension by distraction osteogenesis. Distraction
osteogenesis is a fixture for us to use mechanical force to stimulate the bone
regeneration process clinically. This is achieved by a special form of external fix-
ture called an annular fixture. Ilizarov found that these external frames can be
used in a variety of applications, including post-traumatic and congenital limb
reconstruction, treatment of osteomyelitis, regeneration of bone defects, defor-
mity correction, and complex arthrodesis. These devices take advantage of
Ilizarov’s principle of stretch tissue, relying on a special type of low energy oste-
otomy to preserve local blood vessels. Ideally, only cortical bone fractures are
made, while the medullary vessels and periosteum remain intact at the metaphy-
sis. The initial incubation period allows the osteotomy to begin healing before the
fixture is periodically adjusted to achieve a controlled gradual mechanical stretch.
When the anchor is slowly extended, new bone is formed in the gap created in the
osteotomy by the now familiar distraction osteogenesis process. For example, this
process considers bone reconstruction through bone transport across segmental
defects, using small tensioned Kirschner wires (K-wires) and circumferential ring
supports. When new bone growth occurs at the metaphysis, a healthy bone gradu-
ally shifts to the defect. When the new bone grows out of the metaphysis, the
normal bone gradually shifts to the defect. During the development of similar
stretched tissue, the tension generated by mechanical stretch stimulates new bone
formation, skin, blood vessels, peripheral nerves, and muscles. This impressive
process, bone elongation and regeneration occurs at a rate of about 1 cm per
month. The Ilizarov technique is important in the treatment of nonunion by
mechanical stimulation and regulation of callus and can be used to reconstruct
segmental defects that can be reliably filled far beyond the iliac bone graft. More
importantly, this technology has produced limb salvage with superior quality of
regenerative normal bone.
The circular frame contains the basic components of the rings, the tensioned
wires, and the connected threaded rods. The stability of the frame depends on the
configuration of the components, which will affect the local mechanical environ-
ment around the regenerated bone, and also determining the type, rate, and quality
of the tissue formed. For example, the stability of the structure will change depend-
ing on the type and size of the rings (full ring, partial ring, or arches). Full ring
provides the greatest stability, partially intermediate, and arches the least. The com-
plete ring provides maximum stability, partial middle, and arch. At the very least,
the diameter of the ring is also important, and the smaller ring is more stable than
the larger ring of the same thickness. Stability will also depend on the distance
between the rings, as well as the type and number of ring connectors, such as wires,
rods, and Shantz pins. In clinical cases, different combinations of the circular frame
components are used depending upon the intended application and required
stability.
12 Biomechanics of the Fracture Fixation 321

6.1 Biomechanical Aspects of Fracture Fixation

in Specific Location

6.1.1 Fixation in the Proximal Femur

Fixation of the proximal femur fracture is particularly challenging because during

normal activity, the pressure through the femoral head can reach four to eight times
the body weight [86–89]. This force acts through an important forearm (the length
of the femoral neck) that exerts a large bending load on the fixation hardware [90].
In addition, many of these fractures occur in the elderly, who may have trabecular
bone of low density and poor mechanical quality. In addition, it is generally not pos-
sible to obtain a screw in the cortical bone of the femoral head [91–93].
The major force acting in a basicervical fracture of the femoral neck, fixed with
a sliding hip screw, is the joint reaction force through the femoral head, derived
from body weight and the force generated by muscle movement during walking
[94–96]. The joint reaction force can be divided into two parts. One (Fig. 12.11) is
perpendicular to the axis of the sliding screw, causing the fracture surfaces to shear
along the fracture line, which results in inferior displacement and varus angulation
of the femoral head, and increases the resistance of the screw to sliding. The other
parties parallel to the screw, and the surfaces are joined together by friction and

Total force on
hip

Force component
which creates
binding of screw in
barrel

Force
component
which causes
sliding

135 degress
150 degress

Fig. 12.11 The joint reaction force in the femoral head can be divided into two major components.
The one parallel to the axis of the femoral neck produces sliding and impaction of the fracture
components and the other, transverse to the femoral neck, causes the screw component of the
femoral hip screw to bind, resisting sliding. The higher-angle hip screw has a screw axis more
closely aligned with the joint reaction force so the force component that produces sliding is larger
whereas the transverse force component resisting sliding is smaller
322 Y. Zhang et al.

mechanical interlocking for improved stability. Therefore, the goal of the femoral
neck fixation system is to use the component of the joint force parallel to the femo-
ral neck to encourage the fracture surfaces to slide together. This is the basic prin-
ciple for selecting high angle hip screw when possible.
The following points regarding the sliding hip screw device also apply to the
nail/tension screw device. When the screw slips, since the structure is staggered by
the fracture, the screw is supported by the barrel to prevent the femoral head from
bending down. Adhering to two basic mechanical principles will increase the ability
of the screw to slide within the side plates or nail holes. As mentioned above, higher
angle hip screws are more effective in adjusting slip [97–101]. In addition, the screw
should engage as deep as possible within the barrel. For the force acting on the
femoral end of the screw, if the internal force of the screw in contact with the barrel
is small, the remaining amount of the screw shaft in the barrel is small, and the
internal force in the barrel is increased. This is because the moment (bending load)
generated by the force acting transversely on the screw axis at the femoral head
(Fig. 12.12) acts on the longer force arm or the vertical distance L (the force x is
perpendicular to the edge of the barrel, i.e. the fulcrum)). The balance arm Lb is
shorter because there are fewer screws left in the barrel. Since Fh acts on a longer
arm and F acts on a shorter arm, Fb increases. When the screw is in contact with the
barrel, its internal force Fb produces greater frictional resistance, which requires
more friction to overcome the friction and allow slippage. Sliding hip screws with
two- or four-hole side plates seems to provide an equivalent anti-physiological com-
pression load. There are several factors that affect the fixation strength of the femo-
ral neck using multiple screws, but the number of screws used (3 or 4) is not a
significant factor.
Factors that increase this type of fixed strength include more long-axis screws
with transverse fracture lines, larger femoral skull mass density in the position of
the screw, and less comminuted fractures, shorter arm loads on the arm (shorter The
distance from the center of the femoral head fracture line). However, the most
important factor is the quality of the reduction because of the importance of cortical
support in reducing fracture displacement. Under physiological load, several mech-
anisms of fixed failure were observed (Fig. 12.13). In some cases, the screw bends
downwards, especially when it is unable to support a fracture surface below the
screw due to fracture comminution. If a washer is not used to distribute the screw
load to the bone, when the cortex is thin, the screw head will pass through the cortex
near the greater trochanter. Finally, if the screws do not support well down through
the fracture, they may rotate downwards, causing the femoral head to invert.
Supporting the hypodermis with at least one screw is a mature clinical technique
that may help prevent this from happening.

6.1.2 Fixation Around the Metaphyseal Region of the Knee

Both supracondylar fractures of the femur and tibial plateau fractures are challeng-
ingly stable because they usually involve the fixation of multiple small cancellous
bones [102–104]. Mechanically comparable alternative methods for supraorbital
12 Biomechanics of the Fracture Fixation 323

Hip force Fh
Force of
Le barrel on
screw
Lb

Fb

Fulcrum

Le
Fh
L’b

F ’b

Fh * Le = Fb * Lb = F ’b * L’b

Lb decreases,
Fb increases
If Fb increases,
resistance to sliding
increasese

Fig. 12.12 The greater the length of the sliding screw within the barrel, the lower its resistance to
sliding. In this diagram Fh is the component of the joint reaction force perpendicular to the axis of
the screw. The inferior edge of the proximal end of the barrel is the location of the fulcrum in bend-
ing. An internal force, Fb from the surface of the barrel acts against the screw to counteract Fh. For
equilibrium, the moments produced by Fh(Fh × Le) and Fb(Fb × Lb) must be equal. If Lb, the distance
from the point of application of internal force Fb to the fulcrum, decreases, Fb must increase to
therefore the resistance to screw sliding will increase (Le is the length of the screw beyond
the barrel)
324 Y. Zhang et al.

a b
Moment arm of load
component which
creates bending

Bone density at
screw purchase
sites

Degree of inferior
comminution

Angle of
fracture line

Fig. 12.13 (a) Some factors that decrease the strength of femoral neck fracture fixation include
decreased bone density, a more vertical fracture surface (which reduces buttressing against bend-
ing), and a longer moment arm or distance of the center of the femoral head to the fracture line. (b)
Observed mechanisms of failure of femoral neck fixation using screws include bending of the pins,
displacement of the screw heads through the thin cortex of the greater trochanter, especially if
washers are not used, and rotation of the screws inferiorly through the low-density cancellous bone
of the Ward triangle area until they settle against the inferior cortex

fixation include condylar plates, plates and plates that use lag screws at the fracture
site. All equipment tests seem to provide similar structural stiffness [105–108]. The
most important factor in determining plate fixation is to maintain contact at the
cortex opposite the fixture. A fixed structure without cortical contact is only 20%
harder than a fixed structure with cortical support. It has been found that the use of
a retrograde IM supracondylar nail results in a 14% reduction in axial compression
strength and a 17% reduction in torsional strength compared to fixed-angle side
panels. However, longer nails (36 cm) enhance fixation stability compared to shorter
nails (20 cm). Several new fixation systems have been described as stable for supra-
condylar fractures of the femur. The Minimally Invasive Stabilization System
(LISS) uses a low profile plate with a single cortical screw distal end, which is also
locked to the plate. Compared to a conical screw or a support plate, the LISS plate
produces a structure with greater elastic deformation and less sedimentation.
The tibial plateau fracture is difficult to stabilize [109–111]. Given the patient’s
prognosis, risk factors for reduced reduction have been shown to include patients
older than 60 years, premature weight bearing, fracture comminution, and severe
12 Biomechanics of the Fracture Fixation 325

Screw in
cancellous bone
a Applied
b
load

Tension in screw
with loading

Bending
of plate
Screw in
cortical
bone

Fig. 12.14 Two alternative methods of fixation of tibial plateau fractures: (a) transverse screws
combined with a buttress plate and (b) transverse screws alone. The buttress plate provides addi-
tional support in bending as the tibial fracture component is loaded in an inferior direction and
allows the screws to engage the thicker, more distal cortical bone

osteoporosis [112–114]. Different fixing methods include using a wire or screw

alone (Fig. 12.14), [115, 116] or placing a screw through an L-shaped or t-shaped
plate to support the cortex. Wires of various shapes have been tested and the results
show that the stiffness of the structure increases with the number of wires, regard-
less of the direction of the wires. As shown in Fig. 12.14, when the screw is used
alone and the tibia fragments are pressed to the distal end through the joint, the
screw needs to resist the bending force. By adding plates, not only the load is dis-
tributed to the plate, but also additional screws can be placed at the distal end of the
cortical bone, which is stronger at the metaphysis of the humerus. One disadvantage
of the support plate is that it requires peeling off the soft tissue during application,
[117–120] which may compromise the blood supply [121–124]. Regardless of the
specific configuration of the screw, the I-plate and screw fixing are most resistant to
axial compression loads. Studies of different plate configurations have found that
for bilateral tibial plateau fractures, bilateral (outer and medial) plates can reduce
sag by about 50% under axial loading compared to single-sided locking plates. For
the medial platform fracture, the medial support plate directly supports the load, and
its mechanical properties are significantly better than the outer locking plate. A new
option is the proximal humerus staple with multiple interlocking screws. Under the
combined action of axial load, bending and rotation, the stability of the nail is equiv-
alent to double steel plate, which is higher than the use of locking steel plate, exter-
nal fixator or traditional tibial nail. The device can be used in cases without
significant proximal (joint) comminution [125, 126].
326 Y. Zhang et al.

6.1.3 Fixation of the Humerus

Proximal humerus fractures fixed with a locking plate provided greater stability
against torsional loading, but is similar to blade plate structure when bent, as both
fixation devices are loaded as tension bands in bending [127]. When comparing dif-
ferent types of blade plate structures, the hardest structure uses an eight-hole, low-
contact dynamic compression plate that is shaped into the shape of the blade and
secured with a diagonal screw that is triangular to the end of the blade. This arrange-
ment is quite harder than other blade plates or T-plate and screw structures. A poten-
tial problem is the screw penetration of the subchondral bone in patients with
osteoporosis. Due to the stiffness of the locking plate-screw structure, if there is any
“settling” in the fracture site, the locking screw may penetrate the joint. The inci-
dence of intra-articular screw penetration in the proximal humeral locking plate was
significantly higher than that of conventional implants [14].

6.1.4 Fixation of Spine

For the treatment of spinal fractures, the goals are to reduce the fracture, protect the
neurological function, and accelerate functional recovery [128]. The theory of
3-column model is the basis of the treatment rationale in spinal fractures [129].
Injuries that represent 3-column instability require operative stabilization even if
there is no n­ eurological deficit. The attachments of spinal fixation system consist of
hooks, wires and screws, which produce different types of holding force [130, 131].
Wires could resist tension, hooks could resist driving force against the bone, while
screws could resist forces from all directions except rotation. Therefore, screws are
widely used for spinal fixation because of the superiority.
Posterior internal fixation system with pedicle screws has become popular for the
treatment of spinal fracture. When applying lumbar spinal fixation, some principles
can be considered. Screws are vulnerable to toggling when they are placed into
pedicles. The screw tends to toggle about the base of the pedicle because of the
cortical bone. In order to reduce toggling, the screw head should be locked to the
rod of plate (Fig. 12.15).
Longer fixation could reduce forces acting on the screws because of the effect of
the greater lever arm of a longer rod along with more vertebrae. Whereas it is not
beneficial for a clinical perspective because the reduced spinal motion. It is also
important to add a fusion cage to reduce forces in the fixation. Coupler bars could
connect the fixation rods to form an H configuration, and prevent the rods from
rotating medially or laterally, as shown in (Fig. 12.16). The coupler bars could sig-
nificantly enhance the torsional and lateral bending stability of the implant.

6.1.5 Fixation for Pelvic Fractures

68.3% of pelvic fractures are unstable fractures, which are serious injuries, and the
mortality rate is up to 19%. The stability of the pelvis is mainly related to the integ-
rity of posterior pelvic ring. There are many methods available, including iliosacral
12 Biomechanics of the Fracture Fixation 327

Fig. 12.15 (a) The Pedicle cortex

mechanism of toggling of a a
single pedicle screw
subjected to a Vertical loading
caudocephalad loading. (b)
The fulcrum is at the base
of the pedicle, the
narrowest region with little
cancellous bone. The screw
toggle compresses the bone Fulcrum
within the vertebral body.
(c) Toggling is reduced if
the plate or rod to which b
the screw connects
contacts the vertebra over a
wide surface, which
prevents it from rotating,
whereas the screw head is
locked to the plate or rod

Cancellous bone compression

disengagement from the
screw threads

Vertical loading

Screw head locked in

plate reduced toggling

(IS) screws, sacral bars, tension band plate (TBP), triangular osteosynthesis, and so
on. IS screw fixation is a well-recognized technique for treating the posterior pelvic
ring disruption. It is implanted in the supine or prone position and has such merits
as short operative time, slight trauma, and minimal invasion. However, it remains a
technically demanding procedure, and both doctors and patients are exposed to
large amounts of radiation as continuous fluoroscopic or computerized tomography
(CT) guidance for appropriate screw insertion. In addition, higher rates of iatro-
genic injury is one of the disadvantages, seriously affecting the clinical use of this
technology. To avoid these limitations, our team developed a novel minimally inva-
sive adjustable plate (MIAP) (Fig. 12.17). This MIAP is designed according to the
anatomy of the pelvic ring and simulated the sacroiliac complex structure of
“bridge.” It can be better attached the posterior aspect of the sacroiliac joint without
bending and adjusted the length of the connecting rod to pressure or separation of
328 Y. Zhang et al.

Screws with axes all

parallel
Subconstruct of two F M
Vertebra Applied load
screws securely
Link 3 fastended to a
longitudinal member Link 3
left=link 2, right=link 4
Link 2

Fracture
d
vertebra
Link 4

vertebra
Link 1
Link 1

Fig. 12.16 Without a coupler bar between two longitudinal rods (left), they can rotate when a
lateral moment or axial torsion is applied (right). A coupler connecting the rods to form an H con-
figuration reduces this effect

Fig. 12.17 Structure of

MIAP for posterior pelvic
ring injury

fracture end. Moreover, during the operation, two small incision were made for
placing the MIAP, which can effectively reduce the blood loss and shortened the
operation time.

6.1.6 Fixation for Tibiofibular Syndesmosis Injuries

Operative fixation and anatomic reconstruction of the distal tibiofibular syndesmo-

sis is important to achieving an optimal outcome. An ideal implant to stabilize the
tibiofibular syndesmosis should allow early mobilization for weight-bearing and be
strong enough to maintain reduction in the syndesmosis. The screw fixation has
been considered the standard management which can provide rigidity of the distal
tibiofibular syndesmosis and easily be performed. However, this rigid fixation may
reduce the physiologic motion of the syndesmosis and the screw breakage may
12 Biomechanics of the Fracture Fixation 329

occur. In recent years, the suture button as a flexible fixation has been applied. The
suture button allows physiologic motion in the tibiofibular joint and maintains the
reduction of the ankle. However, the suture between buttons can gradually release
under daily motion. To avoid these drawbacks, our team developed a novel ­technique
called “bionic fixation” (Fig. 12.18). The screw segment may afford an improved
rigidity and stability. The high strength non-absorbable suture located between the

Leading portion

Threaded portion

Break-off groove

Screw nut

High strength
non-absorbable
suture

Fixing button

Fig. 12.18 (1): Schematic diagrams showing the bionic fixation construct (2): Schematic dia-
grams showing the three techniques for fixation of the tibiofibular syndesmosis. (a) A hole was
drilled with a 2.8-mm drill bit from posterolateral fibula to anteromedial tibia. (b, c) A 3.5-mm
cortical screw was then inserted through the hole from the fibular side. (d) After the cortical screw
was removed, the hole was over-drilled with a 4.0-mm drill bit. (e) A 3.5-mm main screw was
passed through the hole from the fibular side and the fixing button of the screw-tail was tightly
attached to the fibula, then the screw nut was installed and adjusted on the tibial side to make the
construct tightened properly. (f) The exposed leading portion of the screw was broken off. (g) The
bionic fixation construct was removed. (h) The non-absorbable suture of the fixing construct was
pulled from the fibular side to the tibial side. (i) The suture was threaded into the tibial button,
looped, traversed through and securely tied over the fibular button. This process was repeated until
there were three independent groups of sutures in the channel
330 Y. Zhang et al.

a b c

d e f

g h i

Fig. 12.18 (continued)

tibia and fibula may retain the motion of the syndesmosis to the maximum degree.
Comparing with the Endo button fixation, the bionic fixation can provide more sta-
ble fixation force and retaining the motion function of syndesmosis. Besides, this
technique has a low cost and is easy to perform.

6.1.7 Fixation for Posterior Column Acetabular Fractures

Operative reduction and internal fixation is the standard treatment for unstable pos-
terior column acetabular fractures to allow early mobilization and decrease the risk
of posttraumatic arthritis. The conventional methods of fixation involve lag screws
and reconstruction plates, or both in combination. Conventional fixation depends on
the structure of the acetabulum and the surgical technique because of the specific
anatomy of posterior column of acetabulum. The conventional reconstruction plates
need to be bended based on the size of the size of the acetabulum. Using screws and
two reconstruction plates to obtain better fixation is a potentially serious traumatic
complication. Our team designed a W-shaped acetabular angular plate (WAAP) for
posterior columns of the acetabulum fractures (Fig. 12.19). This novel fixation
includes a W-shaped locking plate and the guide apparatus. Comparing with other
12 Biomechanics of the Fracture Fixation 331

Fig. 12.19 The W-shaped

acetabular angular plate. R
right, L left

reconstruction plates, the WAAP provides some advantages. First, the WAAP is
anatomically pre-contoured and could match the surface of the posterior acetabu-
lum column properly. Second, the extended fixation range spans from the greater
sciatic notch to the rim of the posterior acetabulum. Third, the WAAP has locking
holes which can achieve angular stability.

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Chapter 13
Biomechanical Principles in Designing
Custom-Made Hip Prosthesis

Jia Hua

Abstract Total hip replacement has increasingly become popular in treating osteo-
arthritis, relieving pain, restoring joint function and correcting the deformities.
However, due to the wide variations of the anatomy in femoral bone between indi-
viduals, the commonly used off-the-shelf standard hip stems cannot consistently
achieve the good fit, thus the clinical outcome is compromised. On the other hand,
an increasing demand for restoring the normal life quality after total hip replace-
ment including play sports and other activities, especially with the coming era of the
precision medicine and digital orthopaedics, and the availability of the advanced
surgical navigation systems and 3-D printing technologies, the patient-specific hip
prostheses have become ever favourable.
The rationale for using the custom stem is not only for the complex cases, but also
for the routine cases in order to achieve better clinical outcomes and longer survivor-
ship. This chapter will focus on how to design a custom hip stem for an individual
patient based on the bone geometry, deformities and pathological conditions. The
advantages and disadvantages of each design options are considered and analysed.

Keywords Hip joint arthroplasty · Total hip replacement · Design of hip stem
Custom hip stem · Osteoarthritis

1 Introduction

Constantly on the rise in quantities and qualities, total hip arthroplasty (THA) has
become ever popular in the treatment of hip diseases, and in relieving pain, restoring
function and correcting deformities [1]. THA is now one of the most successful
surgical intervention in the century for improving life quality of the patients.

