Dental Arch Dimensions in Class II division 1 Malocclusions with Mandibular Deficiency

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1 Originl Article Dentl Arch Dimensions in Clss II division 1 Mlocclusions with Mndibulr Deficiency Omr Gbriel d Silv Filho ; Flávio Muro Ferrri Júnior b ; Terumi Okd Ozw c ABSTRACT Objective: To test the hypothesis tht there is no difference in the dimensions of the upper nd lower dentl rches in Clss II division 1 mlocclusion with mndibulr deficiency compred to norml Clss I occlusion dentl rches. Mterils nd Methods: Photocopies of the dentl rches of 48 ptients exhibiting Clss II division 1 mlocclusion with mndibulr deficiency nd of 51 individuls with norml occlusion were compred. Mndibulr deficiency ws dignosed cliniclly. All 99 individuls were in the permnent dentition. The ges of the subjects rnged from 11 yers 4 months to 20 yers (men ge 12 yers 5 months). Results: When compred to subjects with norml occlusion, the upper dentl rches of the Clss II division 1 ptients presented reduced trnsverse dimensions nd longer sgittl dimensions while the lower rches were less influenced. Conclusion: The hypothesis is rejected. Significnt differences re present between the dimensions of the upper nd lower dentl rches in Clss II division 1 mlocclusion (with mndibulr deficiency nd in the permnent dentition) compred to norml Clss I occlusion dentl rches. KEY WORDS: Mlocclusion; Angle Clss II; Dentl rch INTRODUCTION The rel prevlence of Clss II mlocclusion is difficult to determine becuse of different methods used in studies nd ethnic chrcteristics of the smples. Studies show tht the prevlence of Clss II division 1 nd division 2 mlocclusions vries from 8.6% 1 to 33.7% 2 nd from 0.6% 1 to 6.7%, 3 respectively. An ccurte occlusl nlysis performed in Brzil showed tht Clss II constitutes lmost 50% of the mlocclusions in the deciduous 4 nd mixed 5 dentitions. Clss II mlocclusion cn be constituted by upper dentl proclintion, mndibulr deficiency, or both. A study relting Clss II mlocclusion to fcil nlysis Orthodontist, Hospitl for Rehbilittion of Crniofcil Anomlies, University of São Pulo, Buru, Brzil. b Associte Professor, PROFIS Interceptive Orthodontics Course, Buru, Brzil. c Orthodontist, Hospitl for Rehbilittion of Crniofcil Anomlies, University of São Pulo, Buru, Brzil. Corresponding uthor: Dr Omr Gbriel d Silv Filho, Setor de Ortodonti HRAC/USP, Silvio Mrchione, 3-20 Vl. Universitári, Buru/SP, Brzil (e-mil: ortofce@trvelnet.com.br) Accepted: July Submitted: Februry by The EH Angle Eduction nd Reserch Foundtion, Inc. showed tht bout 15% of the students with mixed dentition in Buru, Brzil, present with mndibulr deficiency, of which 11.5% re division 1 nd 3.5% re division 2. 5 Therefore, Clss II mlocclusion is frequent type of mlocclusion nd my be ssocited with skeletl ptterns I nd II. Figure 1 shows skeletl Clss II mlocclusion with mndibulr deficiency. Prior to the use of cephlometrics in orthodontics, mndibulr deficiency hd lredy been considered prt of the Clss II discrepncy. Cephlometrics confirmed this ide As consequence, functionl orthopedics nd orthognthic surgery gined importnce in the tretment of mndibulr retropositioning. However, mndibulr dvncement shows the posterior crossbite tht frequently ppers due to the constriction of the upper dentl rch in Clss II mlocclusions tht is ssocited with mndibulr deficiency (Figure 2). Some chnges cn be identified in the shpe of the dentl rches to differentite the Clss II mlocclusion. Studies tht refer to the morphology of the upper nd lower dentl rches in Clss II re shown in Tble 1. It is suggested tht the upper dentl rch is vulnerble to Clss II discrepncy. The constriction of the upper rch my be interpreted s trnsverse compenstion to mndibulr retropositioning. Such constriction re- 466 DOI: /

