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Posterior tooth size discrepancy

Arlette OUEISS, Christine MARCHAL-SIXOU, Ahmad DALLOW,Pascal BARON, Jacques FAURE

Address for correspondence:

J. FAURE Faculté de Chirurgie dentaire (UPS, Toulouse III), Service d’Orthopédie dento-faciale 3, chemin des Maraïchers, 31400 Toulouse. faure_ja@club-internet.fr

ABSTRACT

Despite having a correct anterior occlusal relationship between upper and lower teethwith canines in perfect Class I, some patients have imperfect posterior occlusal relation-ships with first molars in positions that are slightly Class II or Class III owing to an archlength discre pancy in the upper and lower buccal segments.

From this study of 62 subjects treated with full banded appliances and no bicuspidextrac tions we were able to determine the ideal relationship of the widths of the lowerbicuspid and molar teeth with their upper antagonists, one that make it possible for theattainment of Class I relationships of both canines and first molars. This ideal value is1.062.

We discuss the therapeutic implications of this finding, notably its influence on extrac-tion decisions and propose solutions for cases of frank disharmony.

KEYWORDS

Occlusal finishing

Tooth size dyscrepancy.

DOI: 10.1051/odfen/20084210009 J Dentofacial Anom Orthod 2008;11:08-22© RODF / EDP Sciences

Article available at http://www.jdao-journal.org or http://dx.doi.org/10.1051/odfen/20084210009

Oueiss A. et al. Posterior tooth size discrepancy9

ARLETTE OUEISS ET AL.

Ideal occlusion is defined as thesimultaneous occurrence of Class Icanine and Class I molar relationships,with an important additional elementassociated with the character of theanterior elements, that is the caninefunction. The tenets of occlusodontiainsist on the dominant importance ofcanine gui dance, which rigorouslyrequires that the canines be in Class Iin closure.

Class I molar relationship is seenin full inter-cuspation in centric rela-tion when the position of the mesio-palatal cusp of the upper first molarlies in the central fossa of the lowerfirst molar. The corresponding buccalposition by classical definitionrequires that the mesio-buccal cuspof the upper first molar should restin the buccal groove of the lowerfirst molar. But many authors haveadopted another definition for anideal molar relationship: the buccalcusp of the upper second bicuspidshould be inserted preciselybetween the lower second bicuspidand lower first molar.

In our daily clinical practice we findthat the simultaneous attainment ofideal anterior and posterior relation-ships is far from routine.

the posterior situation that seemsclearly to have priority.

But in occlusodontia, anterior guid-ance is the dominant element and thetherapist should accord it first consid-eration and then help the buccal seg-ments to come into harmony with theanterior teeth.

This means the practitioner shouldscrupulously regulate anterior guid-ance while keeping posterior teethout of occlusion, in a “pre-eruptive”position or Tweed’s post-therapeuticocclusion, which is a reversal of nor-mal development chronology. In thisconception, molar groups occludeafter the anterior sector does and, it ishoped, do it in accordance with func-tional constraints. This is the thera-peutic stance that we prefer.

1 - INTRODUCTION

1 - 1 - Should orthodontistsfavor one relationshipand, if so, which one?

If one reflects on the developmentof the dentition, it is clear that theinter-cuspation of buccal centricocclusion establishes itself first andthat the anterior occlusion confirmsitself much later in an adaptation to

1 - 2 - How to analyze the frequently observed difference between animperfect Class I molarrelationship accompa-nied by a perfect ClassI canine relationship?

Unless lateral diastemas are pre-sent in one of the arches, this lack ofconcord in the Class I relationships ofthe molars and canines can beexplained by a posterior tooth sizediscrepancy (fig. 1).

