hreaction of maxillofacial complex during protraction

Kong-Geun Lee, DDS, MSD, PhD, a Young-Kyu Ryu, DDS, MSD, PhD, b Young-Chel Park, DDS, MSD, PhD, c and David J. Rudolph, DIDS, MSD, PhD a Nashville, Tenn., Seoul, South Korea, and Los Angeles, Calif.

Most extraoral appliances used for protracting small or retropositioned maxilla do not allow for variazions in the point of force appiication or in its direction. This variation may be necessary to control vertical, anteroposterior, as well as transverse effects. The purpose of this study was to investigate the initial reaction of the maxillofacial complex according to force magnitude, force direction, and point of force application. For this purpose, an antenna-type modified protraction headgear was tested with double exposure holographic interferometry on a dry human skull with well-aligned upper teeth. Fringe patterns of each protraction condition were compared and analyzed. In most cases, upward rotation of the anterior portion of the maxilla changed to translation, or to downward rotation, as force direction was changed from parallel to the occlusat plane to 20 downward to the occlusal plane. Furthermore, a 500 gm force applied 15 mm above and directed 20 below the occlusal plane produced a translation of the maxillary complex, indicated by a typical circular fringe pattern on the holographic plate, which represents the center of resistance of the maxilla. In most cases, with all force variables tested, a protraction of the maxilla with palatal expansion was more effective in producing translation of the maxilla than was protraction without palatal expansion. By varying force magnitude, force direction and point of force application with maxillary protraction, the amount of maxillary rotation and translation might be controlled. (Am J Orthod Dentofac Qrthop 1997;111:623-32.)

Ske leta l Class III malocclusion is charac- terized by either a large mandible, a small maxilla, a retropositioned maxilla, or any combination of the three. Recent studies 13 have noted that 42/{) to 60% of Class III malocclusions are due to maxillary deficiency or retrusion, in combination wilh a nor- mal or mildly prognathic mandible. The treatment of children with developing skeletal Class III real- occlusions is difficult by orthodontic means alone; therefore protraction of the maxilla may be indi- cated to correct the Class III skeletal problem. The optimum application of such forces, however, has not yet been determined.

Class III patients with maxillary deficiency may present accompanying problems such as transverse

Based on a thesis by Kong-Geun Lee submitted to the Department of Orthodontics, College of Dentistry, Yonsei University, Korea, in partial fulfillment of the requirements for the degree of PhD. ~Resident, Orthodontic Center, Vanderbilt University, Nashville, Tenn. bProfessor, Department of Orthodontics, College of Dentistry, Yonsei University, Seoul, Korea. CProfessor and Chairman, Department of Orthodontics, College of Den- tistry, Yonsei University, Seoul, Korea. JAssistant Professor, Section of Orthodontics, School of Dentist~, UCLA, Los Angeles, Calif. Reprint requests to: Dr. Kong-Geun Lee, Vanderbilt University, Ortho- dontic Center, The Village at Vanderbilt, 1500 21st Ave. S., Suite 3400, Nashville, TN 37212. Copyright 1997 by the American Association of Orthodontists. 0889-5406/97/$5.00 + 0 8/1/73161

and vertical deficiency. In these cases, there is a need to control the movements of the maxilla during protraction, on a case by case basis. If no maxillary" rotation is desired, a more effective movement of the maxilla may be achieved if the center of resis- tance of the maxilla can be found and the protrac- tion force can be applied through this center of resistance. Several experimental studies have been performed to find the center of rotation and the center of resistance of the maxilla to protract the maxilla effectively. Burstone and Koenig 4 have suggested that, to obtain optimal stresses in the periodontium, a clear understanding of force magnitude, direction, duration, and point of force application is needed. Christiansen and Burstone 5 further add that these objectives can be achieved only by a clear understanding of the configuration and center of resistance of the teeth to be moved. Nanda 6 reported that, because facial sutures and periodontal tissues behave in a similar manner in response to applied force, these principles can also be applied to the desired movement of craniofacial bones. Nanda 68 also showed that with change in moment and direction of force, the center of rota- tion of the maxilla can be altered and the force variables can play an important role in the attain- ment of a desired directional change of midfacial bones. It is important to have a clear understanding