J. Hua (*)
Department of Natural Science, Faculty of Science and Technology, Middlesex University,
London, UK
e-mail: j.hua@mdx.ac.uk

© Springer Nature Singapore Pte Ltd. 2020 339

C.-K. Cheng, S. L-Y. Woo (eds.), Frontiers in Orthopaedic Biomechanics,
https://doi.org/10.1007/978-981-15-3159-0_13
340 J. Hua

According to the 14th Annual Report of the National Joint Registry, over a hundred
thousand hip surgeries were performed in 2016 across the UK except for Scotland,
a 3.5% increase from the previous year, 90% of which were for the treatment of
osteoarthritis [2]. The joint registry data from the USA showed that 443,219 hip
surgeries have been reported between 2012 and 2017; among them revision surger-
ies accounted for 10.7% [3]. One of the concerns is that some of the revision surger-
ies were performed at very early stages after the first procedure, meaning that the
revision patients are no longer old and inactive; some of them now fall into the
physically active group, while the clinical results for revision THR are still inferior
to that for primary THR [4]. In the past, most cases are performed using standard
off-the-shelf hip stems; only a few of the very difficult cases have used the custom
designed prosthesis to correct deformities and provide best stem fixation and better
hip functions.
However, due to wide variations of anatomy in femoral bone and increasing
demand for the normal function of the hip including sports activity, especially with
the availability of the 3D printing technology, the patient-specific custom designed
hip prostheses have become more favourable. This chapter will focus on how to
design a custom hip stem for an individual patient based on their unique bone geom-
etry, deformities and pathological conditions. For those readers who are not design-
ing hip stems such as surgeons and researchers, may probably find the information
in this chapter can also be very useful.

2 Design Consideration of a Custom Stem

2.1 Determination of Cortical Boundary from Images

In order to design a stem that can exactly fit with the femoral cavity, accurately
determining the boundary of cortical bone from the images, either from normal
X-rays or CT scan, is crucially important. Some of the factors can affect the deter-
mination of the boundary.
For normal plain X-ray images, it should normally include the pelvis and down
to the knee joint on AP and lateral views, with the scaled ruler placed on the side
of the femur at the level of the bone. The opposite side is ideally also included
for comparison. This allows the designer to assess the leg length discrepancy,
orientation of the knee and fixed deformities of the lumbar spine and the knee
joint, as these may affect reconstruction of the new centre of the hip.
The images should be clear with adequate contrast, brightness and resolution in
order for designers to identify the boundary, which involves proper adjustment of
kV and exposure time. However, for digital X-rays that have now been exclu-
sively used, the contrast and brightness can be manipulated on the screen; thus,
13 Biomechanical Principles in Designing Custom-Made Hip Prosthesis 341

the line of boundary showed on the images could be altered as a result, which
may not reflect the true boundary of the cortex. For using of CT scan, the deter-
mination of cortical boundary become critical.
Some of the other factors that could also affect the determination of the boundary
are the nature of the diseases and the density of the bone. For example, young
and active patients with osteoarthritis usually have hard bone, especially for a
band of trabecular bone adjacent to the cortex, which are sometimes too hard to
remove. On the other hand, for rheumatoid arthritis, the bone is quite softer,
especially for those under treatment of steroids. Therefore, the cavity can easily
be overreamed and the stem should be designed slightly tighter than normal. All
these should be considered when assessing the boundary of cortex for designing
custom hip stems.

2.2 Stem Design Inside Medullary Canal (Implant Fixation)

2.2.1 Fit and Fill of the Stem Inside the Cavity

To design a hip stem that achieves the best fit with the cavity is always considered
to be of critical importance in order to obtain a long-term success of the surgery.
This requires the geometry of the stem to match that of the femoral cavity. However,
for a stem to reach 100% fill of the cavity is unpractical in which the stem will not
be able to be inserted. Therefore, the designer should not only focus on which part
of the bone the stem should fit with but also assess whether the stem can be inserted
or not. In principle, the proximal medial curve of the femur in calcar region is
regarded as the most priority region which requires an exact fit in order to achieve
immediate stability of the stem and physiological stress transfer to the bone
(Fig. 13.1). However, this design mostly depends on the condition of the bone being
strong enough to carry the load.
The cortical bone on the lateral side of the femur is equally thick and strong as that
on the medial side due to the tensile stress across this region when the bone is loaded.
The lateral curve can provide stem with additional axial stability due to its wedge effect
and avoid stem from valgus tilt over time. However, one of the considerations is how
far should the stem follow the curve. This really depends on the position of the greater
trochanter and how wide is the opening at the neck resection. If the greater trochanter
is too medialized or the opening of the neck resection is too narrow, the lateral flare of
the stem needs to be reduced in order to facilitate the insertion of the stem.
For the anterior part of the femur, the stem geometry should not completely fol-
low the curve of the femur; otherwise the stem will be too thick to be inserted.
Nevertheless, the anterior curve of the stem is very useful in enhancing the torsional
stability when comparing with the thin and symmetrical design.
The design of the posterior part of the stem is simple; basically it is straight.
342 J. Hua

Fig. 13.1 Radiographic

image shows the calcar
region that a stem should
always fit with in total hip
replacement

2.2.2 The Length of Femoral Stems

From biomechanical and clinical points of view, the stem length should be as short
as possible in order for the femoral cavity being least disturbed. The longer the
stem, the more damage to the bone can occur, which leaves revision surgery more
difficult. However, when the stem being too short it can cause instability and high
stress concentration on the lateral bone at the tip of the stem. In most cases, if the
stem geometry can match the normal proximal medial curve of the bone, a total
length of 90–100 mm (around 2 cm below the lesser trochanter) should be adequate
to provide stem stability as well as the physiological distribution of the stresses.
This is because when the proximal stem is properly supported by the medial calcar
bone, the stem tip will not be tilted under load and distribute lower contact stresses
13 Biomechanical Principles in Designing Custom-Made Hip Prosthesis 343

to the bone. In this regard, the design of the short stem is adequate. However, if the
stem fit in the calcar region is not appropriate or uncertain, then the length of the
stem should be increased to engage more cavity in diaphyseal region to avoid stress
concentration on the bone at the tip of the stem.

2.2.3 Determination of Stem Diameters

In most of the cases, to determine the diameter of the stem should be straightfor-
ward, which simply follows the diameter of the femoral canal. However, sometimes
the diameter needs to be adjusted in certain circumstances. The reason for this is
that the shape of the femoral cavity in the diaphyseal region is more likely oval, but
the distal stem is usually in round shape, so that cross-section of the distal stem will
not completely fit with the canal. Therefore, the diameter of the stem can be custom-
ized depending on how much bone can be overreamed on the narrow side.
In some unusual situations where the canal diameter is too small such as less than
6 mm while the patient has normal body weight, the stem diameter designed accord-
ingly could cause a fracture. In this case, a deliberately overream of the bone may
become necessary in order to increase the diameter of the stem, should the thickness
of the cortical wall and quality of the bone be allowed. If in certain cases that the
increase of the stem diameter being impossible which could cause weakness of the
bone, reducing offset of the neck or changing the material of the implant such as
using Cobalt Chrome instead become an alternative option.
On the other hand, if the diameter of the canal being too large such as over
16 mm, then the distal stem designed for may be too stiff that could lead to stress
shielding of the bone. In order to reduce the stiffness of the stem, a few methods can
be applied. One of the common methods is to make a slot in the middle of the stem,
or to remove part of the metal on the medial side towards to distal so that the shape
of the distal stem looks like a half-moon. Both designs can equally fulfil the pur-
pose, but offer different biomechanical benefits, so which method should be applied
depend on the actual cases.

2.3 Stem Design Outside Medullary Canal (Function

of the Hip)

The design of the stems outside the medullary canal is basically to determine the
centre of the femoral head that mainly involves the height, offset and angle of the
femoral stem neck. Different stem neck angle can influence the range of motions of
the hip joint and impingement between the neck of the stem and acetabular cup or
pelvic bone. The neck angle for the standard implants are usually around 45°, or
135° in neck-shaft angle. However, the neck angle for a custom implant can vary,
which depends on the anatomy of the particular patient and surgical requirement, so
344 J. Hua

that the height and offset of the femoral neck are adjusted in each case to suit for the
patients. Nowadays, the modular femoral heads have been exclusively used; there-
fore if the angle of the neck is more vertical, then any plus heads will increase the
height more than increasing the offset, and vice versa.

2.3.1 Height of the Femoral Head

One of the challenges in designing custom hip stem is to determine the height of the
femoral head. It is always attempted to either maintain or equalize the leg length. In
most of the cases, the contralateral side of the femoral head can be referenced for the
affected side in order to make both leg lengths equal. However, if the leg length dis-
crepancy is too large, then only partial correction may be possible in order to prevent
overstretches of the nerves and vessels. For some of the cases, the soft tissues and joint
capsule may need to be extensively released during surgery to allow for pulling down
the leg and reducing the hip joint. In revision total hip replacements, the leg can nor-
mally be pulled down by 2.5 cm roughly; but in the situation such as developmental
dysplasia of the hip (DDH), only limited leg length can be corrected due to long-
lasting dislocation of the hip and shortening of the nerves, vessels and soft tissues. In
some situations, if the cup needs to be placed into the true anatomical acetabulum to
restore anatomical and biomechanical normality, conducting a sub-trochanteric oste-
otomy and removing a segment of the bone may become necessary.

2.3.2 Offset of the Femoral Head

Often less attention has been paid to adjust and optimize the offset of the femoral
neck when designing a hip stem. However, it can be of paramount importance in
affecting the hip joint biomechanically and functionally. The change of the neck
offset directly affects the forces across the hip joint. If the offset is increased, the
forces across the hip joint will decrease in a single leg stance, because the forces
from the abductor muscles are reduced. This can be calculated based on the balance
of the moments from two sides—the centre of the body weight and the force from
the abduct muscles. However, increasing the offset will increase the bending force
across the hip stem. If the stem diameter is too small, the stem fracture will cause
for concern; then the patients’ body weights need to be taken into consideration.
In the situation that the diameter of the stem cannot be increased due to small
cavity of the femur and overream of the bone is not attempted, in order to avoid stem
fracture, reducing offset of the femoral neck can be one of the choices to reduce
bending force across the hip stem. To do so, the distance of the lever arm of the
abductor muscles is decreased, in which more forces will be generated from the
muscle contraction in order to balance the moment of the hip joint when the patient
is in single leg stance. Therefore, the forces across the hip joint will be increased,
which subsequently increase the wear particles from the bearing surface of the joint.
13 Biomechanical Principles in Designing Custom-Made Hip Prosthesis 345

3 Stress Distribution over the Bone

Stress shielding of the bone following total hip replacements has caused major con-
cerns over the past, and many research projects have been carried out to study the
stem geometries that can distribute the normal stresses over the bone [5]. According
to Wolff’s law, if the bone is under-stresses, bone resorption will occur [6]. The
clinical follow-up study showed that 20% of reduction in bone density at the calcar
region has been observed at 1 year after total hip replacements [7]. This may further
lead to bone fracture or loosening of the implants.
A number of factors can contribute to the stress shielding of the bone following
THR. One of the main reasons is the mismatch of the material modulus between the
implant and the bone so that most of the loads are carried by the implant rather than
the femoral bone. The higher Young’s modulus of elasticity for the implant materi-
als (110 GPa for Titanium alloy; and 230 GPa for Cobalt Chrome) comparing with
the bone (17 GPa for cortical bone at mid-shaft of the femur under compression
load) seem making this occurrence of stress shielding inevitable. In the past, some
of the hip stems have been designed with lower Young’s modulus such as Identifit
implant, but the clinical results were very disappointing, with 17% of revision rates
over the 2 years [8]. The reason for this is that reducing the stiffness of the implant
will increase interface micromotion between the stem and bone, which will inhibit
the bone ingrowth into the stem. Some of the other factors such as stem fails to
closely contact with the bone in the calcar region resulting in less stress transfer to
the bone also play a critical role. Therefore, the match of the stem geometry with the
bone in order to achieve a line-to-line fit and maintain long-­term bone qualities is of
the most importance.
However, some researches have shown a wide variation in the geometry of the
femur between individuals, in which three types of femoral shape have been sum-
marized. The three shapes include normal, stovepipe and champagne bottle, which
represent different ratios in width between proximal and distal canals [9]. For this
reason, the off-the-shelf standard hip stems cannot consistently provide an optimal
fit for each patient.
In the occurrence of loading carried by the distal stem, where the distal fit is too
tight but the proximal bone contact is not achieved, the proximal stem will transfer
less stresses onto the bone. Over the time, the proximal part of the bone will undergo
stress shielding and bone resorption while the distal part will show the formation of
the para-prosthetic pedestal bone [10].
On the contrary, the custom designed hip stem can reliably provide the best fit
and transfer close to normal load onto the bone. A clinical follow-up of custom hip
stems showed that the bone densities measured by DEXA scan at 2 years
­postoperatively were maintained at 97% when compared with that measured imme-
diately after surgery [11].
Therefore, in most of the cases for uncemented fixation, the distal stems should
only be designed for sliding fit to avoid distal loading, in which the function of the
distal stems is only served to prevent the stems from tilting.
346 J. Hua

4 Stem Stability (Relative Motion and Migration)

Among all other factors that may have detrimental effects to the survivorship of the
hip implants, failing to obtain immediate fixation of the stem is the most critical. In
situations where the proximal bone is too poor to load, distal fixation should always
be regarded as an alternative. Primary factors relating to the stability of the stems
include relative motion between stem and bone, and migration of the stem over time.
Relative motion is defined as a recoverable relative position of a component
relative to its host bone after a cyclic loading (Fig. 13.2). This is due to elastic or
plastic deformation of the materials or geometric mismatch between bone and com-
ponent. The amount of relative motion for uncemented stems can vary but should be
around 10–150 μm. It can occur either in localized areas or over the entire interface.
If the motion is over 150 μm, osseointegration and biological fixation of the stem
will unlikely take place [12]. This phenomenon is due to higher tolerance of fibrous
tissue to strain energy in the interface than that of bone tissue. Furthermore, the rela-
tive motion can induce more shear stresses and strains in the bone, which is not
favourable to bone tissue ingrowth.
Therefore, in order to achieve long-term stability and biological fixation of the
stem through osteointegration, immediate mechanical fixation of the stem with the
bone is of critical importance. This to large degrees relies on the geometry of the
stem designed to match the medullary canal. To fit stem in the proximal medial
region of the canal has always been regarded by many designers as the priority for
achieving immediate fixation of the stems.
Migration is defined as a permanent change of position or subsidence of a com-
ponent relative to its host bone after many cyclic loadings over a period of time
(Fig. 13.2), in which the distance between the final position and initial position of
the stem is measured. This can similarly be due to elastic or plastic deformation, but
the geometric mismatch between bone and component plays large roles. In situa-
tions that stems have been in situ for many years, progressive bone resorption and
RELATIVE MOTION BETWEEN

TOTAL MIGRATION
STEM AND FEMUR

AFTER 2500 CYCLES

STEADY STATE

MICROMOTION
MOST MIGRATION AT 2500 CYCLES
OCCURS IN EARLY
CYCLES

NUMBER OF CYCLIC LOADING

Fig. 13.2 Diagram shows axial migration and micromotion of the hip stem in relation to the
femoral bone
13 Biomechanical Principles in Designing Custom-Made Hip Prosthesis 347

extensive osteolysis can also lead to considerable migration of the stem, eventually
causing aseptic loosening and failure of the stems.
Previously a number of studies have shown that early migration of the stem cor-
relates with the long-term clinical success. If the stems were initially stable and only
migrated less than 2 mm within 2 years, they were likely to be successful in long
term; otherwise if the stems were not stable at beginning and migrated over 2 mm
in 2 years, these stems were likely to fail [13–15]. In general, uncemented stems
need more time to stabilize which could take up to 1–3 months after surgery.
Therefore the uncemented stems may be migrated more at early stage which mostly
depends on the geometry of the stem, and also how tightly the stem has been
impacted during surgery. Once the stem has settled, the uncemented stem should be
as stable as the cemented stem for the initial stage. With porous and hydroxyapatite
coating for most of the uncemented stems, bone ingrowth and long-term biological
fixation will take place. Progressive migration of the stems for both cemented and
uncemented fixation indicates that a failure of the stem will soon occur.
The custom-made hip stems have achieved superior results for both relative
motion and migration when compared with the standard stems. A laboratory testing
showed that relative axial motion for custom-made stems was 11 μm in average
after 2500 cyclic loading, while for standard stems was 19 μm [16]. In a clinical
follow-up study, the migration for custom-made primary and revision stems were
less than 2 mm in 2 years, which were more stable than the standard stems [17].
Both relative motion and migration of the stem are three-dimensional referred to
the axis systems in the medullary canal. Relative motion can basically only be mea-
sured in vitro using LVTDs mounted onto the bone and attached to the stem. The
relative motion of the stem along the long axis of the femur, the horizontal motion
at the tip of the stem on both medial-lateral and anterior-posterior direction and the
rotational motion at the neck of the stem are usually measured. The differences in
reading before and after loading in a single cycle are calculated as the magnitude of
the relative motion. A number of cyclic loadings to pre-set the stem into the position
are necessary in order to achieve a stable and consistent reading and to reflect the
true value of relative motion. To measure relative motion after the stem is inserted
into patients is normally impossible, unless two X-rays are taken in a sequence. The
first X-ray is taken when the patient is standing on the effected leg (in loading situ-
ation) and the second X-ray is taken when the patient is standing on the alternative
leg (in off-loading situation). The distance between the stem and bone before and
after the leg is loaded can be measured and compared on the images, and the amount
of difference can be calculated as the value for relative motion.
Migration of the stem can be measured both in vitro using LVTDs and in vivo
using medical images. There are basically three types of methods that can be applied
to measure the migration.
Using the pen to mark the landmarks on the stem and the bone and measure them
by the ruler on plain X-rays. This method is simple and no additional equipment
is required. However, the accuracy is low, which can only be used in clinical for
a gross comparison and general assessment.
348 J. Hua

Applying a digitize technique on the plain X-rays either on the digitize table or
on the computer screen with a specially developed software. This method is
more accurate than using the ruler and pen. A previous study showed that the
accuracy of the method can be up to 0.25 mm if the landmarks on the stem and
bone can be clearly defined [15]. The most benefits of using this method are not
only that it can be more accurate but also that it can be applied for a retrospective
study. This means that all clinical plain X-rays taken in the past years can be used
for the study. However, this method can only measure the axial migration of the
stem, other axes such as rotation and varus-valgus tilt of the stem will not be able
to measure due to the two-dimensional views of the images.
Application of Radiostereometric analysis (RSA) is currently the most accurate
technique to measure the migration of the stems. The study showed that the accu-
racy of the method can reach to 0.15 mm. Moreover, it can also measure the
migration of the stem in three-dimensional planes using plain X-rays [18], so
that it can more truly reflect the status of the stem in situ. However, this method
requires special equipment, technical expertise and analysing software. Therefore
it can only be applied in special centres. The RSA techniques involve injecting a
number of tantalum beads into stem and bone during surgery as specially defined
reference marks for the measurements, and the radiograph has to be taken using
the special method of dual X-ray tubes placed at diagonal planes [19]. In this
way, any studies measuring the migration of the stems using RSA techniques has
to be pre-planned and set up prospectively, so that the study will take long times
to complete.
A most recently developed method of measuring migration of the stem using CT
scan has been studied [20]. The method also relies on the injection of the tanta-
lum beads as reference marks for the measurements; thus, it can only be used for
a prospective study. Instead of using dual X-ray tubes, it measures the reference
marks from the CT scan images. From the study, the femoral head was used as
the reference marks for the stem and the different lengths of the femoral heads
(−3.0, 0.0, 2.5, 5.0, 7.5 and 10 mm) were regarded as the migration of the stem
related to the bone. The accuracy of the method was claimed to be 0.11 mm [20],
even better than the RSA method. However, this method has only been validated
on the cadaveric bone, its real value for clinical application needs further
evaluation.

5 Selecting the Sizes of Femoral Heads

The 28 mm diameter of the femoral head has been mostly used in the past. However,
larger sizes of the femoral heads such as 32 and 36 mm have become more favour-
able for some of the surgeons. According to the report from American Joint
Replacement Registry, 36 mm femoral heads had become the most popular size,
followed by 32 mm [1]. This is because large femoral heads have the advantages of
providing stable joints, being less likely to dislocate, and potentially offering more
13 Biomechanical Principles in Designing Custom-Made Hip Prosthesis 349

range of motion of the hip. It can also increase the bearing surfaces and lead to
decreased contact stresses and thus reduced linear wear; but on the other hand, large
femoral heads cause more volumetric wear and number of wear particles.
Small femoral heads such as 22 mm diameter are usually only used due to the
restriction of the small size of the acetabular cups. However, small femoral heads do
provide biomechanical advantages such as producing lower friction between the
femoral head and the acetabular cup, offering shorter travel distance for the same
range of motion, and thus generating fewer wear particles.

6 Range of Motion of the Hip (Head/Neck Ratio)

Restoring range of motion of the hip should always be part of the design objectives
for the hip replacement. Although how the acetabular cup being placed can affect
the range of motion, the diameter of the femoral heads in relation to the sizes of the
stem neck can be one of the determining factors. In general, the bigger the size of
the femoral head, the more the range of the motion it can achieve, but this is not
always true. Strictly speaking, the range of motion of the hip is only associated
with the head/neck ratio. While for most of the cases where the size of the neck is
constant, the bigger size of the head will obtain more range of the motion. However,
for a small head such as 22.2 mm, it can achieve the same range of flexion and
extension as that for 28 mm head as long as a mini spigot on the anterior and pos-
terior side of the neck is produced, which make head/neck ratio the same as for
28 mm head.

