the apparent contact dimension and covariates among orthodontically treated and nontreated subjects

The Apparent Contact Dimension andCovariates among Orthodontically Treated andNontreated Subjects

VISHNU RAJ, BDS, MSFS*

HARALD O. HEYMANN, DDS, M.Ed†

H. GARLAND HERSHEY, DDS, MS‡

ANDRE V. RITTER, DDS, MS§

JOHN S. CASKO, DDS, MS, PhD¶

ABSTRACTThe apparent contact dimension (ACD), a determinant of dental esthetics, has been purportedto exhibit an esthetic relationship termed the “50:40:30” rule, implying that in an estheticsmile, the ACD between the central incisors, central and lateral incisors, and lateral incisor andcanine would be 50, 40, and 30% of the height of a central incisor, respectively. This studyassessed the existence of this proportion using casts of orthodontically treated (N = 40) andnontreated (N = 27) subjects deemed to possess excellent occlusion. Covariates studied includedtooth size, tooth shape, tip, and torque. The average ACD proportions in this study, relative tothe height of an ipsilateral central incisor, were found to be 49, 38, and 27% between thecentral incisors, central and lateral incisors, and the lateral incisor and canine, respectively. TheACD exhibited a positive correlation (p < 0.05) with the height of the clinical crown and anegative correlation (p < 0.05) with the width/height ratios of the corresponding teeth. Nostatistically significant correlations were evident between the ACD with the shape of the clinicalcrown, tip, and torque. However, the tip and torque did exhibit a statistically significant(p < 0.05) correlation with the height of the clinical crown. This study is the first to validatethe existence and proportions of the ACD.

CLINICAL SIGNIFICANCEThis study validates the existence of the ACD and quantifies the relationship of the ACD withtooth size, tooth shape, mesiodistal crown angulation (tip), and labiolingual crown inclination(torque) among subjects deemed to possess excellent occlusion and alignment. This quantifiable“ideal” and its correlation with the other determinants of dental esthetics may be used inconjunction with various evidence-based paradigms in the esthetic appraisal of the maxillaryanterior teeth.

(J Esthet Restor Dent 21:96–112, 2009)

*Resident, Graduate Orthodontics, School of Dentistry,University of Texas Health Sciences Center at San Antonio

†Professor and graduate program director, Department of Operative Dentistry,School of Dentistry, University of North Carolina at Chapel Hill

‡Professor, Department of Orthodontics, School of Dentistry, University of North Carolina at Chapel Hill§Associate professor, Department of Operative Dentistry, School of Dentistry,

University of North Carolina at Chapel Hill¶Professor, B.F. and Helen E. Dewel Endowed Chair, Department of Orthodontics,

College of Dentistry, University of Iowa, Iowa City

© 2 0 0 9 , C O P Y R I G H T T H E A U T H O R SJ O U R N A L C O M P I L AT I O N © 2 0 0 9 , W I L E Y P E R I O D I C A L S , I N C .DOI 10.1111/j.1708-8240.2009.00240.x V O L U M E 2 1 , N U M B E R 2 , 2 0 0 996

I N T R O D U C T I O N

Esthetics in dentistry has gainedincreasing attention and

prominence over the years, leadingto an almost histological approachto the elucidation of the compo-nents that determine dental attrac-tiveness. Tooth shape, size, andalignment relationships are integralto the attainment of optimal func-tion and esthetics. An estheticsmile is one in which the size,shape, position, and color of theteeth are in harmony, proportion,and relative symmetry to eachother and the elements that framethem.1 Another determinant ofesthetics that has only recentlybeen identified in the dental litera-ture is the so-called “connectorzone” in the maxillary anteriorsextant.2,3 The first apparent refer-ence to the term “connector zone”was in a 2001 publication byMorley and Eubank in which they

delineated the connector zone fromproximal contact points by statingthat, “The connector is a larger,broader area that can be defined asthe zone in which two adjacentteeth appear to touch. The contactpoints between the anterior teethare generally smaller areas (about2 ¥ 2 millimeters) that can bemarked by passing articulatingribbon between the teeth.”2

A source of concern is that theexisting nomenclature (i.e., “con-nector zone”) is descriptivelyambiguous, in that the adjacentteeth do not actually “connect” ortouch throughout the connectorzone. Another potential source ofconfusion derives from the factthat “connectors” are widelydefined and well known as compo-nents of removable and fixed pros-thodontic appliances. Because ofthese concerns, it is recommended

that the perceived area of contactbetween adjacent teeth be termedthe apparent contact dimension(ACD), which is a more preciseand quantifiable description of the“connector zone.” Based on anevaluation of the illustration of the“connector zone” (Figure 1) in theliterature and as a result of a pilotstudy, it was concluded that, foraccuracy and reproducibility, ACDmeasurements be made at 90degrees to each proximal contactarea. Therefore, based on the pilotstudy, it is proposed that the ACDbe defined as the area where theteeth appear to be in contact, whenviewed from the facial aspect at 90degrees to each interproximal area.As an example, the ACD betweenthe central incisors is clearlyevident in Figure 2.

Dentistry is rife with several pur-ported paradigms to guide thetreatment planning process as partof creating or enhancing esthetics.For decades, the prevalent philoso-phy has been to restore or replaceteeth based on vague concepts suchas sex, personality, and age.4

However, in this era of evidence-based health care, it is imperativeto incorporate the tenets ofmodern interdisciplinary researchinto the dental treatment planningprocess. Several investigators haveattempted to provide other guide-lines to facilitate esthetic excel-lence. Magne and colleaguesmentioned the use of certain

Figure 1. Connector zone (reprinted with permissionfrom the Journal of the American Dental Association2001;132(1):39–45).

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subjective and objective criteria,including tooth form, relative toothdimensions, smile symmetry, color,tooth axis, and gingival health.5

Rufenacht proposed a moredynamic approach, where subjectsare provided with orthodontic ele-ments as a part of esthetic recon-struction.6 Nevertheless, thepresence of a quantifiable “ideal”reference is integral to the applica-tion of these esoteric conceptsin dentistry.

Harmony in proportion has beendefined as an esthetic principle,and the golden proportion is oftencited as an exemplar for dentalesthetics. The concept of thegolden proportion was first used inancient Greek architecture, and itsbasic premise is that for tworelated objects to appear naturaland harmonious, the larger to thesmaller should form a ratio of1.6,181 : 1.7 In dentistry, thegolden proportion represents a

62% regression from the mesial tothe distal, with the implication thatif the perceived width of a maxil-lary anterior tooth is approxi-mately 62% of the size of itsadjacent mesial tooth, it is consid-ered esthetically pleasing.4 Asstated by Levin, when viewed fromthe facial, “The width of thecentral incisor should be in goldenproportion to the width of thelateral incisor, and the width ofthe lateral incisor should be goldento the canine and the caninewidth should be golden to thefirst premolar.”8

Other reports have attributed lessvalidity to the golden proportion,and some studies have found thatthe majority of smiles deemed tobe esthetically pleasing clearly didnot coincide with the golden pro-portion.4,7,9 A recent study on den-tists’ preferences of anterior toothproportions found that the goldenproportion was preferable only for

very tall teeth.10 In addition, exces-sive narrowness of the maxillaryarch and compression of lateralsegments have been observed incases of strict adherence to thegolden proportion.5 In an attemptto assess the prevalence of thegolden proportion in the naturaldentition, Preston measured theperceived widths of the maxillarycentral and lateral incisors on 58imaged casts and found thatonly 17% (10) had a perceivedcentral : lateral incisor width ratioin the range of 1.59 and 1.65 : 1.9

The mean perceived central : lateralincisor width ratio was 1.51 : 1.Preston also failed to find anydiagnostic cast with a perceivedmaxillary lateral : canine widthratio within the range of thegolden proportion.9

The ACD of the maxillary anteriorteeth in an esthetic smile has itselfbeen alleged to exhibit a propor-tional relationship, which Morleyand Eubank quantified as the50 : 40 : 30 rule (Figure 1).2 This“rule” defined the ideal ACDbetween the central incisors as50% of the height of the centralincisors, the ideal ACD between amaxillary lateral incisor andcentral incisor as 40% of theheight of a central incisor, andthe ideal ACD between a lateralincisor and a canine as 30% of theheight of a central incisor. No datawere provided to corroborate theseproportions, and it appears that

Figure 2. Apparent contact dimension.

A P PA R E N T C O N TA C T D I M E N S I O N

98© 2 0 0 9 , C O P Y R I G H T T H E A U T H O R SJ O U R N A L C O M P I L AT I O N © 2 0 0 9 , W I L E Y P E R I O D I C A L S , I N C .

the prevalence of this “ideal” pro-portion of 50 : 40 : 30 has notbeen formally investigated. In addi-tion, it is unclear if these propor-tions of the ACD are evident onlywhen viewed from the facialaspect, or individually and at 90degrees to each correspondinginterdental area.

The proportions of the ACD maybe influenced by variations intooth shape and size. For example,a triangular-shaped tooth wouldlikely exhibit a shorter ACD com-pared with a more parallel-shapedtooth, and longer teeth couldostensibly exhibit a greater ACDthan shorter teeth. A recent studyassessed the relative hierarchy ofvarious dental features that con-tribute to overall dental attractive-ness and found that tooth shapewas the feature most strongly asso-ciated with overall dental attrac-tiveness.13 However, it is importantto note that the precise quantifica-tion of specific tooth shapesand their esthetic import has notbeen assessed.

Two additional parameters thatinfluence the perception of theACD are the mesiodistal crownangulation (tip) and the labiolin-gual crown inclination (torque),both of which clearly contribute tothe esthetics of the maxillary ante-rior dentition. Axial inclinations ofmaxillary teeth are perceived rela-tive to the vertical axis of the face

and the maxillary midline, both ofwhich are usually parallel in anesthetic smile. “When the maxillaryanterior teeth tip medially [sic], theoverall esthetic impact is harmoni-ous with the lower lip” (Morleycites Lombardi).2 However, whenteeth incline significantly towardthe midline, the smile appearsnarrow and visually discordant.1 Inthe natural dentition, there is aprogressive increase of anteriorcrown angulations mesially, or amesial tip, as the smile line contin-ues distally from the central inci-sors to the canines. Aberrations inangulation are usually perceptivelytolerable to a minor degree,beyond which they appear dishar-monic and unesthetic. Kokich andcolleagues evaluated perceptions ofalterations in incisor crown angula-tion and found that even minordeviations from the ideal wereconsidered unattractive.14

In a landmark publication,Andrews measured diagnosticmodels of 120 untreated idealocclusion subjects in an attempt toidentify the characteristics consis-tently present in naturally optimalocclusion.15 He then recorded theaverage values or norms for theseparameters, including anteroposte-rior and vertical molar relation-ships, tooth tip, torque, rotations,spaces, and the depth of theocclusal plane. Andrews observedthat in a dentition with excellentocclusion, nearly every tooth type

had a discrete amount of crownangulation and inclination; but theamounts for each tooth type weresimilar among optimal dentitions.16

Andrews’s so-called six keys toideal occlusion were incorporatedinto commercially available ortho-dontic brackets and represented thefirst preprogrammed or straightwire appliance in orthodontics,16

a concept that facilitated toothmovement into desirable positionsbased on carefully documented“ideal” occlusions. Average mesio-distal angulations obtained byAndrews from nonorthodonticallytreated normal models were 5, 9,and 11 degrees for the maxillarycentral incisor, lateral incisor, andcanine, respectively.15 Otherresearchers have reported similaror comparable values of tip andtorque,17,18 and although some dis-parities were evident in the angula-tion and inclination of individualtooth groups, this may be reflectiveof the ethnic diversity apparentin the different populationsstudied (i.e., Caucasian, Asian,and Indian).

Tip and torque discrepancies mayhave significant associated func-tional and esthetic ramifications.The correlation between variationsin angulation and inclination andthe arch height has been reportedby Tuverson.19 The esthetic importof angulation was further empha-sized in a study by Wolfart andcolleagues, who assessed dental

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appearance following changes inincisor angulation and concludedthat symmetric teeth with idealaxes as well as minor variationsin the mesial or distal angulationof the lateral incisors had thegreatest influence on attractiveappearance.20 Brunzel and col-leagues corroborated the signifi-cance of symmetry and axialinclination, specifically variationsin the mesial angulation of thelateral incisors (up to 9 degrees).21

An interesting observation is theconfluence of esthetic and func-tional ideals; the average lateralincisor angulation assessed byAndrews in ideal occlusion casesand the lateral incisor angulationcited by Brunzel and colleagues tobe esthetic are both in the rangeof 9 degrees.

Labiolingual inclination or torquewas defined by Andrews as theangle between the tangent to themiddle of the clinical crown and aperpendicular line dropped on theocclusal plane.17 According toRufenacht, the labial surface of themaxillary central incisors should beperpendicular to the occlusal plane,thus enhancing their estheticappearance by facilitatingmaximum light reflection from thelabial surface.6 In a group of non-orthodontically treated normalmodels, Andrews reported meantorque values for the maxillarycentral incisor, lateral incisor, andcanine as 7, 3, and -7 degrees,

respectively.15 The estheticsignificance of torque was alsodelineated by Mackley in astudy on postorthodontic smileevaluation, in which he foundthat one of the characteristicsthat distinguished the best-judgedorthodontist was the degree ofimprovement in the torque of theupper incisors.22

Esthetics in dentistry is contingenton principles of symmetry and pro-portion, and the inclusion of con-gruent elements may enhance theability to achieve a natural appear-ance. Although each of the afore-mentioned components, includingthe ACD, tooth size, shape, tip,and torque has a contributoryinfluence on esthetics, the interac-tion of these variables has not beenstudied. Therefore, the specificaims of the present study were toestablish the proportions of theACD and to quantify the relation-ship between the ACD and thecovariates of tooth shape, size, tip,and torque using diagnostic castsof nontreated and orthodonticallytreated subjects.

M AT E R I A L S A N D M E T H O D S

Clinical Pilot StudyA pilot study approved by the Insti-tutional Review Board was con-ducted to validate the accuracy ofmeasuring the ACD on the diagnos-tic models compared with intraoralmeasurements. Ten subjects withintact maxillary anterior teeth

comprised the pilot study sample.Subjects with incisal/proximalwear, crowding, rotations, pooralignment, and/or diastemas wereexcluded. The maxillary occlusalplane was used as the horizontalreference to facilitate measurementof the ACD at an angulation of90 degrees to the interdental areabetween the central incisors, centraland lateral incisors, and lateralincisor and canine. Althoughesthetics is not always perceived at90 degrees to each interdental area,this orientation was selected inorder to facilitate measurementaccuracy and reproducibility.

Vertical positioning of the subjectswas standardized by using a Foxplane to orient the maxillaryocclusal plane parallel to the floor.The same vertical head positionwas maintained throughout themeasuring sequence, and the cheekwas reflected using cheek retrac-tors. With subjects seated in thisposition, the investigator was posi-tioned at eye level and at 90degrees to the interdental area ofinterest. The fine tips of an elec-tronic Boley gauge were inserted toengage the incisal convergence ofthe gingival embrasure and the gin-gival convergence of the incisalembrasure (Figure 3). This dimen-sion is analogous to the distancebetween the incisal tip of thepapilla and the incisal terminationof the proximal contact. Readingswere obtained and the measuring



process repeated to obtain asecond reading of the same area.The measuring protocol wasrepeated to measure all interdentalareas between 6/7, 7/8, 8/9, 9/10,and 10/11. The clinical crownheight of teeth #8 and 9 were mea-sured (Figure 4) and recorded induplicate. The ACD was estab-lished as a percentage of the heightof the ipsilateral central incisor.Next, a PolyVinyl Siloxane (PVS)impression of the maxillary archwas made, disinfected, and pouredwith Type III dental stone. ACDmeasurements were performed onthe casts (Figure 5) and convertedto %ACD. The average intraoraland extraoral %ACD was calcu-lated by tooth type, and Pearsoncorrelation was used to establishthe strength of the associationbetween intraoral and extraoralmeasurements. Paired t-tests wereused to assess the existence of sys-tematic measurement differences.

Results of the Pilot StudyTable 1 shows the average ACDmeasurements for each interdentalarea in vivo (intraoral) and in vitro(casts). Pearson correlation indi-cated excellent correlation betweenintraoral and extraoral ACDs ofthe maxillary anterior teeth, withcorrelation coefficients (r) rangingfrom 0.77 to 0.94 (Table 1).Results of the paired t-tests didnot indicate the existence of any

clinically significant differencesbetween intraoral and extraoralACD measurements (Table 2).

Cast EvaluationBased on the results of the pilotstudy, there were no significantdifferences between direct intraoraland plaster cast measurements ofthe ACDs of the six maxillaryanterior teeth. For the main study,the inclusion criteria for the casts

Figure 3. Intraoral apparent contact dimensionmeasurement.

Figure 4. Measurement of clinical crown height.

Figure 5. Apparent contact dimension measurement oncasts.

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were the presence of all six unre-stored and well-aligned maxillaryanterior teeth. Casts with notice-able incisal wear, gingival condi-tions (recession, inflammation),undersized teeth, anterior diaste-mas, rotations, black triangles, andrestorations/crowns were excludedfrom the study. Using these criteria,27 of approximately 90 casts ofnontreated, excellent occlusionsubjects compiled by Dr. John S.Casko at the Department of Orth-odontics, University of IowaCollege of Dentistry, were selectedfor the study. Using the sameaforementioned criteria, additionalcasts (N = 40) representing treatedsubjects with excellent occlusionwere selected from the Department

of Orthodontics, University ofNorth Carolina Schoolof Dentistry.

ACD MeasurementsThe cast was hand positioned, withthe maxillary occlusal plane paral-lel to the floor. The investigatorwas positioned at 90 degrees to theinterdental area of interest, and thefine tips of an electronic Boleygauge were inserted to engage theincisal convergence of the gingivalembrasure and the gingival conver-gence of the incisal embrasure(Figure 5). Readings were obtainedand the measuring process repeatedto obtain a second reading of thesame area. The measuring protocolwas repeated to measure all

interdental areas between 6/7, 7/8,8/9, 9/10, and 10/11. The clinicalcrown height of teeth #8 and 9were measured and recorded induplicate to reduce measurementerror. The ACD was established asa percentage of the height of theipsilateral central incisor using thefollowing equation:

%ACD Measured ACD Height ofipsilateral central incisor

10

= ()

× 00

Tooth SizeTooth size measurements compris-ing the mesiodistal width and theclinical crown height were mea-sured in duplicate using a Boleygauge. The clinical crown heightwas defined as the distance fromthe most apical concavity of thegingival margin to the incisaledge/occlusal surface of a tooth.Width/height (W/H) ratioswere calculated.

Tooth ShapeAlthough tooth shape is not areadily quantifiable variable, it has

TA B L E 1 . AV E R A G E % A C D ( R E L AT I V E T O H E I G H T O F T H E I P S I L AT E R A L C E N T R A L I N C I S O R ) A N D C O R R E L AT I O N

B E T W E E N I N T R A - A N D E X T R A O R A L % A C D .

ACD Location (N = 10) Intraoral (%) Extraoral (%) Correlation Coefficient (r) p-Value

6/7 28.4 26.2 0.88 0.0017/8 37.2 36.3 0.77 0.0048/9 44.7 41.6 0.92 0.0019/10 37.4 36.9 0.94 0.001

10/11 28.7 28.1 0.84 0.001

ACD = apparent contact dimension.

TA B L E 2 . M E A N D I F F E R E N C E B E T W E E N I O A N D E O % A C D .

ACD Location Mean Difference (IO–EO) p-Value

6/7 2.2% 0.0217/8 0.83% 0.4898/9 3.1% 0.0369/10 -0.2% 0.87

10/11 0.62% 0.55

ACD = apparent contact dimension; IO = intraoral; EO = extraoral.



the potential to substantiallyaffect the ACD. For the purposesof this study, teeth were classifiedas parallel shaped (Figure 6A),barrel shaped (Figure 6B), ortriangular shaped (Figure 6C),14

based on the degree ofcervicoincisal divergence.

Facial Axis of theClinical Crown (FACC)As originally proposed byAndrews, the facial (long) axis ofthe clinical crown is judged to bethe mid-developmental ridge,which represents the most promi-nent and centermost portion of thefacial central lobe of all teethexcept molars.16 Clinically, theFACC for all teeth, except molars,can be highlighted with the side ofa pencil lead. The midpoint of theFACC is referred to as the FApoint.16 Andrews reported thatwhen the teeth in an arch are cor-rectly positioned, their FA pointsfall on a plane that closely corre-sponds to the occlusal plane.16 Inthis study, the tip and torque weremeasured at the FACC.

Tooth Inclination Protractor (TIP)Richmond and colleaguesdescribed a disposable device—theTIP—which they used to measurethe inclination of the labialsurface of the maxillary and man-dibular incisors to their respectiveocclusal planes.24 The TIP consistsof an acrylic platform (corre-sponding to the occlusal plane)with a 180-degree protractor sus-pended below it. The perforatedplatform receives a stainless steelwire, which can be cut to lieagainst the labial surface of theincisor, allowing for anatomicalvariations in crown height. Belowthe platform, the other end of thewire rests against the graduatedscale of the protractor.24,25 Thewire pointer is placed againstthe labial surface of the incisorcrown at its maximum convexity(FA point) so that the anglesabove and below the contact areequal. The reading on the scalereflects the inclination of thelabial surface of the maxillaryteeth to their respectiveocclusal planes.

TipThe tip represents the mesiodistalangle formed by the FACC and aline perpendicular to the occlusalplane.7 The tip was consideredpositive when the occlusal portionof the FACC was mesial to the gin-gival portion, and negative when itwas distal.7 The tip was measuredby orienting the cast with theocclusal plane seated on the TIPplatform and the needle aligned atthe FA point (Figure 7). Crownangulation was estimated at2.5-degree intervals.

TorqueCrown inclination or torque repre-sents the labiolingual anglebetween a line perpendicular to theocclusal plane and a line that isparallel and tangent to the FACCat the FA point.8 Crown inclinationis determined from the mesial ordistal, and the line representing theinclination of the FACC should beequidistant from each end of theclinical crown (cervical andincisal), while contacting the FACC(see Figure 8). Crown inclination is

A B C

Figure 6. Tooth shape classification: (A) Parallel, (B) Barrel shaped, and (C) Triangular.

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considered positive if the incisalportion of the crown, tangent line,or FACC is facial to its gingivalportion, and is considered negativeif lingual to the gingival portion.7

Statistical AnalysesPaired t-tests were run to evaluatedifferences between the ACD mea-surements for the right and leftACD locations. Differencesbetween the treated and nontreatedgroups were assessed usingunpaired t-tests. Analysis of vari-ance (ANOVA) was used to studyvariations in the ACD by toothshape. W/H ratios were calculatedfor all maxillary anterior teeth, andthe association between the W/Hand the corresponding ACD (milli-meters) was established usingPearson correlation analysis. Dif-ferences between the treated and

nontreated groups were assessedusing unpaired t-tests. In order toevaluate the relationship betweenthe ACD measurements and toothheight, tip, and torque, the valuesfor each of the covariates wereaveraged across each tooth pairthat comprised an ACD location.A fixed-effects model was used toevaluate correlations between theACD by clinical crown height, tip,torque, and location.

R E S U LT S

The average ACD in millimetersand the %ACD for the orthodonti-cally treated and nontreated groupsare listed in Table 3. As the differ-ences between the treated and non-treated ACD measurements werenot clinically significant (i.e., a fewtenths of a millimeter), the twogroups were pooled by location.

Results of paired t-tests did notreveal statistically significant differ-ences between the ACD measure-ments for the right and left ACDlocations—that is, between 6/7 and10/11 (p = 0.916) and between 7/8and 9/10 (p = 0.268). Therefore,the %ACD values were averagedbetween the right and left locationsto obtain a single average ACD perlocation (Table 3). The average%ACD between the central inci-sors was 49%, between the centraland lateral incisor was 38%, andbetween the lateral incisor and thecanine was 27%.

A statistically significant andnegative correlation was evidentbetween the ACD (millimeter) andthe W/H ratio of each tooth thatcomprised the corresponding ACD(Table 1). One-way ANOVA did

Figure 7. Measurement of crown angulation (tip) using thetooth inclination protractor.

Figure 8. Measurement of crown inclination (torque)using the tooth inclination protractor.



not indicate statistically significantdifferences in ACD values by toothshape. However, statistically sig-nificant differences in the clinicalcrown height of teeth #8(p = 0.016) and 9 (p = 0.049) wereevident across the parallel-(N = 47) and the barrel-shapedgroups (N = 16). Average valuesfor clinical crown height, tip, andtorque for the nontreated andtreated groups are provided inTable 2. For teeth #7, 10, and 11,the average clinical crown heightswere significantly lower (p < 0.05)for the treated group comparedwith that for the nontreated group.The torque was significantly higheracross all six tooth categories inthe treated groups compared withthat in the nontreated group. Fortooth #11, the treated group exhib-ited a lower average degree of tipcompared with the nontreatedgroup (Table 4).

The ACD measurements exhibitedstatistically significant correlationsby location (p < 0.0001) and byheight (p < 0.0001) of the clinicalcrown. Pearson correlation coeffi-cients between the ACD and clini-cal crown height were 0.297,0.511, and 0.478 for the canine/lateral incisor, central/lateral inci-sors, and midline, respectively.Graphs 1 through 3 representvariations in ACD (millimeter)dimensions as a function of theclinical crown height of each toothpair that represents an ACD loca-tion. Clinical crown height exhib-ited statistically significantcorrelations by tip (p = 0.0216),torque (p = 0.0015), and location(p < 0.0001).

D I S C U S S I O N

Symmetry and proportionalityclearly affect the perception ofesthetics, especially in the maxillary

anterior region. Various esthetic“ideals,” such as the golden propor-tion, W/H ratios, and the RecurringEsthetic Dental (RED) proportion,have been proposed.8,10,11 However,in this era of evidence-based den-tistry, it is important that the valid-ity of these “proportions” besubstantiated by research-baseddata. Although the proportions ofthe “connector space” have beenreported and cited in the literature,there were no data presented tovalidate the existence of this pro-portion.2 This study attempted todefine and establish the proportionsof the ACD using casts of non-treated and orthodontically treatedindividuals deemed to possessexcellent occlusion (six keys). Withrespect to method validation toassess the accuracy of measurementon diagnostic models, Lundstrom(as cited by Abdullah and col-leagues), recorded the dimensions

TA B L E 3 . A C D A M O N G T R E AT E D ( N = 4 0 ) A N D N O N T R E AT E D ( N = 2 7 ) S U B J E C T S A N D C O R R E L AT I O N W I T H

W / H R AT I O S .

Location Group Average ACD (mm) Average %ACD ACD (mm) Correlation

with W/H ratios (R)

6/7 Nontreated 2.76 � 0.49 27 � 6.1 -0.245*, -0.166Treated 2.73 � 0.66

10/11 Nontreated 2.73 � 0.59 -0.246*, -0.147Treated 2.74 � 0.68

7/8 Nontreated 4.29 � 0.75 38 � 7.5 -0.293*, -0.243*Treated 3.76 � 0.84

9/10 Nontreated 4.08 � 0.80 -0.287*, -0.372**Treated 3.75 � 0.91

8/9 (midline) Nontreated 5.15 � 0.63 49 � 6.7 -0.404**, -0.367**Treated 4.89 � 0.86

ACD = apparent contact dimension; W/H = width/height.

*p < 0.05; **p < 0.01.

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of six anterior teeth intraorally andon casts, and did not find signifi-cant differences between the twosets of measurements.12 However,

with respect to the actual and per-ceived widths, there appears to be adifference between diagnosticmodels and images. Hasanreisoglu

and colleagues compared themesiodistal width of the maxillaryanterior teeth measured on casts tothe perceived widths measured onthe corresponding images andfound that the actual and perceivedsizes of the anterior teeth whenviewed from the facial differedbecause of the curvature of thearch and angulation of the teeth inrelation to the frontal plane ofthe photograph.4

The selection criteria for this studywere aimed at precluding castswith malaligned teeth, rotations,diastemas, and significant incisalwear. Other exclusionary criteriaincluded maxillary anterior teethwith restorations and evidence ofgingival inflammation or recession,all of which may alter the mesio-distal or incisocervical toothdimensions. The ACD millimeter

TA B L E 4 . C L I N I C A L C R O W N H E I G H T, T I P, A N D T O R Q U E F O R T R E AT E D ( N = 4 0 ) A N D N O N T R E AT E D S U B J E C T S

( N = 2 7 ) .

Tooth # Group Average Height (mm) Average Tip (degrees) Average Torque (degrees)

6 Nontreated 10.0 � 1.08 5 � 3.7 1 � 2.7Treated 9.6 � 0.96 5 � 4.5 3 � 3.3*

7 Nontreated 8.9 � 0.95 8 � 3.5 9 � 4.6Treated 8.4 � 0.90* 8 � 3.2 12 � 5.0*



10 Nontreated 9.2 � 0.83 8 � 3.5 6 � 4.6Treated 8.4 � 0.89* 8 � 3.0 11 � 5.3*

11 Nontreated 10.3 � 0.97 7 � 4.3 -1 � 3.9Treated 9.7 � 1.02* 4 � 4.1* 3 � 3.9*

*Indicates p < 0.05 between treated and nontreated groups.

Clinical Crown Height (mm) of Canine and Lateral Incisors12.0011.0010.009.008.007.00

AC

D (

mm

) b

etw

een

Can

ine

and

Lat

eral

Inci

sors

4.00

3.00

2.00

1.00

Graph 1. Association between apparent contact dimension (ACD) and clinicalcrown height—canine and lateral incisors.



measurements were expressed as apercentage of the height of the ipsi-lateral central incisor. The averageACD proportions established bythis study were 49 : 38 : 27,between the central incisors, thecentral and lateral incisors, and thelateral incisor and canine, respec-tively. This proportion was verysimilar to the 50 : 40 : 30 ratioproposed by Morley and Eubankand was also consistent with theprogressive increase in incisalembrasure dimensions from themidline to the canine, evident inthe well-aligned and unworn max-illary anterior sextant. The ACDproportions exhibited excellentsymmetry with minor and clinicallyinsignificant differences betweenthe left and right sides (Table 3).

A secondary aim of this study wasto assess the effect of crown shape,clinical crown height, tip, andtorque on the ACD. Teeth wereclassified into three groups—parallel shaped (Figure 6A), barrelshaped (Figure 6B), and triangularshaped (Figure 6C)—based on thelabial outline of the maxillarycentral incisor crowns, asdescribed by O’Higgins andKirschen and colleagues.23,26 Theaverage ACD dimensions did notvary across the three groups;however, the parallel- and barrel-shaped groups did exhibit statisti-cally significant differences for theclinical crown heights of the maxil-lary central incisors. On average,

Clinical Crown Height (mm) of the Central and Lateral Incisors12.0011.0010.009.008.007.00

AC

D (

mm

) b

etw

een

th

e C

entr

al a

nd

Lat

eral

Inci

sors

7.00

6.00

5.00

4.00

3.00

2.00

1.00

Graph 2. Association between apparent contact dimension (ACD) and clinicalcrown height—central and lateral incisors.

Clinical Crown Heights of the Central Incisors13.0012.0011.0010.009.008.00

Mid

line

AC

D (

mm

)

7.00

6.00

5.00

4.00

3.00

Graph 3. Association between apparent contact dimension (ACD) and clinicalcrown height—midline.

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V O L U M E 2 1 , N U M B E R 2 , 2 0 0 9 107

parallel-shaped teeth had greaterclinical crown height than barrel-shaped teeth. The small numberof triangular-shaped teeth(N = 4) precluded anyuseful extrapolation.

As the ACD is a function of twoadjacent teeth, in order to evaluatethe relationship between the ACDmeasurements and the covariates(height, tip, and torque), the valuesfor the covariates were averagedacross each tooth pair that com-prised an ACD location. The useof paired adjacent teeth was con-sidered acceptable as there was nosignificant variation when the indi-vidual teeth were used to study theassociation between ACD and thecovariates. The height of the clini-cal crown was significantly associ-ated with the corresponding ACD,thereby implying that taller teethcould have relatively higherACD values compared withshorter teeth.

Interestingly, the orthodonticallytreated group exhibited statisticallysignificant variations in the heightsof the clinical crowns of teeth #7,10, and 11 compared with thenontreated group. This findingmay be attributable to passiveeruption, and according toMorrow and colleagues, passiveeruption may cause an increase inthe clinical crown length of themaxillary central incisors, lateralincisors and canines of subjects up

to 18 to 19 years of age.27 Agedata for the orthodontically treatedgroup was available for 31 of the40 subjects, and 81% (i.e., 25 ofthe 31) of the subjects were age18 or younger at the time of de-bonding. W/H ratios of the maxil-lary anterior teeth exhibited anegative correlation (p < 0.05) withtheir corresponding ACD locations(Table 1), thereby connoting anincrease in ACD dimensions withdiminishing W/H ratios, or viceversa. This was consistent with theaforementioned positive associationbetween the ACD and the heightof the clinical crown.

Variations in the degree of tip andtorque may influence the positionof the proximal contacts.O’Higgins and colleagues suggestedthat increasing the torque of maxil-lary incisors will lead to a palatalmovement of the proximal con-tacts.23 However, according to theresults of the present study, the tipand torque did not appear to influ-ence the ACD proportions. Thismay be because of the fact that theselection criteria for the study werespecifically set to incorporate castsof subjects with excellent occlusionand alignment, thereby narrowingthe range of deviations in tip andtorque. As a point of interest, theincisors in the orthodonticallytreated group had higher averagetorque values compared with thatin the nontreated group. Thisobservation was similar to the

study by Ugur and Yukay, whocompared the crown torque oftreated and normal (untreated)occlusion subjects and foundthat the maxillary incisors wereinclined more labially in thetreatment group.28

In this study, the TIP was used tomeasure the tip and torque of theclinical crown, with the maxillaryocclusal plane as the horizontalreference. Richmond and col-leagues measured crown inclinationon dental casts using the TIP, andreported average intraexaminererrors ranging from 2.2 to 2.6degrees, and interexaminer reliabil-ity (intraclass correlation) valuesabove 0.9 for the maxillary centralincisors.24 A comparison of TIPscores with the upper incisor to themaxillary plane inclination angleindicated that, although the TIPscores were closely related to theupper incisor to maxillary planeangles, the TIP tended to recordthe upper incisor’s axial inclinationapproximately 10.46 degreessmaller than did the lateral cepha-logram.15 Ghahferokhi and col-leagues found a similar diminutionof 14 degrees between thetooth inclination scores whencomparing the TIP withlateral cephalograms.25

Cephalometric assessment ofincisor axial inclination is based onthe premise that a line connectingthe root apex and the incisal edge



reflects the long axis of the tooth.20

Andrews’s method measures thelabial surface inclination relative tothe occlusal plane regardless of theinclination of the root or the longaxis of the entire tooth, and conse-quently, there might be lack ofcongruity between the two mea-sured components that representinclination (i.e., the long axis ofthe tooth and the labial surfaceinclination). Fredericks measuredthe angle formed by a tangent tothe labial surface and the long axisof the tooth (labial surface angle)and found a range of 17 to 38 inhis sample of 30 maxillary centralincisors.30 Similarly, Bryant andcolleagues reported a range of 7 to24 for the labial surface angle of198 central incisors.31 This rangeof variation between the labialsurface inclination and the longaxis of the tooth might explainthe reported differences ininclination between the TIP andlateral cephalograms.

Another factor to be cognizant ofis the potential for angular varia-tions (collum angle) between thelong axis of the crown and thelong axis of the root, for examplein Class II Div II malocclusions.22

Therefore, a tooth that appears tobe proclined on the lateral cephalo-gram might show a retroclinedcrown on the dental cast.20

More recently, Knosel and col-leagues compared incisor inclina-tions obtained using lateral

cephalograms with the NA line asa reference, and inclination valuesobtained from direct cast measure-ments using the TIP on corre-sponding dental casts of 67subjects between 10 and 25 yearsof age.29 They concluded thatdirect dental cast measurementsappear to be more precise andmore valuable than lateral radio-graphs.29 It is important to notethat all three aforementionedstudies did not use subjects withexcellent occlusion, thereby poten-tially affecting the range of discrep-ancy between lateral cephalogramsand direct cast measurements. Apotential limitation of this device(TIP) is that it is challenging tolocate solely by visual means theFACC that is tangential to theFA point and equidistant fromthe occlusal and gingivalextremities of the crown’sfacial surface.6

An additional finding that is ofinterest in this study was the asso-ciation between the height of theclinical crown with the tip andtorque. Andlin-Sobocki and Bodinreported that, when teeth aremoved facially, the facial gingivamay recede, thereby leading to arelative increase in the height ofthe clinical crown.32 Wennströmsuggested that facial tooth move-ment led to a reduced buccolingualtissue thickness, reduced height ofthe free gingival margin, and anincrease in the height of the clinical

crown.33 Similarly, Kornhauser andcolleagues noted that labial tippingof teeth in cross-bite led to a statis-tically significant but clinicallyinnocuous decrease in the width ofthe keratinized and attached gin-giva.34 Kandasamy and colleagues,in a recent study, observed adecrease in papillary height, rela-tive to the control group, afterlabial movement of teeth.35

Therefore, an increase in the labialinclination of the crown maybe associated with a minorincrease in the height of theclinical crown.

The age of subjects in this studyranged from the late teens to thelate 20s. Although age was notevaluated during this study, oneshould remain cognizant of thepotential for age-related variationsin ACD proportions because ofincreased incisal and proximalwear and gingival recession, bothof which are associated withincreasing age. The present studydid not assess other potential vari-ables such as incisal embrasuredimensions and height of the gingi-val papilla. Inchoate ideas forfuture research could include theuse of digitally manipulated imagesto assess the esthetic significance ofdifferent ACD proportions as wellas the investigation of the relation-ship between the ACD, incisalembrasure dimensions, and theheight of the gingival papilla(scallop depth).

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C O N C L U S I O N S

Within the limitations of this study,it is possible to conclude that theaverage ACD proportions betweenthe central incisors, the central/lateral incisors, and the lateralincisor and canine were49 : 38 : 27% of the height of anipsilateral central incisor, respec-tively. The ACD proportions exhib-ited bilateral symmetry and wereconsistent with the ideal propor-tion of 50 : 40 : 30, as proposed byMorley and Eubank. The ACDexhibited a statistically significantand positive association with theheight of the clinical crown. A sta-tistically significant and negativecorrelation was evident betweenthe ACD and W/H ratios of thecorresponding teeth, thereby imply-ing an inverse relationship betweenthe two proportions. No statisti-cally significant correlations werefound between the ACD and shapeof the clinical crown. However, theheight of the clinical crown of themaxillary central incisors didexhibit statistically significantvariations between parallel- andbarrel-shaped teeth. No statisticallysignificant correlations were foundbetween the ACD with the tip andthe torque. The orthodonticallytreated group exhibited a statisti-cally significant (p < 0.05) increasein labial crown inclination com-pared with the nontreated group.The tip and torque did exhibit astatistically significant (p < 0.05)correlation with the height of the

clinical crown, and this may bebecause of the altered position ofthe gingival zeniths or margin,thereby leading to an increase inthe height of the clinical crown.

D I S C L O S U R E

The authors do not have anyfinancial interest in the companieswhose materials are included inthis article.

R E F E R E N C E S

1. Moskowitz ME, Nayyar A. Determinantsof dental esthetics: a rationale for smileanalysis and treatment. Compend ContinEduc Dent 1995;16(12):1164–86.

2. Morley J, Eubank J. Macroesthetic ele-ments of smile design. J Am Dent Assoc2001;132(1):39–45.

3. Sarver DM. Principles of cosmetic den-tistry in orthodontics: part 1. Shape andproportionality of anterior teeth. Am JOrthod Dentofacial Orthop2004;126(6):749–53.

4. Hasanreisoglu U, Berksun S, Aras K,Arslan I. An analysis of maxillary anteriorteeth: facial and dental proportions.J Prosthet Dent 2005;94(6):530–8.

5. Magne P, Gallucci GO, Belser UC.Anatomic crown width/length ratios ofunworn and worn maxillary teeth in whitesubjects. J Prosthet Dent 2003;89(5):453–61.

6. Rufenacht C. Fundamentals of esthetics.Chicago (IL): Quintessence; 1990.

7. Gillen RJ, Schwartz RS, Hilton TJ, EvansDB. An analysis of selected normativetooth proportions. Int J Prosthodont1994;7(5):410–7.

8. Levin EI. Dental esthetics and the goldenproportion. J Prosthet Dent1978;40(3):244–52.

9. Preston JD. The golden proportion revis-ited. J Esthet Dent 1993;5(6):247–51.

10. Rosenstiel SF, Ward DH, Rashid RG.Dentists’ preferences of anterior tooth

proportion–a web-based study. J Prosth-odont 2000;9(3):123–36.

11. Ward DH. A study of dentists’ preferredmaxillary anterior tooth width propor-tions: comparing the recurring estheticdental proportion to other mathematicaland naturally occurring proportions.J Esthet Restor Dent 2007;19(6):324–37.

12. Abdullah MA. Inner canthal distance andgeometric progression as a predictor ofmaxillary central incisor width. J ProsthetDent 2002;88(1):16–20.

13. Ong E, Brown RA, Richmond S. Peerassessment of dental attractiveness.Am J Orthod Dentofacial Orthop2006;130(2):163–9.

14. Kokich VO Jr., Kiyak HA, Shapiro PA.Comparing the perception of dentists andlay people to altered dental esthetics.J Esthet Dent 1999;11(6):311–24.

15. Andrews LF. The six keys to normalocclusion. Am J Orthod 1972;62(3):296–309.

16. Andrews LF. Straight wire: the conceptand appliance. San Diego (CA): LA WellsCo.; 1989.

17. Watanabe K, Koga M. A morphometricstudy with setup models for bracketdesign. Angle Orthod 2001;71(6):499–511.

18. Currim S, Wadkar PV. Objective assess-ment of occlusal and coronal characteris-tics of untreated normals: a measurementstudy. Am J Orthod Dentofacial Orthop2004;125(5):582–8.

19. Tuverson DL. Anterior interocclusalrelations. Part I. Am J Orthod1980;78(4):361–70.

20. Wolfart S, Brunzel S, Freitag S, Kern M.Assessment of dental appearance followingchanges in incisor angulation. Int J Prosth-odont 2004;17(2):150–4.

21. Brunzel S, Kern M, Freitag S, Wolfart S.Aesthetic effect of minor changes in incisorangulation: an internet evaluation. J OralRehabil 2006;33(6):430–5.

22. Mackley RJ. An evaluation of smilesbefore and after orthodontic treatment.Angle Orthod 1993;63(3):183–9.



23. O’Higgins EA, Kirschen RH, Lee RT. Theinfluence of maxillary incisor inclinationon arch length. Br J Orthod1999;26(2):97–102.

24. Richmond S, Klufas ML, Sywanyk M.Assessing incisor inclination: a non-invasive technique. Eur J Orthod1998;20(6):721–6.

25. Ghahferokhi AE, Elias L, Jonsson S, et al.Critical assessment of a device to measureincisor crown inclination. Am J OrthodDentofacial Orthop 2002;121(2):185–91.

26. Kirschen RH, O’Higgins EA, Lee RT. TheRoyal London Space Planning: an integra-tion of space analysis and treatment plan-ning: part I: assessing the space required tomeet treatment objectives. Am J OrthodDentofacial Orthop 2000;118(4):448–55.

27. Morrow LA, Robbins JW, Jones DL,Wilson NH. Clinical crown length changesfrom age 12-19 years: a longitudinalstudy. J Dent 2000;28(7):469–73.

28. Ugur T, Yukay F. Normal facio-lingualinclinations of tooth crowns comparedwith treatment groups of standard andpre-torqued brackets. Am J Orthod Dento-facial Orthop 1997;112(1):50–7.

29. Knosel M, Kubein-Meesenburg D, Sadat-Khonsari R. The third-order angle and themaxillary incisor’s inclination to the NAline. Angle Orthod 2007;77(1):82–7.

30. Fredericks CD. A method for determiningthe maxillary incisor inclination. AngleOrthod 1974;44(4):341–5.

31. Bryant RM, Sadowsky PL, Hazelrig JB.Variability in three morphologic featuresof the permanent maxillary centralincisor.Am J Orthod 1984;86(1):25–32.

32. Andlin-Sobocki A, Bodin L. Dimensionalalterations of the gingiva related tochanges of facial/lingual tooth position inpermanent anterior teeth of children.A 2-year longitudinal study. J ClinPeriodontol 1993;20(3):219–24.

33. Wennström JL. Mucogingival consider-ations in orthodontic treatment. SeminOrthod 1996;2(1):46–54.

34. Kornhauser S, Schwartz Z, Bimstein E.Changes in the gingival structure of maxil-lary permanent teeth related to the orth-odontic correction of simple anteriorcross-bite. Am J Orthod DentofacialOrthop 1996;110(3):263–8.

35. Kandasamy S, Goonewardene M, TennantM. Changes in interdental papillae heightsfollowing alignment of anterior teeth.Aust Orthod J 2007;23(1):16–23.

Reprint requests: Vishnu Raj, UHSCSA,Department of Orthodontics, 7703 FloydCurl Drive, San Antonio, TX 78229-3900.Tel.: 919-259-2360; Fax: 210-567-2614;e-mail: [email protected]

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the apparent contact dimension and covariates among orthodontically treated and nontreated subjects

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