Changes in Occlusal Relationships in Mixed Dentition Patients Treated with Rapid Maxillary Expansion

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1 Originl Article Chnges in Occlusl Reltionships in Mixed Dentition Ptients Treted with Rpid Mxillry Expnsion A Prospective Clinicl Study Jmes A. McNmr,Jr ; Luren M. Sigler b ; Lorenzo Frnchi c ; Susn S. Guest d ; Tizino Bccetti c ABSTRACT Objective: To prospectively mesure occlusl chnges in mixed dentition ptients who underwent stndrdized erly expnsion protocol. Mterils nd Methods: The tretment smple consisted of 500 ptients who were ssigned to three groups ccording to molr reltionship: Clss I (n 5 204), end-to-end (n 5 166), nd Clss II (n 5 130). All ptients were treted with bonded rpid mxillry expnder (RME) followed by removble mintennce plte nd trnspltl rch. Men ge t the strt of tretment ws 8.8 yers (T 1 ), with pre phse 2 tretment cephlogrm (T 2 ) tken 3.7 yers lter. The control smple consisted of the cephlometric records of 188 untreted subjects (Clss 1, n 5 79; end-toend, n 5 51; Clss II, n 5 58). Results: The lrgest chnge in molr reltionship ws noted when the Clss II tretment group (1.8 mm) ws compred with the mtched control group (0.3 mm). A positive chnge ws seen in 81% of the Clss II tretment group, with lmost hlf of the group improving by $2.0 mm. The endto-end tretment group hd positive chnge of 1.4 mm, compred with control vlue of 0.6 mm, nd the Clss I group of bout 1 mm compred with controls, who remined unchnged (0.1 mm). Skeletl chnges were not significnt when ny of the groups were compred with controls. Conclusion: The expnsion protocol hd significntly fvorble effect on the sgittl occlusl reltionships of Clss II, end-to-end, nd Clss I ptients treted in the erly mixed dentition. (Angle Orthod. 2010;80: ) KEY WORDS: Rpid mxillry expnsion; Acrylic splint expnder; Cephlometrics; Clss II mlocclusion; Trnspltl rch Thoms M. nd Doris Grber Endowed Professor of Dentistry, Deprtment of Orthodontics nd Peditric Dentistry, School of Dentistry; Professor of Cell nd Developmentl Biology, School of Medicine; nd Reserch Professor, Center for Humn Growth nd Development, The University of Michign, Ann Arbor, Mich. Privte prctice of orthodontics, Ann Arbor, Michign. b Reserch Assistnt, Deprtment of Orthodontics nd Peditric Dentistry, School of Dentistry, The University of Michign, Ann Arbor, Mich. c Assistnt Professor, Deprtment of Orthodontics, University of Florence, Florence, Itly; Thoms M. Grber Visiting Scholr, Deprtment of Orthodontics nd Peditric Dentistry, School of Dentistry, The University of Michign, Ann Arbor, Mich. d Privte Prctice, Cnton, Mich. Corresponding uthor: Dr Jmes A. McNmr, Jr, The University of Michign, Deprtment of Orthodontics nd Peditric Dentistry, 1011 North University, Ann Arbor, MI (e-mil: mcnmr@umich.edu) Accepted: June Submitted: April G 2010 by The EH Angle Eduction nd Reserch Foundtion, Inc. INTRODUCTION During the lst three decdes, rpid mxillry expnsion (RME) hs grown in populrity mong orthodontists s n importnt orthopedic djunct to fixed pplince therpy. Expnsion protocols hve been dvocted for vriety of purposes, including correction of crossbite, elimintion of dentl crowding, leveling of the curve of Wilson, fcilittion of eruption of the permnent cnines, incresing the size of the nsl irwy, nd reduction of unesthetic buccl corridors. 1 4 One pplince type tht hs been shown to provide effective orthopedic tretment in erly mixed dentition ptients is the bonded crylic splint expnder. A number of rticles hve ppered in the literture in which the crylic splint RME pplince ws used lone 4,5 or in combintion with other pplinces. 6,7 Initilly, the mjor focus of RME tretment ws relted to crossbite correction nd reduction in tooth 230 DOI: /