7 Design Consideration for Developmental

Dysplasia of the Hip (DDH)

Among other complex cases, developmental dislocation of the hip (DDH) is one of
the most challenge cases to design a hip stem for, due to its unusual bone geometry,
with excessive anteversion of the femoral neck, and often accompanied by a mal-­
developed acetabular socket. The disease usually started when the baby is born,
gradually further developed and deteriorated over time. If the proper treatment is
not undertaken in time, the hip joint becomes so deformed that severely affect the
hip functions, and finally requires a total hip replacement. One of the difficulties in
designing a DDH stem is that the proximal medial part of the stem needs to be
gradually anteverted to follow the deformity of the femoral canal, while the stem
neck needs to be retroverted in order for the femoral head to match the normal ori-
entation of the acetabular cup (Fig. 13.3). With this design, the hip can be reduced
and the further dislocation of the hip can be avoided; but the full function of the hip
has still not been restored, because the greater trochanter and abductor muscle are
still at the posterior side of the hip.
350 J. Hua

Fig. 13.3 Hip stem designed for DDH case. The stem follows the geometry of the femoral cavity
and the femoral neck retroverted to the normal position of the acetabular cup

An alternative design is to carry out a de-rotational sub-trochanteric osteotomy, in

which the proximal part of the bone will be rotated internally so that the greater tro-
chanter and abductor muscle can move laterally to their normal anatomical positions.
This design is specially suitable for the anteversion of the hip over 60°, where a simple
retroverted neck may not be able to fully adjust the deformity of the hip. When the
de-rotational osteotomy being performed, the function of the hip should be signifi-
cantly improved and the gait pattern should become more normal [21]. Unfortunately,
none of the studies has been carried out to prove this due to unavailability of the
resources in gait analysis at time to compare patient’s gait before and after operation.
In spite of these advantages in de-rotational osteotomy, some of the concerns
have greatly restricted the wide use of this design. One of the main concerns is the
uncertainty of whether the osteotomy site can be union or not, especially for those
with poor bone qualities and old patients. If the non-union of the osteotomy had
happened, the clinical results could be largely compromised and the revision sur-
gery might be inevitable.
13 Biomechanical Principles in Designing Custom-Made Hip Prosthesis 351

Another concern is how to secure the stem with the cavity below the osteotomy
site. The proximal and the distal part of the bones need to be held together tightly by
the stem, so bone rotation around the stem will occur after the stem undergoes tor-
sional loading. A stem with distal cutting flutes is usually designed to provide the
torsional stability for the distal stem, while the proximal stability is normally
achieved by the geometry fit with the bone. Sometimes, the transverse screws
through the distal bone and stem can be used to provide the torsional stability, pro-
vided the diameter of the stem is large enough for the hole. However, this option has
been less favourable because it may cause destruction and weakness for both bone
and stem. If the diameter of the femoral canal in the diaphyseal region is too small,
both designs may not be suitable. In this situation, two-stage surgeries, with de-­
rotational and bone shortening osteotomy performed first followed by total hip
replacement, may be the choice.

8 Design Consideration for Revision Stems

In overall, the design for revision stems are more complicated than that for primary
stems because there are large variations on the quality of the remaining bone, as
well as the different locations of the bone defects. However, the principles for
designing a revision stem should be kept the same as that for a primary stem, in
which to achieve the initial stability of the stem is the priority. In revision situations,
the design rationales for each case can be different, which are mostly determined by
the condition of the remaining bone. From previous experience of designing custom-­
made hip prostheses, the design rationales for each revision stem have been sum-
marized into four types [12], which were correspondent to Paprosky’s classification
of cavitary defects in revision situation [22].
• Type 1: The quality of the bone is uniformly preserved along the entire femoral
canal. The density of the bone especially in the calcar region is normal which can
be used for load bearing. In this case, the revision stem can be designed short just
like a usual primary stem, regardless of the length of the original stem. The fixa-
tion can be relied on the calcar and metaphyseal bone.
• Type 2A and B: The proximal bone is reasonably maintained. The implant can
be fully or partially supported by the metaphysis. The diaphyseal bone is mostly
intact but there are localized osteolytic lesions, particularly around the previous
distal stem. For this situation, proximal fixation is still obtainable, but the stem
should be designed longer in order to bypass the defects. The optimal length of
stem to bypass the defect should be 2.5–3.0 times the canal diameter in order to
avoid the distally concentrated stresses further weakening the defect and causing
bone fracture. The stress concentration caused by the tip of the stem is mostly
around the lateral side. Therefore, the stem should pass more if the defect is on
the lateral side of the bone.
352 J. Hua

• Type 2C and Type 3: There is further destruction of the bone, leaving an

enlarged proximal cavity with an irregular and thin cortical wall. The distal cor-
tex beyond the level of the original stem has reasonable quality and thickness. In
cases involving a second or even third revision, the length of the bone destruction
may be extended due to the previous use of long stems. Owing to the compro-
mised quality of the proximal femur, fixation and load-bearing are limited, and
stem fixation is primarily achieved in the region below the defective bone. The
distal cutting flutes are usually designed for the stem to enhance the fixation and
provide additional torsional stability. Nevertheless, the proximal part of the
implant is still designed to closely fit (not press-fit) the cavity. Together with the
hydroxyapatite coating, regeneration of bone and long-term stem/bone osteoin-
tegration could be achievable. These design features aim to obtain the maximum
possible fixation in both regions, but initial fixation is obtained by the distal stem.
• Type 4: This situation is rare but severe, in which the cortical bone has severely
been destructed along the proximal and middle parts of the cavity, usually result-
ing from previous multiple revisions involving long-stem implants. The only
portion of the good bone which is good enough for load bearing is in the distal
where the bone shape has flared out. Therefore uncemented fixation of the stem
in this region is intractable. To solve this problem, a long stem reached to femoral
condyle can be designed with distally cemented fixation to obtain immediate
stability in conjunction with a large HA-coated proximal section, with noncon-
forming spaces filled with grafted material. This stem was also suitable when the
femur was longitudinally split for removal of the previous stem.

9 Clinical Results of Custom Hip Implants

Comparing with the clinical results of the standard hip implants, the information for
custom hip implants are much less published. Furthermore, the evaluation of the
clinical results for custom hip stems is more difficult because none of the implants
is designed the same, especially if the stems are designed from the different compa-
nies. In overall, most of the clinical results for custom hip stems are excellent.
A clinical follow-up study of the primary custom hip stems designed by the
author and produced by Stanmore Implants Worldwide (SIW) showed that among
the 114 consecutive CAD-CAM custom-made primary hip stems, inserted by a
single surgeon from one hospital, the survivorship was 100% with the average
13.2 years of follow-up (ranged from 10 to 17 years) and mean age of 46.2 years old
(range from 24 to 62 years old), although after 12 years, some cases have changed
the acetabular liner and femoral head but none of the femoral stems need replace-
ment. A radiographic study showed no aseptic loosening around the stem [23, 24].
Also, a study of the 158 consecutive revision custom hip stems with minimal
10 years follow-up showed that all femoral components were well fixed radiologi-
cally, with 97% survivorship at 10 years. Among the revised cases, some were not
related to the femoral components [23, 24]. One of the observation from the radio-
13 Biomechanical Principles in Designing Custom-Made Hip Prosthesis 353

graphic study showed that there were very little osteolysis occurring, even after
some of the femoral heads and acetabular liners being revised. This suggests that the
close geometric fit of the stem with the cavity may have additional benefits of
achieving layers of osteointegration thus seal the stem-bone interface. If this can
happen, the wear particles generated from the bearing surface will be prevented
from travelling into the femoral cavity, furthermore prevent the macrophages and
osteoclasts from reacting to the wear particles. As a result, osteolysis can be avoided.

10 Disadvantages of Using Custom Stems

Apart from many benefits of using custom stems, some of the disadvantages should
also be considered, which could be the main reasons to prevent the custom stems
from being widely used. However, with the advance of the new technologies, some
of the issues may be able to solve. From surgical point of view, one of the major
disadvantages is that no sequence of the tools can be used to prepare the femoral
cavity and to facilitate insertion of individual implant. Usually only the final shape-
matched custom reamer and rasp can be provided for each case. Therefore, some of
the surgeons may find difficulty to insert a custom hip stem, because all the custom
stems are designed to have line-to-line fit with the cavity, any misalignment at the
initial insertion point will cause the implant jam inside the cavity. With the advance
and wide use of the surgical navigation system, the surgical procedures can be more
precise, accurate and easier. Another disadvantage of using custom stem could be
that the stem may not fit with the bone, in which the stem may be unable to be
inserted. A number of factors can cause this happen. One of the common factors is
the quality of the images makes the boundary of the cortical bone not well defined
or misinterpreted. Other factors could also be possible such as the time between the
images taken and surgery is too long so that the bone geometry has changed since.
Other disadvantages related to the custom stems such as costing and delivery timing
should not be the restricting factors now because the increasingly popular 3D print-
ing technology can make manufacture process of custom stems more quickly, effi-
ciently and economically.

11 Summary

In total hip replacements, the standard stems have been playing a major role for a
long time. However, since individual patients have significantly different require-
ments, such as bone conditions, anatomy, pathologies, clinical problems, and expec-
tations for hip functions/activities/quality of life, custom stems are becoming ever
more popular and demanding in performance. This is true not only for the complex
cases, but also for the routine cases to achieve better clinical outcomes and longer
survivorship. While we are expecting the coming era of precision medicine and
354 J. Hua

digital orthopaedics, advanced surgical navigation systems and 3-D printing tech-
nologies are paving the way for using patient specific custom stems to solve patient
specific clinical problems. Although the advanced and rapid development of future
science and technology will change people’s view and expectation on total hip
replacements, the basic principles of implant design will remain the same. I would
be very pleased if this chapter can be of some contribution and useful to those dedi-
cated to the design of hip stems.

References

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tion in custom designed revision hip stems. Clin Orthop. 2000;373:164–73.
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Chapter 14
Biomechanics of Orthopedic Rehabilitation

Ayman A. Mohamed, Yih-Kuen Jan, Ian M. Rice, Fang Pu,

and Cheng-Kung Cheng

Abstract This chapter discusses four main areas that clinicians should understand to
improve the effectiveness of orthopedic rehabilitation. The first part is about the biome-
chanical factors that affect orthopedic rehabilitation process. The second part is about
the types of exercises during orthopedic rehabilitation and their underlying biome-
chanical principles. The third part is about how to apply these biomechanical principles
to manage common orthopedic disorders. The fourth part is about the biomechanical
guidelines for the use of assistive devices during orthopedic rehabilitation.

Keywords Assistive devices · Biomechanics · Exercise · Musculoskeletal

Orthopedic · Rehabilitation

Biomechanics is defined as the use of the mechanical principles to understand

functions and structures of the biological systems and how these biological
systems can mechanically react to applied forces or loads in both normal and

A. A. Mohamed
Rehabilitation Engineering Lab, Department of Kinesiology and Community Health,
University of Illinois at Urbana-Champaign, Champaign, IL, USA
Department of Basic Science and Biomechanics, Faculty of Physical Therapy,
Beni-Suef University, Beni Suef, Egypt
Y.-K. Jan (*) · I. M. Rice
Rehabilitation Engineering Lab, Department of Kinesiology and Community Health,
University of Illinois at Urbana-Champaign, Champaign, IL, USA
e-mail: yjan@illinois.edu
F. Pu
Advanced Innovation Center for Biomedical Engineering, School of Biological Science
and Medical Engineering, Beihang University, Beijing, China
C.-K. Cheng
School of Biomedical Engineering, Shanghai Jiao Tong University, Shanghai, China
e-mail: ckcheng2020@sjtu.edu.cn
© Springer Nature Singapore Pte Ltd. 2020 357
C.-K. Cheng, S. L-Y. Woo (eds.), Frontiers in Orthopaedic Biomechanics,
https://doi.org/10.1007/978-981-15-3159-0_14
358 A. A. Mohamed et al.

abnormal circumstances. The application of biomechanics to orthopedic reha-

bilitation aims to maximize treatment effectiveness while shortening recovery
time. Biomechanically driven therapies can be applied either during an acute,
recovery, or functional stage of orthopedic rehabilitation [1, 2].

Learning Objectives
After reading this chapter, the readers will be able to:
1. Understand the biomechanical factors of the musculoskeletal tissues (muscles,
tendons, and ligaments) in the human body that can help to improve orthopedic
rehabilitation
2. Understand the biomechanical principles of common exercise types in orthope-
dic rehabilitation
3. Recognize the advantages of applying biomechanical principles to improve
effectiveness of orthopedic rehabilitation
4. Know the common orthopedic disorders of the upper and lower joints and how
biomechanical principles can improve their interventions during orthopedic
rehabilitation
5. Use the biomechanical principles to prescribe appropriate assistive devices
(splints, walkers, crutches, and canes) to improve orthopedic rehabilitation.

1 The Biomechanical Factors Affecting

Orthopedic Rehabilitation

There are several biomechanical factors that should be well understood when per-
forming orthopedic rehabilitation to the human musculoskeletal tissues. This part
discusses the factors that clinicians should understand when applying different
rehabilitation therapies. We provide examples of key factors to clarify the role of
these factors during orthopedic rehabilitation.

1.1 The Viscoelasticity

Viscoelasticity is the main mechanical property of musculoskeletal tissues [3]. It is

defined as the property of any material that exhibits both viscous and elastic charac-
teristics when a stress is applied to it. Viscoelastic materials have time-dependent or
frequency-sensitive stress–strain relations which are dependent on the magnitude,
period of application, and velocity of an applied load. Understanding the viscoelas-
tic characteristics of the musculoskeletal tissues gives us a better understanding of
how the musculoskeletal tissues as viscoelastic materials respond to different types
of the rehabilitation modalities. This section discusses two main phenomena (the
creep [4–6] and the hysteresis [7]) and two main relationships (the stress–relaxation
relationship [8, 9] and the force–velocity relationship [10]).
14 Biomechanics of Orthopedic Rehabilitation 359

1.1.1 The Creep Phenomenon

The creep phenomenon is the first common viscoelastic property that the musculo-
skeletal tissues follow when they are subjected to stress. The creep phenomenon is
defined as the gradual lengthening (shortening) of a viscoelastic material with time
when a constant tensile (compressive) stress is placed on it. When a constant tension
is placed on a muscle for a period of time, this tension is distributed on all of the
sarcomeres in an equal manner. An increase (decrease) in one sarcomere length due
to this tension produces a change in its isometric tension. This causes a lengthening
(shortening) of this sarcomere at a fixed speed that matches the amount of applied
tension (speed of sarcomere change is proportionate to the magnitude of applied
tension). For example, use of splints for stretching shortened musculoskeletal tis-
sues (lengthening effect) functions primarily through the creep phenomena. These
tissues change their shape after a period of time in response to the constant tension
of the applied splint.

1.1.2 The Hysteresis Phenomenon

The hysteresis is the second common viscoelastic property that the musculoskel-
etal tissues follow when they are subjected to stress. The hysteresis can be defined
as the energy loss in the form of heat. It is considered a recovery process after the
removal of a certain load. The amount of energy loss as heat is based on the rate
of applied strain to deform the body tissues. The continual loading and unloading
can explain the increase in the temperature of the viscoelastic material during
loading and unloading (Fig. 14.1). For example, when a shortened ligament is
repetitively stretched with a constant stretching force (stretch then relax then
stretch), hysteresis is developed and the ligament length limit increases with each
cycle. Thus, an extra ligament length occurs in the same session by performing a
repetitive stretching manner.

Fig. 14.1 The hysteresis. When a

viscoelastic material is stretched
(loading) and returns to its original length
(unloading), it (unloading phase) does not
return to the same manner as when it is
stretched (loading phase). The process
Stress

losses energy in the form of heat ing

ad
Lo
g
in
oad
Unl

Strain
360 A. A. Mohamed et al.

1.1.3 The Stress–Relaxation Relationship

The stress–relaxation relationship is the third common viscoelastic property that the
musculoskeletal tissues follow when they are subjected to stress. The stress–relax-
ation relationship can be defined as the reduction in the stress due to the same degree
of strain produced in the viscoelastic tissues. To explain this, when musculoskeletal
tissues (viscoelastic materials) are held under tensile stress for a prolonged time,
there is an increase in this stress over time. Thus, the stress should be increased to
produce the same required strain (Fig. 14.2). For example, in static stretching, when
a constant stretch (strain) is applied on a muscle for a prolonged time, the magnitude
of the stretching force (stress) is less than the firstly applied stretching force.

1.1.4 The Force–Velocity Relationship

The force–velocity relationship is the fourth common viscoelastic property that the
musculoskeletal tissues exhibit when they are subjected to stress. The force–veloc-
ity relationship can be defined as the amount of muscle force in relation to the veloc-
ity of motion or vice versa. Based on this relationship, the maximum possible
tension occurs with the eccentric contraction (Fig. 14.3). This clarifies why it is
easier to lower a load and stop it than lifting it and why it is easier to descend from
a certain height and land than to jump up to the same height.

Viscous material
Relaxation beginning line

Viscoelastic material
Elastic material

Fig. 14.2 The stress relaxation curve. There are differences in the relaxation behaviors for the vis-
cous, elastic, and viscoelastic materials in the stress–relaxation curve (σ = stress, T = time). The
elastic material returns immediately to its original state after relaxation. The viscoelastic material
exhibits some changes in the return way, loses some energy in the form of heat and an alteration in
its original state occurs. The viscous material continues in the state developed by the stress and does
not relax
14 Biomechanics of Orthopedic Rehabilitation 361

Fig. 14.3 The force– Speed = zero

velocity relationship. In
Eccentric
concentric contraction, as Isometric
the load increases, there is
a decrease in the velocity
of contraction. In

Force
concentric contraction, as
the load increases, there is
an increase in the velocity
of contraction Concentric

Elongation Shortening
Speed

Fig. 14.4 The Hill’s a

muscle model. (a) The AC
contraction phase, the SC
parallel component (PC) Contraction phase
and active component (AC) PC
are contracted, while the
elastic component (EC) is
stretched. (b) The b
stretching phase, PC and AC SC
AC are stretched, while the
EC is contracted Stretching phase
PC

1.2 The Hill’s Muscle Model

The Hill’s muscle model is another biomechanical factor that can help us to
understand which muscle tissues are responsible for developing each type of the
muscle tension. The Hill’s muscle model demonstrates that there are two sources
participated in the development of the muscle tension (active and passive). The
active tension is developed by the interaction of actin and myosin filaments in the
muscle, while the passive tension is developed by the connective tissue compo-
nents (fascia and tendon) in the muscle when the muscle length exceeds its resting
length. The Hill’s muscle model demonstrates that the active and passive tensions
are depending on each other and each of them cannot be considered as a separate
structural element of the muscle because the connective tissue matrix of the mus-
cle is relatively complex and connected to each other (within and between the
muscles) [11] (Fig. 14.4).
362 A. A. Mohamed et al.

2 The Biomechanics of the Therapeutic Exercises

The most common exercise types during orthopedic rehabilitation are stretching,
strengthening, ROM, and mobilization exercise.

2.1 Stretching Exercise

Stretching exercise is a critical part of any rehabilitation program applied to increase

the joint range of motion (ROM) and improve the muscle-tendon flexibility. The
application of biomechanical principles into stretching therapies enables orthopedic
rehabilitation team to improve stretching exercise effectiveness, reduce the likeli-
hood of injury, and customize the stretching program to better meet the needs of the
client. Creep, hysteresis, and stress relaxation are all concepts which give us a better
understanding of why the late effect or the prolonged stretch is better than the acute
or short stretch in gaining a stretching effect. This section discusses the biomechani-
cal effects of the stretching exercise, including the immediate [12, 13] and the late
biomechanical effects [11, 14, 15] and the types of the stretching exercise [16].

2.1.1 The Biomechanical Effects of the Stretching Exercise

The Immediate Effects of the Stretching Exercise

The immediate effect of stretching is mainly dependent on two relationships. The

first relationship is the stress–relaxation relationship. The stress–relaxation relation-
ship causes an immediate decrease in the passive tension of the muscle at a particu-
lar joint angle. Stretching a muscle for 20–30 s can result in a decrease in the passive
tension of the muscle because the most percentage of the strain to reduce the stress
effect occurs in the first 20 s of the stretching exercise (stress–relaxation principle).
The stretching exercise can give an immediate 10–30% reduction in the passive
muscle tension. The second relationship is the force–length relationship. The force–
length relationship demonstrates how the force magnitude can be increased by
increasing the prior length of the contracted muscle. When a shortened muscle is
stretched before contraction, the produced force rises considerably. The background
behind the long-lasting rise in the force may be due to alteration in the sarcomere
length that is developed through the activation and after the stretch.

The Late Effects of the Stretching Exercise

The late effects of stretching exercise are much better than the immediate effects.
The first effect is due to the prolonged stretch that causes a significant improvement
(8–12° or 5–31%) in the ROM after 12 weeks of training. This effect is attributed to
14 Biomechanics of Orthopedic Rehabilitation 363

the sarcomere myogenic response. The sarcomere myogenic response demonstrates

that when a muscle is stretched, two possible mechanisms occur. An elongation of
each muscle fiber itself to its maximum resting length until the whole sarcomeres
are fully elongated. Then, a stretch of the connective tissues around it occurs. To
explain this, when the stretching tension increases, the collagen fibers in the con-
nective tissue line up themselves with the same line of force according to the direc-
tion of the applied tension. Thus, prolonged stretching can improve the muscular
functions as it aids in the rearrangement of any disorganized muscle fibers (sarco-
meres and connective tissues).
The second effect, according to the American Council on Exercise [15], stretch-
ing exercise can improve the overall body flexibility. When the stretching exercise
is performed as a daily habit, connective tissues show some elongation. After a
period of time, this elongation in the musculoskeletal tissues increases the ROM for
all body joints. This improvement in the flexibility of muscles and connective tis-
sues reduces the risk of joint degeneration and relieve muscle stiffness. Adding a
stretch after strength training session is significantly effective in maintaining normal
range of motion because it acts as an extra overload stimulus that increases the
strength gain.