623

624 Lee et aL American Journal of Orthodontics and Dentofacial Orthopedics June 1997

Fig, 1. Antenna-type modified protraction headgear. Fig. 2. Fixation of skull to solid metal framework.

of force variables to attain desirable results. How- ever, there have been few attempts to find the response of the maxilla to complex combinations of force variables, and no studies have completely investigated maxillary protraction accompanied by maxillary expansion.

The photographic technique of holography can be used for recording and reconstructing images in such a way that the three dimensional aspect of the object can be retained and recorded as a hologram. In this study, holographic interferometry is used to determine any movement in three dimensions and to measure small bone displacements. Because the initial bone displacement is small with this tech- nique, laser holography was used to accurately mea- sure the movement and to avoid errors found in previous studies of this nature. 9'1

The purpose of this study was (1) to find the center of resistance of the maxilla; (2) to compare the response of the maxillary complex according to the various force systems such as magnitude, direc- tion, and application point of force; and (3) to study the effects of the palatal expansion on the maxillary complex during protraction.

MATERIALS AND METHODS Materials

A dry adult human skull (without the mandible), with well-aligned upper permanent dentition, was used as the experimental model. A modified protraction antenna headgear was made, according to Dermaut's method 9 (Fig. 1). The effects of force variables was investigated,

including the magnitude, point of application, and direc- tion of force on the maxilla. An antenna, instead of an outer bow, was soldered to an inner bow that was totally reinforced by means of casting, with 2.7 mm in diameter porcelain casting metal. Six hooks were soldered at dif- ferent levels of the antenna at intervals of 5 mm to support a nylon wire and to administer various points of force application. Two vertical bars were attached to the base of the metal framework to enable its use in different direc- tions by raising or lowering the face mask simulator. The U-shaped loops were made at the end of the inner bow to enable insertion from the distal side of the maxillary first molar headgear tube.

A Biderman-type Hyrax screw was set on the first premolar band and the first molar band. In addition, a 0.018 0.022-inch stainless steel wire was soldered be- tween the bands on each side, so that the protraction force was transmitted more effectively to the entire maxillary component.

The skull was fixed with nuts and bolts to a heavy metal support by three intermediate modeling compound shields and epoxy cement. Modeling compound shields covered the frontal bone, occipital bone, and both parietal bones (Fig. 2). When fixating the skull, the occlusal plane was kept parallel to the base of the support. The fixed dry skull with heavy metal framework was put on an optical bench that was buffered against minor vibration by rubber tubes. The equipment such as the laser, shutter, beam splitter, beam expander, attenuator, and mirror were set and fixed with a magnetic base on the optical bench (Fig. 3). Before conducting the experiments, the stabilization was checked by double exposure of holography.

American Journal of Orthodontics and Dentofacial Orthopedics Lee et al. 625 Volume 111, No. 6

Fig. 3. Holographic set up.

Methods

The experimental holographic setup is illustrated (Fig. 4). The highly coherent and monochromatic light from the laser source was split into two beams with a beam splitter. One of the beams was directed by mirrors, expanded with a spatial filter (microscope objective and a pinhole assem- bly), and was used to illuminate the object to be recorded. This beam, referred to as the object beam, provided information about the instantaneous condition of the object surface. The second beam, known as tl:~e reference beam, was not modulated by any intervening object. If both of these beams impinge on a surface, they produce a set of fringes, on the surface, as a result of their mutual interference. The fringe pattern gives information about the axis of rotation and the direction of bone deformation. In this study, holographic interferometry was used to measure initial bone displacements. Two images (one before and the other after deformation of the skull) were superimposed, which resulted in the formation of a fringe pattern.

A 20 mW He-Ne laser (NEL GLG 5700; ~ = 0.6328 ~m) was used. The intensity magnification of the refer- ence beam and object beam was 4:1. This He-Ne laser was exposed on the holographic plate (Agfa Gevaert, 8E 75). The holographic plate consisted of a highly sensitized emulsiol~ that coated a glass plate.

A double exposure technique was used. First, the laser was exposed on the fixed skull for 15 seconds and the protraction force was applied for 5 minutes. Tb, e laser was exposed for another 15 seconds to the same holographic plate. Frontal and lateral double exposures were taken. Before the next exposure, the skull was left for a period of 5 minutes after removal of the force to allow conversion from a strain state to a rest state.

After developing and fixing, the plates were bleached in a solution composed of ferric nitrate and potassium bromide, and dried. The completed holographic set of plates consisted of 36 frontal views and 36 lateral views.

Fig. 4. Schematic drawing of holographic set up. a: Laser. b: Beam splitter, c: Beam expander, d: Holo- graphic plate, e: Spatial filter, ob: Object beam. rb: Reference beam.

The fringes recorded on these plates by the double exposure holographic technique were reconstructed with the reference beam and photographs that were taken with an autoexposure camera.

Six points of force applications, two directions of force, and three different amounts of force were tested (Fig. 5). The points of force applications were 15, 10, and 5 mm above the occlusal plane, occlusal plane level, as well as 5 and 10 mm below the occlusal plane. The direction of protraction force was parallel to the sagittal plane and was parallel and 20 below to occlusal plane on the lateral view. The magnitudes of applied force were 300, 500, and 500 gm with a 45 turn to the maxillary jackscrew.

RESULTS Frontal View

The response of the maxillary complex, when protracted parallel to the occlusal plane.

1. The basic structure of the fringe pattern on the maxilla is composed of horizontally par-

626 Lee et al. American Journal of Orthodontics and Dentq[acial Orthopedics June 1997

Fig. 5. Point of application and direction.

allel bands. This indicates that the main movement is a forward and upward rotation of the anterior maxilla around an axis parallel to the direction of the fringes (Fig. 6, A and B).

2. In general, within one bony unit of the skull, the fringe pattern is regular (Fig. 6, A and B). However, the fringe pattern showed interrup- tion of continuity at the sutures. Thus the sutures seemed to behave as adjustment areas in the skulls.

3. There was a slight "A" shape in the area of the teeth, the alveolar process, and the max- illa (Fig. 6, A). This indicates that protraction of the maxilla induces the constriction of the anterior part of the plate. However, when protracting with palatal expansion, the "A" shape changed into a "V" shape (Fig. 6, B). This indicates that expansion of the palate compensated for the constriction of the pal- ate.

4. When protraction was increased, more fringes appeared(Fig. 6, A and B). This indi- cates more rotation of the maxilla.

5. At a higher point of force application, less fringes (Fig. 6, A and B) were formed. This indicates that with a higher point of force application, less upward rotation of the ante- rior maxilla occurs.

6. The direction of the fringes on the zygo- matic bone differed from the pattern on the maxilla. Approximately a 45 difference in angulation of the fringes on the zygomatic bone were produced by a more lateral corn-

ponent of rotation than in the maxilla (Fig. 6, A and B).

The response of the maxillary complex when protracted 20 downward to the occlusal plane:

1. At the point of 500 gm force application, 15 mm above the occlusal plane accompanied with palatal expansion, typical circular fringe patterns appeared. The centers of each of these circular patterns may be referenced from two axes: Through the crista gali per- pendicular, a line drawn through the most inferior points of the zygomaticomaxillary su- tures bilaterally. Thus the centers of each of the fringe patterns can be further described as located laterally at approximately 63% of the distance from the crista gali axis to the infe- rior border of the zygomaticomaxillary suture bilaterally, and approximately 13% of the distance from the zygomaticomaxillary axis to the inferior border of the orbit (Fig. 7, B1). This indicates that a true translation .of the maxilla occurred. The same application point, without expansion, also showed a circular fringe (Fig. 7, A1). However, the circular fringe was not as distinct as with expansion. This indicates that expansion of the palate is more effective in inducing a true translation of the maxilla, during the maxillary protrac- tion.

