2000 Matsui

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O

rthodontic treatment is often achieved more effi-

ciently when the tipping of teeth is minimized.By definition, a force with a line of action passing

through the center of resistance (CR) of a tooth pro-

duces pure translation without rotation of the tooth.1

Further, the tooth subjected to such a force is more

resistant to movement.2 Therefore, tipping will be less

for forces directed near the CR. For normal conditions

of periodontal tissues, the CR for a single root tooth

exists two thirds of the distance from the alveolar

crest to the apex.3 If a force were applied with a line

of action passing through the CR, the tooth would

undergo bodily movement. During canine retraction,

tipping can be eliminated by applying a force and

moment combination to the crown that produces aresultant force that passes through the CR. In the case

of a tooth with multiple roots, such as a maxillary first

molar, the CR is located near the furcation. With these

teeth, bodily movement may be obtained by using a

headgear appliance with the outer bow adjusted so

that the resultant force passes through the furcation

area. Therefore, the orthodontist always considers the

relationship between the location of the CR and the

applied force vector.

A number of investigators have reported on the

location of the CR for single root teeth, determined byvarious theoretical and experimental methods. For

example, Haack and Weinstein3 considered the effects

of forces on the motion of a 2-dimensional model of an

incisor. They concluded that pure translation was

obtained by a single force passing through the CR, or

by a combination of a single force and an appropriate

moment applied at the bracket. Burstone4 reported that

the CR was located at 33% of the distance of the root

length apical to the alveolar crest for an idealized upper

incisor. Using a holographic measuring technique, Bur-

stone and Pryputniewicz5,6 found that the CR of the

upper incisor was located slightly more occlusal when

compared with the theoretical one.2 More recently,Tanne et al7 used a 3-dimensional finite element analy-

sis to determine displacements of teeth with various

root lengths and alveolar bone heights conditions. They

concluded the location of the CR shifted apically as the

alveolar bone height was reduced.

In the case of maxillary molars, bodily movement

was obtained when the traction line of a cervical head-

gear passed through the trifurcation areas. It was con-

cluded that the CR of the upper first molar was located

at this area.8 Burstone et al9 stated that the CR of

mandibular molars was between 30% and 40% of the

distance from the alveolar crest to the apex. Pederson et

al10 also studied mandibular molars, by using displace-

ment transducers on human autopsy material. They

described the relationship between a force system and

the resulting tooth movement by the position of the

center of rotation, the CR, and the angle of rotation. It

was concluded that the CR location depended on tooth

anatomy and the shape and amount of bony support.

On the other hand, significantly less attention has

been given to the CR of a segmented arch. Dermaut and

aAssistant Professor, Department of Orthodontics, School of Dentistry, Meikai

University, Saitama, Japan.bProfessor and Chairman, Section of Biomaterials Science, School of Dentistry,

University of California, Los Angeles.cProfessor Emeritus, Section of Orthodontics, School of Dentistry, University

of California, Los Angeles.dProfessor Emeritus, Department of Orthodontics, School of Dentistry, Meikai

University, Saitama, Japan.

Reprint requests to: Shigeyuki Matsui, Department of Orthodontics, School of

Dentistry, Meikai University, 1-1 Keyakidai, Sakado City, Saitama, Japan 350-

02; e-mail, [email protected]

Submitted, October 1998; Revised and accepted, August 1999.

Copyright © 2000 by the American Association of Orthodontists

0089-5406/2000/$12.00 + 0 8/1/103774

doi:10.1067/mod.2000.103774

171

ORIGINAL ARTICLE

Center of resistance of anterior arch segment

Shigeyuki Matsui, DDS, PhD,a A. A. Caputo, PhD,b Spiro J Chaconas, DDS, MS,c and

Hiroshi Kiyomura, DDS, DMScd

Saitama, Japan, and Los Angeles, Calif

It is important to know the location of the center of resistance (CR) to control tooth movement. In this study,

photoelastic techniques were used to determine the center of resistance. The photoelastic model included the

anterior 4 maxillary teeth, which were interconnected firmly with 6 mm of space between lateral incisors and

canines. Determination of the CR for the anterior arch segment was based on considerations of a wide vari-

ety of load conditions that generated the more uniform stresses in the supporting alveolar bone simulant. For

the arch having the anterior 4 teeth connected, the CR was located within the mid-sagittal plane, 6-mm api-

cal and 4-mm posterior to a line perpendicular to the occlusal plane from the labial alveolar crest of the cen-

tral incisor. (Am J Orthod Dentofacial Orthop 2000;118:171-8)

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172 Matsui et al American Journal of Orthodontics and Dentofacial Orthopedics

August 2000

Bulcke11 used the laser reflection technique and holo-

graphic interferometry in testing 2 types of segmented

arches on a macerated human skull. When the 6 ante-

rior teeth were incorporated in a sectional wire, they

found that the CR was located more to the distal side of the canines; however, it was more difficult to define the

CR of the 4 incisors. They concluded it was situated

just distal to the lateral incisors.