2 IMPROVEMENT IN MOLAR RELATIONSHIP WITH RME 231 size/rch size discrepncies nd control of the verticl dimension. 4 A most interesting observtion following initil efforts in the erly 1980s to expnd Clss II ptients in the erly mixed dentition ws the occurrence of spontneous improvement of the Clss II reltionship during the retention period. 3 The phenomenon of spontneous improvement in sgittl reltionships forced rethinking of the concept of Clss II correction. Trditionlly, clinicins hve viewed Clss II mlocclusion s primrily sgittl nd verticl problem. Tollro nd coworkers 8 hve shown tht most Clss II mlocclusions hve strong trnsverse component s well, with the mxill often 3 to 5 mm nrrower thn it idelly should be reltive to the mndible. In Clss II ptients, significnt deficiency in the dentoskeletl trnsverse width of the mxill hs been demonstrted on posteronterior films. 9 It cn be hypothesized tht the expnsion of the mxill, which subsequently is stbilized with removble pltl plte followed by trnspltl rch (TPA), induces fvorble skeletl nd dentolveolr dpttions in the sgittl dimension, s indicted in previous investigtion. 10 Bsed on yers of clinicl observtion, preliminry outcomes of the study by Wendling nd coworkers, 10 nd cse report describing the sme phenomenon by Lim nd coworkers, 11 rigorous testing of the underlying hypothesis is in order. The im of this prospective study ws to evlute the hypothesis tht expnsion of the mxill in the erly mixed dentition followed by stbiliztion of mxillry chnges leds to improvement in sgittl molr reltionships prior to comprehensive orthodontic tretment in ptients showing Clss II, or end-to-end, or Clss I mlocclusions. MATERIALS AND METHODS Dt on the tretment smple used in this study were gthered prospectively s prt of lrger smple of 1135 consecutively treted ptients who underwent stndrdized expnsion protocol in the erly mixed dentition. All ptients were treted with bonded RME followed by removble pltl plte tht ws worn full-time t lest for 1 yer, nd by the plcement of soldered trnspltl rch during the trnsition to the permnent dentition; the lower rch typiclly ws not retined. The following criteri were pplied for enrollment of subjects in this clinicl tril: N Clss I or Clss II mlocclusion N Erly mixed dentition (ll first permnent molrs erupted, s well s ll erupting upper nd lower permnent incisors) N No other orthodontic tretment provided N Absence of growth problems (crniofcil syndromes, etc) A totl of 547 ptients presented with these specific chrcteristics nd were enrolled in the tril. Two lterl hedfilms of ech ptient were tken: T 1 initil hedfilm, nd T 2 prior to phse 2 tretment. To eliminte leewy spce s fctor, the T 2 film ws tken when ll second premolrs were erupted into occlusion, fter period of pproximtely 4 yers following T 1. When the lterl cephlogrms were nlyzed t the completion of the prospective study, 47 subjects hd to be removed from the tril, becuse there hd been technicl problems with one or both films (19 subjects), problems with mndibulr posture (13 subjects), or lck of relibility in ssessing the molr reltionship (15 subjects). After these technicl dropouts, the finl smple for the treted group (TG) consisted of 500 ptients (224 mles nd 276 femles). Control subjects were chosen from the records of three lrge longitudinl dtbses on orthodonticlly untreted children: the University of Michign Growth Study, the Bolton-Brush Growth Study, nd the Denver Child Growth Study. Inclusion criteri were essentilly the sme s for the tretment group. Prticulr ttention ws pid to the stge of dentl development nd to the intervl between the two hedfilms. The control group (CG) consisted of 188 subjects (101 mles nd 87 femles). TG nd CG were well mtched ccording to the durtion of tretment or observtion (3.7 yers for TG, nd 3.9 yers for CG). The verge ge of TG t T 1 ws yers, nd for CG yers. At T 2, the verge ge of TG ws yers, nd the verge ge of CG ws yers. Cephlometric Anlysis Both lterl cephlogrms of ech ptient were hnd-trced t single sitting on mtte cette using 2H led pencil. Cephlogrms were trced by one investigtor; lndmrk loction nd ccurcy of the ntomic outlines were verified by second. Three occlusl mesurements nd four skeletl mesurements were performed: molr reltionship, overbite, nd overjet; Point A to Nsion perpendiculr (n indiction of the sgittl mxillry position reltive to the crnil bse), Pogonion to Nsion perpendiculr (sgittl position of the mndible reltive to the crnil bse), LAFH (lower nterior fcil height), nd the mndibulr plne ngle reltive to the Frnkfort plne. All mesurements were stndrdized to n enlrgement of 8%. The primry focus of the current investigtion ws to evlute chnges t the level of the nteroposterior

