ORIGINAL ARTICLE

Stress and displacement between maxillaryprotraction with miniplates placed at theinfrazygomatic crest and the lateral nasal wall:A 3-dimensional finite element analysis

Nam-Ki Leea and Seung-Hak Baekb

Seongnam and Seoul, Korea

aAssisNatioof KobProfeInstituThe aucts oReprinDenti#28, JSubm0889-Copyrdoi:10

Introduction: The purpose of this study was to compare the pattern and amount of stress and displacementbetween maxillary protraction with miniplates placed at the infrazygomatic crest and the lateral nasal wall.Methods: Three-dimensional finite element models for the skull and the curvilinear type of miniplate wereconstructed. After a protraction force (500 g/side) was applied to the distal end of the miniplate with a forwardand 30� downward vector to the maxillary occlusal plane, stress distributions in the circummaxillary suturesand displacements of the surface landmarks were analyzed. Results: There was a difference in the maximumstress distribution area according to the site of theminiplate: infrazygomatic crest andmiddle part of themaxilla inthe infrazygomatic crest and paranasal area adjacent to the pyriform aperture in the lateral nasal wall. Stressvalues of the frontonasal, frontomaxillary, zygomaticomaxillary, and pterygomaxillary sutures were greater inthe infrazygomatic crest than in the lateral nasal wall. The site of the miniplate produced differences in the majordisplacement areas: infrazygomatic crest, maxillary dentition, anterior maxilla, and upper part of the maxillarytuberosity in the infrazygomatic crest and the lateral nasal wall, maxillary dentition, anterior maxilla, and lowerpart of the maxillary tuberosity in the lateral nasal wall. The lateral nasal wall exhibited forward, downward,and outward displacements of ANS, Point A, and prosthion. However, the infrazygomatic crest showed forwardand upward displacements of ANS, Point A, and prosthion, and outward displacement of the zygomatic processof the maxilla and the maxillary process of the zygomatic bone. Conclusions: The site of miniplate placementshould be considered to obtain proper stress and displacement values in different areas with maxillaryhypoplasia. (Am J Orthod Dentofacial Orthop 2012;141:345-51)

Therapy with a facemask has been regarded as anappliance of choice to treat growing Class IIIpatients with mild to moderate maxillary hypopla-

sia.1,2 Although facemask therapy can induceadvancement of the maxilla and the circummaxillarycomplex depending on the force generated at thesutures,3,4 more favorable outcomes might be expectedin patients in the deciduous or early mixed dentition

tant professor, Department of Orthodontics, Section of Dentistry, Seoulnal University, Bundang Hospital, Seongnam, Gyeonggi Province, Republicrea.ssor, Department of Orthodontics, School of Dentistry, Dental Researchte, Seoul National University, Seoul, Republic of Korea.uthors report no commercial, proprietary, or financial interest in the prod-r companies described in this article.t requests to: Seung-Hak Baek, Department of Orthodontics, School ofstry, Dental Research Institute, Seoul National University, Yeonkun-dongongro-ku, Seoul, 110-768, Republic of Korea; e-mail, drwhite@unitel.co.kr.itted, March 2011; revised and accepted, July 2011.5406/$36.00ight � 2012 by the American Association of Orthodontists..1016/j.ajodo.2011.07.021

than in those with late mixed dentition.5-7 To transmitthe orthopedic force from the facemask to the maxilla,tooth-borne anchorage with a labiolingual arch,a quad-helix appliance, and rapid maxillary expansionhave been used. However, usage of the maxillarydentition as anchorage cannot avoid unwanted sideeffects such as labioversion of the maxillary incisors,extrusion of the maxillary molars, counterclockwiserotation of the palatal plane, and eventual clockwiserotation of the mandible.8-14

To allow the direct transmission of orthopedic forceto the circummaxillary sutures, intentionally ankyloseddeciduous canines, osseointegrated onplants andimplants, and orthodontic miniscrews have been usedas skeletal anchorage for maxillary protraction.15-20

Since a surgical miniplate can be regarded as a reliableanchorage tool for applying the orthopedic forces tothe maxillofacial skeletal complex, facemask therapywith miniplate anchorage placed at the infrazygomaticarea or the lateral nasal wall of the maxilla has been

345

Fig 1. Three-dimensional finite element model of theskull including the frontonasal, frontomaxillary, zygomati-comaxillary, zygomaticotemporal, zygomaticofrontal, andpterygomaxillary sutures: A, facemask therapy withminiplate anchorage placed at the infrazygomatic area;B, facemask therapy with miniplate anchorage placed inthe lateral nasal wall of the maxilla. Protraction forces(500 g/side) were applied to the distal ends of theminiplate of the infrazygomatic area and the lateral nasalwall models with a forward and 30� downward vector tothe maxillary occlusal plane.