2.1.2 Types of the Stretching Exercise

There are three types of muscle stretching exercise commonly performed in ortho-
pedic rehabilitation (static, dynamic, and pre-contraction). The first type, static
stretching exercise, is most common and regularly used. In static stretching, the
stretching force is constant and includes two subtypes, passive and self-stretching.
Passive stretching exercise occurs when the stretch force is applied by the therapist
or another person. In contrast, self-stretching exercise requires the patient to apply
the stretch force independently.
The second type is the dynamic stretching exercise that occurs when the stretch-
ing force is not constant and includes two subtypes, active and ballistic stretching.
The active stretching exercise is usually applied by moving the limb repeatedly until
the end of the available ROM. The ballistic stretching exercise is conducted by
quick, alternating stretching motions or “bouncing” performed at the end of the
available ROM. This technique is not recommended as there is an increased inci-
dence of the injury to the stretched tissues.

2.2 Strengthening Exercise

A strengthening exercise program should be designed based on the training goals

[17]. This includes the selection of the type of the strengthening exercise, strength-
ening progression features, and injury avoidance. The strengthening exercise should
also be adapted to the stage of the healing status of injured tissues and to the overall
364 A. A. Mohamed et al.

muscle strength of the patient. This section discusses two biomechanical principles
of strengthening exercise [18] and lever systems [19].

2.2.1 Types of Strengthening Exercise

There are three types of the strengthening exercise (isometric, isotonic, and iso-
kinetic types). The isometric strengthening exercise is a static type of the strength-
ening exercise. During isometric strengthening, muscles contract without any
noticeable alteration in either its length or the joint ROM. Although there is no
movement, the amount of force and tension developed can be measured. The sec-
ond type is the isotonic strengthening exercise. Isotonic strengthening is a dynamic
type of the strengthening exercise in which muscle contraction occurs with joint
movement and excursion. It includes two subtypes, the concentric type, in which
the muscle force is produced through contraction (muscle shortening), and the
eccentric type, in which the force is produced during muscle lengthening. The third
type, isokinetic strengthening exercise, is a dynamic type of strengthening exercise
in which muscle contraction occurs about a joint moving at a fixed velocity.
The maximum force generated with eccentric strengthening contraction is more
than during isometric or concentric contraction due to two causes [20]. First, when
a muscle is stretched before contraction, more cross-bridges are included, and thus
more tension is developed than when muscle contracts from a shortened position.
Second, the cross-bridges cycling interaction can occur with less adenosine triphos-
phate (ATP) hydrolysis than in concentric contractions. However, the eccentric con-
tractions are accompanied by a lesser energy cost and high force output and have a
higher tension production that leads to a damage to the muscle-tendon system.
Thus, using the eccentric contraction during orthopedic rehabilitation should be
performed with caution because of a high incidence of injury.

2.2.2 The Lever System

The lever can be defined as a semirigid or rigid segment that moves on a stationary
point (axis) when a force is applied to this segment (not passing through its axis
point) [19]. The lever has a capability to assist or resist the muscle contraction. This
capability is based mainly on its mechanical advantage. The mechanical advantage
of the lever equals the proportion of muscular force to the resistance force. Levers
are classified into three categories by the relative locations of the axis, muscular
force, and resistance. They include three classes.
For the first class, the axis is located between the force and the resistance.
Thus, the force arm can be greater, equal, or less than the resistance arm. For an
example, in the extension of the neck. The axis (the atlantooccipital joint) is posi-
tioned between the resistance (head weight) and the force (deep cervical exten-
sors). The mechanical advantage may be higher than, less than, or equivalent to 1
14 Biomechanics of Orthopedic Rehabilitation 365

depending on the distance of the head to the joint. Thus, the assistance or resis-
tance to the muscle contraction depends on which the lever arm is larger
(Fig. 14.5a).
For the second class, the resistance is located between the force and the axis.
Thus, the force arm is always bigger than the resistance arm. For an example, the
resistance (body weight) is positioned between the axis (the metatarsophalangeal
joints) and the force (calf muscle) during standing on the toes. The mechanical
advantage of the second class is constantly larger than the first class because the
resistance arm is less than the force arm. Thus, it causes an increase in the force
production. It is also called the force multiplier lever (Fig. 14.5b).
For the third class, the force is located between the resistance and the axis. Thus,
the resistance arm is always bigger than the force arm. For an example, the force
(biceps brachii muscle) is positioned between the axis (the elbow joint) and the
resistance (forearm weight) during elbow flexion. The mechanical advantage is con-
stantly less than the first class because the force arm is lesser than the resistance
arm. Thus, it causes an increase in the speed of movement. It is also called the speed
multiplier lever (Fig. 14.5c).
Using lever systems to graduate the strengthening exercise is considered a safe
and effective way during orthopedic rehabilitation. For an example, during strength-
ening exercise for weak shoulder flexors, the strengthening exercise with elbow
flexion is easier than with elbow extension while the weight of the upper limb is
fixed. This is because when the elbow is flexed the resistance arm is only to the
elbow joint; while, when the elbow is extended the resistance arm is to the fingers.
Increasing the lever arm of the resistance increases the demand on the muscle to
counteract this increase.

2.3 Range of Motion Exercise

Range of motion (ROM) exercise is considered to be an important element of

orthopedic rehabilitation and is performed in nearly all orthopedic conditions
[21]. The primary aim of ROM exercise is to maintain or increase the joint
ROM to prevent the development of joint contractions. Joint contractures can be
defined as the limitation in the passive joint range of motion due to a shortening
of the muscles and periarticular connective tissues. Joint contractures often
occur after fractures due to prolonged immobilization. Joint contractures can
limit the passive and active range of motion in one plane or multiple planes. It
is important during the application of the ROM exercise to understand the type
of the joint movements that the ROM exercises performed through, the funda-
mental planes and axes of these movements and the type of the ROM exercise
that is used. This section discusses the types of joint movements and which type
is used during ROM exercises [22], fundamental planes and axes of movements
[22] and types of ROM exercise [23].
366 A. A. Mohamed et al.

R = Head weight
a
F R

A = The atlantooccipital joint A

F = Deep cervical extensors muscles

b
F= Calf muscle
R = Body weight

F R

A = Metatarsophalangeal joints

c
F = Elbow flexors muscles
Bic

R F
ep
s

A = Elbow joint
R = Forearm weight

Fig. 14.5 Types of lever systems. (a) First class lever. As in the action of the deep cervical exten-
sors muscles. The force is performed by cervical deep extensors muscles to overcome the resis-
tance which is applied by the weight of the head, and the axis is the atlantooccipital joint. (b)
Second class lever. As in the action of the calf muscle when standing on the toes. The force is
performed by the calf muscle to overcome the resistance which is applied by the weight of the
body, and the axis is the metatarsophalangeal joints. (c) Third class lever. As in the action of the
biceps muscle when it flexes the elbow joint. The force is performed by the biceps muscle to over-
come the resistance which is applied by the weight of the forearm, and the axis is the elbow joint.
F muscular force, R resistance, A axis
14 Biomechanics of Orthopedic Rehabilitation 367

2.3.1 Types of Joint Movements

Two primary types of movements occur within joints and there are specific exer-
cises for each movement. The first joint movement is the physiological movement,
which is defined as the movement of the two joint bone segments outside the joint
through the available ROM. The second joint movement is the accessory move-
ment; it is defined as the movement of the two joint segments inside the joint cap-
sule through the available ROM “joint play” motion. In the ROM exercises the
focus is on the physiological movement, while the mobilization exercise focuses on
accessory movements.

2.3.2 Fundamental Planes and Axes of Movements

There are three fundamental planes and axes in which physiological movements
occur and orthopedic rehabilitation team should be aware of which physiologi-
cal movement plane is limited such that a ROM exercise plan can be formu-
lated. The first plane is the sagittal plane; it intersects the body into anterior and
posterior halves. The axis perpendicular to the sagittal plan in which move-
ments occur is known as the frontal axis. The primary movements of the sagittal
plane are flexion and extension. The second plane is the frontal plane which
intersects the body into medial and lateral halves and its movement axis is the
sagittal axis. Primary movements occurring in the frontal plane are adduction
and abduction. The third type is the transverse plane, which intersects the body
into upper and lower halves and its movement axis is the vertical axis. The
movements occurring in the transverse plane are rotation, elevation, and
depression.

2.3.3 Types of ROM Exercise

There are three main types of ROM exercise commonly used during orthopedic
rehabilitation. The first type is passive ROM exercise, in which no voluntary con-
traction occurs and an external force is used to move the segment through the avail-
able ROM. The external force can be the other limb, gravity, a machine, or a
therapist. The second type is active ROM exercise, in which no external assistance
is used and the segment is moved through the available ROM with active voluntary
contraction created by the muscles crossing that joint. The third type is the active-­
assistive ROM; it is a combination of both passive and active ROM. In which the
first part of the ROM is actively performed and the second part is passively p­ erformed
because the agonist muscles cannot complete the whole ROM alone due to its
weakness.
368 A. A. Mohamed et al.

2.4 Mobilization Exercise

Mobilization exercise can be defined as a force applied to move the articular sur-
faces inside a joint. It is performed to improve the joints mobility, ROM or to reduce
accompanying pain associated with joint structures via passive or manual accessory
joint movement [6]. In order to perform a successful mobilization exercise, the
rehabilitation team should know three main aspects. The first aspect is understand-
ing how the accessory movements work to form the mobilization exercise. The sec-
ond aspect is the biomechanics of the articular surfaces of the treated joint including
the convex–concave rule and the loose- and close-packed positions of this joint and
the grades for this mobilization exercise. The third aspect is the grades of the mobi-
lization exercise and the indications for each. This section discusses types of joint
play movements [24], the convex–concave rule [25], close- and loose-packed posi-
tions [26], and grades of the mobilization exercise [27].

2.4.1 Types of Joint Play Movements

The accessory or joint play movements, in which the mobilization exercise is

applied, consists of five types. The first type is the rolling movement, in which a new
point on one of the two joint bone surfaces contacts new points on the other bone
surface. The second type is the gliding movement, in which the same point on one
of the two joint bone surfaces contacts new points on the other bone surface. The
third type is the traction movement, in which there is a vertical linear separation of
the joint surfaces away from the treatment plane. The fourth type is the compression
movement, in which there is a vertical linear approximation of the joint surface
toward the treatment plane. The fifth type is the spinning movement, in which there
is a rotation of one joint surface around a stationary axis. This occurs in either clock-
wise or counterclockwise directions (Fig. 14.6).

2.4.2 The Convex–Concave Rule

MacConaill is one of the pioneers of kinesiology; he described the convex–concave

rule for any moving joint. He demonstrated that the convex–concave rules are based
on the shape of the articular surfaces. It includes two conditions depending on
which joint surface moves on the other. The first condition, when the convex sur-
face is moving on the concave surface, rolling occurs in the same direction as the
movement, while sliding movement occurs in the opposite direction. For an exam-
ple, during shoulder (glenohumeral) abduction, the humeral head (convex) rolls
superior to the glenoid fossa (concave). To perform a successful mobilization exer-
cise to increase the shoulder abduction, the mobilization force should be in the
inferior direction (opposite direction) (Fig. 14.7a). The second condition, when the
concave surface is the moving on the convex surface, both the rolling and sliding
movements occur in the same direction. For an example, during distal radioulnar
14 Biomechanics of Orthopedic Rehabilitation 369

a b c d e

Spinning

Compression
Sliding

llin

Traction
Ro

Femur

Tibia

Fig. 14.6 Types of accessory movements. (a) Gliding movement, in which the same point on one
of the two joint bony surfaces contacts new points on the other bone surface. (b) Rolling move-
ment, in which the new point on one of the two joint bony surfaces contacts new points on the other
bone surface. (c) Spinning movement, in which one joint bony surface rotates around a stationary
axis in clockwise or counterclockwise direction. (d) Traction movement, in which there is an
increase in the vertical linear separation between both joint surfaces away from the treatment
plane. (e) Compression movement, in which there is a decrease in the vertical linear separation
between the joint surfaces away from the treatment plane

joint supination, the radius (concave) moves on the ulna (convex). To perform a
successful mobilization exercise to increase distal radioulnar joint supination, the
mobilizing force should be in a posterior direction (same direction) (Fig. 14.7b).

2.4.3 The Close- and Loose-Packed Positions

There are two common positions for any joint. The first position is the close-packed
position; it is a joint position in which the capsule ligaments are taut and there is a
maximum contact between the two contacting bones. It is the most congruent posi-
tion of the joint. The second position is the loose-packed position; it is a joint posi-
tion in which the capsule ligaments are loose and there is a minimum contact
between the two contacting bones. It the loosest position of the joint. The mobiliza-
tion exercise should be performed in the loose-packed position, not in the close-­
packed position, because a greater movement can be achieved in this position.

2.4.4 Grades of the Mobilization Exercise

The grades of the mobilization exercise depend on several biomechanical factors

including speed, movement amplitude, and oscillations degree. The mobilization
exercise has five grades based on the previous factors. Grade 1 is a low speed, small
370 A. A. Mohamed et al.

lide
a b rior g

Inferior glide
Ante
1
1

Humerus,
convex,
Moving. Radius, Ulna,
Scapula,
Concave, Convex,
Concave,
Moving. Fixed.
Fixed
Abduction

ation
Pron
2

Fig. 14.7 The convex–concave rule. (a) Mobilizing force. (b) Movement direction. (a) The mobi-
lizing force for increasing shoulder abduction is performed in an opposite direction to the desired
movement (inferior glide) because the convex humeral head moves on the concave glenoid cavity
of the scapula (convex on concave rule). (b) The mobilizing force for increasing the pronation in
the distal radioulnar joint is performed in a same direction of the desired movement (the anterior
glide) because the concave ulnar notch on the radius moves on the convex ulnar head (concave on
convex rule). 1: mobilization force direction and 2: direction of desired movement

oscillations and small amplitude movements are performed at only the beginning of
the available ROM. It is mainly used to decrease pain. Grade II is a low speed, small
oscillations and large amplitude movements are performed near the middle of the
available ROM. It is mainly used to decrease pain. Grade III is a low speed, small
oscillations and large amplitude movements are performed near the end of the avail-
able ROM. It is mainly used to increase the ROM. Grade IV is a low speed, small
oscillations, and small amplitude movements are performed at the end of the avail-
able ROM. It is mainly used to increase the ROM. Grade V is a high speed, large
oscillations and small amplitude movements are performed beyond the end of the
available ROM. It is called manipulation.

3 Biomechanical Concepts in Orthopedic Rehabilitation

The application of the biomechanical principles in orthopedic rehabilitation helps

the rehabilitation team to perform the rehabilitation of orthopedic disorders in a
more effective and safe manner and to decrease the recovery time for these disorders.
14 Biomechanics of Orthopedic Rehabilitation 371

This part discusses common biomechanical concepts applied to orthopedic rehabili-

tation strategies for upper and lower limb joints.

3.1 The Upper Limbs

The upper limbs consist of several joints, including the shoulder, elbow, wrist, and
hand joints. Upper limb functions typically consist of activities that require a high
degree of mobility.

3.1.1 The Shoulder Girdle

The shoulder girdle is responsible for complex movements which are important for
functional activities. To perform optimally, the shoulder girdle must work together
in a synchronized and coordinated manner in order to perform overhead activities,
such as hair brushing and reaching to a high shelf [28]. This section discusses the
common biomechanical principles utilized in orthopedic rehabilitation for manage-
ment of shoulder joint stiffness [29, 30], shoulder joint dislocations, and sublux-
ations [31, 32].

Shoulder Joint Stiffness

Prolonged immobilization or pain in the shoulder joint often produces shoulder

joint stiffness which limits overhead movements. These complications are often
related to not only stiffness in the glenohumeral joint but also reduced upward rota-
tion of the scapula. To treat the upward rotation limitation of the scapula, the reha-
bilitation team should strengthen all the muscular forces that produce this movement.
The normal scapular rotation movements include two force couples which rotate
about an axis (center of the scapula); each rotation is performed by three muscles.
The upward rotation of the scapula occurs when the glenoid fossa turns upward and
the inferior angle of the scapula move superolaterally away from the spinal column.
Upward rotation of the scapula is performed by the upper fiber of trapezius, lower
fibers of trapezius, and the serratus anterior muscles (Fig. 14.8a). The downward
rotation of the scapula occurs when the inferior angle of the scapula moves infero-
medially toward the spinal column and the glenoid fossa returns to its normal
­position. Downward rotation of the scapula is performed by the levator scapula,
rhomboids, and pectoralis minor muscles (Fig. 14.8b).
The upward rotation moment of the scapula can be calculated by equation of
moments as follows (Eq. (14.1)):

∆M = M 1 + M 2 + M 3 (14.1)

M = F × ma (14.2)
372 A. A. Mohamed et al.

rot ward
n

nt ae
Up tion

atio
wn
rot

l
tra
Up zius

mo scapu
wa
a

Do
pe
per

rd

me
r
ato
Rh ome

lev
sm
om nt
bo
s
tu
ra ior

id
r
Se ter
an

Pe m
cto om
ra en
s
trap er

lis t
eziu
Low

m
ino
r
Center of
rotation

Fig. 14.8 The muscular forces included in upward and downward rotations of the scapula. (a)
Upward rotation of the scapula is performed by action of three moments rotate around a fixed axis
of rotation (center of the scapula). These moments include upper trapezius, lower trapezius and the
serratus anterior moments. (b) Downward rotation of the scapula also is performed by action of
three moments rotate around a fixed axis of rotation (center of the scapula). These moments include
levator scapula, rhomboids, and pectoralis minor moments

∆M = ( F1 × ma1 ) + ( F2 × ma1 ) + ( F3 × ma 3 ) (14.3)

where M: moment, F: force, and ma: moment arm from the center of scapula (center
of rotation).
According to the previous equations, to increase the upward rotation of the scap-
ula during orthopedic rehabilitation, the rehabilitation team should increase the
force of all three muscles responsible for upward rotation of the scapula. Because
theses muscles act together from different directions to induce rotation, any decrease
in the force production due to weakness or pathology can affect scapular rotation.

Shoulder Joint Dislocations or Subluxations

In orthopedic rehabilitation of the shoulder dislocations or subluxations, the orthopedic

rehabilitation team should focus on strengthening the deltoid muscle to minimize the
recurrence of shoulder dislocation or subluxation because the deltoid muscle circles
the shoulder joint from three directions, superiorly, medially, and laterally. The deltoid
14 Biomechanics of Orthopedic Rehabilitation 373

muscle is a multipennate muscle which is advantageous because pennate muscles pos-

sess more muscle fibers oriented in parallel which allows for more force production
than any other type of the skeletal muscle. In pennate muscle, considering the physio-
logical cross-sectional area (PCSA) is more accurate than the anatomical cross sec-
tional-area (ACSA) because the ACSA in these muscles does not represent all muscle
fibers (Fig. 14.9). The PCSA is increased in length with the increase in the pennation
angle and with muscle length. In a pennate muscle, PCSA is always larger than
ACSA. It can be calculated by the following equation [Eq. (14.4)].

PCSA = muscle volume / fiber length (14.4)

In pennate muscles, muscle force can be calculated by these equations Eqs.

(14.5) and (14.6)

Total force = PCSA × specific tension (14.5)

Muscle force = Total force × cos Θ ( angle of pennation ) (14.6)

Medial fibers Middle fibers Lateral fibers

Physiological cross sectional area

Physiological cross sectional area

Tendons

Fig. 14.9 The Deltoid muscle. It is a multipennate muscle that contain several muscle fiber orien-
tations. PCSA is more accurate than the ACSA in the presentation of all its muscle fibers. The
pennation angle (ϴ) is the angle between the tendon and the fiber orientation. Its force production
equals the summation of all forces generated in it, thus its force production is high
374 A. A. Mohamed et al.

The deltoid muscle is also composed of three types of fibers, including anterior,
middle, and posterior. Thus, deltoid muscle force production is greater than the
unipennate muscles. This increases its force production as well. In the case of a
dislocated or subluxated shoulder joint, therapists should prescribe deltoid strength-
ening to increase the compression force inside the glenohumeral joint. Ultimately,
compression force inside the glenohumeral joint increases and glenohumeral joint
stability improves.

3.1.2 The Elbow Joint

The elbow joint consists of three bones, including humerus, ulna, and radius bones.
The articulations between these bones form the elbow complex. The elbow com-
plex consists of four joints, the humeroulnar (main elbow joint), humeroradial,
superior radioulnar, and inferior radioulnar joints. The orthopedic rehabilitation
protocol for the elbow ligaments injuries should focus on offering the injured liga-
ment to be healed maximally while minimizing the hazards of joint stiffness, resid-
ual instability, and posttraumatic arthritis [33]. This section discusses common
biomechanical principles applied to orthopedic rehabilitation specific to the elbow
joint collateral ligaments, the medial (ulnar) [34, 35] and lateral (radial) [36, 37].