3 232 MCNAMARA, SIGLER, FRANCHI, GUEST, BACCETTI Figure 1. Clssifiction of sgittl molr reltionships on cephlometric trcings. Verticl lines re perpendiculr to the occlusl plne. reltionship of the mxillry nd mndibulr first permnent molrs. In those instnces in which dul imges of the molrs were observed, templte of the upper nd lower molrs ws constructed specificlly for tht subject bsed on the more posterior teeth (including the second molrs if present). The templte then ws positioned midwy between the mndibulr first molrs, so tht the loction of the mesil contct point of the lower first molrs could be determined. The process subsequently ws repeted for the mxillry first molrs. Becuse of the criticl nture of the molr reltionship mesurement, the molr reltionship of the entire smple ws mesured independently by two pirs of investigtors (four investigtors in ll). The verge difference between the two sets of mesurements ws,0.1 mm for the entire smple. The method error for the other occlusl mesures s evluted by mens of Dhlberg s formul 12 ws smller thn 0.5 mm; it ws smller thn 1 degree or 1 mm for the cephlometric vribles. Sttisticl Anlysis On the bsis of vlues for the molr reltionships t T 1 (Figure 1), the totl treted smple ws divided into three groups: Clss II group (130 subjects; molr reltion.0.5 mm), end-to-end group (166 subjects; molr reltion $20.5 mm nd #0.5 mm), nd Clss I group (204 subjects; molr reltion,20.5 mm). According to the sme ctegoriztion, control subjects were ssigned to three groups: Clss II group (58 subjects), end-to-end subjects (51 subjects), nd Clss I group (79 subjects). Descriptive sttistics, including mens nd stndrd devitions, were clculted for the vlues t T 1, s well s for the chnges between T 1 nd T 2 of the seven cephlometric mesures for the three treted groups nd the three control groups. Dt were nlyzed with sttisticl softwre pckge (Sttisticl Pckge for the Socil Sciences [SPSS], version 16.0; SPSS Inc, Chicgo, Ill). Sttisticl significnce ws tested t P,.05, P,.01, nd P,.001. Following ssessment of the norml distribution of the dt (Shpiro-Wilks test), independent smple Student s t-tests were used to exmine between-group differences in mens of the cephlometric mesures of the strting forms for ll groups. Comprison of T 2 T 1 chnges over time between treted nd untreted groups ws ccomplished by wy of independent smple Student s t-tests. Z-tests on proportions were used to nlyze sttisticlly the proportions of ptients vs untreted controls who presented with improvement in the molr reltionship during the T 1 to T 2 intervl in ech of the three groups, ccording to initil molr reltion. Given the smple sizes of ll tretment nd control groups nd subgroups nd P vlue of.05, the power of this study ws 100%. RESULTS Descriptive dt nd sttisticl comprisons for strting forms nd cephlometric chnges for ll groups from T 1 to T 2 re given in Tbles 1 through 6. Anlysis of Strting Forms Occlusl reltionships. The verge differences in molr reltionships between treted nd control Clss II, end-to-end, nd Clss I groups were within 0.1 mm in ll instnces (Tbles 1 through 3). No differences in initil overbite or overjet were observed between groups, with the exception of slightly deeper overbite (3.4 mm) in the end-to-end CG thn in the corresponding TG (2.6 mm; P,.05; Tble 2). Skeletl reltionships. When skeletl reltionships of the three subgroups were evluted, only minor differences were noted in strting forms. Although no difference in LAFH ws seen between Clss I groups, the mndibulr plne ngle ws 26.7 degrees in the tretment group nd 25.1 degrees in the control group (P,.05; Tble 3). LAFH ws longer (61.6 mm) in the end-to-end TG thn in corresponding controls (60.0 mm; P,.05; Tble 2). A similr difference in LAFH ws noted between the Clss II groups (P,.01; Tble 1).