If the sum of the mesio-distalwidths of the groups of upper bicus-pids and molars is greater than thetotal over-all widths of the corre-sponding lower teeth, when thecanine teeth are in Class I the molarswill have to be in Class III, or if the

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POSTERIOR TOOTH SIZE DISCREPANCY

molars are in Class I the canines willhave to be in Class II. We believe thatthe first, a Class I canine and Class IIImolar is preferable. We often note,

with some dismay, that when wehave completed treatment with awell-seated Class I molar relationship,that the canines are slightly in Class II

Figure 2The upper and lower anatomic ele ments responsible for the lack of conformity betweenthe Class I molar relationship and the Class I canine relationship.

Figures 1 a and bThe responsibility of the posterior arch length discrepancy in the establishment of a ClassIII in cases of excess maxillary tooth substance;a: occlusion with Class I molars and canines;b: occlusion with Class I canine and “Andrew key” molar relationship.

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ARLETTE OUEISS ET AL.

and that a minor overjet remains. Thetreating orthodontist had certainlyremoved the appliances without com-pleting a finishing stage when itwould have been advisable to add astage of Class II mechanics and,doubtless, lighten the molar contacts!Some authors suggest, especially inClass II type patients, that at termina-tion of treatment the upper molarsshould be left in a slight Class III rela-tionship and angled with a forward tipas they “embrace” the lower molars.

It is surprising that this positioning isunderlined proudly: if the molars occu-py such a position it is because there isa slight tooth size posterior discrepancy(upper exces). It is interesting to notethat the occlusion Tweed advocated,upper molars tipped back and distalcusps out of occlusion, arrives sponta-neously as an Andrews key threemonths after removal of appliances,when there is an excess of upper toothmaterial (for example fig. 4)!

Therefore, the observation of anAndrews key in a finished case withperfect anterior relationships doesn’tresult from an exquisite treatment fin-ishing of the occlusion, but from ananatomic accident (an excess of pos -terior maxillary tooth material).

molar and in part to the distance inthe mandible between the canine-bicuspid space and the buccal grooveof the first molar (fig. 2). These quan-tities correspond respectively tothese totals:

– Distal half of the canine, mesio-distal width of the premolars,mesial portion of the first molar(distance mesio-buccal cusp/mesialcontact point).

– Mesio-distal widths of the pre-molar-mesial portion of the firstmolar (distance buccal groove/mesial contact point).

In this study, the interactionbetween the bicuspid-molar groups isonly an approximation: the completeintegration of their anterior portionscan be accomplished only if their mor-phology is not atypical.

We explain our not including theupper demi- canine in the study by oursample’s presentation of uniformlyperfect canine Class I, a testimony tothe standardization of canine mor-phology.

1 - 3 - What teeth are responsible for the archlength discrepancy that created imbalance inthe anterior and poste-rior Class I relationship?

The lack of concord between thequalities of the Class I canine and theClass I molar relationships may berelated n part to the distance in themaxilla between the canine cusp andthe mesio-buccal cusp of the first

1 - 4 - What factors areinvolved in extractionchoice when an archlength discrepancy is present?

Some members of the orthodonticcommunity point an accusatory fingerat the extraction of first bicuspid teeth.In a view widely shared by clinicians,they affirm that the first premolar is amore important tooth in the maxillaryarch than the second bicuspid, whilethe lower second bicuspid plays amore important functional role thandoes the mandibular first bicuspid. Theextraction of first bicuspids in the max-illa subtracts more tooth substance

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ARLETTE OUEISS ET AL.

Figures 3 a to sManagement of a complex arch length discrepancy case, with a deliberate decision to fin-ish with an “Andrews key” occlusion of the molars.This patient, who originally had a Class III malocclusion with a complex arch length dis-crepancy, was treated in two stages, with extraction of the premolars (15-25-34-44) andthe third molars. Thesefindings were, present:

– an anterior arch length discrepancy with excess mandibular tooth material, managedby stripping from canine to canine, finished with a much reduced anterior overbiteand a rigorously maintained canine Class I relationship;

– a posterior arch length discrepancy (maxillar excess) that was left intact with noreshaping or stripping of teeth and the molars left in a slight Class III “Andrews key”relationship.