Medial (Ulnar) Collateral Ligament

MCL exercise should be performed with the forearm in pronation. Elbow flexion
from a pronated position increases the force production of the biceps muscle and
increases the axial compressive force inside the elbow joint. Biceps brachii muscle
inserts into the radial tuberosity. With forearm pronation, the radial tuberosity
moves away and this increases the length of the biceps muscle. This increases the
compression force between the trochlear notch of the ulna and the trochlea of the
humerus. Also, during elbow flexion exercise, this lengthening in the biceps brachii
before its contraction causes an increase in its force production that increases the
level of the compression force inside the elbow joint during exercises.
Passive mobilization of the deficient MCL should be performed when the fore-
arm is in supination because the forearm supination generates an external rotation
moment on the ulna that closes the medial side of the elbow effectively and this
increases the stability of the elbow joint. The movements of the radius and ulna are
related to each other and it takes place around an axis that passes from the center
of the head of the radius to the base of the styloid process of the ulna. External
rotation of the ulna takes place with forearm supination and internal rotation of the
ulna takes place with forearm pronation. In a forearm supination, the external rota-
tion moment pulls the ulna medially inside the elbow joint; this increases the pull
on the ulna inside the joint and gives a more elbow stability (Fig. 14.10).
14 Biomechanics of Orthopedic Rehabilitation 375

a b

Internal rotation
Internal rotation
moment
moment

Axis of rotation

Pronation
Supination

Fig. 14.10 Types of moments placed on the ulna during elbow supination and pronation. The
movements of the radius and ulna are related to each other and they take place around an axis that
passes from the center of the head of the radius to the base of the styloid process of the ulna.
External rotation of the ulna takes place with forearm supination and internal rotation of the ulna
takes place with forearm pronation. In a forearm supination, the external rotation moment pulls the
ulna medially inside the elbow joint; this increases the pull on the ulna inside the joint and gives a
more elbow stability

The Lateral (Radial) Collateral Ligament

The LCL is a key stabilizer which resists both the varus stresses and the rotational
instabilities which prevents elbow joint laxity. Forearm pronation helps to stabilize
the LCL lacking while the arm is passively flexed in a vertical orientation because
the internal rotational torque placed on the wrist to keep the forearm in a pronation
causes the ulna to be hinged over the intact soft tissues on the medial side of the
elbow. This overlapping closes the valgus stress on the lateral side of the elbow.
Thus, patients with acute posterolateral rotatory instability can be actively and pas-
sively mobilized early by keeping the elbow in a full pronation.
Patients with LCL injuries should exercise with the arm positioned in a gravity-­
loaded overhead position, because in this position, the gravity and contraction of
the biceps brachii, brachialis, and triceps brachii increase axial compression, con-
gruency, and stability of the elbow joint. When elevating the arm above head, the
gravity and these previous muscles that connect the humerus to the ulna or radius
apply downward forces. These forces help to approximate the joint surface and
increase the compression force inside the elbow joint and consequently improve its
stability.
376 A. A. Mohamed et al.

3.1.3 Wrist and Hand Joints

Wrist and hand are complicated structures that contain high numbers of joints to
allow performance of several fine motor activities such as writing, painting, and
grasping. All of these joints are inter-related and must work together in harmony to
achieve optimal functioning at the hand and wrist. Good understanding of the bio-
mechanics of the hand and wrist joints is crucial to treat these injuries. This section
discusses common biomechanical concepts applied to wrist injuries [38] and in the
carpal tunnel syndrome [39, 40].

Splints for Treatment of the Wrist Injuries

Splinting is an effective rehabilitation tool for treatment of wrist injuries. Splints

usually follow the rule of the first-class lever systems through use of three points
of pressure techniques. The first force is located on the wrist joint and the two
other forces are located proximally (forearm component) and distally (palmar
component) to the wrist joint. These proximal and distal force components pro-
vide a counterforce against the opposing applied middle force. The forearm com-
ponent represents the force arm, and the palmar aspect represents the resistance
arm (the weight of the hand). Before applying the splints to the wrist joint, the
three points of pressure must always be well defined. The force applied on the
proximal end of the wrist splint can be calculated by measuring the length of the
forearm component, the length of the palmar component, and the average weight
of the hand.

F × Fa = R × Ra (14.7)

Thus,

F = ( R × Ra ) / Fa (14.8)

The mechanical advantage,

Fa / Ra (14.9)

where F: Force applied by the splint, Fa: length of the forearm component, R:
weight of the hand, and Ra: the length of the palmar component (Fig. 14.11).
According to the previous equations, increase in forearm component length is
recommended to decrease the stress on the healing tissues and to increase the
patient’s comfort level. Increasing the forearm component length decreases the
force required to counteract the weight of the hand to support the splint, and
consequently the resultant stress applied to the healing tissues is less. Reduced
stress on the healing tissues has been associated with increased comfort and
decreased pain.
14 Biomechanics of Orthopedic Rehabilitation 377

RA
FA

Fig. 14.11 The wrist splint. Wrist splint is considered as the first class lever. The forearm piece
should be large to increase the lever arm of the force. This decreases the force needed to overcome
the hand weight of the hand. F splint force, FA force arm, R resistance (hand weight), RA resis-
tance arm

Splints for Treatment of the Carpal Tunnel Syndrome

Carpal tunnel syndrome is one of the most common injuries to the wrist joint in
which the median nerve is narrowed across the carpal tunnel between the radial and
ulnar bursa and the synovial membranes of the extrinsic finger flexor tendons.
Extension or flexion of the wrist increases the contact stress and motion friction
between the tendons on the palmar and dorsal surfaces of the carpal tunnel. The
dorsal surface includes the distal head of the radius and the carpal bones. While the
volar surface includes the median nerve and the flexor retinaculum.
In carpal tunnel syndrome, the rehabilitation team should focus on relieving the
stress on the median nerve. The median nerve is more compressed during wrist
flexion than extension because it is located more on the volar side of the carpal tun-
nel. The resultant compression force on the median nerve during flexion can be
calculated by assuming the tendons and nearby structures as a low friction pulley-­
belt mechanism (Fig. 14.12). The load distribution for the contacting surfaces, FL, is
related to tendon load, Ft, and the anatomical pulley radius, r:

FL = Ft / r

Thus, the resultant force, FR, on the pulley construction is connected to the ten-
don load and angle of contact between the pulley and the tendon [41].

FR = 2 Ft sin (θ / 2 ) (14.10)

Based on the previous equations, wrist splints should be adjusted at angles of

“neutral” to 20° of wrist extension to avoid the higher pressure presented on the
median nerve during flexion.
378 A. A. Mohamed et al.

FR

FL

θ
Ft r

Fig. 14.12 Calculations of the forces applied on the median nerve during wrist flexion. If the
tendons and nearby structures are considered as a low friction pulley-belt mechanism, the resultant
force FR is calculated by measuring the load distribution for the contacting surfaces (FL), the
related tendon load (Ft), the anatomical pulley radius (r) and the angle of inclination (θ)

3.2 The Lower Limbs

The main function of the lower limbs is the locomotion and body weight support.
Thus, orthopedic rehabilitation should focus on providing more strength to support
the body weight. The lower limb consists of several joints the hip, knee joints, and
ankle and foot joints.

3.2.1 The Hip Joint

The hip joint has special biomechanical characteristics; it is formed by the articu-
lation between the acetabulum and the femoral head. The acetabulum is deep in
order to apply more stability to the hip joint to enable it to carry the weight of the
body. Osteoarthritis of the hip joint is commonly due to weight-bearing [42].
Total hip arthroplasty can be a treatment to overcome the severe pain and degen-
eration with severe hip osteoarthritis. This section discusses common biomechan-
ical concepts that should be applied during orthopedic rehabilitation after total
hip arthroplasty [43–45].
The main aims of orthopedic rehabilitation after total hip arthroplasty are to min-
imize the pain, return function, and decrease possible deformities in the hip joint.
The hip abductor peak moment reduction is one of the problems occurring with the
total hip arthroplasty that can affect stride length and gait pattern. There are three
elements which can cause a decrease in the hip abduction peak moment at the hip.
14 Biomechanics of Orthopedic Rehabilitation 379

The first one is the muscle strength related to soft tissue damage. The second one is
the surgical approach, as it is supposed that the posterior approach leads to fewer
damage to the hip abductor muscles and consequently improved postoperative gait.
The third one is the vertical distance between the point of action of the abduction
force and the axis of hip rotation.
In total hip arthroplasty, the rehabilitation team must increase the strength of the
hip abductors because during walking it counteracts three times the weight of the
body during normal standing. To maintain the body in equilibrium during any phase
of waking, the muscular moment should counteract the weight of the body moment,
according to the equilibrium equation of moments.
In normal standing,

( M R × M ma ) + ( M L × M ma ) = W × Wma (14.11)

In single limb support,

( M × M ma ) = W × Wma (14.12)

where MR: the muscular force of the right hip abductors, ML: the muscular force of
the left hip abductors, Mma: muscle moment arm, W: body weight force, and Wma: is
the weight moment arm. The moment arm is defined as the line between the force
and the center of the affected hip joint.
Both hip abductors contract to counteract the body weight during the double leg
support. In single limb support, the hip abductors of the supporting limb should
increase its force to compensate for the other hip abductor force and movement of
the weight line of action away from the supporting limb. Thus, the hip abductor of
the supporting limb counteracts approximately three times greater body weight than
the body weight that placed on it during normal standing. The other element is the
distance of the vertical distance between the hip abductors and the center of the hip
joint. According to Eq. (14.11), decreased femoral offset decreases the hip abductor
moment arm, and consequently increases the hip abductors force to counteract the
weight of the body. Thus, in orthopedic rehabilitation after total hip arthroplasty, if
the femoral offset is smaller than the normal femoral neck, the rehabilitation team
should increase the strength of the affected hip abductors muscles to counteract the
decrease in the femoral offset (Fig. 14.13).

3.2.2 The Knee Joint

The knee joint consists of two joints, the tibiofemoral and the patellofemoral joints.
The rehabilitation exercise for the knee joint is mainly conducted in two forms, an
open kinetic chain (OKC) and a closed kinetic chain (CKC) exercises. The OKC
exercise is described as the movement of the knee joint in which the distal segment
(tibia and fibula) is freely moving. Non-weight-bearing exercise is considered a
380 A. A. Mohamed et al.

a b
Hip abductors moment

Normal femoral offset

Decreased femoral offset

Fig. 14.13 The difference in femoral offset effect on the hip abductors. A decreased femoral offset
decreases the hip abductor moment arm. This increases the work required from the hip abductor
muscles. (a) Decreased the femoral offset. (b) Normal femoral offset

regular OKC exercises, such as knee extension from seating on a leg extension
machine. The CKC exercise is described as the movement of the knee joint in which
the proximal segment (femur) is moving or the movement in which the distal seg-
ment of the joint encounters significant resistance. The weight-bearing exercise is
considered a typical CKC exercise such as a squat or step-up. This section discusses
the effect of these two exercises on the stability of the tibiofemoral and patellofemo-
ral joints [46].

The Tibiofemoral Joint

The tibiofemoral joint is formed by the articulation of the femur and the tibia. This
section discusses the effect of these two types of exercises on the anterior cruciate
ligament (ACL) [46–48] and posterior cruciate ligament (PCL) injuries and recon-
structions [45, 49].
14 Biomechanics of Orthopedic Rehabilitation 381

Orthopedic Rehabilitation of ACL Injuries or Reconstruction Surgery

In orthopedic rehabilitation after ACL injuries or reconstruction surgery, OKC and
CKC should be performed correctly to avoid applying overloads on the healing
ACL or on ACL graft. During OKC knee extension, OKC exercise should not be
performed in the last 45° of knee extension. The OKC exercise is provided by con-
traction of the quadriceps muscles, which causes an anterior translation of the tibia.
When a load is conducted vertically to the distal region of the leg, a resultant poste-
rior shear movement of the femur (anterior shear of the tibia) occurs. The anterior
cruciate ligament (ACL) resists about 85% of the restrictive force to this anterior
tibial shear movement. The stress on the ACL increases during the last 45° of knee
extension due to an increase in the anterior tibial translation in this range. Thus, any
exercise in this range should be avoided following ACL reconstruction as it places
an adverse effect on the ACL graft or on the injured ACL. After 45°, the tibial trans-
lation is decreased at 60° and 75° of knee flexion because the patellar tendon exerts
approximately a vertical torque (0°) on the tibia in an upward direction (Fig. 14.14).
Thus, in this range, quadriceps contraction cannot cause either an anterior or poste-
rior tibial translation.
The degree of strain applied on the ACL during the OKC exercise depends in
addition to the angle of knee flexion, also on the level of quadriceps activity.
Isometric OKC contraction of the quadriceps at 15° and 30° causes an average
peak of a strain of 4.4% and 2.7%, respectively, whereas at 60° and 90° of knee
flexion there is no ACL strain. Therefore, it is recommended to use the exercises
that produce no to low strain on the ACL. This exercise involves quadriceps muscle
strengthening with a flexed knee at 60° or higher, or unloaded knee movement
amid 35° and 90° of flexion. The healing graft of ACL is susceptible to be failed if
exercises are aggressive.

a b
Fe
mu
r

Angle of pull of the

patellar tendon

Tibia

Fig. 14.14 The anterior tibial translation during 45° and 75°. (a) At 45° of knee flexion, there is a
large anterior transition tension which is not recommended during early ACL rehabilitation. (b) At
75° of knee flexion there is a decrease in the anterior transition force because the patellar tendon
exerts approximately a vertical torque (0°) on the tibia in an upward direction
382 A. A. Mohamed et al.

OKC of knee flexion is produced by the contraction of the hamstrings muscle.

During OKC isometric hamstring contractions there is no to low strain on the
ACL. Thus, all OKC knee flexion exercises produce insignificant stress on the ACL
and should be utilized carefully during the rehabilitation after ACL injury or
reconstruction.
CKC exercise is commonly prescribed by clinicians after ACL injuries or recon-
struction surgery because CKC exercise decreases the tibiofemoral shear stress by
raising the joint compression and muscular co-contraction between the hamstring
and the quadriceps. This decreases the stress on the injured ACL. During CKC, the
line of force is positioned more centrally in comparative to the tibia. This minimizes
the axial compression and the shear forces on the ACL. Consequently, the joint
displacement is minimized. Weight-bearing exercise causes a small anterior tibial
displacement in comparative to non-weight-bearing exercise. All squat types
(power, front, and lunge) produce a back tibiofemoral shear stress. The effect of
load on the injured or reconstructed ACL is nonsignificant during weight-bearing
exercise because the total anteroposterior translation is decreased by about 50–66%
in healthy ACL and by about 42–71% in unhealthy ACL. During squatting, both
quadriceps and hamstring contract to resist the flexion moment. The quadriceps
muscle resists the flexion moment at the knee and the hamstrings contracts to resist
it at the hip joint.
CKC exercises can be performed without co-contraction between the quadriceps
and hamstring muscles. In squats with straight leg, the body is located posterior to
the knee joint. So, quadriceps must resist the increase in knee flexion moment. In
contrast, in the upright squat, the body is located somewhat back to the knee, Thus,
a co-contraction is raised among the quadriceps and hamstring muscles. Also, bicy-
cling is considered a type of CKC exercise. Throughout bicycling the values of
mean peak ACL strain were relatively low (1.7%). Thus, bicycling can be used for
increase thigh musculature strength without harming ACL.

Orthopedic Rehabilitation of PCL Injuries or Reconstruction

PCL injuries are less common than ACL injuries. During OKC knee flexion, the
contraction of the hamstring causes a posterior translation of the tibia; this exerts a
stress on PCL. The posterior translation of the tibia is minimum at full extension
and progressively increases with increasing the knee flexion angle to be 11.4 mm at
90° of knee flexion. The posterior shear force exerted on the tibiofemoral joint
throughout the entire range of flexion reaches its peak at 75° of knee flexion. The
isometric OKC exercise of flexion should be performed at full knee extension or it
should be avoided in the earlier periods of PCL injuries or reconstruction.
The synchronized knee and hip extension in CKC exercise, when it is performed
from a flexed position makes two actions, elongates the rectus femoris across the
hip joint and shortens it across the knee joint. However, the hamstring elongates
across the knee and shortens across the hip; the resultant eccentric and concentric
contraction at the origin and insertion of the muscle produce a “pseudo isometric
contraction” which is called “concurrent shift.” This type of contraction is useful for
14 Biomechanics of Orthopedic Rehabilitation 383

functional activities such as gait, run, stair climb, and jump and cannot be regener-
ated by isolated OKC exercises. Thus, CKC exercises are safely related to anterior
shearing forces placed on the tibia and it can be performed safely in the early phase
of orthopedic rehabilitation following PCL surgery.

The Patellofemoral Joint

The patellofemoral joint is composed of the articulation between the femur (proxi-
mal) and the patella (distal). The stability of this joint is based mainly on the active
and passive restraints within the knee. The main passive restraints include the lateral
patellar and the medial patellofemoral ligaments. It accounts for about 60% of the
whole restrictive force. The lateral retinaculum accounts for 10% and the medial
patellomeniscal ligament accounts for 13% of the resistive components to the lateral
displacement of the patella. While for medial patellar translation, the main passive
resistive components to it are the structures that make the profound and superficial
lateral retinaculum. The deep retinaculum is made by the lateral patellofemoral liga-
ment, the lateral patellotibial ligament, and the deep fibers of the iliotibial band. The
superficial retinaculum is made by fibers from the iliotibial band and vastus lateralis.
In knee flexion training, during CKC flexion training, with the increase in the
flexion, the knee flexion moment arm increases. This requires a high quadriceps and
patellar tendon tension to offset the increase of the flexion moment arm. This leads
to a higher patellofemoral joint reaction force (PFJRF) with knee flexion. During
gait, the PFJRF is equal to the half of the body weight. In ascending and descending
stairs, the PFJRF is about 3–4 times the body weight. In squatting, the PFJRF is
about 7–8 times the body weight. This data can illustrate the increase in patello-
femoral pain with activities that include progressive knee flexion with
weight-bearing.
During OKC extension, there is an increase in the knee flexion moment arm with
a decrease in the patellar extension moment arm. This increases the request for the
quadriceps force to make the knee extension, particularly at full range. This illus-
trates the extensor lag that occurs with quadriceps weakness as in poliomyelitis.
In OKC knee extension, the peak PFJRF at 36° of flexion is 4 times of the weight
of the body. It is decreased to half of the weight of body with full extension. Thus,
the straight leg raise and short arc quadriceps exercises are recommended to per-
form from 20° to 0° during the initial phase of orthopedic rehabilitation. The PFJRF
and patellofemoral contact stress are higher with OKC leg extension exercise in
comparison with the leg press from 0° to 45° knee flexion. While, from 50° to 90°
knee flexion, the PFJRF and contact stress were higher for the leg press in compari-
son with the OKC leg extension exercise.
In knee extension training, with OKC exercises, the forces across the patella
are minimum at 90° knee flexion. With knee extension from 90° of flexion, the
PFJRF rises, and there is a decrease in the patellofemoral contact area. This
causes more contact stress with knee extension until about 20° because the
patella is non-­contacting the trochlea. With CKC exercise, there are minimum
384 A. A. Mohamed et al.

a b
Quadriceps moment arm
Femur

Patella

Patellar tendon moment

Tibia

Fig. 14.15 The patellofemoral resultant compression force. The compression force on the patella
increases with the increase in knee flexion (a). Thus, in the painful proximal lesion of the patella,
exercises should be avoided from 60° to 90° of flexion (b). (c) Resultant compression force

forces across the patella at 0° of extension. With knee flexion, PFJRF increases
with an increase in the patellofemoral contact area. This initial increase in the
PFJRF causes a reduction in contact stress, then, the contact stress increases
with flexion progression subordinate to the increase in joint reaction force
(Fig. 14.15).
Both CKC and OKC exercises are performed to treat the patients with patello-
femoral pain if conducted in the pain-free range. CKC exercises for the patello-
femoral joint are better tolerated during 0–45° of knee flexion. During this range,
CKC exercise includes leg presses, step-ups, and mini-squats. In contrast to CKC
exercises, OKC training for the patellofemoral joint is better tolerated in the ranges
during 20–0° and 90–50° of knee flexion. During these ranges, exercises may
include straight leg raises, quadriceps sets, multiple angle isometrics, and short arc
isotonic. The aim of the exercising in these previous ranges is to load the quadriceps
muscles with lower degrees of the stress exerted on the patella.

3.2.3 The Ankle Joint

Ankle and foot articulations are considered as a closed chain system, in which
each bone segments are interdependent and interrelated on each other, and thus
their functions are dependent on each other and cannot move autonomously of the
others. Hypomobility at any joint affects the whole movement of all joints through
a compound sequence of compensations that disturb all other joints.
14 Biomechanics of Orthopedic Rehabilitation 385

a b

Line of gravity

Fig. 14.16 The line of gravity course with normal and supinated foot (posterior view). During
supination, the line of gravity moves medially, this increases the stress applied to the lateral side of
the ankle and causes a lateral ankle sprain. (a) Supinated foot. (b) Normal foot

Lateral collateral ligament sprain is a common ankle injury [50]. It results from
an increase in the supination moment across the subtalar joint, which results from
increasing the magnitude of the upright ground reaction time during initial foot
contact. At this position, if the center of plantar pressure deviates more medially to
the axis of the subtalar joint, a higher moment arm occurs across the subtalar joint
axis. Thus, more supination moment is occurred due to sudden aggressive ankle
supination. When the foot is plantarflexed, the initial touch is performed with the
forefoot. This increases the moment arm between the resultant joint torque and the
subtalar joint axis. Consequently, the sudden aggressive twisting movement results;
this causes ankle sprain injury. Thus, during the rehabilitation, ankle taping or brac-
ing for correcting the ankle joint position at stance phase provides more ankle
mechanical support [51] (Fig. 14.16). Ankle taping or bracing should apply a varus
stress to reduce the stress on the healing tissues and increase the patient comfort.

4 Biomechanics of Assistive Devices

This part discusses assistive devices that are mainly used for ambulation in patients
with lower limbs orthopedic disorders. Early ambulation is an essential component
to orthopedic rehabilitation because it decreases postoperative complications and
386 A. A. Mohamed et al.

length of stay. Thus, the rehabilitation team should have a complete understanding
of assistive device prescription and the biomechanical advantages associated with
each. The rehabilitation team should prescribe an appropriate assistive device for
each patient in accordance with his/ her abilities and needs and at the correct time
during orthopedic rehabilitation. Assistive devices can also be used to decrease
pain, decrease inflammation, and compensate for muscle weakness in the lower
limbs. The assistive devices include the wheelchairs, walkers, crutches and canes.