4 IMPROVEMENT IN MOLAR RELATIONSHIP WITH RME 233 Tble 1. Comprison of Strting Forms Clss II Smple Cephlometric Mesures Clss II RME (n 5 130) Clss II CG (n 5 58) Clss II RME vs Clss II CG Men SD Men SD Men Difference P Vlue Occlusl 6/6, mm NS OJ, mm NS OB, mm NS Skeletl Pt A-N perp, mm NS Pg-N perp, mm NS Mndibulr plne, degrees NS LAFH, mm * Independent smple Student s t-test. NS indictes not significnt. * P,.01. Tble 2. Comprison of Strting Forms End-to-End Smple Cephlometric Mesures End-to-End RME (n 5 166) End-to-End CG (n 5 51) End-to-End RME vs End-to-End CG Men SD Men SD Men Difference P Vlue Occlusl 6/6, mm NS OJ, mm NS OB, mm * Skeletl Pt A-N perp, mm NS Pg-N perp, mm NS Mndibulr plne, degrees NS LAFH, mm * Independent smple Student s t-test. NS indictes not significnt. * P,.05. Anlysis of Tretment Effects Occlusl reltionships. Chnges for the overjet nd the overbite showed no significnt differences in ny of the comprisons between tretment groups nd controls. The only exception ws significntly greter increse in overbite in end-to-end TG when compred with the corresponding CG (Tble 5), which, however, compensted for the significnt difference in overbite in the strting forms (Tble 2). In the nlysis of the dt regrding molr reltions (Figures 2 through 5), the distribution of the chnges Tble 3. Comprison of Strting Forms Clss I Smple Cephlometric Mesures Clss I RME (n 5 204) Clss I CG (n 5 79) Clss I RME vs Clss I CG Men SD Men SD Men Difference P Vlue Occlusl 6/6, mm NS OJ, mm NS OB, mm NS Skeletl Pt A-N perp, mm NS Pg-N perp, mm NS Mndibulr plne, degrees * LAFH, mm NS Independent smple Student s t-test. NS indictes not significnt. * P,.05.

5 234 MCNAMARA, SIGLER, FRANCHI, GUEST, BACCETTI Tble 4. Comprison of Chnge During Time of Observtion Clss II Smple Cephlometric Mesures Clss II RME (n 5 130) Clss II CG (n 5 58) Clss II RME vs Clss II CG Men SD Men SD Men Difference P Vlue Occlusl 6/6, mm * OJ, mm NS OB, mm NS Skeletl Pt A-N perp, mm NS Pg-N perp, mm NS Mndibulr plne, degrees NS LAFH, mm ** Independent smple Student s t-test. NS indictes not significnt. * P,.001; ** P,.05. Tble 5. Comprison of Chnge During Time of Observtion End-to-End Smple Cephlometric Mesures End-to-End RME (n 5 166) End-to-End CG (n 5 51) End-to-End RME vs End-to-End CG Men SD Men SD Men Difference P Vlue Occlusl 6/6, mm * OJ, mm NS OB, mm ** Skeletl Pt A-N perp, mm NS Pg-N perp, mm NS Mndibulr plne, degrees NS LAFH, mm *** Independent smple Student s t-test. NS indictes not significnt. * P,.001; ** P,.01; *** P,.05. (ie, negtive, neutrl, positive) ws considered, s ws the evlution of verge vlues: N A negtive chnge ws defined s chnge in molr reltionship greter thn 1 mm towrd Clss II (,21.0 mm) between the first nd second films. N No chnge (neutrl) is movement of 21.0 mm to 1.0 mm ($21.0 mm nd #1.0 mm), regrdless of the direction of chnge. N A positive chnge is shift greter thn 1 mm (.1.0 mm nd,2.0 mm) towrd Clss I. An extremely positive chnge is shift of 2 mm or greter ($2.0 mm) towrd Clss I. Clss II Groups (Figure 2) The lrgest chnge ws noted in the Clss II tretment group (n verge positive chnge of Tble 6. Comprison of Chnge During Time of Observtion Clss I Smple Cephlometric Mesures Clss I RME (n 5 204) Clss I CG (n 5 79) Clss I RME vs Clss I CG Men SD Men SD Men Difference P Vlue Occlusl 6/6, mm * OJ, mm NS OB, mm NS Skeletl Pt A-N perp, mm ** Pg-N perp, mm NS Mndibulr plne, degrees NS LAFH, mm NS Independent smple Student s t-test. NS indictes not significnt. * P,.001; ** P,.01.