a, b and c: portraits at the beginning of treatment: 2/94, 9a 7m; d, e and f: intra-oral views at the beginning of treatment: 2/94, 9a 7m;g, h and i: portraits at the end of the full-banded treatment: 2/2000, 15a 7m;j, k and l: intra-oral views on the day of band removal: 2/2000, 15a 7m;m: headplate at the end of full-banded treatment: 2/2000, 15a 7m;n: cephalometric findings at the close of bull-banded treatment: 2/2000, 15a 7m;o: cephalometric changes: Steiner analysis;p: cephalometric changes: Tweed analysis;q, r and s: intra-oral views three years after treatment, showing good stability: 8/2003, 19a 1m.

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POSTERIOR TOOTH SIZE DISCREPANCY

Figures 4 a to fUndetected posterior arch length discrepancy with excess maxillary tooth material. This was a severe hyperdivergent Class II malocclusion with an arch length discrepancycaused by excess maxillary tooth structure.A Tweed type occlusion was achieved fairly quickly as shown on the day of band removal.The rigorous Class I canine relationship remained unchanged, but the originally “pre-erup-tive” molar teeth changed rapidly into a characteristic “Andrews key” relationship:a, b and c: intra-oral views on the day of band remo- val;d, e and f: intra-oral views five years after treatment. The extractions (14-24-34-44) did notplay a role one way or another in the arch length discrepancy caused by an excess of pos-terior maxillary tooth material. This case was present in a thorough fashion in the Revued’Orthopédie Dento-Faciale, 2005;39:449-76.

If it is clear that an arch length dis-crepancy is responsible for the non-conformance of the quality of the ClassI relationship in the canine and molarregions, its extent must be measuredand corrected when it is large:

– by augmentation in the formof a prosthe sis or a restora-tion;

– by reduction through inter-proximal strip ping;

than would removal of second bicus-pids, but less in the mandible. Theextraction of mandibular first bicus-pids, therefore, would effect an excessof lower tooth structure and contributeto a Class II tendency. The sacrifice oflower second bicuspids would havethe opposite effect.

So a selective variation of extrac-tion candidates would be less disturbing to molar relationshipsthan extraction of the same tooth ineach quadrant. But the literaturedoes not agree in a confirmation ofthe existence of significant differ-ences4,5,7,8,9,11.

1 - 5 - Should we make harmonious extraction choices routinely?

2 - MATERIALS AND METHODS

Our study sample consisted of 62nonextraction cases treated with amultiband appliance.

We obtained the records from anorthodontic office whose three practi-tioners have all earned certificates ofexcellence or from the Toulouse-Rangueil Department of Orthodon-tics for cases students had presentedfor the CECSMO national examina-tion.

The criterion for inclusion in thestudy was a standard occlusion withperfect Class I canine relationship andnormal incisor positioning thatremained stable in the post-treat-ment period.

The criteria for exclusion were:– extractions of bicuspids or ante-

rior teeth. Cases with third molarextractions were accepted;

– a non-standard terminal occlu-sion, usually documented tohave been the result of lack ofcooperation as documented inthe administrative record.

We measured the mesio-distaldiameters of all the teeth with a calipers that was accurate to 0.05 mm.

We evaluated the optimal Rpivalue of the relationship of the sixlower posterior teeth with the sixupper posterior teeth 6PL6PU withthree different methods:

– an “anatomic” based on the idealrela tionships defined by Boltonfor the anterior region, Rai, and forthe entire dentition Rti;

– an “average anatomic” thatused as an average value of therelationship Rp=6PI/6PS as areference base;

– an occlusal that examined therelationship between the Class Iqualities of the canines and themolars.

• An “anatomic” based on the Bolton IndexThe Bolton Index is defined as the

ideal relationship between anteriorgroups of six teeth Ra=6LA/6UA) andthe complete dentition, with the sec-ond molars excluded, Rt= 12L/12U.