4.1 Wheelchairs

The main goal of any orthopedic rehabilitation program is to make patients as inde-
pendent as possible. Wheelchairs are the main way of ambulation for patients who
are unable to ambulate because of both lower limbs amputations. There are several
patterns of wheelchair propulsion that patients can use. This section discusses
guidelines for wheelchair prescription [52] and biomechanical concepts associated
with wheelchair use [53–55].

4.1.1 Guidelines for Wheelchair Prescriptions

Wheelchair prescriptions significantly rely on the relationship between three vari-

ables, including the wheelchair user (abilities, needs, and preferences), wheelchair
technology (light or heavy), and the environment (home, work, or study) in which
the wheelchair is utilized. Numerous factors must be considered when selecting a
wheelchair. Firstly, the chair width should be narrow but without applying compres-
sion against the hips. A wheelchair which is too tight fitting laterally increases the
pressure on the patient hips and waist while a wheelchair that is too wide may
increase the side-to-side movement of the patients inside. This increases the friction
between the patient and chair. Secondly, the chair length should usually be 5 cm
from the back of the chair to knee in order to provide enough length to support the
legs. This distributes the weight on a larger surface area, thus decreasing the pres-
sure on the ischial tuberosity and preventing the development of pressure sores.
Pressure is calculated by dividing the force (weight of the body) over the area on
which the patient sits (chair length) [Eq. (14.13)].

P= F /a (14.13)

where P pressure, F body weight, and a chair length.

Thirdly, chair back height should be 2 cm beneath the inferior angle of the scapula
to allow the scapula to move easily while supporting the back maximally. Fourthly,
the patient’s head should be in the middle between both shoulders and hips, knees,
and ankles at right angles to prevent the development of back deformities as a result
of changing the line of gravity to adapt alterations in their positions. Fifthly, the feet
14 Biomechanics of Orthopedic Rehabilitation 387

should be supported to avoid overwork of the dorsiflexors which works to keep the
feet in a horizontal position and to prevent planterflexor contractures.

4.1.2 Biomechanical Concept of Wheelchair Propulsions

Wheelchair propulsion includes two phases, including the push (stroke, drive) and
the recovery phases. The push phase (the force production phase) occurs when the
hands are in contact with the hand rims. The second phase is the recovery phase (the
non-propulsive phase), in which the hands are repositioned to start the push
phase again.
The wheelchair propulsion pattern is mainly determined via the recovery phase
during the push phase because the upper limbs are moving in a closed kinematic
chain. Movement patterns are mainly two patterns, namely “semicircular” or
“pumping” patterns. The semicircular push pattern occurs when the hand passes
below the push rim through the recovery phase, producing a semicircular move-
ment. The pumping push pattern occurs when the hands only pass slightly below
push rim during the recovery phase. There are two additional propulsion patterns
identified, including single loop over (SL) and double loop over (DL). The SL pat-
tern occurs when the hands rise above push rim through the recovery phase. The DL
pattern occurs when the hands rise above push rim and then cross over and drop
under the push rim through the recovery phase (Fig. 14.17).
Understanding propulsion pattern is important because it can help maximize an
individual’s quality of life through repetitive strain injury minimization and
performances optimization. Importantly, the semicircular propulsion pattern is
­

a b c d

Pushing Phase

Recovery phase

Fig. 14.17 Wheelchair propulsion patterns. (a) The semicircular push pattern occurs when the
hands pass below the push rim through the recovery phase. (b) The pumping push pattern occurs
when the hands only pass slightly below push rim during the recovery phase. (c) The single loop
over (SL) pattern occurs when the hands rise above push rim through the recovery phase. (d) The
double loop over pattern occurs when the hands rise above push rim and then cross over and drop
under the push rim through the recovery phase
388 A. A. Mohamed et al.

thought to be superior to the other population patterns because it is associated with

larger push angles. Increased push angles lends to a higher effective force, reduced
force loading, and reduced stroke frequency. Ultimately, these biomechanical char-
acteristics may protect from overuse injuries.

4.2 Walkers

Walkers are the most stable assistive devices used for gait training and usually
orthopedic rehabilitation begins with it. Walkers have several advantages over
crutches and canes, including increasing the patient base of support, anterior sta-
bility, and lateral stability and decreasing the weight-bearing and joint reaction
forces. This section discusses the main guidelines for walker description [56] and
the main biomechanical concepts in weaker-assisted gait [54, 56].

4.2.1 Guidelines for Walker Prescriptions

Walkers’ height should be adjusted by the alignment of the top of the frame with the
ulnar styloid process. This technique has been shown to provide between 20° and
30° of elbow flexion. This slight elbow flexion permits the patients for a powerful
downward push on the walker. This downward push permits patients to bear some
of the body weight through the upper limbs. Extended elbow (no flexion angle)
causes a decrease in the downward push force. Excessive elbow flexion angle causes
the patient to excessively bend at trunk anteriorly. Anterior bending of the trunk can
prevent hip extension during the stance phase of gait by moving the center of gravity
anterior to the hip joints (Fig. 14.18).

4.2.2 Biomechanical Concept of Walker-Assisted Gait

Strengthening of the elbow extensors should be prescribed by clinicians for all patients
that use walker-assisted gait because maximum elbow extension moment far exceeds
those at the shoulder or wrist joints. Shoulder flexors and adductors should be strength-
ened too. The eccentric moment of the shoulder flexors is needed because this repre-
sents the eccentric demand on the shoulder flexors to control the deceleration and
downward movement of the walker frame. While shoulder adductors counteract the
shoulder abduction moment, this abduction moment increases the distal to proximal
moment arm away from joint centers and increasing the influence of distal joint forces.
Walker-assisted gait should be explained by clinicians to patients because going
too much into the walker during the gait moves the center of gravity backward and
increases the tendency to fall backward. The proper technique for walker use
involves the patients moving the walker slightly forward first followed by move-
ment of the affected leg forward and finally movement of the unaffected leg comes
forward to meet the affected leg.
14 Biomechanics of Orthopedic Rehabilitation 389

Fig. 14.18 Guidelines for

walker prescriptions.
Elbows should be flexed
about 30°. A slight trunk
bending forward is
required to move the center
of rotation anteriorly to
prevent falling backward.
Too anterior bending of the
trunk could also prevent
the hip extension during
the stance phase of gait.
The patient should avoid
going too much into the
walker, as this moves the
center of gravity backward
and increase the tendency 30°
to fall backward

4.3 Crutches

Crutches are commonly used in couples. Crutches are commonly used to assist
locomotion by decreasing the load on injured tissue, compensating for the loss of
muscular control or alleviating pain. This section discusses the guidelines for
crutches prescription [54] and the common biomechanical concepts in crutch-­
assisted gait [57, 58].

4.3.1 Guidelines of Crutch Prescriptions

The main types of crutches are the axillary, triceps, platform, and forearm crutches.
The first type is the axillary crutch which is the most common type. In axillary
crutches, the patient must avoid complete weight-bearing on the crutch over the
axilla during walking to avoid excess pressure on the blood vessels and superficial
nerves. This excessive pressure increases incidence of injuries. This excessive
390 A. A. Mohamed et al.

pressure can be decreased by two considerations. Firstly, the upper end of the
crutch must be two to three fingers widths under the patient’s axilla when the
patient is standing with a 30° of elbow flexion. Secondly, putting a sponge rubber
to cover the upper end of the crutch to minimize stress against the user’s chest. The
design of the crutch should include a longer upper end than the lower end to
increase the support area on the chest and reduce energy consumption in the initial
few minutes of walking. The lower end of the crutch should be padded with a rub-
ber to prevent patient slippage during walking. The crutch should be adjusted to
that the lower end of the crutch to be 15 cm from the outside of the patient’s feet to
avoid the ankle trauma caused by the contact of the crutch with the patient legs
during gait (Fig. 14.19).
The other types are less common and each one has a particular purpose. The
second type is the triceps crutches. They are prescribed by clinicians for patients
with paralyzed shoulder muscles. The proximal part has lateral and medial supports
merged with a couple of posterior bands. These supports perform the same action of
the triceps muscle to maintain the elbow in extension. The third type is platform

a b c d

90°

30°
30°

Fig. 14.19 Different types of crutches. All types should be well padded and include a sponge
lower tip to prevent the slippage during gait. (a) Axillary crutch is the common ones, in which
elbow angle is 30°. (b) Triceps crutch is used to help the weak triceps muscles, in which elbow
angle is 0°. (c) Forearm crutch is used when a partial weight bearing only is required, in which
elbow angle is 30°. (d) Platform crutch has a flat support for loading the weight on the forearm, in
which elbow angle is 90°
14 Biomechanics of Orthopedic Rehabilitation 391

crutches; they have a flat support for loading the weight on the forearm. These
crutches are prescribed for patients with the inability to bear weight transmission
over the hand, wrist, or forearm. The fourth type is the forearm crutch, they are
prescribed by clinicians to patients who have mild orthopedic problems and need
only a partial weight-bearing gait.

4.3.2 Biomechanical Concept of Crutch-Assisted Gait

Crutches should be prescribed by clinicians to adequately fit the crutch to the

patients’ needs and abilities. There are four patterns of crutche-assisted gait, includ-
ing 2 points, 3 points, 4 points, swing-through and swing-to patterns. The com-
monly used patterns are swing-through and 3 point patterns.
Through the swing-through crutch gait, the energy requirements for crutch walk-
ing are more than the normal gait. The partial weight-bearing crutch gait demands
about 33% more energy than normal gait, and the non-weight-bearing crutch gait
demands about 78% more energy. The external flexion moment that acted around
the elbow during crutch gait is counteracted by an extension moment provided by
the upper arm muscles, particularly the elbow extensors. The mechanical work
through the swing-through crutch gait was almost the same as in normal gait; how-
ever a higher percentage of this work is done by the upper extremities. The upper
limbs muscles are fatigued more quickly than the lower limbs muscles because they
are not functionally designed to support the weight of the body. Thus, strengthening
exercise to the upper limb muscle particularly elbow and shoulder extensors should
be prescribed by clinicians before the use of axillary crutches to avoid early and
quick fatigue of these muscles.
Energy consumption of the upper limb during swing-through crutch-assisted gait
is greater than during normal gait. This increased energy consumption results in
health problems in patients due to crutch-assisted gait, such as upper-limb joint
degeneration or nervous system injuries like bilateral ulnar nerves neuropraxia. The
possible mechanism to reduce these health problems is to decrease the vertical
movement between the body and the crutch tip to make the motion to be performed
with less difficulty.
Through the three-point crutch-assisted gait, a decrease in the energy consump-
tion occurs because of the useful kinematic alterations that occur due to adaptation
to the crutch-assisted gait. These kinematic alterations include a decrease in the
trunk and pelvis rotation and lateral movements, hip flexion and adduction, knee
flexion, and ankle plantarflexion at the toe-off. In contrast, the unaffected side
exhibits a slight increase in hip abduction and external rotation, and knee flexion.
This is because of the movement of the center of gravity away from the affected side
slightly to the affected side. Thus, strengthening exercise for both lower limbs
should be prescribed by the clinician, not just the affected lower limb, to accom-
modate the required increase in the unaffected lower limb force.
Three-point crutch-assisted gait is commonly prescribed by clinicians because it
offers for different levels of weight-bearing ranging from non-weight-bearing to
392 A. A. Mohamed et al.

full-weight-bearing. In three-points gait pattern, both crutches are moved forward

simultaneously, then the affected side is moved and lastly the unaffected side is then
moved. The swing-through gait pattern includes moving the crutch forward; then
both legs are moved together forward to a point slightly anterior to the crutches.

4.4 Canes

Canes are considered the simplest assistive devices used for ambulation. It is com-
monly used by older people or people with lower limb osteoarthritis. This section
discusses the main guidelines for cane prescription [54, 59, 60] and the biomechani-
cal concepts in cane-assisted gait [61, 62].

4.4.1 Guidelines of Cane Prescriptions

Canes are available with several kinds of handles. The basic one is the inverted U
shape which allows patients to suspend the cane on a forearm or back of a chair
while it is not in use. Other handle designs include the pistol grip handles which are
designed to increase the contact area, thus decreasing the pressure on the hand [Eq.
(14.13)]. This design helps to increase comfort and decrease pain. The shaft of the
cane can be folded, height adjusted, depending on the subject height. The cane’s
base should be rubbered with broad deep grooves to prevent its slippage. It should
be kept clean to offer ultimate traction. The base can be single or quadruped. The
quadruped base increases the base of support and gives more stability to the patients.
The cane should be grasped as its handle’s height should permit semi-flexed
elbow about 30°. The cane’s tip should be at a distance of 15 cm forward and
5–10 cm lateral to the foot. Prolonged use of the cane causes a backward bend of the
subject or can interfere with a proper weight that should the cane alleviates. Canes
which are too short cause excessive anterior bending in patients. For canes with a
wide base, the clinicians should ensure that the base edge of the cane is laterally
away from the foot enough to avoid hitting the ankle by the cane base through the
swing phase of gait.

4.4.2 Biomechanical Concept of Cane-Assisted Gait

People with lower-limb instability usually use the cane on their ipsilateral side,
while people with muscle weakness or pain use the cane on their unaffected side
(contralateral). The contralateral use of the cane decreases the hip contact forces
more efficiently and encourages the normal reciprocal gait pattern. The decrease
in hip contact forces during cane-assisted gait is mainly argued to the increase in
the moment arm of the cane which decreases the demand on the abductor mus-
cles of the affected side (Fig. 14.20). The hip abductor muscle force is required
14 Biomechanics of Orthopedic Rehabilitation 393

Fa
Fc Fa Fc

B B

C C

Affected side
Affected side

Fw
Fw

Fig. 14.20 The side of holding a cane in a person with an affected hip joint. The cane should be
held in the contralateral side to decrease pain of the affected hip and increase the force of the hip
abductor muscle on the affected side. Using the cane on the contralateral side increases the moment
arm of the cane and decreasing the need of the affected hip abductors. Fc force of the cane, A
moment arm of the cane, Fw force of the body weight, C moment arm of the body weight, Fa force
of affected hip abductor muscle and B moment arm of hip abductor muscle

to balance the pelvis during unilateral stance. When the cane is grasped on the
affected side, the force of the hip abductor muscles can be calculated by the fol-
lowing equation.

Fw × C = ( Fc × A ) + ( Fa × B )) (14.14)

where Fa: hip abductor force, Fc: cane force, Fw: body weight, A: moment arm of
cane, and B: moment arm of the hip abductor and C: moment arm of the body
weight. By increasing (A) there is an increase in the (Fa); this leads to a decrease in
the demand on the hip abductors to produce high force.
It is shown that the hip contact forces can be decreased up to 56% and the gluteus
medius moment can be decreased up to 31.1% with using the cane on the contralat-
eral side in comparison with the normal gait. Thus, clinicians should prescribe the
use of the cane on the unaffected side during cane-assisted gait because the use of
394 A. A. Mohamed et al.

the cane on the uninvolved side significantly decreases demands on the hip a­ bductors
and consequently decreases compression forces inside the hip joint accompanied
with hip adductors contraction.

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Chapter 15
Biomechanics of Osteo-Synthetics

Chia-Ying James Lin, Heesuk Kang, and Scott J. Hollister

Abstract Osteo-synthetics play critical roles in skeletal tissue regeneration by sup-

porting mechanical integrity as well as enhancing cell–tissue interaction to facilitate
tissue formation. These roles can be fulfilled by the functional design of porous
architectures to provide proper load bearing and mass transportation for the neo tis-
sue formation. These require a simultaneous design for mechanical and mass trans-
port properties. In this chapter, trends for introducing osteo-synthetics in the clinical
setting, design parameters for capable implants, and influence of implant physical
characteristics on osteointegration are extensively reviewed, followed by introduc-
tion of a novel numerical approach to integrate all these factors. We applied a
homogenization-based topology optimization scheme to design the three-­
dimensional unit microstructures for the desired scaffolds. The target effective bulk
modulus and isotropic diffusivity are obtained by the optimized porous microstruc-
ture. Cross-property bounds between the desired bulk moduli and diffusivities are
adapted to determine the defined targets for a given porosity.

Keywords Osseointegration · Multifunctional microstructure · Homogenization

Topology optimization · Cross-property bounds

1 Trends in Osteo-Synthetics

Osseointegration occurs when a direct structural and functional connection between

ordered, living bone and the surface of a load-carrying implant takes place.
However, osseointegration is particularly challenging in traumatic injury and spinal

C.-Y. J. Lin (*)

Department of Orthopaedic Surgery, University of Cincinnati, Cincinnati, OH, USA
e-mail: chia-ying.lin@uc.edu
H. Kang
Ford Motor Company, Dearborn, MI, USA
e-mail: hkang11@ford.com
S. J. Hollister
Department of Biomedical Engineering, Georgia Institute of Technology, Atlanta, GA, USA
e-mail: scott.hollister@bme.gatech.edu

© Springer Nature Singapore Pte Ltd. 2020 397

C.-K. Cheng, S. L-Y. Woo (eds.), Frontiers in Orthopaedic Biomechanics,
https://doi.org/10.1007/978-981-15-3159-0_15
398 C.-Y. J. Lin et al.

arthrodesis where excessive instrumentations are normally required. Spine arthrod-

esis or fusion has been performed to manage pathological spine disorders and ver-
tebral instability. The number of the procedures increases dramatically to nearly
one ­million cases performed each year [1]. An extensive study in 2001 [2] revealed
that in the United States alone, approximately 360,000 patients underwent certain
types of spinal arthrodesis. Indications for spine arthrodesis are mostly low back
pain, spondylosis and spondylolisthesis, rheumatoid instabilities, postdiscectomy,
unstable fractures, trauma, and other lesions. Each of the aforementioned presents
different challenges for surgeons in improving the solid integrity as permanent fixa-
tion with successful osseointegration to immobilize the interfered motion segments.
Efforts have been made with various approaches to achieve successful bone
union. Although autologous bone grafting still remains as the gold standard, ongo-
ing efforts have been pursued to improve healing and decrease the morbidity cre-
ated during bone harvesting. New design and fabrication techniques with compliant
biocompatible or biodegradable materials create less rigid but still mechanically
sound systems. Additionally, porous architecture has been incorporated in implants
to scaffold ingrown tissue while promoting specific biological interactions to
enhance bony reunion. Gene transfer, recombinant protein delivery, and therapeu-
tic cell-­based transplantation also provide novel opportunities to replace conven-
tional grafting strategies. All the attempts have collectively pushed the new
development of osteo-synthetics that will contribute to successful osseointegration .

2 Potential Design Variable Modifications

for Osteo-Synthetics Development

The primary function of osteo-synthetics is to provide immediate stability to the

motion segment until arthrodesis is complete so that the existing mechanical defor-
mation will be corrected.
Porous implants made with osteo-synthetics are typically designed with an exter-
nal shape, surface topography, and pore dimension. These parameters in turn deter-
mine the overall performance including mechanical integrity and the integration of
tissue ongrowth and ingrowth. Besides the dimensional factors of design, the limita-
tions of the base material presents another big concern. Stress shielding, migration
of the implant, and pseudoarthrosis of the motion segment lead to complications
that result in problems in osseointegration. The highlight in this chapter is to mag-
nify the request of the rigidity and stability without sacrificing essential compliance
as the favorable stimulation for tissue regeneration. A further attempt is to create the
implant to be a porous-matrix-like structure as a scaffold to increase osteoconduc-
tion and achieve biofactor delivery as bone graft substitutes, such as genes, proteins,
growth factors, and/or cells. In all, the goal herein is to develop a triplet construct
with osteo-synthetics to maintain segmental stability, deliver therapeutic biofactors,
and therefore enhance bone union.
15 Biomechanics of Osteo-Synthetics 399

2.1 Motion, Ingrowth, and Stability

Functional osseointegration is highly related to the local mechanical environment at

the footprint of implants on bone. Indeed, the way by which the induced motion
perform will determine the patterns of the tissue formation. Cuillinane et al. [3]
conducted a precisely controlled motion in an experimental mid-femoral defect and
reported that the defect of mechanical treatment group failed to achieve union, but
instead the neoarthroses formed. The structural composition of molecular compo-
nents within the newly formed tissue are influenced by their local mechanical envi-
ronment, which has been investigated with a deep-to-superficial polarity on
subcondral bone arcades and a flattened morphology in the midline. This pattern
was directed by the applied symmetrical bending motion, which mimicked the
mechanical environment in utero join development. Pilliar et al. and Simmons et al.
[4–6] pioneered the limited movement between the implant and the surrounding
tissue within as a necessary criterion for bone formation onto implants with porous
surface. They have then elucidated the morphological change of the tissue-implant
interface from radiographs and animal models.
An early report [7] from the group in 1981 showed that excessive movement
prevents the calcification of the tissue within the pores and resulted in implant
attachment by fibrous tissue only. However, they suggested that the implant fixation
supported by fibrous tissue ingrowth can be adequate. In the follow-up studies
[5, 6], they concluded different bone formation patterns corresponded to respective
local mechanical environment. Appositional bone formation occurred when the
strain components at the tissue-host bone interface were less than 8%, while local-
ized, de novo bone formation occurred when the distortional tissue strain is approxi-
mately <3%. The studies illustrated that controlled motion in devices with adjacent
bone tissue provide some extent of manipulation of bone formation patterns and
new construct stability.

2.2 Stress

The bone tissue structure significantly contributes to bone mechanical properties.