2 DENTAL ARCH DIMENSIONS IN CLASS II 467 Figure 1. Orthodontic dignosis is bsed on fcil (1A), rdiogrphic (1B), nd occlusl (1C to 1K) nlyses. Ptient hs Clss II division 1 mlocclusion with mndibulr deficiency. quires tht the trnsverse dimensions of the upper dentl rch re incresed during Clss II tretment 8,15,16 whenever mndibulr dvncement is plnned. Involvement of the upper dentl rch in Clss II mlocclusions hs been shown from the time of the deciduous dentition 8,15 18 or from 7 yers of ge, 18,19 nd it does not self-correct until the individul reches mixed 8,16 or permnent 15,18 dentition. Studies of permnent dentition demonstrte the influence of the sgittl discrepncy on the intr-rch reltionship. Buschng et l 20 found tht the upper dentl rch is nrrower nd longer in women with Clss II division 1 who re between 17 nd 68 yers old. Syin nd Turkkhrmn 21 found constriction in only the inter upper second premolr nd inter upper molr widths nd n increse in the inter lower cnine width in Clss II division 1 women in the permnent dentition t n verge ge of 16 yers. Stley et l 22 noticed constriction of the upper dentl rch in the intercnine nd intermolr distnces in Clss II mlocclusions, without ny dimensionl chnge in the lower dentl rch widths in young dults. Uysl et l 23 found constriction in the trnsverse dimensions of the upper dentl rch nd in the widths of the inter lower premolrs nd inter lower molrs of young dults with Clss II division 1. Studies lso show tht the lower dentl rch is more vulnerble to Clss II division 2. When Uysl et l 23 compred Clss II division 1 nd 2 mlocclusions, they found tht the inter-lower cnine nd inter-lower premolr widths were nrrower while the inter-upper molr widths were wider in the division 2 in comprison to division 1. Buschng et l 20 found reduced interlower cnine nd inter-lower molr distnces in the Clss II division 2 relted to division 1 nd to Clss I. Wlkow nd Peck 24 found nrrower inter-lower cnine distnces in the Clss II division 2 mlocclusions with deep overbite when relted to division 1.

3 468 DA SILVA, FERRARI, OZAWA Figure 2. Dentl cst models representing Clss II division 1 (A E). Simultion of the mlocclusion correction (F H) with mndibulr dvncement shows the posterior crossbite tht ppers due to the mxillry trnsverse deficiency. Stley et l 22 suggested tht the reduced trnsverse dimension of the upper dentl rch in Clss II division 1 constriction is due to the picl bses, similr to the dt found by Alrshi et l 19 nd de Lux et l 18 in nteroposterior rdiogrphs. Contrrily, Syin nd Turkkhrmn 21 stted tht the upper constriction is due to dentl positioning only, s they found no difference in the lveolr widths between women with Clss I nd Clss II mlocclusions. The current study tests the hypothesis tht there is no difference in the dimensions of the permnent dentition of upper nd lower dentl rches in Clss II division 1 mlocclusion with mndibulr deficiency compred to norml Clss I occlusion dentl rches. MATERIALS AND METHODS Before onset, this retrospective study ws revised nd pproved by the Institutionl Review Bord of the Hospitl for Rehbilittion of Crniofcil Anomlies (HRCA), University of São Pulo, Buru, Brzil. All ptients were consecutively selected from n orthodontic rchive tht belongs to our hospitl (HRCA). The experimentl group ws composed of models of the upper nd lower dentl rches of 48 ptients exhibiting Clss II division 1 mlocclusion with mndibulr deficiency, eqully mtched for gender nd rnging in ge from 11 yers 4 months to 18 yers 4 months. All subjects in this group were Cucsins in permnent dentition, with the second molrs either erupted or erupting, nd the ptients demonstrted untreted Clss II division 1 mlocclusions with symmetric sgittl discrepncy of t lest 4 mm in the premolr reltionship. The selection of individuls ws clinicl nd bsed on soft-tissue profile nlysis, with specil ttention to the nsolbil ngle, which indictes prticiption of the mxill in the mlocclusion. All ptients of the smple presented stisfctory nsolbil ngle, showing tht the Clss II mlocclusion

4 DENTAL ARCH DIMENSIONS IN CLASS II 469 Tble 1. Author Studies Relting the Dentl Arch Behvior to Clss II Mlocclusion Yer Clss II Smple Age Bccetti et y 8 mo nd 8 y 1 l 8 mo (longitudinl Bishr et l Stge 1: 5.1 M, 5 F Stge 2: 8.2 M, 8.5 F Stge 3: 12.7 M, 12.8 F (longitudinl n 25 (13 M, 12 F) 37 (15 M, 22 F) Control Smple Age n Origin Mesurements 5 y 5 mo nd 7 y 8 mo (longitudinl Stge 1: 4.9 M, 5 F Stge 2: 7.8 M, 8.1 F Stge 3: 13 M, 13.1 F (longitudinl 22 (9 M, 13 F) University of Michign/ University of Florence 55 (28 M, 27 F) University of Iow lower dentl Sgittl nd trnsverse lower dentl Buschng et l Between 17 nd 25 y 145 F Between 17 nd 25 y 241 F Sgittl, trnsverse, nd condition of the incisors Between 25 nd 35 y 121 Cl II/2 Between 25 nd 35 y More thn 35 y 24 Cl II/1 More thn 35 y Lux et l 18b 2003 From 7 to 15 y (longitudinl Syin nd Turkkhrmn 21 Cl II/1: 17 (8 M, 9 F) Cl II/2: 12 (8 M, 4 F) From 7 to 15 y (longitudinl CL I: 37 (19 M, 18 F) Norml occlusion: 18 (10 M, 8 F) Belfst Growth Study y 30 F y 30 F University of Suleymn Demirel, Turkey Stley et y M, 18 yers F 39 (20 M l 22 nd 19 F) Uysl et l y (Cl II/1) 18.5 y (Cl II/2) Cl I/1: 106 (45 M, 61 F) Cl II/2: 108 (45 M, 63 F) Wlkow nd y 23 Cl II/2 Peck 24 (20 M, 3 F) Most studies were mde on the bsis of cst models. b The method included nteroposterior rdiogrphs y M, 16 y F 36 (19 M, 17 F) 21.6 y 150 (72 M, 78 F) 12.4 y 46 (pired with Cl II/2 group) University of Iow University of Selcuk, Turkey Hrvrd University lower dentl lower dentl lower dentl lower dentl ws due to mndibulr deficiency. To stndrdize the smple, ptients with protrusive mxills (ie, obtuse nsolbil ngle) were not included. Figures 1 nd 2 illustrte the chrcteristics of the Clss II smple. The control group ws composed of cst models of the upper nd lower rches of 29 femles nd 22 mles (n 51) with norml occlusion nd hrmonious fces rnging in ge from 11 to 20 yers. The men ge for the experimentl nd control groups ws 12 yers 5 months ( 1 yer 3 months). All cst models were selected from the rchive of the HRCA. The control norml occlusion ptients were selected from the norml occlusion rchive of the HRCA. The trnsverse nd sgittl dimensions of the dentl rches were mesured on photocopies of the upper nd lower cst models of the experimentl nd control groups. All dentl csts were plced on the centrl prt of the glss surfce of photocopy mchine (PRO 40; Xerox, Hertfordshire, UK) with the occlusl spects of the teeth fcing the glss. Photocopies of the models were obtined in stndrdized mnner. Cre ws tken to mintin the occlusl plne of the models prllel to the glss copying surfce. Previous studies hve shown no distortion in imges obtined from photocopies. 16,25,26 The imges of the models were mesured with digitl cliper. The trnsverse distnces of the cnines were mesured between their cusp tips. The premolr widths were mesured between their buccl cusps. The molr widths were mesured between the mesiobuccl cusps of the first molrs. The sgittl dimension of the models ws determined by the distnce from the midpoint of the centrl incisors to the midpoint of

5 470 DA SILVA, FERRARI, OZAWA ws close to 0.5 mm, which gives high relibility to the mesurements obtined in this study. Descriptive sttistics were illustrted by mens of tbles nd grphs. A Student s t-test ws used to check whether gender nd mlocclusion influenced the dimensions of the dentl rches. Significnce levels were 5% (P.05) nd 1% (P.01). Figure 3. Assessment of the dimensions of the upper nd lower rches obtined from the mesurement of the intercnines (3-3), inter first premolrs (4-4), inter second premolrs (5-5), inter first molrs (6-6), nd sgittl dimensions. line tngent to the distl spect of the first molrs (Figure 3). Mens nd stndrd devitions were obtined for the trnsverse (3-3, 4-4, 5-5, 6-6) nd sgittl dimensions for the upper nd lower dentl rches in both groups. The mesurements were repeted by two exminers in some pirs of rndomly selected models within 1 week. In ll mesurements, the error of the method RESULTS Mens nd stndrd devitions were obtined for the trnsverse nd sgittl mesurements of the upper nd lower dentl rches of the smple groups, seprted by gender. A Student s t-test ws pplied to verify sexul dimorphism. Sttisticl vlues re expressed in Tbles 2 nd 3. Tble 2 shows tht ll dimensions of the upper nd lower dentl rches with norml occlusion presented higher vlues for mles, bout 2.25 mm for the upper rch nd 1.6 mm for the lower rch. Tble 3 shows the results for the study group nd demonstrtes tht the widths of the inter upper first premolrs, inter upper molrs, inter lower cnines, inter lower first premolrs, nd inter lower second premolrs showed sttisticlly significnt differences relted to gender. Figures 4 nd 5 depict the mesurements shown in Tbles 2 nd 3 for the upper nd lower dentl rches, respectively. Tbles 4 nd 5 show the differences in the Clss II nd norml occlusion groups. The mesurements of the upper (Tble 4) nd lower (Tble 5) dentl rches were compred seprtely for the groups with norml occlusion nd Clss II division 1. Except for the intercnine distnce in the femles, ll mesurements of the upper dentl rch in ptients with Clss II were different from those of subjects with norml occlusion. Tble 6 presents the differences in the sgittl nd trnsverse dimensions of the upper rch with Clss II when compred to the norml occlusion group, while Tble 7 shows tht the verge difference between the dentl rch widths in the norml occlusion group grdully decreses from 8.7 mm in the cnine re to 6.7 mm in the molr re. This difference is clerly Tble 2. Mens (), Stndrd Devitions (), nd Student s t-test for the nd Sgittl Dimensions of the Upper nd Lower Dentl Arches in the Norml Occlusion Group, According to Sex Dimension Mle (n 22) Upper Dentl Arch Femle (n 29) Mle (n 22) Lower Dentl Arch Femle (n 29) Anteroposterior ** ** Intercnines ** ** Inter first premolrs ** ** Inter second premolrs ** ** Inter first molrs * * * Significnt t 5%. ** Significnt t 1%.

6 DENTAL ARCH DIMENSIONS IN CLASS II 471 Tble 3. Mens (), Stndrd Devitions (), nd Student s t-test for the nd Sgittl Dimensions of the Upper nd Lower Dentl Arches in the Clss II Group, According to Sex Dimension Mle (n 24) Upper Dentl Arch Femle (n 24) Mle (n 24) Lower Dentl Arch Femle (n 24) Anteroposterior NS NS Intercnines NS * Inter first premolrs ** * Inter second premolrs NS * Inter first molrs ** NS DP indictes ; NS, nonsignificnt. * Significnt t 5%. ** Significnt t 1%. Figure 4. Sgittl nd trnsverse dimensions of the upper rch in norml nd Clss II division 1 mles nd femles. smller in the Clss II group (Tble 8), decresing from 6.8 mm to 4.2 mm. DISCUSSION This study imed to determine the influence tht the Clss II mlocclusion with mndibulr deficiency hs on the dimensions of the dentl rches. Studies rrely include Clss II ptients with mndibulr retropositioning; thus, we decided to stndrdize our smple on the bsis of mndibulr deficiency. All 99 cst models nlyzed represented the occlusion of subjects with Figure 5. Sgittl nd trnsverse dimensions of the lower rch in norml nd Clss II division 1 mles nd femles. permnent dentition. Forty-eight subjects exhibited untreted Clss II division 1, while 51 showed norml occlusion. The smple included ptients in permnent dentition becuse the sgittl nd trnsverse dimensions of the dentl rches t this time re prcticlly defined nd becuse this is the ge when most ptients seek orthodontic tretment. Longitudinl studies suggest tht the dimensions of the dentl rches tend to stbilize fter 13 yers of ge in girls nd 16 yers in boys, 9,27 30 lthough the dimensionl chnges tht Tble 4. Sttisticl Comprison (Student s t-test) for the nd Sgittl Dimensions of the Upper Dentl Arch Between Norml nd Clss II Groups for Mles nd Femles Dimension Norml (n 22) Mles Clss II (n 24) Norml (n 29) Femles Clss II (n 24) Anteroposterior ** ** Intercnines * NS Inter first premolrs ** ** Inter second premolrs ** ** Inter first molrs ** ** NS indictes nonsignificnt. * Significnt t 5%. ** Significnt t 1%.

7 472 DA SILVA, FERRARI, OZAWA influence the intr-rch dentl positioning re unpredictble nd my occur nytime in norml occlusions. 31 The results in Tble 2 show higher vlues for mles nd re consistent with prior studies tht ssessed dentl rch dimensions However, in our study, the Clss II group did not show the sme differences (Tble 3). Only the widths of the inter upper first premolrs, inter upper molrs, inter lower cnines, inter lower first premolrs, nd inter lower second premolrs showed sttisticlly significnt differences relted to gender. Clss II mlocclusion seems to minimize the influence of gender on the dimensions of the lower nd, minly, upper dentl rch. Therefore, sexul dimorphism influenced ll sgittl nd trnsverse dimensions of the dentl rches in individuls with norml occlusion nd some trnsverse dimensions in Clss II individuls. Becuse mny dimensions were influenced by gender, the norml occlusion nd the Clss II groups were compred ccording to gender. This comprison is shown in Tbles 4 nd 5. Clss II mlocclusions seem to induce chnges in the dimensions nd, consequently, the upper dentl rch shpe. With regrd to the sgittl dimensions, the findings show sttisticlly significnt differences between the norml nd Clss II groups. Subjects with Clss II mlocclusion presented with longer upper dentl rches, most likely due to the proclintion of the upper incisors. The upper dentl rch in the Clss II subjects presented with lesser trnsverse dimensions (Tble 4) nd typicl tringulr shpe (Figures 1 nd 2). A sttisticlly significnt difference ws noticed in ll mesurements except in the upper intercnine distnce in femles. Tble 6 shows the sgittl nd trnsverse differences between both groups, which indicte the verge mount of expnsion needed in the upper rch to trnsversely fit it to the dvnced mndible in Clss I ptients. Therefore, constriction of the upper dentl rch is not generlly ccompnied by posterior crossbite in the Clss II division 1 ptients. It hs been suggested tht constriction of the upper rch in the Clss II ptients is due to constriction of the nsomxilry complex, identified in posteronterior rdiogrphs. 19,25 Frontl cephlogrms show ltertions in the upper dentl rch with no trnsverse chnges in the mndible nd lower dentl rch. 19,25 Similr to other reserchers (Tble 1), Fröhlich 32 studied longitudinl smple of 51 children ged 6 to 12 yers nd noticed tht the sgittl discrepncy remined during the follow-up period, with n increse of the overjet nd overbite fter eruption of the permnent incisors. However, no difference ws found in the dimensions of the dentl rches with Clss II. Such contrdiction is probbly explined becuse the Clss II divisions 1 nd 2 subjects were gthered together in tht smple. The current reserch does not confirm Fröhlich s 32 results. On the contrry, our results gree with severl other studies tht hve shown chnges in the shpes of dentl rches with Clss II mlocclusion. 19,21 23,27 Despite other fctors relted to the upper rch constriction, such s orl brething, prolonged sucking hbits, nd indequte positioning nd function of the tongue, the trnsverse dpttion of the upper rch to the lower rch my not be neglected. Such dpttion hppens nturlly s trnsverse compenstion of the upper rch to the retropositioning of the lower rch nd is typicl of Clss II division 1 mlocclusions. Therefore, dentl compenstion in Clss II is neither restricted to the sgittl dimensions nor to the incisors. An ccurte orthodontic tridimensionl morphologic evlution (Figures 1 nd 2) would provide complete nd correct interprettion of the sgittl, trnsverse, nd verticl ltertions found in Clss II mlocclusions. The current study focuses on the trnsverse chnges nd corrobortes the need for expnding the upper rch prior to mndibulr dvncement. The clinicl confirmtion of the upper rch constriction is evidenced by the posterior crossbite tht results when the Tble 5. Sttisticl Comprison (Student s t-test) for the nd Sgittl Dimensions of the Lower Dentl Arch Between Norml nd Clss II Groups for Mles nd Femles Dimension Norml (n 22) Mles Clss II (n 24) Norml (n 29) Femles Clss II (n 24) Anteroposterior NS ** Intercnines NS NS Inter first premolrs NS NS Inter second premolrs NS * Inter first molrs * * NS indictes nonsignificnt. * Significnt t 5%. ** Significnt t 1%.

8 DENTAL ARCH DIMENSIONS IN CLASS II Tble 6. Differences in the nd Sgittl Dimensions of the Upper Dentl Arch Between Norml nd Clss II Groups (mm) Anteroposterior Intercnines Inter First Premolrs Inter Second Premolrs Inter First Molrs Mles Femles Men The numbers represent the error in the upper dentl rch in Clss II mlocclusion. Tble 7. Differences Between the Dimensions of the Upper nd Lower Dentl Arches in the Norml Occlusion Smple (mm) Mles Femles Men Anteroposterior Intercnines Inter first premolrs Inter second premolrs Inter first molrs Tble 8. Differences Between the Dimensions of the Upper nd Lower Dentl Arches in the Clss II Smple (mm) Mles Femles Men Anteroposterior Intercnines Inter first premolrs Inter second premolrs Inter first molrs mndible is dvnced nd implies the chievement of well-blnced finl lterl reltionship between the upper nd lower rches following mndibulr dvncement. The lower dentl rch in Clss II mlocclusion (Tble 5) shows more subtle chnges tht re restricted to its greter length nd to the smller interpremolr nd intermolr dimensions, with sttisticl significnce for femles only. The longer lower rch is due to proclintion of the lower incisors, which chrcterizes the dentl compenstion in Clss II. The wide vrition in the positioning of the lower incisors in Clss II, from proclintion to retroclintion, hs possibly cmouflged the sttisticl significnce in mles. Therefore, even if the lower rch tends to be longer, the difference between the upper nd lower rches in comprison to norml occlusion (Tble 7) is greter in Clss II (Tble 8). The tendency for posterior constriction of the lower rch my be interpreted s ccommodtion to the upper rch constriction. In our study, the chrcteristic of the lower rch ws similr to tht registered by Uysl et l, 23 who found reduced interpremolr nd intermolr widths. Our results re not similr to those found 473 by Syin nd Turkkhrmm 21 nd Fröhlich. 32 The former uthors noticed chnges in the lower intercnine width in women (men ge 16 yers) tht were greter in Clss II subjects, while the ltter did not find ny influence of Clss II on the lower dentl rch in growing children. Constriction of the upper dentl rch in Clss II division 1 mlocclusion is reflected in the differences between the trnsverse dimensions of the upper nd lower rches. CONCLUSION The hypothesis is rejected. Significnt differences re present between the dimensions of the upper nd lower dentl rches in Clss II division 1 mlocclusion (with mndibulr deficiency nd in the permnent dentition) compred to norml Clss I occlusion dentl rches. REFERENCES 1. Almeid RR, Fêo PS, Mrtins DR. Influênci d fluoretção n prevlênci de más oclusões. Estomt Cult. 1970;4: Erickson DM, Grzino FW. Prevlence of mlocclusion in seventh grde children in two North Crolin cities. JAm Dent Assoc. 1966;73: Krzpow AB, Liebermn MA, Modn M. Prevlence of mlocclusion in young dults of vrious ethnic bckgrounds in Isrel. J Dent Res. 1975;54: Silv Filho OG, Silv PRB, Rego MVNN, Silv FPL, Cvssn AO. Epidemiologi d má oclusão n dentdur decídu. Ortodonti. 2002;35: Silv Filho OG, Freits SF, Cvssn AO. Prevlênci de oclusão norml e má oclusão em escolres d cidde de Buru (São Pulo). Prte I: relção sgitl. Rev Odontol Univ São Pulo. 1990;4: Anderson DL, Popovich F. Lower crnil height vs crniofcil dimensions in Angle Clss II mlocclusion. Angle Orthod. 1983;53: Angle EH. Tretment of Mlocclusion of the Teeth: Angle s System. Phildelphi, P: White Dentl Mnufcturing; 1907: Bccetti T, Frnchi L, McNmr JA Jr, Tollro I. Erly dentofcil fetures of Clss II mlocclusion: longitudinl study from the deciduous through the mixed dentition. Am J Orthod Dentofcil Orthop. 1997;111: Bishr SE, Jkobsen JR, Treder J, Nowk A. Arch width chnges from 6 weeks to 45 yers of ge. Am J Orthod Dentofcil Orthop. 1997;111: Brodie AG. The Angle concept of Clss II, division 1 mlocclusion. Angle Orthod. 1931;1: Hitchcock HP. A cephlometric description of Clss II, division 1 mlocclusion. Am J Orthod. 1973;63: McNmr JA Jr. Components of Clss II mlocclusion in children 8 10 yers of ge. Angle Orthod. 1981;51: Oppenhein A. Prognthism from the nthropologicl nd orthodontic view points. Dent Cosmos. 1928;70: Vle DMV, Mrtins DR. Avlição ceflométric ds estruturs dento-esquelétics em jovens portdores de clsse II,

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