2. The number of fringes decreased significantly compared with protraction parallel to the occlusal plane (Figs. 8 and 9). This means that an upward rotation of the anterior portion of the maxilla changes to translational, or down- ward, rotation as the force direction changes from parallel to the occlusal plane to 20 downward.

3. Protraction when the point of force applica- tion was 10 mm above the occlusal plane shows a downward rotation of the anterior portion of the maxilla (Fig. 7,A2, A3, B2, B3). This rotation increased as the point of force application was lowered.

4. At the points above the occlusal plane, the direction of the fringes on the zygomatic bone showed reversal or vertical angulation com- pared with that of parallel protraction (Figs. 6, A,B and 7, A,B).

Lateral View

The fringe pattern showed a A shape on the zygomatic arch from the zygomaticotemporal su-

American Journal of Orthodontics and Dentofacial Orthopedics Lee et al. 1}27 Volume 111, No. 6

Fig. 6. Response of maxillary complex when protracted parallel to occlusal plane with 500 gm. (Frontal view) AI: 15 mm above to occlusal plane. A2: Occlusal plane. A3:10 mm below to occlusal plane. BI: 15 mm above to occlusal plane + expansion. B2: Occlusal plane + expansion. B3:10 mm below to occlusal plane + expansion. (Lateral view) C1:15 mm above to occlusal plane. 02: Occlusal plane. C3:10 mm below to occlusal plane.

ture, in two opposite directions. This indicates that the suture was acting as a hinge axis (Figs. 6, C, and 7, C).

In the area of the zygomaticotemporal suture, both bones (zygomatic process of the temporal bone

and temporal process of the zygomatic bone) were sheared relative to each other (Figs. 6, C, and 7, C).

Without expansion, the fringes ran horizontally on the maxilla. This indicates that the protraction force was transmitted to the maxilla as one unit in

628 Lee et al. American Journal of Orthodontics and Dentofacial Orihopedics June 1997

Fig. 7. Response of maxillary complex when protracted 20 downward to occlusal plane with 500 gm. (Frontal view) AI: 15 mm above to occlusal plane. A2: Occlusal plane. A3:10 mm below to occlusal plane. BI: 15 mm above to occlusal plane + expansion. B2: Occlusal plane + expansion. B3:10 mm below to occlusal plane + expansion. (Lateral view) C1:15 mm above to occlusal plane + expansion. 02: Occlusal plane + expansion. 03:10 mm below to occlusal plane + expansion.

one direction. However, during anterior rotation with expansion, the fringe pattern changed to a more vertical pattern. Furthermore, it divided in different ways from the first premolar area to the inferior area

of the zygoma and also to the pterygomaxillary fissure area (Figs. 6, C, and 7, C). This indicates that the protraction force probably was transmitted two ways, as primary and secondary stress areas.

American Journal ~?f Orthodontics and Dentofacial Orthopedics Lee el al. 629 Volume 111, No, 6

20

No. of

fringes

10

u15 u l0 u5 0 b5

Point of force application

Fig. 8. Number of fringes: parallel to occlusal plane.

bl0

30

20

No. of

fringes

10

300gin 500gin 500grn + Exp.

u15 ul0 u5 0 b5

Point of force application

bl0

Fig. 9. Number of fringes: 20 downward to occlusal ;)lane.

