TISSUE BIOMECHANICS

STRUCTURE OF BONE

Bone

Cellular Component

Extracellular Component

Osteoblasts ( bone forming cells)

Osteoclasts (Bone resorbing cells)

Osteocytes (Mature and inactive osteocytes

Organic (Collagen type 1)

Inorganic (Hydroxyapatite) Ca5(PO4)3OH

Triple helix tertiary twisted structures. High tensile strength and flexibility.

Crystals are aligned along the axis of the collagen fibres provide reinforcement. Provide strong and tough composite

Cortical bone

Trabecular bone

more dense ( porosity 5% to 10%) found on surface of the bones ( shaft of long bones, forms outer shell around cancellous bone at the end of the joints and vertebrae) structural and functional unit is called the osteon

Less dense ( porosity 50% to 90%) Found in end of long bones, vertebrae and flat bones. Also found in the inside of the bone. Structural and functional unit is called the trabecula

Cortical Bone

Haversian System ( Osteon) - Microstructure

Lamellae

Bands or layers of bone ( 3 7 mm thick)

Arranged concentrically around the central haversian canal Contain type 1 collagen fibres and mineral

Osteocyte Lacunae ( 10 to 20 mm in diameter)

holes within the bone matrix which contain bone cells(osteocytes) and their processes. Osteoblasts become entrapped and mature into osteocytes during the process of mineralization, ellipsoidal structure. Within the lacunae the osteocytes sit within the extracellular fluid.

Osteocyte Canaliculi

small tunnels that connect one lacunae to the other. These interconnections provide a pathway though which osteocytes can communicate information.

Cement lines ( 1 to 5 microns thick)

Only found in secondary bone result of remodelling. Occurs at the point bone resorption ends and bone formation begins. Devoid of collagen type 1 CEMENT LINES MAY SERVE TO ARRESST CRACK GROWTH IN BONE BEING THAT THEY ARE VERY COMPLIANT AND LIKELY TO ABSORB ENERGY

Source: http://training.seer.cancer.gov/anatomy/skeletal/tissue.html

Source: Grays Anatomy of the Human Body from the classic 1918 publication available online at Bartleby.com. Coloured and modified using Adobe Illustrator

Trabecular Bone
Structural unit Trabacula - Components are the same as that of cortical bone. - Difference lies in the organization of microstructures. - Trabacula is 200nm in thickness and 1000nm long. - Do not contain central canal with blood vessel. Blood vessels surround the trabacula. - Lamallae are not concentrically arranged but arranged longitudinally along the trabacula.

BIOMECHANICS OF BONE

Two unique mechanical characteristics of bone

Anisotropy Bone responds differently depending on the direction of applied load.

Viscoelasticity Bone responds differently depending on the duration of load application.

Stress vs strain curves differ depending on the load direction.

Stress vs strain curves differ depending on the duration of load application

 The whole bone properties are called extrinsic biomechanical properties. Bone tissue properties are called intrinsic properties.

Source: Biomechanics of Bone: Determinants of Skeletal Fragility and Bone Quality C. H. Turner

Source: Biomechanics of Bone: Determinants of Skeletal Fragility and Bone Quality C. H. Turner

Anisotropic behaviour of human cortical bone

Loading mode (Longitudinal )

Ultimate strength

Tension

133 MPa

Compression

193 MPa

Shear

68 MPa

STRAIN
The amount of deformation in the material, relative to its original length, is called strain.

Material is pulled, it gets longer - tensile strain Material is pushed together, it shortens - compressive strain Layers in the materials slide against each other, occurs with torsion or bending - Shear

Absolute magnitudes of peak strains in bone during vigorous activity can be on the order of 3500 micro strain in compression (0.35% strain), 1200 micro strain in tension.

Material A

Material A is stiffer compared to B. - Steeper slope Material B has a higher yield strain than A - more linear relation between stress and strain ( Yield Failure)

Material B

Material A has a higher ultimate strain when compared to B - gives the Ultimate Failure. Material A is more brittle than B - Area under the graph gives the toughness of the material

MODULI

Stiffness is determined by the relative proportions of the hydroxyapatite crystals and the collagen fibres that make up the composite. The steeper the slope of the stress vs strain graph, the greater is the modulus and bone deforms much less.

The modulus of mature cortical bone is on the order of

i) ii) iii)

18 GPa in the longitudinal direction 12 GPa in the transverse direction, 3.3 GPa in shear The material properties of cancellous bone are influenced by trabecular orientation, connectivity and bulk density The elastic modulus of trabecular bone can range from 0.1 to 3.5 GPa. The degree of mineralization (e.g., immature or woven bone) or porosity (e.g., old bone) will compromise the stiffness of the bone and thereby lower the elastic modulus.

Young's modulus of trabecular bone as a function of density of bone. Bone density is expressed in g/cm3 and Young's modulus E in MPa

YIELD FAILURE

When strain is no longer proportional to stress, the material loses it ability to resume its original shape. In the bone, yield failure arises through ultra structural micro cracks within the hydroxyapatite and the disruption of collagen fibrils. The yield stress is approximately 130 MPa. The yield strain of cortical bone is on the order of 6800 micro strain.