346 Lee and Baek

introduced to treat patients with Class III malocclusionwith maxillary hypoplasia or hypodontia.21-24

Three-dimensional (3D) finite element model analysiscan enumerate the biomechanical variables such as stress,strain, and displacement in the maxillofacial complex in-duced by various conditions of force and direction inmax-illary protraction.25-27 Several studies have evaluated thebiomechanical changes of the maxillofacial structureswith facemask therapy combined with tooth-borneanchorage.28-31 However, few biomechanical studieshave been undertaken about the effects of facemasktherapy with miniplate anchorage on the maxillofacialstructures in the infrazygomatic area and the lateralnasal wall. Since these models have different positions ofthe miniplates in the maxillofacial skeletal structure,there can be differences in stress distribution in thecircummaxillary sutures and in displacement of thesurface landmarks in the maxillofacial bones.

Therefore, the purpose of this study was to comparestress distribution in the circummaxillary sutures anddisplacement of the surface landmarks in the maxillofa-cial bones between the infrazygomatic area and thelateral nasal wall models by using 3D finite elementmodel analysis. The null hypothesis was that there areno differences in the pattern and amount of suturalstress and landmark displacement according to theposition of the miniplates.

MATERIAL AND METHODS

Computed tomography scans (SCT-6800TXL;Shimadzu, Tokyo, Japan) (120 kVp, 230 mA, 1:1.2 pitch,scanning time of 1.5 seconds, 3-mm intervals in the axialdirection, parallel to the Frankfort horizontal plane) ofthe skull of a girl (age, 13.5 years) who had a retrusivemaxilla and an anterior crossbite were taken to obtainthe horizontal images from the maxillary occlusal planeto the superior margin of the cranium. A surface 3Dmodel of the skull was reconstructed from the computedtomography images by using a 3D imaging process soft-ware package (Mimics 7.10; Materialise, Leuven, Bel-gium). This geometric model (STL format) was editedand meshed into a 3D finite element model by usingSimulation software (version 2011; SolidWorks,Concord, Mass).

Six craniofacial sutural systems were integrated intothe model. After the nodes corresponding to the ana-tomic sutures (frontonasal, frontomaxillary, zygomati-comaxillary, zygomaticotemporal, zygomaticofrontal,and pterygomaxillary) were identified, pairs of nodeswere created along the entire suture length. The thick-ness of each suture was modeled with an even thicknessof 0.5 mm. This modeling can allow stress displacementin the sutural system and independent displacement of

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the surface landmarks at the bony structures in responseto simulated orthopedic forces.

Also, a 3D finite element model for a curvilinear typeof surgical miniplate with 6 holes (thickness, 0.80 mm;length, 31.65 mm; hole diameter, 2 mm; distance be-tween the centers of the holes, 5.50 mm; curvature,0.04 mm−1; LeForte system, Jeil Medical, Seoul, Korea)was designed based on 3D computer-aided designdata and fixed according to the anatomic shape of theinfrazygomatic crest and the lateral nasal wall of themaxilla by the projection method. In the lateral nasalwall model, the distal end of the miniplate was placed2 mm above the gingival crest of the alveolar bone be-tween the maxillary lateral incisor and the canine, and

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Table I. Young’s modulus and Poisson’s ratio forvarious materials in this study

Material Young’s modulus (MPa) Poisson’s ratioCortical bone 1.37 3 104 0.30Cancellous bone 7.9 3 103 0.30Miniplate 1.05 3 105 0.33Miniscrew 1.05 3 105 0.33Suture 7 0.40Tooth 2.07 3 104 0.30

Fig 2. A, Suture points: 1, frontonasal suture; 2, fronto-maxillary suture; 3-5, zygomaticomaxillary suture (supe-rior, middle, and inferior); 6 and 7, zygomaticotemporalsuture (superior and inferior); 8 and 9, zygomaticofrontalsuture (anterior and posterior); 10 and 11, pterygomaxillarysuture (superior and inferior). B, Surface landmarks of themaxilla: 1, frontal process; 2, ANS; 3, Point A; 4, prosthion;5, inferior orbital rim;6-8, zygomaticprocess (superior,mid-dle, and inferior); 9, PNS; zygomatic bone: 10 and 11, fron-tal process (anterior and posterior); 12-14, maxillaryprocess (superior, middle, and inferior); 15 and 16, tempo-ral process (superior and inferior); frontal bone: 17 and 18,zygomatic process (anterior and posterior); temporal bone:19 and 20, zygomatic process (superior and inferior).