DISCUSSION

Kragt w'l~ has reported the similarity in initial responses of dry skull and human skull to orthope- dic force by means of a holography study. Although some differences of biomechanical behavior be- tween this type of model and the patient may be expected, a sulficient degree of similarity exists to use it as a simulation tool.

With holographic interferometry, parallel hori- zontal bands on the maxilla would indicate that the

main movement with protraction headgear is a forward with upward, or downward, rotation of the anterior portion of the maxilla around an axis parallel to the direction of the fringes. Ichikawa and associates 1~ reported similar outcomes when a pro- traction force was applied parallel to the occlusal plane. However, the fringe pattern in this study was not made up of purely straight horizontal bands. Furthermore, the distances between bands often differed, thus indicating that a protraction of the

630 Lee et al. American Journal of Orthodontics and Dentofacial Orthopedics June 1997

maxilla results in unequal amounts of rotational forces in different areas. This may be due to effects of sutures and variations in bone shape and density. Dermaut 13 reported the same result in his holo- graphic investigation during retraction with Class II elastics on a dry skull.

The A-shaped fringe pattern on the maxilla during protraction in this study indicates a compres- sional movement of the anterior palatal constriction accompanied by a forward translation and upward rotation of the anterior maxilla. This fringe pattern supports the results of Ichikawa; t2 Hata, 14 and Itoh. 15

It is very interesting to compare these results with Dermaut's experiment. ~3 He reported a slight V-shaped fringe at the same area during retraction with Class II elastics on a dry skull. He concluded that this phenomenon leads to the backward tipping of teeth and, to some extent, movement in a lateral direction, depending on the localization of the axis of rotation. The fringe pattern changed from a A to a V shape when protracting with palatal expansion. This indicates that palatal expansion compensates for palatal constriction that results from maxillary protraction. Hata 14 suggested that intraoral expan- sion devices be used whenever maxillary protraction appliances are used, based on his study that showed palatal constriction during protraction. There have been no clear demonstrations to prove this theory. Proffit .6 reported that the maxilla may move forward in response to transverse widening alone, but the average change is only 0.5 mm and posterior move- ment is as likely as anterior moment. However, the clinical importance of expansion during protraction may not be in its forward response only, but also in its compensating effect on maxillary constriction. The net effect is a change in the direction of bone bending from constriction to expansion.

MikP v and Hirato ~s reported that the location of the center of resistance in the midface of the human skull is between the first and second upper premo- lars anteroposteriorly, and between the lower mar- gin of orbitale and the distal apex of the first molar vertically in the sagittal plane. However, the above results were theoretically deduced with mechanical tests on a simulated human skull. Hata and associ- ates t4 reported that protraction 5 mm above the palatal plane produces a relatively straight forward movement of maxilla, but they were unable to find the force system that could induce a true translation of the maxilla.

When 500 gm force was applied 15 mm above and 20 downward to the occlusal plane and was

accompanied with expansion, typical circular fringe patterns appeared in the frontal view. The centers of each of these circular patterns may be referenced from two axes: Through the crista gali perpendicu- lar, a line drawn through the most inferior points of the zygomaticomaxillary sutures bilaterally. Thus the centers of each of the fringe patterns can be further described as located laterally at approxi- mately 63% of the distance from the crista gali axis to the inferior border of the zygomaticomaxillary suture bilaterally, and approximately 13% of the distance from the zygomaticomaxillary axis to the inferior border of the orbit. In the lateral view, three different fringe patterns appeared. The center of the neutral area of these patterns is located on a line passing through the distal contact of the maxillary first molar perpendicular to the functional occlusal plane, and 50% of the distance from the functional occlusal plane to the inferior border of the orbit. This point is coincident with the line of action of the 500 gm protraction force (Fig. 7, C1). The frontal and lateral fringe patterns indicates the center of the maxilla.

The same application without expansion also showed a circular fringe. However, this circular fringe pattern was not as distinct as with palatal expansion. This indicates that during maxillary pro- traction, expansion of the palate is a more effective method to induce pure translation of the maxilla.