Ultimate Failure

As the loading continues in the plastic region, the material will eventually reach ultimate failure and fracture. The point at which the bone breaks can be viewed as either the ultimate strain. - 10,000-15,000 micro strain in tension - the ultimate stress i) 140 MPa in tension ii) 200 MPa in compression iii) 65 MPa in shear

Toughness

The area under the stress strain graph gives the energy per unit volume possessed by the material at any given point.The area gives the energy required to break the object i.e. it gives the work to failure. The property is measured as the toughness of the material. The composite nature of Haversian, circumferential and interstitial lamellae play an important role in defining the toughness of the bone.

The amount of post-yield strain that occurs before ultimate failure is a measure of the material's ductility, reflecting its ability to resist the propagation of cracks.

Osteopetrosis : Brittle bone disease. The bone undergoes little deformation before fracture. This disease causes stiff, brittle bones.

Osteomalacia : This results in weak, ductile bone. Bones can deform considerably before the fracture. The bones bend under load and deform ( bowed long bones)
Both osteopetrosis and osteomalacia , the bone is unable to absorb energy before breaking. i.e there is reduced work to failure.
Source: Biomechanics of Bone: Determinants of Skeletal Fragility and Bone Quality C. H. Turner

Effect of mineralization on bone

Increased mineralization affects a number of biochemical properties of bone - stiffness is increased. - ultimate displacement is decreased.
Increased mineralization improves structural rigidity if bone while at the same time makes the tissue more brittle. Properly mineralized bone has the best combination of stiffness and brittleness.

Source: Biomechanics of Bone: Determinants of Skeletal Fragility and Bone Quality C. H. Turner

Porosity and bone strength

Increase in porosity causes disproportionate decreases in bone strength, i.e. small increase in porosity can decrease bone strength. Power law proportion: Strength=k(1- P)N

Where, k = constant, P =porosity Strength porosity relationship for bone, the value on N falls between 2 and 3.

Source: Biomechanics of Bone: Determinants of Skeletal Fragility and Bone Quality C. H. Turner

Stiffness and toughness are the basic requirements of a bone. It is not possible to attain high stiffness and toughness simultaneously. There is an inevitable trade-off between both the properties. A delicate balance between resistance to propagate cracks provided by collagen and resistance to deformation ( given by the hydroxyapatite crystals).

Compression
The cortical bone is stronger in compression than in tension. The strain to failure is about 3% for cortical bone under compressive loading regardless of whether the load is applied travresely across the bone or longitudinally along the bone.

When the bone is loaded transversely in tension, the strain to failure and strength is reduced substantially.
Transverse specimens are much weaker and exhibit much lower strain-to-failure than longitudinal specimens.

Property
Compressive strength(MPa)
Tensile strength Strain to failure Youngs Modulus Fracture toughness

Cortical Bone
100-200
50-150 1-3 7-30 2-12

Cancellous Bone
2-12
10-20 5-7 0.5-0.05

Source: Table 8.2, The skeletal system, LARRY HENCH Biomaterials, Artificial Organs and Tissue Engineering

Trabecular structures of vertebrae in a 36 year old woman

Trabecular structures of vertebrae in a 74 year old woman

Viscoelastic Behaviour of Bone

Viscosity Fluids Elasticity Solids

Viscoelasticity is a phenomena of time dependent strain exhibited by amorphous materials. Viscoelasticity has been attributed to viscous-like motion at the cement lines and the presence of a water phase. Viscoelasticity can be explained in terms of Creep Stress relaxation Viscoelastic parameters : Elastic (storage) modulus : The ability of a material to store energy Viscous (loss) modulus : The ability of a material to dissipate energy.

Creep
It is a tine dependent increasing strain response to a constant applies stress.

Stress Relaxation
It is a time dependent reduction of stress response to a constant applied stain.

BONE REMODELLING

Need for bone remodelling

Adjust bone architecture to meet changing mechanical needs. Modification of bone in response to stress other biomechanical forces. Helps to repair micro damages in bone matrix by preventing the accumulation of old bone. Maintaining plasma calcium homeostasis.

Cortical Bone

Trabecular Bone

Cylindrical 2,000m long and 150200m wide Speed of 20-40 m/day 2% to 5% of cortical cone is remodelled each year.

More actively remodelled Trench of depth 40-60m Larger surface to volume ratio Speed of 25m/day

Osteoblasts and osteoclasts arranged in BMU (site of bone remodelling). BMUs vary from cortical bone to trabecular bone(morphology).

Bone Remodelling ( Turn over)

Involves the removal of mineralized bone by osteoclasts followed by the formation of bone matrix through osteoblasts that subsequently become mineralized. Bone resorption Bone deposition

Resportion

Formation

Reversal

References:
1. Biomechanics of Bone: Determinants of Skeletal Fragility and Bone Quality , C. H. Turner Biomechanics and Biomaterials Research Center, Indiana University, Indianapolis, USA 2. Bone Remodeling DIMITRIOS J. HADJIDAKIS AND IOANNIS I. ANDROULAKIS Second Department of Internal Medicine, Propaedeutic, and Research Institute, Athens University, Attikon University General Hospital, Athens, Greece 3. biomech.byu.edu/Portals/83/docs/exsc362/.../bone_biomech.pdf 4. www.engin.umich.edu/class/bme456/bonestructure/bonestructure.htm 5. http://www.feppd.org/ICBDent/campus/biomechanics_in_dentistry/index.htm#index 6. http://www.teambone.com/biomechanics.html