Lee and Baek 347

the mesial end of the miniplate was located 3 mm fromthe pyriform aperture. In the the infrazygomatic areamodel, the distal end of the miniplate was placed 2mm above the gingival crest of the alveolar bone be-tween the maxillary canine and first premolar, and themesial end of miniplate was located 5 mm anterior tothe infrazygomatic crest. The part of the miniplatearound the upper 3 holes was simulated to be rigidlybonded to the bony surface area as if 2-mm diameterminiscrews were inserted through the upper 3 holes.

The 3D finite element model in this study consistedof 317,572 first tetrahedral elements, 64,772 nodes,and 194,316 degrees of freedom (Fig 1). The mechanicalproperties of cortical and cancellous bones, teeth,sutures, miniplate, and miniscrews in the 3D finiteelement model are shown in Table I.25,30,32

Restraints were established at all other nodes of thecranium lying on the symmetrical plane. In addition,a zero-displacement boundary condition was imposedon the nodes along the foramen magnum (Fig 1).

Protraction forces (500 g/side) were applied to thedistal ends of the miniplates of both models with a 30�

downward and forward vector to the maxillary occlusalplane, respectively (Fig 1). Stress distribution in thecircummaxillary sutures and displacement of the surfacelandmarks in the maxillofacial bone were analyzed byusing ANSYS software (version 12.1; Belcan Engineer-ing, Cincinnati, Ohio). The locations of the suture pointsand the surface landmarks in the maxillofacial bone areshown in Figure 2.

RESULTS

Although both models did not show stress concentra-tion in themaxillary dentition, therewas a difference in thepatterns of stress distribution between the infrazygomaticarea and the lateral nasal wall models. The stress was con-centratedmainly on the infrazygomatic crest and themid-dle part of the maxilla in the infrazygomatic area model(Fig 3,A) andon the roots of themaxillary canines andfirstpremolars and the paranasal area adjacent to the pyriformaperture in the lateral nasal wall model (Fig 3, B).

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Fig 3. Pattern of stress distribution (MPa 3 10�6) in A,the infrazygomatic area model and B, the lateral nasalwall model. The stress was concentratedmainly on the in-frazygomatic crest and themiddle part of themaxilla in theinfrazygomatic area model and on the roots of the maxil-lary canines and first premolars and the paranasal areaadjacent to the pyriform aperture in the lateral nasal wallmodel.

Table II. Von Mises stress in the circummaxillarysutures in maxillary protraction with miniplates placedat the infrazygomatic area (MP-IZ) and the lateralnasal wall (MP-LN) of the maxilla

Suture MP-IZ (MPa) MP-LN (MPa)Frontonasal 2.09E-03 1.86E-03Frontomaxillary 1.20E-03 9.61E-04ZygomaticomaxillarySuperior 5.98E-04 4.57E-04Middle 2.12E-03 1.01E-03Inferior 1.79E-03 1.89E-03

ZygomaticotemporalSuperior 5.90E-04 5.84E-04Inferior 2.82E-03 2.68E-03

ZygomaticofrontalPosterior 2.55E-04 3.17E-04Anterior 2.35E-04 2.63E-04

PterygomaxillarySuperior 4.83E-03 3.69E-03Inferior 4.44E-03 3.28E-03

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Both models showed the maximum von Misesstresses at the pterygomaxillary, zygomaticotemporal,zygomaticomaxillary, and frontonasal sutures in de-scending order (Table II). However, the stress values ofthe frontonasal, the frontomaxillary, the zygomatico-maxillary (superior and middle portions), and the ptery-gomaxillary sutures were higher in the infrazygomaticarea model than in the lateral nasal wall model (Table II).