The precise definition of the anteri-or and posterior occlusal relationshipsdepends on a pre-determination offour dimensional para meters: 6LA,

2 - 1 - Material and the measurement method

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ARLETTE OUEISS ET AL.

– by appropriate selectiveextractions.

Considerable interest has beenevidenced in the literature ininciso-canine relationships andways of managing anterior lack ofhar- mony1,2,3,4,5,6,10. But studiesincluding the posterior region are,

to date, quite rare1,2. Very few authorshave considered the occlusal conse-quences of tooth to tooth inharmony5.Accordingly, we concluded that aninvestigation into the relationshipbetween arch length discrepancy andocclusal malrelationships would beworthwhile.

2 - 2 - Mathematical methodof evaluating the optimal Rpi relationship

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POSTERIOR TOOTH SIZE DISCREPANCY

We calculated the averages andthe standard deviations of the mesio-distal widths of each tooth. Wedescribed the distribution, averageand standard deviation, of the dentalgroups being considered, 6UA, 6LA, 6UP, 6LP, 12U, 12L, as well as the distribution of the signifi cant relation-ships, Ra, Rp, Rt and the ante- rior/total: RatU and RatL, were evaluated.

We also assessed the significantcharacter of the differences betweenfirst and second bicuspids in the two arches by means of a Student t test.

The correlation coefficients of thetype of molar relationship with RatUand RatL, measured by a t test, were

6UA, 6LP, 6UP (or possibly 6LA, 6UA,12L, 12U because 6LP=12L-6LA and6UP=12U-6UA). If one of these para -meters is known, the values of thethree others can be calculated byusing the relationships Ra and Rp (orpossibly Rt), but in addition the rela-tionship of anterior dentition/totallower dentition or of anterior den-tition /posterior dentition must beadded. We use the relationship anteri-or denture/total lower denture,RatL=6LA/12L, or upper, RatU= 6UA/12U=Rt.RatL/Ra.

We at first studied the relationshipbetween the parameters and the pos-terior occlusal relationships anddefined the ideal relationships RatUior RatLi.

For the theoretical reason we havealready stated the relationship of thesix lower posterior teeth to the sixupper posterior teeth, 6LP/6UP, can-not be expressed solely with the helpof the Bolton indices Ra et Rt, therelationship of the anterior dentitionto the total must also be included.

A dentition in equilibrium is definedas one in which there is an ideal rela-tionship between its anterior elementsand its totality, Rai and Rti. With a deter-mination of the ideal relation ships RatUior RatLi, a calculation of the corre-sponding ideal value Rpi can be made.

• The average anatomic methodWith a calculation of the sums of

the dia meters of the posterior teeth(4-5-6) of the two arches we wereable to determine the ave rage dimen-sional relationship, which should cor-

respond to what would be expectedin a dentition in equilibrium.

• Occlusal method seekingaccord between the Class I of the canines and the Class I of the molarsThe dentitions of our study sample

were in perfect Class I canine rela-tionship but their molar relationshipshad changed from a mode rate Class IIto a moderate Class III. The relation-ship of the over-all dimensions of thegroup of upper posterior teeth to theover-all dimensions of the group oflower posterior teeth, Rp = 6LP/6UP,pre-disposed a priori the final molarrelationships. A study of the relation-ships between the extent of themolar Class II and the Rp relationshipwould make it possible to determinethe optimal occlusal relationship, thatis one capable assuring both a Class Icanine and a Class I molar inter- cuspation.

2 - 3 - Statistical methods

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ARLETTE OUEISS ET AL.

significant after the values 0.245/0.315/0.391 with respective confi-dence levels of 5%/1%/1%o. Withregres sions we were able to moreeffectively pin point the optimumvalue for Rp.

The regression rate of the molarclass with respect to the Rp relation-ship precisely defines the ideal valuefor this relationship.

For this study we re-grouped theright and left observations and ana-lyzed the variation of unilateral Rpwith the extent of the correspondingClass II relationship. The sample consisted of 124 individuals. The significance thresholds for r were:0.174/0.227/0.288 at the same confi-dence levels.

3 - RESULTS

The correlation coefficient betweenthe over-all occlusal Class III (Right +Left) and the relationship RatL is highlysignificant. The rate of regressionshows that the Class I is acquired by

RatLi = 0.4133 (fig. 5), very close tothe other reference, the average valueof RatL.

The correlation with RatU is notsignifi cant.

The correlations of Rp with RatLor RatU show the role that the rela-tionship between the anterior denti-tion and over-all dentition plays in

3 - 1 - “Anatomic” methodbased on the Boltonindices

Figure 5 Regression graph of the molar relationship (the extent of the Class III) as a function of theanterior den- tition/total lower dentition relationship (RatI).The correlation coefficient is highly significant (0.519); the value corresponding to Class Iis 0.4133.

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Table IAverages and standard devi-ations of the study sample:

Ra: 6LA/6UA;Rt: 12L/12U;Rp: 6LP/6UP;RatU: 6UA/12U;RatL: 6LA/12L.

Mean Stand. Dev.

Ra 0,7638 0,0216

Rt 0,9154 0,0184

Rp 1,0658 0,0322

RatS / RatU 0,4975 0,0085

RatI / RatL 0,4151 0,01

Mean Stand. Dev. Mean Stand. Dev.

16 9,826 0,465 46 10,875 0,687

15 6,57 0,477 45 7 0,438

14 6,854 0,396 44 6,956 0,425

13 7,754 0,544 43 6,68 0,406

12 6,773 0,542 42 5,733 0,361

11 8,594 0,443 41 5,185 0,296

21 8,6 0,509 31 5,243 0,29

22 6,81 0,497 32 5,764 0,369

23 7,727 0,427 33 6,706 0,4

24 6,892 0,407 34 7,031 0,38

25 6,68 0,476 35 6,985 0,415

26 9,888 0,467 36 10,914 0,621

6AS/6UA 46,258 2,358 6AI/6LA 35,31 1,681

12S/12U 92,968 4,332 12I/12L 85,073 3,754

3PSD/3RUP 23,25 1,116 3PID/3RLP 24,831 1,251

3PSG/3LUP 23,46 1,175 3PIG/3LLP 24,931 1,221

6PS/6UP 46,71 2,255 6PI/6LP 49,762 2,442

Table IIAverages and standard deviations of the study sample for the different teeth andthe different groups of teeth:– anterior groups (6UA and 6LA);– arches (12U et 12L);– right and left posterior groups (respectively 3RUP and 3RLP/3LUP and 3LLP);– complete posterior groups (6UP and 6LP).

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ARLETTE OUEISS ET AL.

The relationships of the sums ofthe dia meters 4-5-6 on the lower withthe upper give (table II):

Rpi = 1.0658+/-0.0322

The equation or the regression rateimmediately records a perfect Class I(fig. 6):

Rpi= 1.0699

3 - 2 - “Anatomic average”method

3 - 3 - Occlusal method seeking an accordbetween Class I canineand Class I molar

the occlusal relationships of thepos terior teeth, respectively r =-0.497 and r = 0.357).

The average values for RatL andRatU are respectively 0.4151 and0.4975 (table I).

The recording of these values inthe 1 and 2 formulas by means of theideal Bolton values for Rai and Rtimake it possible to calculate the Rpi.

From the formulas 1 and 2 weget, res- pectively, for the Rp rela-tionship.

Rpi = 1.0526andRpi= 1,0489

Figure 6 Regression graph of the molar relationship (the extent of the Class III) as a function of thelower posterior dentition/upper posterior dentition (Rp).Le correlation coefficient is highly significant (-0.583); the value corresponding to Class Iis 1.0699.

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4 - 3 - What value should the Rpi have?