Pedersen et al12 also determined the location of the

CR of various consolidated units of maxillary anterior

teeth on human autopsy material by means of a dis-

placement measuring device. The units studied con-

sisted of 2 central incisors, 4 incisors, and 6 anterior

teeth, and they described the changes of the location of

the CR for each of the arch segment units. The results

of these studies are not in complete agreement on the

location of the CR in segmented arch units.

None of these techniques makes any estimations of

internal stress within the supporting structures around

the teeth that would lead to biologic alterations. When

the induced stresses are uniform, biologic changes take

place that lead, in time, to translational motion.13 In

this study, the quasi-3-dimensional photoelastic tech-

nique was used.14 This modeling technique allows for

visualization of internal stresses developed within the

model around the loaded teeth. By rotating the model,

visual access to stresses in various locations, including

mediolateral directions, is enhanced.

Therefore, it was the purpose of this investigation todetermine the CR of a maxillary anterior arch segment

based on observations of stress distributions around teeth

in simulated periodontal tissues of a photoelastic model.

MATERIAL AND METHODS

Photoelastic Materials and Frame Work

A compound photoelastic 3-dimensional model of a

maxilla was used in this study. Impressions were made

of a maxilla and maxillary teeth by using a silicone mold

material. Different plastic simulants were used to fabri-

cate the individual components of the model. As shown

in Table I, PL-1 (Photolastic Division, Measurements

Group, Raleigh, NC) was used for the teeth, PL-2 (Pho-tolastic Division) for alveolar bone, and Solithane

(Uniroyal Chemical Co, Inc, Middlebury, CT) for the

periodontal membrane.14-16 After being assembled, the

model was fixed firmly, with epoxy resin, to a support-

ing plate at the zygomatic and frontal processes.

As shown in Figs 1 and 2, the model had 6-mm

spaces between the lateral incisors and canines. The

model simulated the treatment stage of an extraction

case after the canine retraction was completed. The

wax pattern for the framework was directly fabricated

on the model. Small pins were attached on the vertical

part of the framework every 5 mm from the level of the

alveolar crest to the apex on each side. The wax pattern

of the framework was made as symmetrical as possi-

ble. After casting the wax pattern in a chrome-cobalt

alloy, the framework was the firmly connected to the 4

anterior teeth with a resin cement.

Load Conditions

The model was loaded by dead weights connected to

the framework with nylon lines (Fig 3). A 1-pound (454

Table I. Mechanical properties of simulant materials

Materials E (MPa) v

Tooth Epoxy resins 2931 0.36

(PLM-1)

Alveolar bone Epoxy resins 207 0.42

(PL-2)

Periodontal Urethane 7 0.40

membrane (Solithane)

E(MPa), M odules of elasticity v Poisson’s ratio.

Fig 1. Test setup. Shaded area represents framework fixing 4 anterior teeth. Note 6-mm space

between lateral incisor and canine representing a stage of orthodontic treatment in extraction case.

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American Journal of Orthodontics and Dentofacial Orthopedics Matsui et al 173Volume 118 , Number 2

gm) weight was applied to each side of the arch. Various

directions of pull were obtained by altering the position

of pulleys affixed posterior to the model, as shown in Fig

3, and the location of the hooks to which the lines were

connected. Loads were applied to the framework in a

posterior direction at various angles to the occlusal

plane. These force directions were obtained by adjusting

the position of the line on the framework from A to D,

and by changing the pulley location from 2.0 to 4.0. Fig

3 A, shows an example of direction 2.0-A, which means

that the position of the line on the frame is A, and pulley

location is 2.0. Vertical loads also were applied perpen-

dicular to the occlusal plane at 2-mm increments from

the anterior alveolar ridge of the central incisor (Fig 3 B).

Photoelastic Experiment

All loading was performed in the field of a circu-

lar polariscope, with the model immersed in a tank of

mineral oil to facilitate isochromatic fringe observa-

tion (Fig 4). These isochromatic fringes are distrib-

uted 3-dimensionally in response to the intensity of

internal stress. Stress is high in an area when many

lines are seen and concentrated when distance

between fringes is small. Presentation of the photoe-

lastic data was facilitated by schematic representa-

tions of the stress distributions. In these diagrams,

areas of high stress concentration are denoted by the

darkest shading and lower stresses are shown with

light shading. Further, since there was almost com-

Fig 2. Photoelastic model used: (a) anterior segment; (b) chromium-cobalt frame; (c) pulley.

Fig 3. Diagrammatic representation of directions of pull applied to arch segments. A, Distal load.The

arrrow shows an example of direction of pull 2.0-A. B, Vertical load.

A B

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August 2000

In general, the various force vectors applied to the

framework produced different degrees of lingual

crown tipping, as manifested by nonuniform fringe

patterns within the periodontal membranes and alve-

olar bone simulants. Fig 5 shows the comparison

of the stress distributions for 2.0-A loading (distal,

parallel to the occlusal plane) on the left, with load-

ing 2.0-D (distal, toward the occlusal plane) on the

right. Load 2.0-A concentrated stress at both sides of

the central incisor root, being higher on the distal.

Stress also was localized distally along the lateral

incisor and the mesial part of the canine root. These

high-stress areas were toward the crestal one-third of

the roots. This stress distribution reflects lingual

crown tipping.

plete symmetry of the stress fields about the midline,

only the right-side data are presented.

From all of the test conditions, the load was sought

that produced a relatively uniform stress distribution

pattern in order to determine the general area of the

CR. Because of the symmetry of the model and the

applied loads, the location of the CR can be expected to

lie in the mid-sagittal plane.

RESULTS

Examination of the unloaded model in the circular

polariscope revealed an almost stress-free condition

(less than one-half fringe order maximum). Conse-

quently, the stress patterns observed on load applica-

tion were due to the effects of the applied loads.

Fig 4. Circular polariscope arrangement for visualization of isochromatic fringes. LS, Light source;

D, diffuser; P, polarizer; M, model; Q, quarter-wave plate.

Fig 5. A comparison of stresses generated by 2 pull directions.The width of the periodontal ligaments

in the diagram is exaggerated to facilitate presentation of fringes. Note nonuniform stress distributions.

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A different distribution resulted from 2.0-D loading.

Here, the highest stress concentrations occur along the

middle half of the distal aspect of the root of the central

incisor. This distribution is indicative of labial crown tip-

ping and is in contrast to the lingual effects of load 2.0-A.

A relatively uniform distribution pattern was

observed when the position of the pulleys was 4.0 and

the lines for loading were attached between B and C

of the framework, as shown in Fig 6. This uniform

stress distribution indicates that the vertical location

of the CR exists close to this axis.

Fig 7 shows the stress distributions resulting from

forces applied vertical to the occlusal plane. When a

load α was applied at the anterior region (Fig 7 A),

Fig 6. Stresses resulting from 4.0-BC direction of pull. Note uniformity of stress distribution.

Fig 7. Comparison of stress distributions of different locations of vertical pull. A, Load α; B, load γ ;

C, load ε; D, location of vertical directions of pull.

A B

C D

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stress concentrations were found at the distal parts of

the roots of the anterior teeth. When a load ε was

applied at the posterior part of the anterior segment

(Fig 7, C ), higher stress concentrations were observed

at the distal parts of the roots of the lateral incisors and

within the alveolar crest between laterals and canines.

The stresses generated by load γ midway between α

and ε are shown in Fig 7, B. This load produced high

stresses uniformly distributed to the middle one third of

the distal aspect of the central incisor root, the distal of

the lateral incisor, and to the distal part of the canine.

Therefore, the horizontal location of the CR exists

close to this direction of pull.

Fig 8 shows the estimated position of the CR. The

CR was located at the intersection of the vertical force

that produced more uniform stresses (force γ ) with the

distally directed force that also produced a more uni-

form stress field (force 4.0-BC). This intersection, and

thus the CR, is located within the mid-sagittal plane

approximately 6-mm apical and 4-mm posterior to a

line perpendicular to the occlusal plane from the labial

alveolar crest of the central incisor.

DISCUSSION

Selection of Photoelastic Technique

The photoelastic technique was selected for this

investigation because: (1) 3-dimensional and compli-

cated shapes can be reproduced and modeled in mate-

rials that provide individual simulation of orofacial

structure and that provide visualization of stresses

under load, and (2) stresses throughout the entire

model (whole-field observation) can be examined.

However, the materials used as simulants are isotropic

in nature, and it is not possible to perfectly model allcharacteristics of the mechanical properties.

It should be noted that finite element analysis (FEA)

and laser holography also have the characteristic of

whole-field observation. Further, FEA has the capacity

of including anisotropic mechanical properties in the

analysis,7 while laser holography has the potential for in

vivo examinations.17,18 While these techniques have the

potential for high accuracy, their application is not an

easy matter. For example, the anisotropic input data of

the individual elements of the orofacial complex, which

is required for utilization of the strengths of the FEA,

are not known. On the other hand, laser holography,

while inherently extremely accurate in measuring dis-

placements, is complicated to apply in vivo because of

the difficulty in fixating the head. In addition, this tech-

nique cannot predict any internal effects.