Similar to the stress distribution, the positions of theminiplates affected the pattern of displacement. The in-frazygomatic area model showed greater displacementsof the infrazygomatic crest area, the maxillary dentition,the anterior maxilla, and the upper part of the maxillary

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tuberosity (Fig 4, A), whereas the lateral nasal wallmodel exhibited the main displacements on the lateralnasal wall area, the maxillary dentition, the anteriormaxilla, and the lower part of the maxillary tuberosity(Fig 4, B).

In the sagittal plane, maximum forward displace-ments were observed at the anterior nasal spine (ANS),Point A, prosthion, and posterior nasal spine (PNS) inthe maxilla in both models (Table III). These valuesshowed an increasing tendency in the infrazygomaticarea model and a decreasing tendency in the lateral nasalwall model from ANS and Point A to prosthion (Table III).However, forward displacement values of the surfacelandmarks in the inferior orbital rim and zygomatic pro-cess of themaxilla, the zygomatic bone, the frontal bone,and the temporal bone were almost same (Table III).

In the vertical plane, the infrazygomatic area modelshowed the maximum upward displacements at ANS,Point A, and prosthion in the maxilla, and the maximumdownward displacement at PNS in the maxilla (Table III).However, the lateral nasal wall model showed the max-imum downward displacements at ANS, Point A, pros-thion, and PNS in the maxilla (Table III). Thesefindings mean that there were different patterns of ver-tical displacement according to the position of the mini-plates. However, the frontal process of the maxilla, thefrontal and maxillary processes of the zygomatic bone,and the zygomatic process of the frontal bone, whichwere remote from the miniplates, did not show signifi-cant differences in vertical displacements (Table III).

In the transverse plane, the infrazygomatic areamodelshowed the maximum outward displacement of thezygomatic process (middle and inferior) of the maxilla

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Fig 4. Pattern of displacement of the surface landmarks(mm) in A, the infrazygomatic area model and B, the lat-eral nasal wall model.

Lee and Baek 349

and the maxillary process (superior, middle, and inferior)of the zygomatic bone (Table III). However, the lateral na-sal wall model showed the maximum outward displace-ment at ANS, Point A, and prosthion in the maxilla(Table III). These findings imply different patterns oftransverse displacement according to the positions ofthe miniplates. However, the inferior orbital rim of themaxilla, the frontal and temporal processes of the zygo-matic bone, and the zygomatic process of the temporalbone, which were remote from the miniplates, did notshow significant differences in transverse displacements(Table III).

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DISCUSSION

The infrazygomatic area model had the orthopediceffect with maximum stress distribution in the infrazy-gomatic crest and the middle part of the maxilla (Fig3,A). But the lateral nasal wall model showed the ortho-pedic effect in the paranasal area adjacent to the pyri-form aperture (Fig 3, B). Therefore, the position of theminiplate might result in a different effect on estheticimprovements in the midface.

Both models showed the maximum von Mises stressesat the pterygomaxillary, zygomaticotemporal, zygomati-comaxillary, and frontonasal sutures in descending order(Table II). These results are in accordance with those ofTanne and Sakuda33 and Gautam et al.31 The pterygo-maxillary suture had the maximum von Mises stressvalues, with the superior portion having higher stressesthan the inferior portion in both models (Table II); thisimplies that disarticulation of the maxilla from the sphe-noid bone might be more pronounced at the superior re-gion of the pterygomaxillary suture. These findingsindicate that the maxilla might be separated from thepterygoid process at the pterygomaxillary fissure level.

The finding that the stress values of the frontonasal,frontomaxillary, zygomaticomaxillary (superior andmiddle portions), and pterygomaxillary sutures werehigher in the infrazygomatic area model than in thelateral nasal wall model (Table II) suggests that the infra-zygomatic area could transfer the orthopedic force moreeffectively to these sutures than the lateral nasal wall.