Itoh and associates 1~ reported that the best usage of protraction appliances should include a combina- tion force of a forward and downward vector to protract the maxilla and to minimize the upward rotation of the anterior portion of the midface. Prof- fit 16 reported that most children with a maxillary deficiency are deficient vertically as well as anteropos- teriorly. This implies that a slight downward direction of an elastic traction is usually desirable between the intraoral attachment and the face mask frame.

When a 20 downward pull from occlusal plane was applied, the number of fringes decreased signif- icantly in comparison to protraction parallel to the occlusal plane. This means that upward rotation of the anterior portion of the maxilla changed to translation or downward rotation as force direction changed from parallel to the occlusal plane to 20 downward. This phenomenon was similar to the findings of Itoh and associates. 15 They reported that a 20 downward pull from molar and premolar ar- eas, decreased the rotation of the palatal plane.

The fringe pattern showed a A on the zygomatic arch from the zygomaticotemporal suture in two opposite directions on the lateral view. This reveals

American Journal of Orthodontics and Dentofacial Orthopedics Lee et al. 63"~ Volume H1, No. 6

that the suture was acting as a hinge axis. There was a difference in the lateral movement on both sides of the suture, meaning that the suture functioned as a hinge axis. Bishara and associ- ates 19 reported that it is important for the clini- cian to remember that the main resistance to a midpalatal suture opening is probably not in the suture itself but in the surrounding structures, particularly the sphenoid and zygomatic bones. In the area of the zygomaticotemporal suture, both bones (zygomatic process of the temporal bone and the temporal process of the zygomatic bone) had sheared relative to each other. This is in agreement with the findings of I~agt and associ- ates, 11 who found a comparable movement in the zygomatic area after having applied headgear forces on a macerated skull.

On the lateral view, the fringe pattern showed a horizontal direction on the maxilla. This may indi- cate that the protraction force is transrnitted to the maxilla as one unit, in one direction. However, during the protraction with expansion, the fringe pattern changed vertically and divided in different ways from the first premolar area, to the inferior area of the zygoma, and to the pterygomaxillary fissure. This indicates that the protraction force probably transmitted in two ways, as primary and secondary stress areas.

The following suggestions were developed from this study so that an effective forward dis- placement of the maxilla through the, center of resistance could be obtained clinically. For pure translation, an optimum force system includes a 500 gm force applied at a point 15 mm above the occlusal plane, directed 20 downward from the occlusal plane with palatal expansion. ]-'his type of force application is especially desirable if the face height is normal and a rotation of the maxilla is contraindicated.

Conversely, in deep overbite cases in which an opening of the bite is necessary, a forward pull with a concomitant upward rotation of the anterior part of the maxilla will aid in file treatment of these malocclusions. This was seen when 500 gm of force was applied at every point of application when the force was directed parallel to the occlusal plane with palatal expansion. The lower the point of applica- tion, the greater the magnitude of the resultant upward rotation.

Furthermore, in open bite, maxillary vertical deficiency, or short lower face height cases, a downward rotation of the anterior part of the maxilla is desirable. This can be achieved in this study with a

500 gm force applied at or below the occlusal plane directed 20 downward to the occlusal plane with palatal expansion. Downward displacement of the maxilla increases face height and rotates the mandible downward and backward. This contributes to the cor- rection of a skeletal Class III relationship.

Therefore the vertical control of the maxilla can effectively be obtained by the type of force variables applied to the midface. Each patient needs to be evaluated to determine the desired maxillary move- ment. In addition, dental movements should also be taken into account.