Bone structure, on the other hand, can be altered to respond stress as described by
Julius Wolff [8]. In Wolff’s law, the structure will align along the direction of prin-
cipal stress and the orientation could change if there is a change in mechanical stress
direction. This discovery revealed the bone adaptation to mechanical environment.
Essentially, Wolff’s law implied that bone tissue continues to self-optimize by the
remodeling process, attempting to obtain maximum mechanical efficiency with
minimum mass.
During fracture healing, the tissue differentiation is related to mechanical stimu-
lus accompanied through the fracture healing history, as postulated by Carter et al
[9]. The relation of mechanical stimulus to tissue growth, remodeling, and healing
400 C.-Y. J. Lin et al.

is based upon the level of vascularity. Earlier, the group also developed an osteo-
genic index and applied the theory on the numerical models to judge the occurrence
of bone, cartilage, and fibrous tissue [10].
Followed by the healing, stress still plays an determinant role in bone remodel-
ing. As noted in the Wolff’s law, the bone structure still undergo an optimization to
fit in the demand of mechanical requirement without redundancy in the intricate
architecture. Guldberg et al. developed an in vivo model of hydraulic bone chamber
in their canine metaphyseal trabecular bone and found convincing evidence of
microstructural adaptation during trabecular bone repair form microcomputed
tomography images [11]. The microstructural adaptation within the bone chamber
was similar to that observed in the spinal cage during bony bridge formation.
Therefore, if the designed internal architecture of osteo-synthetics could provide a
controlled and predictable mechanical stimulation, more reliable construct strength
would be obtained.
Implants can share the load applied to bone, and hence stress on the tissue is
reduced. This phenomenon is known as stress shielding. According to the Wolff’s
law, bone would adapt itself by reducing its mass, either by becoming more porous
(internal remodeling) or by making the structure thinner (external remodeling), to
respond to the decreased load. During spinal fusion, it remains unclear whether the
bone quality of the developing interbody fusion mass will be affected due to the
shield-stress, and if so, what the threshold of the adequate mechanical load would
be required to prevent bone mass loss over the long period. In a more than 8-year
postoperative investigation, Cunningham et al. showed the histological composition
of cervical interbody fusion in thoroughbred horses and they discovered significant
decrease in bone mineral density at the fusion site within the cage compared with
the adjacent vertebral bodies [12]. Similarly, a series of clinical reports showed
resorption in a manner of reduced cortical thickness and increased porosity were
observed in most patients who received noncemented total hip arthroplasty. On the
contrary, van Dijk et al. showed that reduced stiffness of cage contributed to the rate
of lumber interbody fusion [13]. The group used polymeric material poly(l-lactic
acid) (PLLA), which possess an apparently lower elastic modulus (4.2 GPa) com-
pared to titanium (110 GPa), to fabricate a cage with an identical geometry. They
found reduced stiffness significantly enhanced interbody fusion as compared with
titanium cages after 6 months. The results from their large quadrupedal animal mod-
els showed significant improvement in the arthrodesis rate and the quality of tra-
becular bone in the new constructs [13–15]. This result implied that reduced stiffness
of the cage compensates the loss of strain energy to bone tissues.
The relationship between the change of bone density and strain energy was suc-
cessfully quantified in a remodeling algorithm propose by Huiskes et al. [16]. The
model included the idea of a lazy or homeostatic zone where a certain threshold
interval exists. Bone mass increases when the strain energy density is above a cer-
tain level inferring to the modeling from stress fractures. Below a certain threshold,
there is excessive remodeling or absorption of bone; in between these levels is
maintenance of bone structure. Therefore, the reduction of shielded stress would
15 Biomechanics of Osteo-Synthetics 401

ensure bone tissue adjacent to the implant to acquire sufficient energy to maintain
bone mineral density when the rigidity requirement is still placed first in the priority.

2.3 Porosity

In tissue regeneration, porosity, pore size, and interconnectivity of the scaffolding

constructs as the factors are critical for nutrient supply to transplanted cells. Large
void volume is favorable to vascularization, extracellular matrix deposition, and
maximal cell population. Internal pore connection increases diffusion rates to and
from the center of the scaffold and enhances the vascularization that improves the
mass transportation such as metabolic waste removal and nutrient supply. It has
been postulated that bone tends to infiltrate into the pores of an inert porous system
[17]. Hence, by creating a highly porous scaffold, bone ingrowth will be more aug-
mented to stabilize the construct of bone and implants. Designing high porous struc-
ture for spinal cages would facilitate fusion rate and restabilize the affected segment,
especially when cellular grafting is performed as an alternative biological
component.

3 Implantology and Osteoconduction

3.1 Influence of Implant Surface Geometry

on Osseointegration

It has been shown earlier in series of in vivo studies that implant surface geometry
as a design variable significantly influences long-term implant performance [18–
20]. Early in 1979, Bobyn and colleagues examined the optimal pore size for the
fixation of porous surfaced metal implants by the bone ingrowth [21]. The pore size
was investigated to influence the rate of bone ingrowth and the retained maximum
fixation strength. They concluded that in the shortest period (8 weeks) a pore size
range of approximately 50–400 μm ended up to provide the optimum or maximum
fixation strength of 17 MPa. In an earlier report, the group also showed the surface
configuration played as an additional role affecting the tensile strength of fixation of
implants by bone ingrowth [22]. The results indicated implants with the multiple
particle layer surface configuration develop a greater tensile strength of fixation
than that provided by implants with the single particle layer surface configuration.
Also, they suggested this fixation strength develops more quickly if the cortical
bone is petaled prior to implantation. In a more microscopic investigation, Simmons
et al. reported the differences in osseointegration caused by surface geometry can be
attributed to the alteration of local tissue strains [6]. In their computational model-
ing, local tissue strain was predicted in two different designs of plasma-sprayed and
402 C.-Y. J. Lin et al.

porous-surfaced. The result indicated that porous surface structure provided a larger
secure region that experienced low distortional and volumetric strains, whereas the
plasma-sprayed implant provided little local strain protection to the healing tissue.
Coincident with Pilliar’s study, low distortional and volumetric strains are believed
to favor osteogenesis.
In a more cellular-based study, Carter and Giori suggested that proliferation and
differentiation of the mesenchymal cells responsible for surrounding tissues forma-
tion of implants are regulated by the local mechanical environment [19]. Put
together, the mesenchymal cells tend to be more osteogenic when experiencing low
distortional strain and low compressive hydrostatic stress, provided under an ade-
quate vascularity.

3.2 Porous Material

To regenerate tissues and organs with high vascularity, porous structure has been
considered as a desirable feature of scaffolds because of high void ratio and surface
area. Many biomaterials have been fabricated into porous structures with defined
global and local pore sizes as well as interconnected pore network. In 1972, Hulbert
and the colleagues investigated the tissue reaction with porous ceramics versus non-
porous ones [23]. Tissue around discs of porous ceramics healed faster and pre-
sented a thinner fibrous encapsulation than the impervious implants. Blood vessels
invasion were more rapid in those discs with pore size of 100 to 150 μm, constitut-
ing a richer blood supply.
Currently biodegradable polymers such as poly(lactic-co-glycolic acid) have
been prevalently used in tissue engineering. Peter et al. developed porous, poly-
meric bone flaps with attached vascular pedicle to reconstruct defects and found
blocks of vascularized bone were formed 6 weeks after implantation [7]. Hacking
et al. also showed complete tissue ingrowth throughout a porous tantalum implant.
Tissue ingrowth and sufficient vascularity were noted over time and the attachment
strength was three- to sixfold greater compared to a similar study where the implant
was treated with porous beads [24].

4 New Design Strategy: Topology Optimization

4.1 Introduction of Topology Optimization

and Homogenization Theory

The multiple factors in osteo-synthetics that can be determinant for osseous integra-
tion suggest that new synthetic implants can be optimized to concurrently enhance
stability, biofactor delivery, and mechanical tissue stimulation. Modern structural
optimization can be traced back to 1940s, when the discipline was initially d­ eveloped
15 Biomechanics of Osteo-Synthetics 403

in the aerospace industry. In order to design with light-weighting aircraft structural

components with possibly maximal stiffness, the researchers developed a variety of
optimization approaches for simple as well as complex structures, based on analyti-
cal procedures to a specified type of geometry. Until 1960s when modern computers
and finite element method (FEM) became more available, the structural analysis
with mathematical programming embedded became possible. The structural optimi-
zation, however, was still limited to size and shape optimization of the structure
during the period. A more generalized and nonparametric optimization method
which can simultaneously select the best geometric layout and topological configu-
ration was not available until late 1980s. Such an optimization method named
“topology optimization” (or layout optimization) is more superior in saving signifi-
cant amount of materials to avoid redundancy over those designed by the size and
the shape optimizations.

4.2 Topology Optimization

Structural topology optimization, which is a generous design method to find the

optimal structural layouts in a nonparametric fashion, is truly a milestone for
mechanic structural design. It involves simultaneous optimization of the topology
and the shape of internal boundaries in porous composite continua. The topology
optimization is based on the image-based representation that consists of a macro-
scopic variation of solid material and void in a fixed reference design domain. It is
also called material distribution approach or black-and-white design since the den-
sity of structure is given by either 0 or 1, representing void or solid.
Ever since the epochal contribution by Bendsøe and Kikuchi [25] in 1988, the
topology optimization method has progressed with a significant breakthrough from
theoretical into practice. A FE-based numerical topology optimization scheme was
implemented to solve structural design problem with a homogenization-based
method. Many practical engineering problems have been successfully addressed
with the breaking algorithm over the past decades. Neves et.al [26] presented two
computational models to design the periodic microstructure of lattice materials with
optimal elastic properties. Kikuchi et al. [27] furthered the approach to design the
optimal layout and microstructure of composite materials. Topology optimization
method is now leading to a well-acceptable methodology in many industrial
applications.

4.3 Homogenization Theory

The homogenization theory allows the effective properties of periodic composite

materials to be calculated without enforcing the restriction on the geometry of the
given composite structure. The mathematical formulation assumes that the
404 C.-Y. J. Lin et al.

c­ omposite is composed of the periodic microstructures, and the microscopic scale is

much smaller compared to the global dimension, namely the macroscopic domain.
Hence, from the macroscopic view, the composite looks like a “homogeneous”
material. The homogenization theory is a key foundation to conduct topology opti-
mization [25].
The homogenization theory was established by a school of French mathemati-
cians in 1970s [28]. They cooperated homogenization method with the G-convergence
theory and solved many mechanical problems in linear elasticity, heat, and wave
equations. Sanchez-Palencia addressed the fluid flow in porous media, elasticity,
electromagnetism, and vibration of solid mechanics by using the theory [29]. Later,
a numerical homogenization method for elasticity was implemented by Guedes and
Kikuchi [30] using an adaptive finite element method. The homogenization-based
topology optimization was considered a building block in structural optimization
field, and was wildly implemented in different disciplines and applications.

5 Materials for Osteo-Synthetics

5.1 Metals

Metals are perhaps the most common materials used in modern orthopedics. Among
the metals, stainless steel and titanium have been prevalently used for instruments,
particularly when load bearing and mechanical integrity of the new constructs are
required. In spinal applications, anterior interbody cages are often titanium cylin-
ders that are placed in the intervertebral disc space. The cages made of titanium
offer a superior rigidity, and therefore in most single-level fusion cases, additional
instrumentation (e.g., pedicle screws) or postoperative back braces for support are
not needed.
Although biocompatible metals provide desired load bearing, the dense mate-
rial has also created certain obstacles in the real practice . Potential image arti-
facts have been observed in the vicinity of the cage during magnetic resonance
imaging (MRI) and computed tomographic (CT) scanning [31, 32]. Although the
CT images with titanium or titanium, aluminum, and vanadium (Ti-6Al-4V)
alloy present a better result, the amount of MR image artifacts is still comparable
to that with stainless steel [33, 34]. How, lesser field strength and the use of fast
spin–echo techniques have been found to effectively remedy the problem
[35–37].
The second concern with these materials is that solid fusion cannot be easily and
definitely determined from simple radiographic analysis alone. The devices made of
metals are not radiolucent and thus bring the difficulty to determine whether solid
osseous fusion has occurred (osseous trabeculation, evidence of bone formation in
and around the device) on radiographs. Complementary histological examinations
15 Biomechanics of Osteo-Synthetics 405

of the tissue obtained in the hollow spaces from retrieved cages in the studies of
Lange et al. [38] and Carvi et al. [39] confirmed sufficient bone growth in these
areas. However, the reexamination is not feasible in the real practice.
Like the common complication with the use of any metallic device, stress shield-
ing significantly contributes to the relatively high incidence of cage subsidence.
Stress shielding in the segmental fusion achieved by rigid stabilization techniques
with transpedicular screws has been noticed to be associated with disuse osteopenia
in fused vertebra in dog models [40–45]. This osteopenia will likely lead to screw
loosening and instrumentation failures [41]. The mechanically shielded environ-
ment resulted from thick wall or cylindrical thread in conventional cage designs
allows lower intracage pressure propagation [46], which leads to significant bone
mineral density decrease in long term [12]. Consequently, increased incidence of
postoperative complications has been reported such as stress-shielding, the migra-
tion or dislodgement of the cage, pseudarthrodesis, or the combined adverse symp-
toms [14].

5.2 Allograft

Allogenic grafts using corticocancellous blocks [47, 48], corticocancellous dowels

[49, 50], and femoral ring allografts [51] have been commonly integrated in the
segmental reconstruction. Biological contents such as growth factors are well pre-
served after dementalization process. To the context, allografts have been tailored to
accommodate the existing fusion systems. O’Brien et al. devised a hybrid interbody
graft consisting of a biological fusion cage (femoral cortical allograft ring) packed
with autogenous cancellous bone graft [51]. It was thought that the femoral allograft
ring provides the instant stability of the fusion construct, while the autogenous can-
cellous bone graft help induce long-term stability achieved by later complete
arthrodesis. Femoral cortical dowels have been fabricated using cadaveric femurs
that is machined in a dowel formation with a hollow intramedullary region for graft-
ing bone [52]. They are cut along the weight-bearing axis of the bone to provide
structural stability. Because the femoral cortical dowels are not metallic, fusion can
be assessed radiographically. The device have also been shown to have osteocon-
ductive properties. The intramedullary region can be filled with autogenous cancel-
lous bone or bone morphogenetic protein (BMP) allowing the hybrid to be
osteoinductive. The two components synergistically stimulate proper bone ingrowth
within the graft and the ongrowth over a resorptive surface that is integrated with
adjacent bone to form bony union. The femoral cortical dowels provide adequate
mechanical strength as they have been shown to withstand forces of up to 25,000 N. It
should be noted that although cases are extremely rare with current screening
­techniques, using femoral dowel is with risks of pathogen propagation and disease
transmission.
406 C.-Y. J. Lin et al.

5.3 Carbon Fiber Reinforced Polymer

To overcome the major problems of image distortions in the postoperative assess-

ment and stress-shielding induced complications commonly observed with the use
metallic cages as previously described, a family of implants made of a carbon fiber
reinforced polymer (CFRP), PEEK-Optima (Invibio Inc., Greenville, SC) derived
from polyetheretherketone, have been developed since the mid-1980s by Dr. John
Brantigan [53]. The Brantigan CFRP cage is radiolucent, allowing postoperative
visualization of the bone graft healing. The more compliant stiffness close to native
bone properties decreases the incidence of complications resulted from stress
shielding, and a series of clinical reports have shown favorable outcomes [54, 55].
However, it should be noted that device made with PEEK alone does not provide
sufficient fixation and therefor additional posterior pedicle screws are normally
necessary.

5.4 Biodegradable Polymers

In order to address the complications associated with excessive stiffness aforemen-

tioned, biodegradable/bioabsorbable polymers, when used to fabrication implants,
should possess several advantageous characteristics compared to their metallic
counterparts. First, the immediate stability should be still acquired in the segment
where the device is implanted, with the stiffness retained through the degradation.
Second, the implant should be radiolucent without postoperative image interference
as presented in the metallic counterpart. The biodegradable implant should also be
capable of transferring stress during tissue formation by a dynamic equilibrium that
as the implant degrades and its mechanical properties decline, the compromised
strength must be compensated by the tissue regenerate. This main advantage of a
degradable/resorbable material confers initial and intermediate stability without
long-term complications, e.g., stress shielding or migration, of metallic implants.
Finally, the metabolites by implant breakdown should be able to be incorporated
into normal cellular processes without inciting a metabolic derangement that pos-
sesses mutagenic or immunogenic properties to their host cells [56]. A number of
adverse effects with the use of bioabsorbable implants have been reported, includ-
ing synovitis, osteolysis, hypertrophic fibrous encapsulation, and sterile sinus tract
formation. These have brought up concerns with bioabsorbable implants to incite
aseptic inflammatory reactions during the resorption process [57–60].
The class of bioabsorbable materials that has been most studied is alpha-poly
hydroxyl esters. These include the two mostly used polymers in biomedical
­applications, poly(glycolic acid) (PGA) and poly(lactic acid) (PLA). Both materials
have been shown with complete absorption in bone [61–63]. However, different
degradation byproducts and inflammatory reactions were found with the two poly-
mers. PGA has been shown to induce more inflammatory tissue reactions than PLA
15 Biomechanics of Osteo-Synthetics 407

[64, 65]. In addition, degradation patterns and half-lives are also different for stereo-
isomers belonging to the same compound [63, 66, 67].
The idea to incorporate bioabsorbable polymers in the surgical implants was first
introduced by Kulkarni et al. [68]. A variety of other applications were then invented,
including sutures, repair of craniofacial defects, appendicular fracture fixation, and
soft-tissue repair [59, 61, 62, 67, 69–73]. A recent attempt also included to fabricate
a PLA interbody fusion cage with the same geometry from the titanium [14, 74, 75].
The use of bioabsorbable materials in skeletal reconstruction has aroused signifi-
cant interests in clinic. The dynamic load transition has been show to lead to higher
bone formation rates, further improving clinical outcomes in specific applications.
Clinical studies are currently underway to evaluate the feasibility to extend their use
in more practice of orthopedic surgery.

6 Osteo-Synthetics with Designed Architecture Possessing

Solid–Fluid Bi-phasic Properties of Native Bone

6.1 Introduction

The effects of how porous features of a scaffold such as pore size, pore shape, and
interconnectivity affect tissue regenerates have been well studied. These micro-
structural parameters are correlated with mechanical and mass transport properties
of the scaffolds. One delicate way to achieve a viable tissue regenerate is to find
optimal microstructures that achieve prescribed mechanical and mass transport
properties.
To obtain the overarching aim, hierarchical scaffold design appears to be an
adapting optimization scheme to include all these diverse design goals [76]. In the
hierarchical scaffold design scheme, unit microstructures, or unit cells (structural
unit, not biological cells) are selected from unit cell libraries and assembled to form
a scaffold with a global shape that fits into anatomical geometries. The mechanical
and fluidic properties of the scaffold are calculated using the homogenization theory
based on double-scale asymptotic expansion [77, 78]. Furthermore, the pore archi-
tectures can be designed with predefined geometries such as three orthogonal cylin-
drical pores or spherical pores. Hollister et al. optimized pore diameters of scaffolds
with three orthogonal cylindrical pores using the homogenization method and
empirically fitted polynomials that relate pore diameters and the effective stiffness
tensor [79]. The requirements for mass transport were considered by applying a
lower-bound constraint to the porosity.
In more general cases, new microstructures with target properties can be created
using topology optimization [80–82]. Topology optimization distributes material
within a unit microstructure with compose of the final, global architecture that ful-
fills the targeted performances. Lin et al. adapted the topology optimization to find
scaffold microstructures that reach the targeted anisotropic elastic constants [83].
408 C.-Y. J. Lin et al.

Hollister and Lin further extended the method by introducing effective permeability
to the optimization scheme to design scaffolds with the maximized permeability
[84]. However, in that initial attempt, the permeability was not coupled with the
mechanical property in the optimization procedure, so that maximizing permeabil-
ity could affect the mechanically optimized microstructure.
Recently, several multifunctional material design schemes based on the topology
optimization have been reported. Guest and Prevost illustrated a general 3D micro-
structure design scheme using the topology optimization method to achieve maxi-
mized bulk modulus and isotropic permeability [85]. They optimized microstructures
by differentially weighting mechanical and transport terms in the objective, allow-
ing designers to tailor the material properties. de Kruijf et al. found optimal struc-
tures with maximized bulk modulus and thermal conductivity by minimizing both
mechanical and thermal compliance in 2D [86]. The authors explored Pareto opti-
mality by varying weights for mechanical and transport properties. Challis et al.
presented the design of isotropic unit structures with maximized bulk modulus and
isotropic conductivity by a level set method [87]. The authors also explored changes
in design with different combinations of weighting factors.
The design approaches of multifunctional material structures with maximized
properties have gained increasing interests in many engineering fields. Tissue engi-
neering scaffolds, for example, have been tailored to meet a wide range of mechani-
cal and mass transport properties, including cross property relationships that fall
well within the cross-property bounds. For instance, cartilage needs low mass trans-
port and mechanical properties, which lay well within the interior of the mass trans-
port and mechanical cross-property bounds [88].
Thus, in order to design microstructures with ranges of mechanical and mass
transport properties, we adapted a local microstructure topology optimization
scheme based on the SIMP method for target optimization. The target properties
were selected within defined cross-property bounds connecting effective bulk mod-
ulus and isotropic diffusivity. Various microstructures were designed and utilized
within the tissue engineering scaffolds. A porous biodegradable interbody fusion
cage was designed as a biomedical application of multifunctional microstructures
by integrating the layout from the global topology optimization with the local opti-
mized microstructure. The final integrated structures were then built using solid
free-form fabrication techniques.

6.2 Tailoring Scaffold Properties

6.2.1 Material Interpolations

Microstructure topology optimization computes the optimal topology of a scaffold

microstructure by distributing material density within the unit cell domain under
design objectives and constraints. The design domain is discretized with the finite ele-
ments assigned with density values, ranging from 0 through 1. In this relaxed problem,
15 Biomechanics of Osteo-Synthetics 409

material laws should be defined to relate element densities and local material proper-
ties. In addition, the intermediate density values are penalized to have a final discrete
design. The most common local material law is the Solid Isotropic Microstructure
with Penalization (SIMP) [89]. We utilized the SIMP method for elasticity:

Cijkl = ρ pCijkl
base
, ( p > 1)
where Cijkl is the element stiffness tensor, ρ is the element density, p is a penalization
base
factor, and Cijkl is the stiffness tensor for the base material. For the diffusivity, a
SIMP-like material law can be applied to the interpretation of the intermediate den-
sities with penalization,

Dij = (1 − ρ ) Dijbase ,
p
p >1

where Dij is the element diffusivity tensor, ρ is the element density, p is a penaliza-
tion factor, and Dijbase is the free diffusivity tensor for the fluid phase. With the local
material laws defined for both stiffness and diffusivity, the objective function and
sensitivity derivatives are derived with respect to material density ρ, and the optimi-
zation problem can be solved by updating ρ at each iteration.
For the phase base material, we used unit isotropic diffusivity, D = 1 for the void
phase. For the base material solid phase, we chose Poisson’s ratio equal to 1/3 with
a Young’s modulus of 1, which yields a bulk modulus of 1. In this case, the designed
properties could be easily compared within the cross-property bounds normalized to
base material properties.

6.2.2 Problem Statement for Target Optimization

In order to tailor the material properties directly, the optimization problem was
defined to minimize the error between the target and the effective bulk moduli and
diffusivities, with constraints on porosity:

2 2
 KH   DH 
minimize f = w1  ∗ − 1  + w2  ∗ − 1  + w3 fcubic
K  D 
N
1 − ρi
subject to φlb ≤ ∑ ≤ φub ,
i =1 N
0 < ρi ≤ 1

where KH is the homogenized bulk modulus, K∗ is the target bulk modulus, DH is the
homogenized isotropic diffusivity, D∗ is the target isotropic diffusivity, fcubic is the
cubic error function and wi (i = 1, …, 3) are weighting factors, ϕlb and ϕub are the
upper and lower bounds of porosity, ρi is ith element density, and N is the total num-
ber of elements.
410 C.-Y. J. Lin et al.

Imposing isotropic or cubic symmetric material microstructures, the effective

bulk modulus was converted from elastic stiffness tensor components assuming iso-
tropic/cubic symmetry in the final result.

1  C H + C2222
K H =  1111
H
+ C3333
H
+
H
(
2 C1122 + C2233
H
+ C1133
H
) 
3 3 3 
 

In the same way, the effective diffusivities were evaluated as average of the diag-
onal terms in diffusivity tensor.

D11H + D22
H
+ D33H
DH =
3

The cubic error function is defined to minimize the differences among three nor-
mal components, three off-diagonal terms, and three shear terms in the stiffness
tensor components, respectively.
2 2 2
 CH   C3333
H
  C1111
H

fcubic =  2222
H
− 1 +
  H − 1   H − 1
+
 C1111   C2222   C3333 
2 2 2
 CH   C1133
H
  C1122
H

+  2233
H
− 1  +  H
− 1  +  H
− 1
 C1122   C2233   C1133 
2 2 2
 CH   C1212
H
  C2323
H

+  1313
H
− 1  +  H
− 1  +  H
− 1
 C2323   C1313   C1212 
H
where Cijkl are the components of the homogenized stiffness tensor. This multi-­
objective formulation can be easily converted to a formulation in which one of the
target properties is optimized while the other is constrained.

6.2.3 Implementation

Topology optimization, in its relaxed formulation, still requires additional treatments

to avoid known numerical instabilities such as checkerboard patterns and mesh depen-
dencies [90]. We applied a nonlinear filtering scheme to the sensitivity derivatives to
prevent checkerboard patterns and mesh dependency as proposed by Sigmund [91].
Assuming unit cell size of 1 mm in each direction, a filter radius of 3 elements was
chosen to maintain a minimum physical feature size (0.15 mm) for the 40 × 40 × 40
element unit cells. When the mesh resolution was increased to 60 × 60 × 60, the filter
radius was increased to 4 elements to maintain the minimum physical feature size
(0.13 mm). Finally, to solve the optimization problem, the Method of Moving
Asymptotes (MMA) was adopted to provide greater efficiency in solving problems
with a large number of variables and a small number of constraints [92].
15 Biomechanics of Osteo-Synthetics 411

6.3 Design Results

Our results demonstrate that the properties of the microstructures can be tailored to
meet various scaffold requirements such as stiffness and mass transport using topol-
ogy optimization with SIMP interpolation and sensitivity filtering. Target design
points were chosen close to the cross-property upper bounds. Figure 15.1 illustrates
various microstructural architectures obtained in this study and the achieved proper-
ties are presented in Table 15.1. The mesh resolution for microstructures (a), (c), (e),
(g), and (f) was 60 × 60 × 60, and the mesh resolution for the other microstructures

a b c

d e f

g h

Fig. 15.1 Microstructures obtained by targeting bulk modulus and diffusivity close to the upper
cross-property bounds, for 30% porosity (a, b, and c), 50% porosity (d, e, and f), and 60% porosity
(g, h). (With permission from “Structural and Multidisciplinary Optimization”, Springer Nature)
412 C.-Y. J. Lin et al.

Table 15.1 Properties of microstructures tailored with target bulk moduli and diffusivities (With
permission from “Structural and Multidisciplinary Optimization”, Springer Nature)
Microstructures Porosity Diffusivitya Bulk modulusa Young’s modulusa Poisson’s ratio
A 0.2825 0.1276 0.3734 0.4875 0.2824
B 0.3030 0.1340 0.3565 0.5273 0.2535
C 0.2935 0.1616 0.3317 0.4277 0.2851
D 0.4831 0.3016 0.1512 0.2258 0.2511
E 0.4828 0.3156 0.1624 0.1955 0.2994
F 0.5037 0.3330 0.1522 0.2251 0.2535
G 0.5802 0.3556 0.1246 0.2442 0.1734
H 0.5882 0.4164 0.1114 0.0973 0.3544
The values are normalized to the base material properties
a

Fig. 15.2 Microstructures 0.6

designed to achieve
properties close to the
upper cross-property 0.5
Effective Bulk Modulus, K/K1

bounds are specified within

the cross-property bounds.
(With permission from 0.4
“Structural and
Multidisciplinary
Optimization”, 0.3
Springer Nature)

0.2

0.1

0 0.1 0.2 0.3 0.4 0.5 0.6

Effective Diffusivity, D/D2

was 40 × 40 × 40. The designed microstructures were identified within the cross-­
property bounds in Fig. 15.2.
Note that the porosities of the designed microstructures satisfied the constraints
despite the lack of an exact match in the corresponding cross-property bounds. This
is because the porosity constraints were set at a small range around the target poros-
ity. For example, the porosity constraints were set less than 52% and greater than
48% for the design of 50% porosity microstructures. Nonetheless, there was excel-
lent agreement between the target and designed bulk moduli and diffusivities
(Fig. 15.3).
Because of the theoretical cross-property bounds for 50~60% porosities, the
maximum normalized diffusivities are 0.4 and 0.5, respectively. Thus, we may con-
sider diffusivity over 0.3 as high diffusivity for 50~60% porosity materials.
15 Biomechanics of Osteo-Synthetics 413

Fig. 15.3 The achieved a Effective Diffusivities

diffusivities (a) and bulk 0.5
moduli (b) were compared
with target properties for

Normalized Diffusivity
0.4
the mirostructures
presented in Fig. 15.1
(a–h, respectively). 0.3
(With permission from
“Structural and 0.2
Multidisciplinary
Optimization”,
0.1
Springer Nature)

0
A B C D E F G H
Microstructures

Target Diffusivity Achieved Diffusivity

b Effective Bulk Modulus

0.5
Normalized Bulk Modulus

0.4

0.3

0.2

0.1

0
A B C D E F G H
Microstructures
Target Bulk Mod Achieved Bulk Mod

6.3.1 Microstructures with High Diffusivity

Microstructures with relatively high diffusivity designed for either 50% or 60%
porosity approached the cross-property upper bound, as depicted in Fig. 15.1d–h.
The properties of the microstructures illustrated in these figures were isotropic. It
should be noted that the designed microstructures have different topologies while
the achieved properties were close to each other. Interestingly, the property pair of
the microstructure in Fig. 15.1f is the closest to the cross-property upper bound,
implying that the structure is optimal. Furthermore those microstructures designed
to have 60% porosity showed lower bulk modulus of approximately 0.1 of that of
the solid phase. When the structures were specified within cross-property bounds,
414 C.-Y. J. Lin et al.

both structures again have near optimal properties because the properties are close
to the upper bounds (Fig. 15.2).

6.3.2 Microstructures with Low Diffusivity

Microstructures targeted a low diffusivity for 30% porosity were also near the cor-
responding cross-property upper bounds (Fig. 15.1a–c). The optimized structures
have thick diagonal in the unit cell domain to obtain a high bulk modulus and small
pore diameter to decrease diffusivity. The normalized diffusivities of these micro-
structures were between 0.12 and 0.17 (Table 15.1). These low diffusivity structures
were also close to the upper cross-property bounds due to high bulk moduli
(Fig. 15.2).

6.3.3 Microstructure Targeting Low Diffusivity and Low Bulk Modulus

For cartilage tissue engineering applications, microstructures with low modulus

and low diffusivity are desired. Such microstructures lie within the interior of
the cross property bounds, distant from the upper limits that are more often tar-
gets of other multiphysics microstructural topology optimizations. These targets
present significant challenges as the increase of material will increase bulk
modulus while decreasing diffusivity, reaching the opposite end of the
design goal.
To eliminate the intermediate densities, we used a post processing technique. We
designed a microstructure with a low diffusivity of 0.1 and a low bulk modulus of
0.1, respectively. However, the result of the post processing had changed the initial
properties set as targets. The intermediate density values were interpolated using the
SIMP model. After applying a threshold, the properties shifted toward cross-­
property upper bounds.
One interpretation for intermediate densities were generated is that the algo-
rithm converged to a local minimum before all densities were penalized. We
employed the convention of Sigmund’s continuation method to avoid convergence
to a local minimum [82]. However as expected, this essentially heuristic approach
could not sufficiently penalize the intermediate densities: the final mechanical and
transport properties were with a diffusivity of 0.12 and a bulk modulus of 0.1,
which were not a totally satisfactory solution to the problem. The full structure and
1/eighth of the structure are shown in Fig. 15.4a, b, respectively. In addition, repre-
sentative cross-­sectional view of the density distribution are illustrated in Fig. 15.4c.
There are significant amounts of gray elements at convergence, which may indicate
local minima. There are very weak connections between large spheres at the
corners.
15 Biomechanics of Osteo-Synthetics 415

a b

z=1 z=10 z=20 (center)

Fig. 15.4 (a) Microstructures with low diffusivity and low bulk modulus, (b) 1/8 of the designed
microstructure, and (c) representative cross-sectional view of the structure. (With permission from
“Structural and Multidisciplinary Optimization”, Springer Nature)

6.3.4 Microstructures with the Same Porosity But Different Bulk

Modulus and Diffusivity

A particular strength of the targeted optimization is the capability to create micro-

structures of the same porosity, but with a range of bulk moduli and diffusivities.
Here, we demonstrated a series of microstructures that were successfully designed
with 45~50% porosity with diffusivities ranging from 16 to 33% and effective bulk
moduli ranging from 12 to 24% of the base properties, respectively (Fig. 15.5). This
endorses the argument that our developed algorithms is capable of distributing the
same amount of material in different layouts to dramatically retain different effec-
tive mechanical and mass transport properties. The microstructures in Fig. 15.5 can
be experimentally tested to evaluate the effect of material distribution on load bear-
ing and mass transport without changing the porosities.
416 C.-Y. J. Lin et al.

Fig. 15.5 Microstructure Cross–Property Bounds (Porosity=0.5, n1=1/3)

designs with ranges of 0.3
diffusivities for 50%

Effective Bulk Modulus, K/K1

porosity. (With permission 0.25
from “Structural and
Multidisciplinary 0.2
Optimization”,
Springer Nature)
0.15

0.1

0.05

0
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4
Effective Diffusivity, D/D2

6.3.5 Comparison of Designed Properties

with Experimental Measurements

Using SFF technique, we fabricated the designed scaffolds with PCL/HA compos-
ites for compression tests. Because the scaffold microstructures were represented
using voxel elements, a three-dimensional version of pixels, the geometry of the
optimized scaffolds was generated by simply repeating the corresponding voxels
using an image-based modeling technique. The dimension of the specimens tested
were 8 mm × 8 mm × 16 mm, with unit microstructures of
2.67 mm × 2.67 mm × 2.67 mm, which represents 3 × 3 × 6 units of microstructures.
The voxel representation of the specimens was then converted to STL files to
accommodate the SFF technique.
A selective laser sintering technique was utilized to fabricate the specimens by
sintering PCL and HA in a powder bed. As shown in Fig. 15.6, the specimens
(a)~(h) corresponds to microstructures (a)~(h) in Fig. 15.1. Compression tests were
conducted with the fabricated specimens and the results were compared to the
designed properties. MTS Alliance RT30 electromechanical test frame (MTS
Systems Corp., MN) was used with a strain rate of 1 mm/min under a preload of
1 lb. TestWorks4 software (MTS Systems Corp., MN) was used to collect load-­
displacement responses. Average stress was obtained from the recorded load divided
by the undeformed cross-sectional area of the specimen (~64 mm2). In the similar
manner, average strain was calculated from the displacement divided by the unde-
formed height (~16 mm).
The stress–strain curve is presented in Fig. 15.7. The experimental modulus was
then calculated based on the slope of a line that connects the origin and 1% strain
point. The moduli obtained by the average stress and strain were compared with the
designed Young’s modulus, which was calculated from bulk modulus and Poisson’s
ratio because the optimized microstructures were all cubic symmetric (Table 15.2).
15 Biomechanics of Osteo-Synthetics 417

a b c d

e f g h

Fig. 15.6 Scaffolds with optimal microstructures illustrated in Fig. 15.1 (a–h, respectively) were
designed and fabricated using SFF

Fig. 15.7 Stress–strain 10

A
curves obtained from B
compression tests of the C
D
fabricated scaffolds E
designed with the optimal 8 F
G
microstructures H

6
Stress (MPa)

0
0 0.05 0.1 0.15 0.2
Strain
418 C.-Y. J. Lin et al.

Table 15.2 Comparison of Theoretical

theoretical Young’s modulus Young’s Experimental
calculated from the Microstructures modulusa Young’s modulusb
homogenization method, and
A 0.4875 0.2167
experimental Young’s
modulus measured B 0.5273 0.4424
compression tests C 0.4277 0.2479
D 0.2258 0.1284
E 0.1955 0.2186
F 0.2251 0.1373
G 0.2442 0.1509
H 0.0973 0.0571
a
Values are normalized to the base material
Young’s modulus
b
Experimental Young’s moduli are normalized to experi-
mental Young’s moduli of bulk specimen (295 MPa)

Fig. 15.8 Theoretical 0.6

Young’s modulus was
correlated to experiments
0.5
Experimental Yound’s Modulus

0.4
y = 0.6151x + 0.013
R2 = 0.6845
0.3

0.2

0.1

0.0
0 0.1 0.2 0.3 0.4 0.5 0.6
Theoretical Young’s Modulus

As shown in Fig. 15.8, the theoretical Young’s moduli were correlated to experi-
mental Young’s moduli, although the latter were lower than the former. It should be
noted that small geometric features such as struts and pores in the microstructures
were not accurately fabricated in some cases. For example, disconnected struts were
identified between unit microstructures in Figs. 15.6, 15.7, and 15.8. In the selective
laser sintering process, the laser beam scanning speed and particle size of the pow-
der have been found to affect the energy exposure at a spot, which determines the
minimal curing path size. Geometric features, smaller than the minimum path size,
were skipped based on the preset accuracy of the machine. Considering these manu-
facturing defects, the theoretically designed properties seemed to provide upper
bound for the experimental properties.
15 Biomechanics of Osteo-Synthetics 419

6.4 Discussion

It is hypothesized that scaffolds should provide mechanical and mass transport

properties as close as possible to native tissues to enhance tissue regeneration [93].
As an active component, scaffolds should be able to provide a proper mechanical
withstanding to maintain structural integrity at the defect site as well as transpass
appropriate mechanical stimuli to newly generated tissues [94–96]. In addition,
scaffolds should provide appropriate mass transportation that can support cellular
functions, tissue ingrowth, and supply of nutrition [93, 97]. However, it is still
unclear what optimal properties the scaffold should possess in order to obtain the
best outcome of tissue regeneration. For example, there have been inconsistent sug-
gestions from different prior studies on the optimal pore size or porosities for tissue
regeneration. Moreover, different levels of fluidities have been also shown to result
in different cell differentiations [98].
In order to rigorously investigate correlations between functional environments
and tissue regeneration, the ability to design scaffolds with controlled mechanical
and mass transport properties is essential. In this study, we demonstrated a devel-
oped approach to tailor these properties using topology optimization. Cross-property
bounds provide a favorable yet also feasible domain in the intersection of the bulk
modulus and diffusivity. Thus, topology optimization with cross-property bounds
make it a powerful design tool for creating microstructures with desirable, precise
controls.
To avoid numerical instabilities inherent to the process, we introduced a nonlin-
ear sensitivity filter proposed by Sigmund [91]. Filtering techniques are known to
avoid known instabilities such as checkerboard patterns and mesh dependence. The
downside of the technique is that the final structure often contains intermediate
densities spanning solid-void boundaries due to the blurring effect of the filter.
However, in our case, we found 0 and 1 were successfully distinguished with the
nonlinear sensitivity filter. We measured the convergence of the intermediate densi-
ties toward 0 or 1 by:

1 N ρi − 0.5
Rconv = ∑
N i =1 0.5

Rconv approaches 1 as the intermediate densities are penalized toward either 0 or

1. With the SIMP topology optimization and sensitivity filter, we were able to obtain
microstructures with an Rconv index over 0.95, which can be considered converged.
If Rconv is less than 0.95, the designed properties may shift toward upper cross-­
property bounds after the post-processing. From a practical viewpoint, this could be
beneficial because the premature solution still serves as a design choice. However,
achieving a discrete solution is more desirable in terms of tailoring the material
properties and creating a manufacturable design. In this regard, other techniques can
be applied such as density filtering with a Heaviside step function [99] or addition
of a nonlinear diffusion term to the objective function [100].
420 C.-Y. J. Lin et al.

Several studies for microstructure design have shown the composite or porous
structures that are near or on the cross-property upper bounds [85–87]. In these
previous works, two competing properties were maximized simultaneously.
However, one of our main interests in this study was to design microstructures
whose properties are far from the upper bounds.
In particular, our main interest was the design of microstructures with low dif-
fusivity and low bulk modulus. As presented in the result, our design converged to
a minimum. Typically the Rconv index was less than 0.8. If we targeted a design point
far from the upper cross-property bounds, the Rconv index became even smaller. To
evaluate the difficulty of achieving this inner design point, we tested three design
points: (1) K = 0.2 and D = 0.3, (2) K = 0.15 and D = 0.2, and (3) K = 0.1 and
D = 0.15. We used the same problem statement and control parameters for filtering
until convergence at a local minimum was achieved.
The outer point or the point on the upper bounds was easily achieved with an
Rconv index of almost 0.99. For the middle design point, the Rconv index was 0.93,
which means the final design contained a blurry solid-void boundary. However, for
the innermost design point case, the Rconv index was 0.71 and the structure exhibited
a clear gray layer in addition to the black solid structure. This can be noticed in the
histogram as shown in Fig. 15.9 where the number of elements with given densities
were plotted in bins. The case with the inner design point generated a large amount
of elements containing around 0.3–0.4. One possibility was that the presence of the
gray regions represented sub-microstructures were with higher degrees of freedom
in reaching the interior targets than the distinct 0 or 1. This would be more relevant
in the hierarchical structure of biologic tissues, where the feature sizes can range
from the nanometer to centimeter scale.
Another important factor is the practical aspect for manufacturing. Particularly
for the designs with low diffusivities designs, small holes would become the case
that in turn limits the overall diffusivity. Considering the size of unit cells (typically
around 1 mm) in the skeletal tissue scaffolds, the small holes may not be manufac-
turable due to the default resolution of the machine.

Fig. 15.9 Histograms of Histogram of Element Densities

densities of three 5000
microstructure designs
targeting K = 0.2 and K=0.2 ,D=0.3
4000 K=0.15 ,D=0.2
D = 0.3, K = 0.15 and
Element Counts

D = 0.2, and K = 0.1 K=0.1 ,D=0.1

and D = 0.1 3000

2000

1000

0
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
Density
15 Biomechanics of Osteo-Synthetics 421

In our study, diffusivity was considered in our design process because the char-
acteristics of diffusion in the scaffold can affect many critical cellular behaviors,
such as migration. The property will also influence mass transportation such as
oxygen and nutrient delivery as well as metabolic waste removal. Mathematical
models of cell migration and tissue regeneration have adapted diffusion in the simu-
lations [101, 102]. In addition, diffusivity and permeability of scaffolds are well
correlated [103]. There are also known cross-property bounds on the effective dif-
fusivity and bulk modulus, suggesting the necessity to include them as design
characteristics.
As a temporary substitute for the extracellular matrix, scaffolds are expected
to provide a favorable milieu to promote new tissue formation. More experi-
mental data are warranted to elucidate what are considered as optimal condi-
tions to augment tissue regeneration as ambiguities have been noticed in
different observations. For example, conflicting findings have been reported
regarding the effect of oxygen diffusion on cartilage regeneration [97]. In this
regard, the method of microstructural topology optimization emerges as a new
platform tool to further this type of studies and help explore the most relevant
scaffold properties.

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