The findings that the lateral nasal wall modelsshowed forward and downward displacement at ANS,Point A, prosthion, and PNS (Table III and Fig 4) andthat the lateral nasal wall model showed forward andupward displacement at ANS, Point A, and prosthionand forward and downward displacement at PNS(Table III and Fig 4) mean that there were different pat-terns of vertical displacement according to the positionsof the miniplates during maxillary protraction. Theresults of this study suggest that the lateral nasal wallmight be favorable to minimize the counterclockwise ro-tation of the maxilla compared with the infrazygomaticarea. Kircelli et al21 and Kircelli and Pektas23 insisted thatthe lateral nasal wall of the maxilla might be a proper sitefor miniplate placement because it is anterior to the cen-ter of resistance of the nasomaxillary complex, allowingthe force vector to be near the center of resistance. Incontrast, the infrazygomatic area model seems to showa slight tendency for counterclockwise rotation of thenasomaxillary complex. Therefore, changing the forceapplication point to a more forward position and theforce vector to a more downward direction might be

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Table III. Displacement of the surface landmarks in the maxillofacial structures in maxillary protraction withminiplates placed at the infrazygomatic crest (MP-IZ) and the lateral nasal wall (MP-LN)

Region Surface landmarks

MP-IZ MP-LN

X (mm) Y (mm) Z (mm) X (mm) Y (mm) Z (mm)Maxilla Frontal process �7.24E-08 9.72E-06 2.23E-04 �9.65E-08 7.89E-06 2.23E-04

ANS �3.44E-07 7.17E-05 3.77E-04 3.05E-05 �6.90E-05 4.31E-04Point A �7.64E-06 6.56E-05 4.06E-04 3.53E-05 �7.24E-05 4.27E-04Prosthion �2.08E-05 7.87E-05 4.32E-04 2.68E-05 �8.02E-05 4.11E-04Inferior orbital rim 1.68E-05 2.07E-05 2.70E-04 1.57E-05 1.47E-05 2.64E-04Zygomatic process, superior 1.80E-05 2.12E-05 2.70E-04 1.64E-05 1.37E-05 2.64E-04Zygomatic process, middle 2.56E-05 2.30E-05 3.13E-04 2.12E-05 1.31E-05 3.04E-04Zygomatic process, inferior 2.43E-05 �1.98E-06 3.33E-04 1.82E-05 �1.01E-05 3.25E-04PNS 1.61E-05 �7.39E-06 3.90E-04 2.52E-7 �7.28E-05 4.16E-04

Zygomatic bone Frontal process, anterior 3.02E-06 1.84E-06 2.14E-04 1.17E-06 3.51E-08 2.14E-04Frontal process, posterior �6.27E-06 �7.98E-06 2.03E-04 �6.59E-06 �9.73E-06 2.04E-04Maxillary process, superior 2.60E-05 8.15E-06 2.70E-04 2.06E-05 3.45E-06 2.65E-04Maxillary process, middle 3.12E-05 6.25E-06 2.91E-04 2.49E-05 1.67E-06 2.84E-04Maxillary process-inferior 2.61E-05 �7.12E-06 2.99E-04 1.99E-05 �1.05E-05 2.91E-04Temporal process, superior �9.10E-06 �3.20E-05 2.29E-04 �1.07E-05 �3.24E-05 2.29E-04Temporal process, inferior �1.85E-05 �3.91E-05 2.49E-04 �1.96E-05 �3.84E-05 2.46E-04

Frontal bone Zygomatic process, anterior 1.31E-06 3.86E-06 2.12E-04 2.11E-7 2.86E-06 2.12E-04Zygomatic process, posterior �7.99E-06 �3.73E-06 2.01E-04 �8.23E-06 �4.66E-06 2.02E-04

Temporal bone Zygomatic process, superior �2.28E-05 �4.49E-05 2.19E-04 �2.39E-05 �4.45E-05 2.19E-04Zygomatic process, inferior �2.26E-06 �4.03E-05 2.11E-04 �3.55E-06 �3.97E-05 2.10E-04

X, Transverse plane; Y, vertical plane; Z, sagittal plane.Positive value (1) indicates outward, upward, and forward displacement in relation to the X, Y, andZ planes, respectively; negative value (�) indicatesinward, downward, and backward displacement in relation to the X, Y, and Z planes, respectively.

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recommended to minimize the unwanted counterclock-wise rotation tendency of the nasomaxillary complex.

In addition, our findings of different patterns of max-imum outward displacement according to the positionsof the miniplates—the infrazygomatic area model atthe zygomatic process of the maxilla and the maxillaryprocess of the zygomatic bone and lateral nasal wallmodel at ANS, Point A, and prosthion in the maxilla(Table III and Fig 4)—imply that the lateral nasal wallmight induce expansion of the anterior part of themaxilla and the infrazygomatic area, and expansion inthe middle part of the maxilla during maxillary protrac-tion. Therefore, if there is maxillary hypoplasia witha constricted arch, especially in the anterior part, the lat-eral nasal wall could be helpful to resolve these problemscombined with a quad-helix or rapid maxillary expan-sion appliance. If the maxillary constriction is not amajorissue during protraction, the infrazygomatic area can beused with a lingual arch.

Our results showed different amounts and patterns ofsutural stress and landmark displacement between theinfrazygomatic area and the lateral nasal wall (Tables IIand III; Figs 3 and 4) because the infrazygomatic areaand the lateral nasal wall might have different forcevectors with respect to the relationship between thecenter of resistance for the maxillofacial skeletalcomplex and the position of the miniplates.

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Although these results could offer information aboutthe patterns of initial stress distribution and displace-ment in maxillary protraction with miniplates placed atdifferent positions, the real treatment outcome mightbe different from these 3D finite element model resultsbecause we did not consider the soft tissues in modeling.In addition, since both the infrazygomatic area and thelateral nasal wall models exhibited different patterns ofstress distribution and displacement of the surface land-marks, combined use of the infrazygomatic area and thelateral nasal wall might provide a better treatment resultfor growing Class III patients with moderate to severemidface hypoplasia. Therefore, further studies are re-quired to investigate the appropriate site of miniplateplacement for these patients with varying horizontaland vertical skeletal discrepancies.

CONCLUSIONS

1. The null hypothesis of no differences in the patternand the amount of sutural stress and landmark dis-placement according to the position of the mini-plates was rejected.

2. Although the biologic outcome can be differentfrom the results of this 3D finite element modelstudy, it would be more advantageous to performmaxillary protraction with a miniplate placed in the

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Lee and Baek 351

infrazygomatic crest area in patients who need moreadvancement in the middle part of the zygomatico-maxillary complex, and maxillary protraction witha miniplate in the lateral nasal wall area in patientswho need more advancement in the paranasal areaand the lower part of zygomaticomaxillary complex.

REFERENCES

1. McNamara JA. An orthopedic approach to the treatment of Class IIImalocclusion in young patients. J Clin Orthod 1987;21:598-608.

2. Baik HS. Clinical results of the maxillary protraction in Koreanchildren. Am J Orthod Dentofacial Orthop 1995;108:583-92.

3. Kambara T. Dentofacial changes produced by extraoral forwardforce in the Macaca irus. Am J Orthod 1977;71:249-77.

4. Nanda R. Protraction of maxilla in rhesus monkeys by controlledextraoral forces. Am J Orthod 1978;74:121-41.

5. Kapust AJ, Sinclair PM, Turley PK. Cephalometric effects of facemask/expansion therapy in Class III children: a comparison of threeage groups. Am J Orthod Dentofacial Orthop 1998;113:204-12.

6. Saadia M, Torres E. Sagittal changes after maxillary protractionwith expansion in Class III patients in the primary, mixed, andlate mixed dentitions: a longitudinal retrospective study. Am JOrthod Dentofacial Orthop 2000;117:669-80.

7. Westwood PV, McNamara JA Jr, Baccetti T, Franchi L, Sarver DM.Long-term effects of Class III treatment with rapid maxillaryexpansion and facemask therapy followed by fixed appliances.Am J Orthod Dentofacial Orthop 2003;123:306-20.

8. Itoh T, Chaconas SJ, Caputo AA, Matyas J. Photoelastic effects ofmaxillary protraction on the craniofacial complex. Am J Orthod1985;88:117-24.

9. Hata S, Itoh T, Nakagawa M, Kamogashira K, Ichikawa K,Matsumoto M, et al. Biomechanical effects of maxillaryprotraction on the craniofacial complex. Am J Orthod DentofacialOrthop 1987;91:305-11.

10. Chong YH, Ive JC, �Artun J. Changes following the use ofprotraction headgear for early correction of Class III malocclusion.Angle Orthod 1996;66:351-62.

11. Ngan PW, H€agg U, Yiu C, Wei SH. Treatment response andlong-term dentofacial adaptations to maxillary expansion andprotraction. Semin Orthod 1997;3:255-64.

12. Ngan P, Yiu C, Hu A, H€agg U, Wei SH, Gunel E. Cephalometric andocclusal changes following maxillary expansion and protraction.Eur J Orthod 1998;20:237-54.

13. Kapust AJ, Sinclair PM, Turley PK. Cephalometric effects of facemask/expansion therapy in Class III children: a comparison of threeage groups. Am J Orthod Dentofacial Orthop 1998;113:204-12.