6 IMPROVEMENT IN MOLAR RELATIONSHIP WITH RME 235 Figure 2. Chnge in molr reltionship: Clss II groups. 1.8 mm vs 0.3 mm for the untreted Clss II group), with n verge 1.5 mm difference tht ws sttisticlly significnt (P,.001; Tble 4). This difference ws chrcterized by significnt effect size. 13 The effect size ws lrger thn 1, which mens tht the verge effect ws greter thn the interindividul vribility expressed by the verge stndrd devition. Fourteen percent of the controls presented with negtive chnge; 60% of the untreted Clss II smple hd no chnge in molr reltionship from T 1 to T 2, wheres 26% hd positive chnge. On the other hnd, only 2% nd 17% of the Clss II tretment group hd negtive chnge or remined unchnged, respectively; 81% hd positive chnge towrd Clss I. The sttisticl comprison between the proportion of ptients who presented with n improvement in the molr reltion in treted nd untreted smples ws significnt (Z ; P,.001; Figure 5). Almost hlf of the treted smple presented with n extremely positive chnge in molr reltionship ($2 mm); in contrst, only 5% of the untreted Clss II smple presented with n extreme improvement. End-to-End Group (Figure 3) The end-to-end tretment group hd n overll positive chnge of 1.4 mm in comprison with the control group (0.6 mm), for net difference of 0.8 mm (P,.001; Tble 5). Sixty-nine percent of the treted group hd positive chnge, with 23% showing extreme improvement; 30% remined unchnged. In the end-to-end control group, 29% demonstrted positive chnge, wheres 63% hd no chnge in molr reltionship. The difference in the proportion of subjects showing n improvement in molr reltionship ws significnt (Z ; P,.001; Figure 5). Eight percent of the end-to-end control group hd negtive chnge between T 1 nd T 2, nd only 1% of the tretment group hd negtive chnge. Clss I Group (Figure 4) The smllest chnge ws noted in the Clss I group, with virtully no chnge noted in the control group (0.1 mm); the Clss I tretment group demonstrted positive chnge of 1.1 mm, with net verge difference between treted nd untreted subjects of

7 236 MCNAMARA, SIGLER, FRANCHI, GUEST, BACCETTI Figure 3. Chnge in molr reltionship: end-to-end groups. 1mm (P,.001; Tble 6). Nineteen percent of the untreted Clss I smple showed improvement (only 1% improved by 2 mm or more), nd 67% remined unchnged. For the Clss I treted smple, 58% improved (29% improved by $2 mm) nd 34% remined unchnged. Differences in the proportions of subjects showing positive chnge were significnt once gin (Z ; P,.001; Figure 5). It is interesting to note tht the molr reltionship of 14% of the Clss I control group nd 8% of the Clss I tretment group presented with negtive chnges during the tretment or observtion intervl. Skeletl Reltionships Across groups, no chnges were noted in the sgittl reltionships of the mxill (Tbles 4 through 6), with the exception of Point A to the Nsion perpendiculr, which showed greter increse in Clss I controls. Increses in lower nterior fcil height were significntly smller in the Clss II (3.4 mm; Tble 4) nd end-to-end (3.2 mm; Tble 5) tretment groups thn in their respective control groups (4.2 mm in both groups; Tbles 4 nd 5). Although sttisticlly significnt, these sgittl nd verticl differences cn be regrded s cliniclly insignificnt (within 1 mm). No differences were noted in the mndibulr plne ngle (Tbles 4 through 6). DISCUSSION This prospective clinicl study evluted lrge number of ptients who underwent stndrdized expnsion protocol tht included bonded crylic splint RME pplince nd trnspltl rch t the end of the trnsition to the permnent dentition. The results of this investigtion, which included comprison of substntil number of ptients (n 5 500) vs lrge group of untreted control subjects (n 5 188), indicted tht the tretment protocol used induced positive chnges in molr reltionship in most ptients (Clss III mlocclusion ws not included in this study). Of prticulr interest were the occlusl chnges noted in Clss II nd end-to end ptients, in whom

8 IMPROVEMENT IN MOLAR RELATIONSHIP WITH RME 237 Figure 4. Chnge in molr reltionship: Clss I groups. Figure 5. Prevlence rtes for positive chnge in molr reltionships in TG vs CG subgroups within ech mlocclusion group.