Consequently, each of these techniques is seen to

possess inherent advantages and disadvantages. The

ideal situation would be to apply all of the techniques

to all biomechanics problems in orthodontics, which is

generally not accomplished because of practicality.

Fig 8. Estimated position of the CR. The CR for the 4-tooth segment was located within the mid-

sagittal plane, approximately 6-mm apical and 4-mm posterior to a line perpendicular to the occlusal

plane from the labial alveolar crest of the central incisor.

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Photoelasticity has had a long history of applications indentistry and has been shown to be predictive of many

clinically observed phenomena.

CR Determination and Location

In this study, a photoelastic technique was used to

determine the CR of a maxillary anterior arch segment

based on observations of stress distributions around teeth

in simulated periodontal tissues of a photoelastic model.

The location of the CR was determined by observing

isochromatic patterns. If an applied force produces a rel-

atively uniform fringe pattern in the periodontal mem-

brane and surrounding tissues, the force must pass close

to the CR. Therefore, the CR was established as the pointof intersection of the lines of action of the forces, both

perpendicular and inclined to the occlusal plane, that

produced uniform stress distributions around the teeth. A

pure translation of teeth would occur if the stresses

around the periodontal tissues and surrounding bones

were uniform.13 The CR is located within the mid-sagit-

tal plane, approximately 6-mm apical and 4-mm poste-

rior to a line perpendicular to the occlusal plane from the

labial alveolar crest of the central incisor.

These findings are different from those found by

Pedersen and colleagues12 and Vanden Bulcke et al.19,20

Fig 9 compares the locations of the CR determined by

these investigators with the CR determined in this study.

A major difference was in the configuration of the arches

studied. The model used in the present study had 6-mm

spaces between the lateral incisor and canines and filled

with simulated alveolar bone, which represented an

orthodontic treatment stage just before the retraction of

the 4 incisors in extraction case. The situation considered

by the above-mentioned investigators did not include a

comparable orthodontic treatment stage. Further, these

investigators used techniques that monitor the displace-ment of the crowns of teeth of human skulls, either dried

or fresh autopsy material. These techniques cannot

ensure the development of uniform stresses that is essen-

tial for pure translation of the teeth to occur.13 An advan-

tage of the photoelastic approach, used in this investiga-

tion, is the ability to observe the stresses generated

around the teeth during loading. Consequently, it is

expected that the position of the CR as determined in

this study can be used as a clinical guideline.

Effect of Framework Stiffness

A chrome-cobalt alloy was selected for the framework

because of its high modulus of elasticity. If the frame tofix teeth is not stiff enough, the teeth will move individu-

ally and an accurate determination of the CR becomes

almost impossible. This experimental difficulty was

recognized by Vanden Bulcke and associates.11,19,20

Because of the stiffness of the framework used in the pres-

ent investigation, this problem was obviated and a good

estimate of the CR for the arch segment was obtained.

Clinically, when 4 anterior teeth are to be moved, it is

most often desirable to move them bodily. To accomplish

this bodily motion, it is necessary to use the stiffest wire

possible and zero wire-slot clearance. If the wire selected

is not sufficiently stiff, the CR of the segment will not be

uniquely defined, because each tooth moves separately.

When this situation occurs, control of the anterior seg-

ment is lost. On the other hand, as the stiffness of the wire

increases, the position of the CR of the 4 teeth becomes

stable and control of the segment will be achievable.

CR Application

Many factors make the precise understanding of the

CR difficult. In the clinical situation, it is almost

Fig 9. Comparison of the position of the CR with fixation of 4 anterior teeth: (a) present study; (b)

Vanden Bulcke et al study19,20; (c) Pedersen et al study.12

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August 2000

impossible to keep the direction and the amount of

applied force constant. In addition, factors that alter the

position of the CR of 4 anterior teeth are the shape of

surrounding bone, root morphology, position of each

tooth, and structure of the periodontal attachment. Since

these factors generally will be different for each patient,the location of the CR of anterior arch segments in these

patients also will be different. One of the advantages of

the model system used in this study is the fact that all

these variables are kept constant. Thus, the experimental

results will give us a specific position of the CR for this

configuration. The values from this investigation may

not be extrapolated directly to a particular clinical situa-

tion, but they will provide a guideline for determining

the CR of the anterior arch segment for each case.

CONCLUSION

A 3-dimensional photoelastic model of a maxilla

with individual simulants for teeth, bone, and peri-odontal ligament was used to determine the CR of a 4-

tooth anterior arch segment. The CR was specified

from the forces that produced more uniform stresses

around the teeth. The CR for the 4-tooth segment was

located within the mid-sagittal plane, approximately

6-mm apical and 4-mm posterior to a line perpendic-

ular to the occlusal plane from the labial alveolar crest

of the central incisor.

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