14. Keles A, Tokmak EC, Erverdi N, Nanda R. Effect of varying the forcedirection on maxillary orthopedic protraction. Angle Orthod 2002;72:387-96.

15. Kokich VG, Shapiro PA, Oswald R, Koskinen-Moffett L, Clarren SK.Ankylosed teeth as abutments for maxillary protraction: a casereport. Am J Orthod 1985;88:303-7.

American Journal of Orthodontics and Dentofacial Orthoped

16. Smalley WM, Shapiro PA, Hohl TH, Kokich VG, Br�anemark P.Osseointegrated titanium implants for maxillofacial protractionin monkeys. Am J Orthod Dentofacial Orthop 1988;94:285-95.

17. Singer SL, Henry PJ, Rosenberg I. Osseointegrated implants as anadjunct to face mask therapy: a case report. Angle Orthod 2000;70:253-62.

18. Enacar A, Giray B, Pehlivanoglu M, Iplikcioglu H. Facemask therapywith rigid anchorage in a patient with maxillary hypoplasia and se-vere oligodontia. Am J Orthod Dentofacial Orthop 2003;123:571-7.

19. HongH, Ngan P, Han G, Qi LG,Wei SH. Use of onplants as stable an-chorage for facemask treatment. Angle Orthod 2005;75:453-60.

20. Vachiramon A, UrataM, Kyung HM, Yamashita DD, Yen SL. Clinicalapplications of orthodontic microimplant anchorage in craniofa-cial patients. Cleft Palate Craniofac J 2009;46:136-46.

21. Kircelli BH, Pektas ZO, Uckan S. Orthopedic protraction withskeletal anchorage in a patient with maxillary hypoplasia andhypodontia. Angle Orthod 2006;76:156-63.

22. Cha BK, Lee NK, Choi DS. Maxillary protraction treatment ofskeletal Class III children using miniplate anchorage. Korean J Or-thod 2007;37:73-84.

23. Kircelli BH, Pektas ZO. Midfacial protraction with skeletallyanchored facemask therapy: a novel approach and preliminaryresults. Am J Orthod Dentofacial Orthop 2008;133:440-9.

24. Baek SH, Kim KW, Choi JY. New treatment modality for maxillaryhypoplasia in cleft patients. Protraction facemask with miniplateanchorage. Angle Orthod 2010;80:595-603.

25. Tanne K, Hiraga J, Kakiuchi K, Yamagata Y, Sakuda M. Biome-chanical effect of anteriorly directed extraoral forces on the cranio-facial complex: a study using the finite element method. Am JOrthod Dentofacial Orthop 1989;95:200-7.

26. Tanne K, Hiraga J, Sakuda M. Effects of directions of maxillaryprotraction forces on biomechanical changes in craniofacial com-plex. Eur J Orthod 1989;11:382-91.

27. Tanne K, Matsubara S, Sakuda M. Location of the centre of resis-tance for the naso-maxillary complex studied in a three-dimen-sional finite element model. Br J Orthod 1995;22:227-32.

28. Miyasaka-Hiraga J, TanneK,Nakamura S. Finite element analysis forstresses in the craniofacial sutures produced bymaxillary protractionforces applied at the upper canines. Br J Orthod 1994;21:343-8.

29. Ko JS, Kim JC. Effects of maxillary protraction on the displacementof the maxilla. Korean J Orthod 1995;25:543-55.

30. Yu HS, Baik HS, Sung SJ, Kim KD, Cho YS. Three-dimensionalfinite-element analysis of maxillary protraction with and withoutrapid palatal expansion. Eur J Orthod 2007;29:118-25.

31. Gautam P, Valiathan A, Adhikari R. Skeletal response to maxillaryprotraction with and without maxillary expansion: a finite elementstudy. Am J Orthod Dentofacial Orthop 2009;135:723-8.

32. Erkmen E, Simsek B, Y€ucel E, Kurt A. Three-dimensional finiteelement analysis used to compare methods of fixation aftersagittal split ramus osteotomy: setback surgery-posterior loading.Br J Oral Maxillofac Surg 2005;43:97-104.

33. Tanne K, SakudaM. Biomechanical and clinical changes of the cra-niofacial complex from orthopedic maxillary protraction. AngleOrthod 1991;61:145-52.

ics March 2012 � Vol 141 � Issue 3