CONCLUSION

Laser holography was used on a human dry sknll to find the force system that could induce true translation through the center of resistance of the maxilla during protraction. The response of the maxillary complex was analyzed by using various force systems, such as the force magnitude, the direction of force, and the application point of force. The effects of palatal expansion on the maxillary complex were also studied during protraction. The following conclusions Were reached: When the point of force application was 15 mm above and directed 20 dowaaward to the ocdusal plane with a force of 500 gm, along with palatal expansion, true translation through the center of resistance of the maxilla occurred. By varying the force system, the amount and direction of maxillary rotation might be controlled. During maxillary protraction, the expansion of the palate performed a compensating action for the maxillary constriction ten- dency and was effective in inducing pure translation of the maxilla.

REFERENCES

1. Ellis E, McNamara J Jr. Components of adult Class IU malocclt~sion. Am J Oral Maxillofac Surg 1984;42:295 305.

2. Guyer EC, Ellis E, McNamara JA, Behrents GG. Components of Class IIl malocclusion in iuveniles and adolescents. Angle Orthod /986;56:7-30.

3. Jacobson A, Evans WG, Preston CB, Sadowsky PL. Mandibular prognathism. Aan J Orthod 1974;66:140-71.

4. Bnrstone CJ, Koneig HA. Force systems t?om an idea arch. Am J Orthod 1974;65:270-89.

5. Christiansen R, Burstone CJ. Centers of rotation within the periodontal space. Am J Orthod 1969;55:353-69.

6. Nanda R, Goldin B. Biomechanical approaches to the study of the alterations of facial morphology. Am J Orthod 1980;78~213-26.

7. Nanda R. Protracting of maxilla in rhesus monkey by controlled extraoral forces. Am J Orthod 1978;74:121-41.

8. Nanda R. Biomechanical and clinical consideration of a modified protraction headgear. Am J Orthod I980;78:125-30.

9. Dermaut LR. Experimental determination of the center of resistance of the upper first molar in a macerated dry human skull submitted to horizontal headgear traction. Am J Orthod Dentofac Orthop 1986;90:29-36.

10. Kragt G, Duterioo HS, Ten Bosch JJ. The initial reaction of a macerated skull caused by orthodontic cervical traction determined by laser metrology. Am J Orthod 1982;81:49-56.

l 1. Kragt G, Duterloo HS, Ten Bosch JJ. the initial effect of the orthopedic forces: a study of alterations in the craniofacial complex of a macerated human skuI1 owing to high-pull headgear traction. Am J Orthod 1982;81:57-64.

I2. Ichikawa K, Nakagaw M, Kamogashira K, Hata S, Itoh T, Matsumoto M. The effects of orthopedic forces on the craniofacial complex utilizing maxillary protrac- tion. J Jpn Orthod Soc 1984:43:325-36.

13. Dermaut LR, Beerden L. The effect of class elastic force on a dz2 skull measured by holographic interferometry. Am J Orthod 1981;79:296-304.

632 Lee et al. American Journal of Orthodontics and Dentofacial Orthopedics June 1997

14. Hata S, Itoh T, Nakagawa M, Kamogashira K, Ichikawa K, Matsumoto M, et al. Biomechanical effects of maxillary protraction on the craniofacial complex. Am J Orthod Dentofac Orthop 1987;91:305-11.

15. Itoh T, Chaconas SJ, Caputo AA, Matyas J. Photoelastic effects of maxillary proreaction on the craniofacial complex. Am J Orthod 1985;88:117-24.

16. Protfit WR. Contemporary orthodontics. St Louis: CV Mosby, 1993. 17. Miki M. An experimental research on the directional of the nasomaxillary complex

by means of the external rome--two dimensional analysis on the sagittal plane of the craniofacial skeleton. J Tokyo Dent Coll 1979;79:1563-97.

18. Hirato R. An experimental study on the center of resistance of nasomaxillau complex-two dimensional analysis on the coronal pane of the dry skull. J Tokyo Dent Coil 1984:84:1225-62.

19. Bishara SE, Staley RN. Maxillary expansion: clinical applications. Am J Orthod Dentofac Orthop 1987;91:3-14.

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