9 238 MCNAMARA, SIGLER, FRANCHI, GUEST, BACCETTI positive chnge towrd norml occlusion is desirble. In 81% of Clss II ptients nd 69% of end-to-end ptients, significnt positive chnge ws noted, with chnge of 2 mm or greter observed in 49% nd 23% of Clss II nd end-to-end ptients, respectively. It should be remembered tht Clss II molr correction or improvement ws not the primry intent of the expnsion protocol; rther it my be considered fvorble side effect of expnsion therpy followed by spce mintennce regimen. The primry focus of this lrge-scle investigtion hs been evlution of chnges in sgittl occlusl reltionships, with molr reltionship, overjet, nd overbite mesured. Only four skeletl mesures were considered, nd they did not show ny consistent trend in treted ptients vs controls. These outcomes re in greement with previous long-term longitudinl dt on subjects treted with RME in the lte mixed dentition followed by fixed pplince therpy. 14 Additionl studies re wrrnted to elucidte individul vritions in mxillomndibulr skeletl response to the expnsion protocol, especilly with regrd to the possibility of forwrd positioning of the mndible in the postexpnsion period, s suggested in previous study. 10 The significnt prevlence of improvement in molr reltionship following RME tretment ppers to be cliniclly beneficil in subjects showing mild to moderte Clss II mlocclusion in the mixed dentition. The possible role of the trnspltl rch in voiding the physiologic mesil drift of mxillry molrs during the trnsitionl phse of occlusion deserves to be considered. The TPA hs been shown to lck significnt effect in improving nchorge in extrction cses, 15 lthough it my be effective s spce mintennce device to ssist the improvement in molr reltionships induced by the RME protocol. CONCLUSIONS N The expnsion protocol evluted in mixed dentition ptients, which included the use of bonded crylic splint expnder nd trnspltl rch just prior to phse 2 tretment, results in n improvement in sgittl reltionships in Clss II, end-to-end, nd Clss I ptients in comprison with their mtched control groups. N Positive chnges were observed in 81% of Clss II ptients, 69% of end-to-end ptients, nd 58% of Clss I ptients. N Forty-nine percent of Clss II ptients, 29% of endto-end ptients, nd 23% of Clss I ptients demonstrted n improvement in sgittl molr reltionships of 2 mm or greter. Less thn 5% of corresponding control groups hd positive chnges of 2 mm or greter. REFERENCES 1. Hs AJ. Pltl expnsion: just the beginning of dentofcil orthopedics. Am J Orthod. 1970;57: Wertz RA. Chnges in nsl irflow incident to rpid mxillry expnsion. Angle Orthod. 1968;38: McNmr JA Jr. Mxillry trnsverse deficiency. Am J Orthod Dentofc Orthop. 2000;117: McNmr JA Jr, Brudon WL. Orthodontics nd Dentofcil Orthopedics. Ann Arbor, Mich: Needhm Press; Srver DM, Johnston MW. Skeletl chnges in verticl nd nterior displcement of the mxill with bonded rpid pltl expnsion pplinces. Am J Orthod Dentofc Orthop. 1989;95: McNmr JA Jr. An orthopedic pproch to the tretment of Clss III mlocclusion in young ptients. J Clin Orthod. 1987;21: McNmr JA Jr, Howe RP. Clinicl mngement of the crylic splint Herbst pplince. Am J Orthod Dentofc Orthop. 1988;94: Tollro I, Bccetti T, Frnchi L, Tnsescu CD. Role of posterior trnsverse interrch discrepncy in Clss II, Division 1 mlocclusion during the mixed dentition phse. Am J Orthod Dentofc Orthop. 1996;110: Frnchi L, Bccetti T. Trnsverse mxillry deficiency in Clss II nd Clss III mlocclusions: cephlometric nd morphometric study on postero-nterior films. Orthod Crniofc Res. 2005;8: Wendling LK, McNmr JA Jr, Frnchi L, Bccetti T. Shortterm skeletl nd dentl effects of the crylic splint rpid mxillry expnsion pplince. Angle Orthod. 2005;75: Lim RM, Lim AC, de Olivers Ruells AC. Spontneous correction of Clss II mlocclusion fter rpid pltl expnsion. Angle Orthod. 2003;73: Dhlberg G. Sttisticl Methods for Medicl nd Biologicl Students. New York: Interscience Publictions; Cohen J. Sttisticl Power Anlysis for the Behviorl Sciences, 2nd ed. Hillsdle, NJ: Lwrence Erlbum; Chng JY, McNmr JA Jr, Herberger TA. A longitudinl study of skeletl side effects induced by rpid mxillry expnsion. Am J Orthod Dentofc Orthop. 1997;112: Zblocki HL, McNmr JA Jr, Frnchi L, Bccetti T. Effect of the trnspltl rch during extrction tretment. Am J Orthod Dentofc Orthop. 2008;133: