Which Hard and Soft Tissue Factors Relate with the Amount of Buccal Corridor Space during Smiling?

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1 Originl Article Which Hrd nd Soft Tissue Fctors Relte with the Amount of Buccl Corridor Spce during Smiling? Il-Hyung Yng ; Dong-Seok Nhm b ; Seung-Hk Bek c ABSTRACT Objective: To investigte which hrd nd soft tissue fctors relte with the mount of buccl corridor re (BCA) during posed smiling. Mterils nd Methods: The smples consisted of 92 dult ptients (19 men nd 73 women; 56 four first bicuspids extrction nd 36 nonextrction tretment cses; men ge 23.5 yers), who were treted only with fixed pplince nd finished with Angle Clss I cnine nd molr reltionships. To eliminte the crowding effect on the buccl corridor re, lterl cephlogrms, dentl csts, nd stndrdized frontl posed smile photogrphs were obtined t debonding stge nd 28 vribles were mesured. Person correltion nlysis, multiple liner regression nlysis, nd independent t-test were used to find vribles tht were relted with buccl corridor re rtio (BCAR). Results: Among the lterl cephlometric nd dentl cst vribles, FMA, lower nterior fcil height, upper incisor (U1) exposure, U1 to fcil plne, lower incisor (L1) to mndibulr plne, L1 to N-B, Sn (subnsle) to soft tissue menton (Me ), Sn to stomodium superius (stms), stms to Me, nd interpremolr width were significntly negtively correlted with BCAR. Occlusl plne inclintion nd buccl corridor liner rtio did not show ny significnt correltion with BCAR. Multiple liner regression nlysis generted three-vrible model: Sn to Me, U1 exposure, nd sum of tooth mteril (STM) (R ). There ws no significnt difference in BCAR between extrction nd nonextrction groups. Conclusions: To control the mount of BCA for chieving better esthetic smile, it is necessry to observe the verticl pttern of the fce, mount of upper incisor exposure, nd sum of the tooth mteril. KEY WORDS: Posed smiling; Buccl corridor re; Buccl corridor re rtio INTRODUCTION Although there hve been numerous soft tissue nlyses of the fce, 1 8 those mostly delt with the soft tissue profile in the sgittl plne. However, Arnett nd Grdute student (PhD), Deprtment of Orthodontics, School of Dentistry, Seoul Ntionl University, Seoul, South Kore. b Professor Emeritus, Deprtment of Orthodontics, School of Dentistry, Seoul Ntionl University, Seoul Breum Dentl Clinic, Seoul, South Kore. c Associte Professor, Deprtment of Orthodontics, School of Dentistry, Seoul Ntionl University, Seoul, South Kore. Corresponding uthor: Seung-Hk Bek, DDS, MSD, PhD, Associte Professor, Deprtment of Orthodontics, Dentl Reserch Institute, School of Dentistry, Seoul Ntionl University, #28 Yeonkun-dong, Jongro-Ku, Seoul, , South Kore (e-mil: drwhite@unitel.co.kr) Accepted: Februry Submitted: December by The EH Angle Eduction nd Reserch Foundtion, Inc. Bergmn, 7 Arnett et l, 8 nd Proffit 9 emphsized the importnce of the esthetics in the frontl view. Therefore, it is necessry for orthodontists to shift the focus from the sgittl plne to the frontl plne during evlution of their ptients when plnning nd ssessing orthodontic tretment. 10 In ddition, orthodontic ptients re concerned with not only their sttic ppernces, but lso with their dynmic ppernces during converstion nd smile The smile designing in orthodontic tretment is the socil posed smile, which is known to be repetble nd reproducible. 12,16 19 The buccl corridor is one of the evlution points in smile esthetics It is spce between the mxillry lterl teeth nd the corner of the mouth during smile, which ppers s blck or drk spce. 16,23 The nrrow mxillry rch 13,14,24 25 nd extrction in the upper dentition 26 were thought to be cuses of the buccl corridor. Others suggested tht the nterior-posterior DOI: /

2 6 YANG, NAHM, BAEK position of the mxill nd the rottion of the upper molrs could be influencing fctors on the buccl corridor. 11,12,15,19,20 Since the buccl corridor is ctully two-dimensionl on frontl view nd cn be seen differently ccording to light condition, quntifiction of the smile from the frontl photogrphs cn be done using liner mesurements, propoprtions, 12,15,16,19 21,27 nd mesh digrm with the extrpoltion method. 15,19,28 Therefore, it is necessry to quntify color nd density of the pixel unit of the buccl corridor in histogrm nd to mesure two-dimensionlly the buccl corridor re (BCA). The purpose of this study ws to quntify two-dimensionlly the BCA nd to determine which hrd nd soft tissue fctors re relted with the mount of BCA during posed smiling. MATERIALS AND METHODS The smples consisted of 92 dult ptients (19 men nd 73 women; 56 four first bicuspids extrction nd 36 nonextrction tretment cses; men ge: 23.5 yers) to eliminte growth chnges of the hrd nd soft tissues. The ptients hd been treted only with fixed pplince nd finished with Angle Clss I cnine nd molr reltionships. The ptients with fcil symmetry (chin point devition 4 mm), temporomndibulr joint disorder, cleft lip nd plte, or ny other syndromes, orthognthic surgery experience, nd more thn two missing teeth were excluded becuse these might result in bnorml neuromusculr ctivities during smile. Also, to get rid of ny crowding effect on BCA, lterl cephlogrms, dentl csts, nd stndrdized frontl posed smile photogrphs were obtined t the debonding stge. Lterl cephlogrms were tken with the ptient s Frnkfort horizontl (FH) plne prllel to the floor nd with centric occlusion nd unstrined lips. The trcings were digitized with digitizer (Intuos2 grphic tblet, Wcom Technology Co, Vncouver, Cnd) nd nlyzed by V-Ceph (Cybermed, Seoul, Kore). Reference lines nd cephlometric lndmrks re listed in Figures 1 nd 2. For lterl cephlometric mesurements, seventeen vribles of the nteroposterior position of the mxill, skeletl verticl pttern, denture pttern, nd soft tissue verticl lengths were used nd re listed in Figure 3. The vlues were mesured up to 0.05 nd 0.05 mm. For mesurements of the dentl csts, the mesiodistl width of ech tooth from the upper right to left first molr ws mesured with digitl vernier cliper (Mitutoyo, Auror, Ill) in 0.01 mm units nd their sum clculted. The intercnine, interpremolr, nd bsl rch widths were recorded. The ngultion nd inclintion of the upper incisors nd cnines were me- Figure 1. Reference lines. (1) Frnkfort horizontl plne (porion to orbitle). (2) Nsion perpendiculr line (N-perp, line perpendiculr to FH plne through nsion). (3) Subnsle perpendiculr line (Snperp, line perpendiculr to FH plne through subnsle). Figure 2. Cephlometric lndmrks. (A) Skeletl nd dentl lndmrks: 1. S (sell); 2. N (nsion); 3. Or (orbitle); 4. Po (porion); 5. Ar (rticulre); 6. Go (gonion); 7. Me (menton); 8. Pog (pogonion); 9. ANS (nterior nsl spine); 10. PNS (posterior nsl spine); 11. Point A (subspinle); 12. Point B (suprmentle); 13. Occlusl plne point; 14. U1E (incisor superius); 15. L1E (incisor inferius); 16. U1A (root pex of the upper centrl incisor); 17. L1A (root pex of the lower centrl incisor). (B) Soft tissue lndmrks: 18. Gl (glbell); 19. N (soft tissue nsion); 20. Sn (subnsle); 21. stms (stomion superius); 22. Me (soft tissue menton).

3 QUANTIFICATION OF THE BUCCAL CORRIDOR SPACE 7 Figure 3. (A) Vribles of nteroposterior position of mxill: 1. A to N-perpendiculr (mm); 2. A to Sn-perpendiculr (mm). (B) Vribles of the skeletl verticl pttern mesurements: 1. Fcil height rtio [(S-Go/N-Me) 100, %]; 2. Frnkfurt mndibulr plne ngle (FMA, degrees); 3. Lower nterior fcil height (LAFH, ANS-Me, mm); 4. Overbite depth indictor (ODI, degrees). (C) Vribles of denture pttern: 1. Upper incisor (U1) to fcil plne (mm); 2. Occlusl plne to S-N (degrees); 3. U1 to Sn-perp (mm).; 4. U1 exposure (mm); 5. Lower incisor (L1) to A-Pog (mm); 6. L1 to N-B (mm). (D) Vribles of the soft tissue verticl length: 1. N to Me (mm); 2. N to Sn (mm); 3. Sn to Me (mm); 4. Sn to stms (mm); 5. stms to Me (mm). sured with n ngultion- nd inclintion-mesuring guge (InvisiTech Co, Seoul, Kore) in 0.1 units. Vribles of dentl csts re listed in Figure 4. The cephlometric nd cst mesurements were relible ccording to the results of Dhlberg s formul. Posed smile photogrphs were tken with Nikon FM2 nlog film cmer (Nikon, Tokyo, Jpn) nd KODAK Elite Chrome 35mm slide film (Estmn Kodk Co, Rochester, NY). The ptients were positioned with the FH plne nd the interpupillry line prllel to

4 8 YANG, NAHM, BAEK Figure 4. Vribles of dentl csts. (A) Mesurement of the inclintion nd ngultion of the teeth with n ngultion- nd inclintion-mesuring guge (Invisitech Co, Seoul, Kore) in the units of 0.1. Vribles re s follows: IA (verge ngultion of the upper centrl nd lterl incisors of both sides), CA (verge ngultion of upper cnines of both sides), CI (verge inclintion of upper cnines of both sides), PI (verge inclintion of upper first nd second premolrs of both sides), occlusl plne ws used s reference plne. (B) Mesurement of the rch widths nd mesiodistl width of ech tooth on the dentl cst with digitl vernier cliper (Mitutoyo, Auror, Ill). Vribles re s follows: ICW (intercnine width between cusp tips of upper cnines), IPW (verge interpremolr width t contct point between first nd second premolr in nonextrction cse nd interpremolr width t second premolrs in extrction cse), ICBAW (intercnine bsl rch width between the upper cnines), IPBAW (interpremolr bsl rch width t centroid between the upper first nd second premolrs), Sum of tooth mteril (sum of the mesiodistl widths of the teeth from the upper right to left first molrs, STM). the floor nd were sked to touch their teeth slightly nd to smile. When we took picture of the posed smile, we creted stndrdized repetble nd reproducible method. The imginry center line of the ptient s fce ws ligned to the center verticl line on the grid of the viewfinder nd both sides of the ptient s ers showed the sme mount to prevent trnsverse rottion. Since the buccl corridor cn be seen differently ccording to different light conditions, ll procedures were crried out in studio under stndrdized light conditions to get the ctul BCA. The photogrphs were developed nd fixed by professionl. They were then scnned with Epson Expression 1680/pro scnner (Epson, Long Bech, Clif) under 24-bit color mode nd 600 dpi. The scnned imges were sved s JPEG files (stndrd bseline formt) t the mximum qulity s set t level 12. The mouth re in ech photogrph ws mgnified to fill the screen of 14.1 inch TFT SXGA monitor ( pixels, Fltron L1720B, LG, Seoul, Kore), using Adobe Photoshop 7.0 softwre (Adobe Systems Inc, Sn Jose, Clif). Vribles of posed smile photogrphs re listed in Figure 5. For clcultion of the buccl corridor liner rtio (BCLR), intercnine nd intercommissurl widths were mesured in 0.01 mm units with the liner mesuring tool in Adobe Photoshop 7.0 softwre. For precise re mesurements, polygonl lsso to select the smile res nd mgic wnd (options: tolernce [15 25], nti-lised [on], nd contiguous [on]) were used to decide the buccl corridors. The pixel number in both res ws ttined in the pixel histogrm menu nd the buccl corridor re rtio (BCAR) ws clculted. These were verified with the relibility test; r.999 for the smile re, r.989 for the buccl corridor re. To nlyze the test-retest relibility of the BCAR mesurement techniques, the smile re nd BCA of 30 rndomly selected smile photogrphs were mesured 4 weeks fter initil mesurement. Intrclss correltion coefficient ws computed for ssessment of the test-retest dt, which ws (P.01) for BCA using the mgic wnd tool nd (P.01) for the smile re using the polygonl lsso tool. The result substntited the relibility of these computerided re mesurement techniques. To find vribles tht were relted with the BCAR, Person correltion nlysis ws performed. Independent t-test ws performed to compre the mens of BCAR between extrction nd nonextrction groups. With the vribles showing the sttisticlly significnt correltion, multiple liner regression nlysis ws used to remove its intercorreltion mong these independent vribles s well s to discover the more importnt vribles which could predict the mount of BCA. RESULTS According to Person correltion nlysis, FMA (P.05), LAFH (P.01), U1 exposure (P.01), U1

5 QUANTIFICATION OF THE BUCCAL CORRIDOR SPACE Figure 5. Vribles of posed smile photogrphs. (A) Buccl corridor liner rtio ([C to C / Ch to Ch] 100 [%]), C mens distl surfce of the upper cnine; Ch, corner of the mouth. (B) Buccl corridor re rtio ([buccl corridor re / smile re] 100 [%]). Smile re mens re between upper nd lower lip; Buccl corridor re, Totl re of right nd left buccl corridors. to fcil plne (P.01), L1 to mndibulr plne (P.01), L1 to N-B (P.05), Sn to Me (P.01), Sn to stms (P.05), nd stms to Me (P.01) were significntly correlted with the BCAR (Tble 1). Among the dentl cst mesurements, the sum of tooth mteril (P.05) nd interpremolr width (P.05) were significntly correlted. Occlusl plne inclintion nd buccl corridor liner rtio did not show ny significnt correltion with BCAR. There ws no sttisticlly significnt difference in BCAR between the extrction nd nonextrction groups (Tble 2). Multiple regression nlysis produced three-vrible model, which consisted of Sn to Me, U1 exposure, nd sum of tooth mteril with the djusted R (Tble 3). DISCUSSION To mesure the ctul re insted of the liner rtio of the buccl corridor spce, the BCAR ws used s dependent vrible for correltion nlysis in this study (Tble 1). In Person correltion nlysis for determining the correltion between BCAR nd the other vribles (Tble 1), the vribles for the nteroposterior position of the mxill (A to N perp nd A to Sn perp) nd the inclintion of the occlusl plne did not show sttisticlly significnt correltions, which conflicted with results of former studies ,20 Among the vribles for the skeletl verticl pttern, FMA (P.05, Tble 1) nd LAFH (P.01, Tble 1) showed sttisticlly significnt negtive correltions. There were lso significnt negtive correltions in the vribles of the soft tissue verticl length; Sn to Me (P.01, Tble 1), Sn to stms (P.05, Tble 1), nd stms to Me (P.01, Tble 1). However, there ws no significnt correltion in N to Sn. Therefore, verticl length in the lower hlf of the soft tissue profile ws significntly negtively correlted with the mount of BCAR. A possible reson why stms-me showed the strongest correltion ws the possible reltionship with the ctivities of the lips. During smiling the lower lip showed lrger extent of motion thn the upper lip. Together with these results the long fce cn be sid to hve tendency for less buccl corridor. Among the denture pttern mesurements, there were sttisticlly significnt negtive correltions in U1 exposure (P.01, Tble 1), U1 to fcil plne (P.01, Tble 1), L1 to mndibulr plne (P.01, Tble 1), nd L1 to N-B (P.05, Tble 1). These suggest tht the more nteriorly nd downwrdly positioned the upper incisors nd nteriorly nd upwrdly positioned the lower incisors were, the less the BCAR ws. These incisor positions could be prt of the dentl compenstion effect of the hyperdivergent tendency in skeletl verticl pttern. In dentl cst mesurements, interpremolr width (P.05, Tble 1) showed sttisticlly significnt negtive correltion with BCAR. The nrrower the interpremolr width ws, the lrger the BCAR. This ws in ccord with the results of former studies. 13,14,24,25 Although sum of tooth mteril (P.05, Tble 1) showed negtive correltion coefficient, which suggested the extrction group hd high possibility of hving lrge buccl corridor, there ws no sttisticlly significnt difference of the BCAR between the extrction nd nonextrction groups (Tble 2). This ws in discord with the results of former studies. 26 Those findings men tht the mount of buccl corridor spce did not correlte with whether extrctions were done or not, but with the sum of tooth mteril. If the size of ech tooth ws slightly lrger thn norml in extrction cses, eventully the sum of tooth mteril could be lrger thn norml nd vice vers for the nonextrction group. These discords 12 15,20,26 nd ccords 13,14,24,25 to former studies were minly due to the newly-introduced method of mesuring the buccl corridor spce in this study. Former methodology ws horizontl liner mesurement, but the method used in this study delt with two dimensions. This is the reson the verticl com- 9

6 10 YANG, NAHM, BAEK Tble 1. Correltion Between Buccl Corridor Are Rtio nd Other Vribles Vribles Men SD Person Correltion Coefficient b Anteroposterior position of the mxill A to N-perpendiculr, mm A to Sn-perpendiculr, mm Skeletl verticl pttern Fcil height rtio (FHR) Frnkfurt mndibulr plne ngle (FMA), degrees * Lower fcil height rtio (LAFH), degrees ** Overbite depth indictor (ODI), degrees Occlusl plne inclintion Occlusl plne to S-N, degrees Denture pttern U1 Exposure, mm ** U1 to Fcil plne, degrees ** U1 to Sn-perpendiculr, mm L1 to A-Pog, mm L1 to Mndibulr plne, mm ** L1 to N-B, mm * Soft tissue verticl length N to Sn, mm Sn to Me, mm ** Sn to stms, mm * stms to Me, mm ** Dentl cst Sum of tooth mteril (STM), mm * Incisor ngultion (IA), degrees Cnine ngultion (CA), degrees Cnine inclintion (CI), degrees Premolr inclintion (PI), degrees ICW, mm IPW, mm * ICBAW, mm IPBAW, mm Smile photogrphs BCLR, % BCAR, % * P.05. ** P.01. SD indictes stndrd devition; U1, upper centrl incisor; L1, lower centrl incisor; STM, sum of tooth mteril which is sum of the mesiodistl widths of the teeth from the upper right to left first molrs; IA, verge ngultion of the upper centrl nd lterl incisors of both sides; CA, verge ngultion of upper cnines of both sides; CI, verge inclintion of upper cnines of both sides; PI, verge inclintion of upper first nd second premolrs of both sides; ICW, intercnine width between cusp tips of upper cnines; IPW, verge interpremolr width t contct point between first nd second premolr in nonextrction cse nd interpremolr width t second premolrs in extrction cse; ICBAW, intercnine bsl rch width between the upper cnines; IPBAW, interpremolr bsl rch width t centroid between the upper first nd second premolrs; BCLR, buccl corridor liner rtio; BCAR, buccl corridor re rtio. b Person correltion nlysis. In this study the correltion coefficients greter thn 0.20 nd less thn 0.20 hd sttisticl significnce (r.26, r.26, P.01; r.20, r.20, P.05, 2-tiled). ponents of the cephlometric nd cst mesurements hd n importnt effect on the BCA. In multiple liner regression nlysis of BCAR (Tble 3), the hrd nd soft tissue fctors ffecting the mount of BCAR were the soft tissue verticl length (Sn to Me ), the mount of upper incisor exposure, nd sum of tooth mteril. The reson why these three vribles were selected follows: The vribles in the skeletl verticl pttern (FMA nd LAFH) were excluded becuse of the collinerity with Sn to Me. Tht is, Sn to Me cn explin the verticl pttern of the underlying skeletl structures. Becuse most of the persons Tble 2. Comprison of Buccl Corridor Are Rtio Between the Nonextrction nd Extrction Groups Vrible Nonextrction Group (N 36) Men SD Extrction Group (N 56) Men SD P Vlue Significnce (2-Tiled) BCAR NS Independent t-test, BCAR indictes buccl corridor re rtio; SD, stndrd devition; NS, nonspecific. Tble 3. Multiple Liner Regression Anlysis of Buccl Corridor Are Rtio Significnt Vribles Coefficient Adjusted R 2 P vlue Sn-Me, mm U1 exposure, mm Sum of tooth mteril, mm Multiple liner regression nlysis. N 92, P.05, djusted R U1 indictes upper centrl incisor.

7 QUANTIFICATION OF THE BUCCAL CORRIDOR SPACE with lrge Sn to Me tend to hve lrge Sn to stms nd stms to Me, these two soft tissue verticl length vribles were lso excluded in the multiple liner regression nlysis. The vribles on the position of the lower incisors (L1 to mndibulr plne nd L1 to N-B) were excluded becuse the lower incisors were well locted in given smll rnge of position ccording to the position of the upper incisors fter orthodontic tretment. Becuse sum of tooth mteril hd strong correltion (r 0.720, P.001) from the correltion mtrix, the interpremolr width ws excluded from the regression model. CONCLUSIONS With the newly-introduced method for BCA, the buccl corridor is multifctoril phenomenon. To control the mount of BCA for chieving better esthetic smile, it is necessry to observe the verticl pttern of the fce, mount of upper incisor exposure, nd sum of the tooth mteril. Extrction or nonextrction tretment did not ffect the mount of BCA. 11 REFERENCES 1. Burstone CJ. The integumentl profile. Am J Orthod. 1958; 44: Ricketts RM. Cephlometric synthesis. Am J Orthod. 1960; 46: Merrifield LL. The profile line s n id in criticlly evluting fcil esthetics. Am J Orthod. 1966;52: Scheidemn GB, Bell WH, Legn HL, Finn RA, Reisch JS. Cephlometric nlysis of dentofcil normls. Am J Orthod. 1980;78: Holdwy RA. A soft-tissue cephlometric nlysis nd its use in orthodontic tretment plnning. Prt I. Am J Orthod. 1983;84: Powell N, Humphreys B. Proportions of the Aesthetic Fce. New York, NY: Thieme-Strtton Inc; 1984: Arnett GW, Bergmn RT. Fcil keys to orthodontic dignosis nd tretment plnning. Prt I. Am J Orthod Dentofcil Orthop. 1993;103: Arnett GW, Jelic JS, Kim J, Cummings DR, Beress A, Worley CM Jr, Chung B, Bergmn R. Soft tissue cephlometric nlysis: dignosis nd tretment plnning of dentofcil deformity. Am J Orthod Dentofcil Orthop. 1999;116: Proffit WR. The soft tissue prdigm in orthodontic dignosis nd tretment plnning: new view for new century. J Esthet Dent. 2000;12: Kerns LL, Silveir AM, Kerns DG, Regennitter FJ. Esthetic preference of the frontl nd profile views of the sme smile. J Esthet Dent. 1997;9: Ackermn JL, Proffit WR, Srver DM. The emerging soft tissue prdigm in orthodontic dignosis nd tretment plnning. Clin Orthod Res. 1999;2: Ackermn MB, Ackermn JL. Smile nlysis nd design in the digitl er. J Clin Orthod. 2002;36: Srver DM, Ackermn MB. Dynmic smile visuliztion nd quntifiction: prt 1. Evolution of the concept nd dynmic records for smile cpture. Am J Orthod Dentofcil Orthop. 2003;124: Srver DM, Ackermn MB. Dynmic smile visuliztion nd quntifiction: prt 2. Smile nlysis nd tretment strtegies. Am J Orthod Dentofcil Orthop. 2003;124: Ackermn MB, Brensinger C, Lndis JR. An evlution of dynmic lip-tooth chrcteristics during speech nd smile in dolescents. Angle Orthod. 2004;74: Hulsey CM. An esthetic evlution of lip-teeth reltionships present in the smile. Am J Orthod. 1970;57: Rigsbee OH 3rd, Sperry TP, BeGole EA. The influence of fcil nimtion in smile chrcteristics. Int J Adult Orthodon Orthognth Surg. 1988;3: Morley J. Smile design terminology. Dent Tody. 1996;15: Ackermn JL, Ackermn MB, Brensinger CM, Lndis JR. A morphometric nlysis of the posed smile. Clin Orthod Res. 1998;1: Ackermn MB. Buccl smile corridors. Am J Orthod Dentofcil Orthop. 2005;74: Ritter DE, Gndini LG, Pinto Ados S, Locks A. Esthetic influence of negtive spce in the buccl corridor during smiling. Angle Orthod. 2006;76: Prekh SM, Fields HW, Beck M, Rosenstiel S. Attrctiveness of vritions in the smile rc nd buccl corridor spce s judged by orthodontists nd lymen. Angle Orthod. 2006; 76: Lombrdi RE. The principles of visul perception nd their clinicl ppliction to denture esthetics. J Prosthet Dent. 1973;29: Snyder RJ. Clss II mlocclusion correction: n Americn bord of orthodontics cse. Am J Orthod Dentofcil Orthop. 1999;116: McNmr JA. Mxillry trnsverse deficiency. Am J Orthod Dentofcil Orthop. 2000;117: Ghfri JG. Emerging prdigms in orthodontics n essy. Am J Orthod Dentofcil Orthop. 1997;111: Snow SR. Esthetic smile nlysis of mxillry nterior tooth width: the golden percentge. J Esthet Dent. 1999;11: Nylor CK. Esthetic tretment plnning: the grid nlysis system. J Esthet Restor Dent. 2002;14:76 84.