A reassessment of force magnitude in

orthodontics Dr. Quinn

Robert 9. Quinn, D.M.D., M.D.S.,* and

D. Ken Yoshikawa, M.S., D.D.S., M.D.S.**
San Francisco, Calif.

The relationship between the force magnitude delivered by orthodontic appliances and the rate of orthodontic
tooth movement is controversial. This paper critically reviews the experimental data base that has shaped this
controversy and graphicaNy presents four hypotheses proposed to represent the relationship between force
magnitude and the rate of tooth movement. The clinical implications of each hypothesis for treatment planning
and space-closing mechanics are discussed. The authors’ analysis of the data from six heavily cited clinical
studies in the orthodontic literature appears to support one of the four pruposed hypotheses (No. 4, Fig. 2).
Acceptance of this hypothesis leads the clinician to a rational approach in manipulating the final position of teeth.
Anchorage can be conserved by means of treatment strategies that reduce stress magnitudes in the
periodontium of the posterior teeth while maximally efficient stress is maintained on the anterior teeth. Appliances
with Jaw load-deflection rates and relatively constant moment/force ratios allow the clinician to take advantage
of the type of tooth movement proposed in this hypothesis.

Key words: Mechanical stress/strain,tooth movement, orthodontic appliances

M echanical strategies in orthodontics are

largely drawn from clinical empiricism. Although not
without merit, this method for the acquisition of knowl-

93
edge has serious limitations. A limited number of ob-
servations, made with inadequate measurement tech-
niques, complicated by observer bias, and unduly
influenced by extreme cases, can yield inaccurate
conclusions. In most disciplines empiricism has given
way to controlled experimentation and the reliability of
data has improved. This transition has been incomplete
in a critical area of orthodontics. The important question
of how the magnitude and distribution of force from
orthodontic appliances influence the rate of tooth dis-
placement has received little experimental study. When Fig. 1. Compressive stress patterns in the periodontal ligament
it has, the data reported from these few experiments under different force systems. A, Pure force applied at the
bracket. B, Force and moment applied at the bracket equivalent
have been difficult to interpret. As a result, there is no
to a force through the center of resistance.
clear consensus on the most efficient way to move teeth.
Most clinical strategies to move teeth are based on
the assumption that a force magnitude, or range of tooth there is a force that will move that tooth at a
magnitudes, exists that, when delivered to the peri- maximum rate. Acceptance of this assumption has pro-
odontal tissue, will yield the most rapid rate of tooth found clinical implications. Its effects on considerations
movement. In other words, the rate of movement is of wire cross section and material, loop design, and
sensitive to changes in force magnitude and for a given elastic size are obvious. It also influences basic treat-
ment planning decisions. For example, the decision to
From the Department of Growth and Development, School of Dentistry, Uni- remove second, rather than first, premolar teeth in a
versity of California, San Francisco.
*Assistant professor. minimum anchorage extraction case is predicated on
**Assistant clinical professor. the belief that changing the distribution of teeth on

252
Volume 88 Reassessmentof force magnitude 253
Number 3

Hypothesis 1 Hypothesis 3

/\

Hypothesis 2 Hypothesis 4

STRESS MAGNITUDE

Fig. 2. Possible hypotheses of the relationship between stress magnitude and the rate of tooth move-
ment are graphically represented.

either side of the extraction site will change the force ously mentioned influenced the conclusions these au-
distribution. Since the assumption holds the rate of thors drew from their studies. Where the published data
movement to be force-dependent, the teeth will move support the conclusions, we have drawn alternative
into the extraction site at different rates, with the molars ones.
protracted more than the anterior teeth are retracted. If The investigations of Smith and Storey’ more than
the assumption is invalid, treatment strategies of this 30 years ago were afflicted by virtually all of these
type are ineffective. problems, some of which have been discussed by other
In this article we critically examine several key stud- authors. 3v4Smith and Storey concluded that there is a
ies that are relevant to this assumption. We then use range of force or “pressure” that produces the maxi-
these studies to evaluate four hypotheses that can be mum rate of tooth movement. Below this range there
proposed to describe the relationship between force is little movement and above it, at least in the short
magnitude and tooth movement and discuss the clinical term, movement is slowed.
implications of each hypothesis for treatment planning The retraction mechanism used by Smith and Storey
and appliance design. delivered a simple force through the canine bracket and,
as expected, the canines tipped into the extraction site.
REVIEW The molar and premolar were unable to tip, but moved
Three major problems complicate clinical studies on a sliding yoke that produced a more translatory
of force magnitude and tooth movement. First, inves- movement. The force levels on either side of the ex-
tigators have not been able to control the type of tooth traction site were equivalent, but the distribution of
movement (that is, tipping vs. translation) caused by those forces to the alveolar bone and periodontal lig-
their appliances. Second, because of the nonlinear, ament may have been unequal. Force against the canine
time-dependent course of tooth movement following root was likely concentrated at the alveolar crest,
appliance activation, ’ measurements of tooth movement whereas the molar and premolar roots would have had
that are not coordinated with activations can system- more uniform force distributions along their surfaces.
atically bias the data. Third, the large measurement Force distribution is critically important in a discussion
errors, as well as the large variation in the rate of tooth of tooth movement because the biologic system that
movement both between patients and between quad- allows teeth to move is activated by, and responds to,
rants in an individual patient, make statistically signif- local changes in stress (force per unit area) and the
icant findings difficult to achieve. associated local strain (unit deformation) delivered to
The studies abstracted in Table I were selected for the system. So, although the forces were equal in Smith
review because of their quality as well as their fre- and Storey’s appliance, tbe stress and strain in the peri-
quency of citation in the orthodontic literature. Our odontium of the canine and molar units may have been
discussion attempts to show how the problems previ- quite different. This may have exaggerated the differ-
 Am. J. &thud.
September 1985
254 Quinn ad Yoshikawa

Fig. 6.

Flg. 7.

Flg. 4.

Ng. 6.
Fig. 6.
Volume 88 Reassessment of force magnitude 255
Number 3

Table I. Selected clinical studies measuring the effect of force magnitude on orthodontic tooth movement
Patients Observation
Author (no.) (weeks) Measurement technique Mechanics Force levels Results

Smith and Storey’ 4 to 10 Observation-weekly See Fig. 3. 185 gm vs. Cuspid displacement greater than
Measurement-calipers, 238 gm” the molar at both force
intraoral levels.“,’
Reference-opposite Heavy forces yielded greater
arch molar displacement than light
forces.“,’
Andreasen and 10 Observation-weekly See Fig. 4. 100 to 150 gm Heavier forces showed greater
Zwanzige? Measurement-calipers, vs. 400 to molar displacement.“,b
intraoral 500 gm
Reference-incisors
Hixon et al.’ 8 Observation-biweekly See Fig. 5. 300 gm vs. 0 Higher forces produce greater
Measurement-calipers, to 1,500 gm tooth displacement up to
models 300 gm.
Reference-25” cepha-
lograms, endosseous
implants
Hixon et a1.6 Observation-3 times See Fig. 6. 300 gm vs. 0 Higher forces yielded greater
per week to 1,000 gm tooth displacement.
Measurement-calipers,
models
Reference-2S” cepha-
lograms, endosseous
implants
Boester and Johnston4 Observation-weekly See Fig. 7. 55 gm, 140 55-gm force yielded less tooth
Measurement-calipers gm, 225 movement than higher forces.d
intraoral, models gm, 310 gm Above 140 gm no increase in
Reference-22.5” tooth displacement was
cephalogram, struc- observed.
tural references
Andreasen and Observation-weekly See Fig. 8. 200 gm vs. Higher force levels yielded
Johnson’ Measurement-calipers, 400 gm 2.5 x the tooth displacement
intraoral of the lower force.’
Reference-incisors

“Reviewers’ interpretation of original data.

bP < 0.05 paired t test (2 tail).
‘P < 0.01 paired t test (2 tail).
dP < 0.05 ANOVA.

ences in movement they observed between the canine from Smith and Storey’s conclusions. “Light” and
and the molar. “heavy’ ’ forces produced statistically indistinguishable
The force magnitudes used in the Smith and Storey movement of the canine, but the “heavier” forces
experiment have been critically reviewed.4 The mean moved the molar segment further than did the light
force values over the duration of their experiment (see forces (P < 0.01). At both force levels, the canine
table III of Smith and Storey’) which we calculated as moved more than the molar (P < O.Ol), but the
238 gm (heavy) and 18.5 gm (light) are statistically difference was greater with the “light” springs
different (P < 0.05, t test), but do not appear clinically (ZJ< 0.01).
distinct. The initial activations, however, that averaged A larger study reported by Andreasen and Zwan-
475 gm (heavy) and 235 gm (light) may have been zige? in 1980 attempted to answer the same questions
sufficiently different to cause early tissue changes that addressed by Smith and Storey. In spite of their sliding
may not have equilibrated over the short experimental edgewise mechanics (Table I), the amount of tooth
period of 4 to IO weeks. When the data in Smith and movement over a lo-week period indicates that in most
Storey’s table III* is analyzed with a two-tailed t test casesthe teeth were moved with some degree of tipping.
for paired data, the results (Table I) differ somewhat With their appliances stress distributions in the perio-
256 Quinn and Yoshikawa

dontium for the molar and the canine should have been canines move at a faster rate than their mandibular
qualitatively the same. The rate of movement was con- counterparts.’ The large mean square residuals in Boes-
trolled as well as possible by the use of low, load- ter and Johnston’s table III4 point to a large measure-
deflection rate springs, along with weekly observations ment error that they have not described. These factors,
and activations. The forces used in their study, 100 to when combined, make it unlikely that the study could
150 gm versus 400 to 500 gm, must be considered yield subtle differences in rates of tooth movement.
approximate values since frictional reductions in force Despite these limitations, the study was an improve-
magnitude have never been calculated in situ. ment on the existing data base and the data reported
Measurement error, which must be considered sig- (Table I) are generally compatible with the conclusions
nificant, was not discussed by the authors. Most of their we have derived from other studies. The canine teeth
published graphs show teeth moving up to 0.5 mm in were observed to move more than the molar teeth.
a direction opposite to the applied force at some point Boester and Johnston concluded that there was a direct
during the study. This phenomenon is difficult to ex- relationship between the magnitude of the applied stress
plain except as measurement error. A systematic error and the rate of tooth movement. But they also observed
may also have been introduced when the incisor teeth that once a certain stress level was reached, further
were used as a “stable” reference point. It seems rea- increases in stress failed to produce continued increases
sonable to assume that some posterior repositioning of in the rate of movement.
the mandibular incisors occurred as the canines were In the most easily interpreted study on this subject,
retracted. If this is true, canine movement in the system Andreasen and Johnson7 reported on the displacement
would be underestimated and anchorage loss overesti- of maxillary molars as effected by an asymmetric head-
mated. This would obscure any differences in displace- gear. They used the Haack-Weinstein headgear design’
ment of the canine relative to the molars. to deliver 400 gm of force to the first molar on one side
Like Smith and Storey, Andreasen and Zwanziger of the arch and 200 gm to the contralateral tooth.
did not apply statistical analysis to their data. A paired Although variation among patients was large, the
comparison of the patients in the study shows no dif- paired design and analysis demonstrated a difference
ference between the two force levels in canine displace- (P < 0.01) between these force levels in the amount
ment, but molar movement was greater with the higher of movement produced. The authors’ data are consistent
force value (P < 0.05, two-tailed t test for paired data). with their conclusion that the molar subjected to the
These findings are consistent with Smith and Storey’s higher force moved a greater distance (2.5 X) during
data. So is the finding that the majority of the patients the 12-week experimental period.
showed more canine than molar movement at both force The studies of Hixon et al? were characterized by
levels, but in this study the difference was not statis- a detailed analysis of tooth movement in a relatively
tically significant. This may have been due to the mea- small number of patients. In their 1970 study.h the au-
surement problems discussed earlier since other studies thors used an appliance system that ensured a more
fail to support this observation. uniform stress distribution throughout the periodontal
Aware of the difficulties encountered by forerun- ligament, thus partially eliminating this important vari-
ners, Boester and Johnston4 reported a carefully con- able as a source of bias. The study was, however, hand-
structed study designed to reexamine the relationship icapped by the small sample size (6 patients) and the
between force magnitude and tooth movement. They short observation period (8 weeks), allowing, in most
did not specify the type of tooth movement in this study, cases, less than 1 mm of canine movement. The authors
but for two reasons we presume it to have been tipping. concluded that, although heavier forces seemed to move
First, the extraction sites measured intraorally closed 6 teeth at a greater rate, the individual variation in met-
to 7 mm over the lo-week period; it seems unlikely the abolic response was so large that it overshadowed any
teeth could have translated at this rate. Second, weekly differences caused by force magnitude. Hixon et al.’
activations of the Ricketts spring would keep moment/ also made the observation that teeth showing translatory
force ratios low and not permit translation. Moment/ movement were displaced at a slower rate than teeth
force ratios are also different for upper and lower that were tipped. Although this had been known em-
springs and, since quadrants were randomized in the pirically for some time, they demonstrated experimen-
experimental design, this difference detracted from the tally the importance of stress distribution.
discriminatory power of the experiment. The random-
FORCE MAGNITUDE AND STRESS/STRAIN
ized block design may have further reduced the sen-
sitivity because it assumes that maxillary and mandib- Force magnitude is a popular concept because it is
ular quadrants behave identically; however, maxillary easily understood and conveniently measured. HOW-
Volume 88 Reassessmentof force magnitude 257
i’lumber 3

ever, it is an incomplete way to describe the forces assumptions about tooth movement. Some of the pos-
delivered by an orthodontic appliance. The true me- sible relationships between stress magnitude and rate
chanical parameter in tooth movement is not the mag- of movement have been graphically illustrated in Fig.
nitude of the force per se, but rather the magnitude of 2. In the following discussion, we will examine these
the stress generated by the appliance in the surrounding relationships and the clinical strategies that follow from
periodontium. Stress is defined as force per unit area each.
(for example, gm/cm*) and strain is the unit deformation Hypothesis 1 shows a constant relationship between
that occurs in the tissue as a result of the stress. This rate of movement and stress. The rate of movement
concept is illustrated in Fig. 1. In A, when a tooth is does not increase as the stress level is increased. The
tipped (for example, with an elastic on a light wire), clinician operating under this assumption controls an-
the stress distribution in the periodontium is uneven, chorage only through interarch and/or extraoral me-
there is high Icompressive stress in the cervical and chanics. To place more teeth into the anchorage unit or
apical thirds of the ligament, and lower stress in the extract teeth in a more anterior position in the arch does
middle third. 111B, when the appliance delivers a couple not affect the final tooth position. If elastics are used
as well as a force (for example, as with a canine re- for retraction, only one size is necessary. Loop designs
traction spring), the stress distribution is more uniform. are not critical and can be simple and uncomplicated
It is then evident that, although the force magnitude by helices. Intrarch mechanics cannot be altered to
applied to the tooth in each of these examples is the change final tooth position. An extraction site, regard-
same, the tooth movement is not identical. While these less of where it lies in the arch, is always evenly closed
stress distributions have yet to be measured in vivo, by retraction of the teeth anterior to it and protraction
centers of rotation have been determined by means of of the teeth posterior to it. The periodontium is sensitive
laboratory photoelastic models’ and holographic inter- only to force direction and not to force or stress mag-
ferometry.” These data support the stress patterns de- nitude .
picted in Fig. I . A similar situation prevails in the case Hypothesis 2 is more complex. The relationship
of individual canine retraction as compared with here calls for a linear increase in the rate of tooth move-
en masse anterior retraction. Because the average stress ment as the stress increases. Operating under this hy-
magnitude varies inversely with the area over which pothesis, the clinician would, in order to shorten treat-
force is applied, the additional root area in the en masse ment time, use appliances that generated the highest
retraction would result in stress values for these six stress values. In this system intraarch anchorage could
teeth that are lower than those surrounding the single be manipulated by adding teeth (second molars) to the
root of the canine. anchorage unit or moving the extraction site-for ex-
It is important to understand that tooth movement ample, second versus first premolars. This would dis-
occurs through a cellular response and that the intensity tribute the stress over a larger root surface, lowering
and duration of the response is mediated by the local the local stresses and slowing the rate of tooth move-
stress and stra:in generated in the tissue by appliance ment. Arch wires designed for space closure would be
activation. It is the local stresses and strains that set up fabricated from large, cross-section steel wire with clos-
piezoelectric potentials, change blood flow, trigger cell ing loops activated to generate large stresses. The ap-
membrane-mediated metabolic responses, and cause pliance that delivered the highest stresses would close
the production and release of chemical resorption me- extraction sites most rapidly.
diators-all of which ultimately result in the remod- Hypothesis 3 depicts a relationship in which in-
eling of the periodontal structures and clinical tooth creasing stress causes the rate of movement to increase
movement. ‘I When considering the issue of force mag- to a maximum. Once this optimal level is reached,
nitude in orthodontics, either by a review of published additional stress causes the rate of movement to decline.
work or the formulation of clinical strategies to improve This hypothesis was originally proposed by Smith and
retraction mechanics, it is imperative that the concept Storey’ and clinical strategies have evolved to take ad-
of stress be understood. vantage of its implications. Some clinicians assume the
validity of the latter part of the curve in this hypothesis
HYPOTHESES OF THE STRESS-MOVEMENT where light forces move teeth “optimally” and an in-
RELATIONSHIP crease of stress slows movement. These clinicians use
The effect of periodontal stress magnitude on the light forces, for example, to retract canines and prevent
rate of tooth movement is an important issue in plans anchorage loss while using heavy forces to protract
to control the displacement of posterior teeth. Clinicians posterior teeth and “anchor” the canines. The ortho-
base their strategies for controlling anchorage on their dontist who operates under this hypothesis theoretically
 Am. J &that.
258 Quinn and Yoshikuwu
Sentember 1985

has a great deal of control over anchorage and final segment. Because of its smaller root surface, the mean
tooth position without resorting to extraoral or interarch stresseson the canine can be assumed to be higher than
mechanics. those on the posterior unit. At the stress levels evaluated
Hypothesis 4 is a composite of some of the fore- in these experiments then, an increase in stress appeared
going concepts. Here the relationship of rate of move- to cause an increase in the rate of movement. The avail-
ment and stress magnitude is linear up to a point; after able literature suggests that hypothesis 3 may not be an
this point an increase in stress causes no appreciable accurate representation of the data.
increase in tooth movement. Because the rate of move- The evidence for hypothesis 4 is more compelling.
ment is dependent on changes in stress, anchorage can Virtually all the reports examined in Table I support
be controlled within the arch. Change of extraction the idea that increasing mean stress produces a higher
patterns, addition of teeth to the anchorage unit, and rate of tooth movement. Both Smith and Storey’ and
modification of intraarch retraction mechanisms to fit Andreasen and Zwanzige? demonstrated greater dis-
the anchorage requirements are all effective means to placement of the posterior teeth as the force level was
determine the final tooth position. For example, oper- increased. This finding is consistent with the hypothesis
ating under this hypothesis, a clinician could enhance since the molar segment, under less stress because the
canine retraction by (1) extracting first premolar teeth force is distributed over a larger area, would be on the
instead of second premolars, (2) incorporating second ascending portion of the curve and would move at a
molars into the posterior segment, and (3) adjusting the greater rate when the stress level was increased. Inter-
stress delivered by the retraction mechanism so that the estingly, neither study provided evidence of a statisti-
stress level at the canine would coincide with the max- cally significant difference in canine movement at the
imal rate of movement. The stress on the posterior teeth two force levels. This might indicate that the canine
would be distributed over a greater root area, lowering was moving at a near maximum rate at the lower force
the local stresses and producing a rate of movement and that increasing the force did not increase the rate
less than maximal. of movement. These data, along with those of Boester
and Johnston,4 Hixon et al.’ (discussed earlier), and
EVALUATION OF HYPOTHESES Burstone and Groves,” provide evidence that beyond
None of the studies listed in Table I support hy- a certain stress level increasing stress no longer alters
pothesis 1. All of the results show that, to varying the rate of tooth movement.
extents, changing the mean stress magnitude will pro- Biologically, the concept is appealing. The removal
duce changes in the rate of tooth movement. Andreasen of tissue from areas of compression is cell-mediated
and Johnson,’ and Hixon et al6 perhaps showed this and it is reasonable to suppose that the resorptive pro-
most convincingly (see Table I). cess has a maximum rate dependent on the number of
Hypothesis 2 is difficult to disprove because most cells participating as well as their resorptive capacity.
studies used only two force magnitudes and were unable The shape of the curve proposed in this hypothesis is
to describe the behavior of the curve as the stress consistent with many other biologic processes that show
reached higher levels. Boester and Johnston4 did dem- stimulation-dependent activity before becoming satu-
onstrate, however, that in their system forces above 140 rated. A theoretical argument can also be presented in
gm produced no measurable increase in tooth move- support of hypothesis 4. As a tooth undergoes a tipping
ment. This study, along with that of Hixon et al.’ which movement, the stress pattern varies along the length of
suggested a 300-gm plateau, casts serious doubts on the root (Fig. 1, A). High compressive stresses are
the validity of the continuing linear relationship pro- generated near the cervical region and at the apex on
posed in hypothesis 2. the opposite side of the root, while stresses become
Hypothesis 3, the original Smith and Storey pro- zero near the middle of the root. This stress pattern
posal,’ can no longer be considered viable in light of correlates well with the observed movement of the
subsequent data. A more rigorous analysis of their tooth. In other words, a simple force applied to the
report’ shows that their data did not justify their con- crown of a tooth produces a gradation of stress in the
clusions. As pointed out earlier, the canine moved fur- periodontal ligament. It is this difference in stress mag-
ther than the molar at both the high and low force levels nitude along the length of the root that allows the tooth
and there is no evidence for the rate of movement to to move greater distances at the cervix and apex than
suddenly reverse as the stress levels increase past a at midroot. This commonly observed clinical example
certain “optimum” value. Furthermore, in all the ca- supports hypotheses No. 2 and 4, which contend that
nine retraction experiments listed in Table I, the rate the biologic response in tooth movement is dependent
of canine movement was greater than that of the molar on the magnitude of the mechanical stimulus (stress).
Volume 88 Reassessmentof force magnitude 259
Number 3

Also of interest in this discussion is the data of is to use an appliance system that can deliver relatively
Weinstein and associatesI on equilibrium tooth posi- continuous stresses in the range described earlier. Ex-
tion. They were able to show that forces as small as 4 cessive stress produces an increase in the rate of move-
gm can move teeth at a measurable rate-approxi- ment of posterior teeth without increasing retraction of
mately 0.1 mm/week. Weinstein and associates’ data anterior teeth. Appliances that have a high load-deflec-
suggest that the origins of the hypothetical curves in tion rate are unable to achieve a difference in the rate
Fig. 2 are quite close to zero on both the x and y axes. of tooth movement. Low load deflection-rate mechan-
They also suport the concept that tooth movement is ics, on the other hand, can maintain stresses in the
force-dependent, as suggested by hypotheses 2, 3, 4, desired range and maximize the difference in the rate
because the studies cited in Table I show that force of movement. Appliance systems that deliver a rela-
levels above 4 gm cause a rate of movement greater tively constant moment/force ratio also seem to have
than 0.1 mm/week. an advantage in that they maintain local stresses in the
The slope of the curve and the position of the plateau desired range and prevent excessive stress concentra-
in hypothesis 4 are difficult to establish, given the prob- tion from occurring in the apical or cervical areas of
lems in interpretation of the clinical studies. The slope the periodontal ligament. Orthodontic appliances can
in hypothesis 4 cannot be determined from the available best achieve these design characteristics by means of
data and yet it is critically important for the clinical low modulus materials and appropriate closing loop
implications of this hypothesis. A steep slope would geometries. I5
yield dramatic: changes in tooth movement for minor
SUMMARY
variations in induced stress. It would be difficult to
adjust our current appliances, with their relatively high Four hypotheses have been presented in an attempt
load-deflection rates, to the tolerances necessary to take to describe the relationship between stress/strain mag-
advantage of such a system. If the slope were suffi- nitude and orthodontic tooth movement. The existing
ciently steep, tooth movement with our present appli- clinical data may best support the interpretation pro-
ances would occur only on the plateau portion of the vided in hypothesis 4. Acceptance of this hypothesis
curve and for practical purposes be similar to that in carries important clinical implications both for planning
hypothesis 1. A shallower slope makes appliance ad- treatment mechanics and the achievement of treatment
justment less demanding, but makes differential move- objectives. The clinician operating under this hypothe-
ment of teeth less dramatic. sis can enhance anchorage in two ways-first, by in-
Our best estimate of a maximally efficient canine creasing the root surface area of the posterior teeth
retraction force from the clinical data is between 100 either by adding second molars to the posterior unit or
and 200 gm. This would yield mean compressive by extracting teeth in a more anterior position in the
stresses for the average cuspid rootI (assuming one arch (these strategies will decrease the stress and strain
half of the root surface to be under compressive stress) on the posterior teeth and slow their rate of movement
of approximately 70 to 140 gm/cm*. during space closure) and second, by means of an ap-
If hypothesis 4 with a clinically useful slope and a pliance system that can deliver continuous stresses in
plateau in the 100 to 200 gm range is thought to be a the desired range with a relatively constant moment/
valid model, there are two clinical strategies that would force ratio. This will allow retraction to proceed at a
maximize anchorage within the arches. The first is to near maximal rate while the stress on the posterior unit
lower the stress delivered to the posterior teeth. This remains submaximal.
can be done bly increasing the root surface area, either The authors wish to thank Evangeline Leash for her ed-
by incorporation of second molars into the anchorage itorial assistanceand Teny Rodden for preparation of the
unit or by making extractions more anteriorly in the manuscript.
arch. For example, when a canine is retracted, the ratio
of root surface area between the posterior teeth and the
REFERENCES
canine can be increased from 2.6 to 4.4 by the addition 1. Burstone CJ: Biomechanics of tooth movement. In Kraus BS,
of a second molar to the anchorage unit. I4 The decrease Riedel RA (editors): Vistas in orthodontics. Philadelphia, 1962,
in stress obtained by increasing the root surface area of Lea & Febiger, pp 197-213.
the posterior teeth will slow their rate of movement and 2. Smith R, Storey E: The importance of force in orthodontics: The
design of cuspid retraction springs. Aust Dent J 56: 291-304,
allow more canine retraction. The same rationale makes
1952.
extraction of second premolar teeth a logical choice in 3. Hixon EH, Atikian H, Callow GE, McDonald HW, Tracy RJ:
minimum anchlorage cases. Optimal force, differential force, and anchorage. AM J ORTHOD
The secondi strategy for minimizing anchorage loss 55: 437-457, 1969.
260 Quinn and Yoshikawa Am. J. Orthod.
September 1985

4. Boester CH, Johnston LE: A clinical investigation of the concepts 11. Roberts WE, Goodwin WC, Heiner SR: Cellular response to
of differential and optimal force in canine retraction. Angle orthodontic force. Dent Clin North Am 2% 3-17, 1981.
Orthod 44: 113-119, 1974. 12. Burstone CJ, Groves MH: Threshold and optimum force values
5. Andreasen GF, Zwanziger D: A clinical evaluation of the dif- for maxillary tooth movement. J Dent Res 39: 695, 1961.
ferential force concept as applied to the edgewise bracket. AM 13. Weinstein S, Haack DC, Lightle MY, Snyder BB, Attaway HE:
J ORTHOD78: 25-40, 1980. On equilibrium theory of tooth position. Angle Orthod 33: l-
6. Hixon EH, Aasen TO, Arango J, Clark RA, Klosterman R, 26, 1963.
Miller SS, Odom WM: On force and tooth movement. AM J 14. Freeman DC: Root surface area related to anchorage in the Begg
ORT~OD57: 476-489, 1970. technique, Master’s thesis, University of Tennessee, 1965.
7. Andreasen G, Johnson P: Experimental findings on tooth move- 15. Burstone CJ: The segmented arch approach to spaceclosure. AM
ments under two conditions of applied force. Angle Orthod 37: J ORWOD 82: 361-378, 1982.
9-12, 1967. Reprint requests to:
8. Haack DC, Weinstein S: The mechanics of centric and eccentric
Robert S. Quinn, D.M.D., M.D.S.
cervical traction. AM J ORTHOD44: 346-357, 1958. Department of Growth and Development
9. Baeten LR: Canine retraction: A photoelastic study. AM J
Room C-734 UCSF
ORTHOD67: 11-23, 1975. San Francisco, CA 94143
10. Burstone CJ, Pryputniewicz RJ: Holographic determination of
centers of rotation produced by orthodontic forces. AM J ORTHOD
77: 396-409, 1980.

SOUND VOLUMES AVAILABLE TO S Ns

Bound volumes of the AMERICAN JOURNALOF ORTHODGNTTCS are available to
subscribers (only) for the 1985 issues from the Publisher, at a cost of $44.65
($53.85 international) for Vol. 87 (January-June) and Vol. 88 (July-December).
Shipping charges are included. Each bound volume contains a subject and author
index and all advertising is removed. Copies are shipped within 30 Pays after
publication of the last issue in the volume. The binding is durable buckram with the
journal name, volume number, and year stamped in gold on the spine. Payment
must accompany all orders. Contact The C. V. Mosby Company, Circulation
Department, 11830 Westline Industrial Drive, St. Louis, Missouri 63146, USA;
phone (800) 325-4177,
subBcriptions IImst
inplaceofareg&rJ