At the beginning of treatment,orthodontists should review morphol-ogy of premolars and molars withconsiderable vigilance, in order tomake a de visu assessment of thepossible presence of any substantialposterior arch length discrepancy. Thisdoes not mean that they should rou-tinely and systematically measure themesio-distal widths of all the teeth tocalculate the Ra, Rp and Rt.

Unfortunately, in actual practiceorthodontists usually do not discern aposterior arch length discrepancy prob-lem until they have finished the bulk oftreatment and are approa- ching thefinishing stage, the warning sign beinga lack of concordance between theClass I relationships in the canine andin the molar areas. Most often practi-tioners rejoice in having obtained afrank Class I molar relationship andthen desperately try to improve thecanine situation, which is slightly ClassII with a modest remaining anterioroverjet or the opposite, an end-to-endanterior occlusion. More rarely theanterior relationships are perfect butthe molars seem stuck in a slight ClassII or modest Class III.

The observation of an averageanterior rela- tionship Ra, close to theBolton value, confirms the orthomor-phic nature of the sample table II). Theweak observed standard deviationtype is related to patients having aperfect Class I canine, making itimpossible for the Bolton Index tovary much from the ideal value.

We have already criticized themethod we adopted utilizing the sumof the mesio-distal diameters of thepremolars and the first molar for cal-culating the Rp. The highly significantcorrelations between Class II occlusaland Rp show that the approximationadopted was justified.

4 - DISCUSSION

4 - 1 - Criticism of the method

4-2- The role of the choice of extractions of bicuspidsin the creation or correc-tion of a posterior archlength discrepancy

The mesio-distal diameters werecorded are very close to those citedin the literature 7,8,9,11; the differencebetween the first and second pre-molars is significant in the maxilla(0.248 mm, t = 8.847) but it is not inthe mandible.

These results support the concep-tion that choosing the upper right andleft first bicuspids for extraction con-tributes to an excess of maxillary toothsubstance and a Class II molar rela-tionship while selection of the upperright and left second bicuspids leads toa deficit in maxillary tooth material anda Class III molar relationship.

The average of the three determi-nations, very close to each other, canbe kept for reference:

Rpi = 1.062

4 - 4 - What clinical considera-tions should this studyhave for practitioners?

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ARLETTE OUEISS ET AL.

At that time the orthodontist oughtto quantify the arch length discrepan-cy by calculating the Rp index, whichhelps to assess the excess of toothsubstance in one arch or defi cit in theother. Thus in the present an increa-sed Rp, the orthodontist can either:

– consider the inferior arch to becorrect and then calculate theideal maxillary value: 6UPi=6LP/Rpi and thus the upperdeficit would be: 6UPi-6UP;

– consider the superior arch to becorrect and then calculate theideal mandibular value: 6LPi=6UPxRpi and thus the mandibu-lar excess: 6LP-6LPi.

The primary therapeutic objectiveis the establishment and the comfort-able implemen tation of a canine ClassI and of perfect anterior guidance. Asfor the posterior relationships, whichwould then be out of kilter, the thera-peutic stance to adopt would dependupon the severity of the arch lengthdiscrepancy and the patient’s willing-ness to undergo additional treatment.

– In the pursuit of an ideal treat-ment result, the orthodontistwould correct the lack of mor-phological harmony if possible

by removing inter-proximalenamel by stripping or, effective-ly, increasing enamel mass withcomposite fillings, remakingprostheses, or appropriatelyadapting mesio-occlusal andmesio-distal restorations.

– By accepting an imperfect ClassI molar relationship but rigorous-ly adjusting the occlusion in cer-tain cases, for example amodest Class III molar relation-ship in a patient with a Class IIItype face to secure a stableocclusion (fig. 3), especiallywhen anterior occlusion is per-fect.

– When the observed imperfec-tions are indications of over-cor-rection, for example, a modestClass III finish of a mal-occlusionthat was originally Class II (fig.4), this situation is “no risk”. Theorthodontist has only to adjustthe anterior occlusion scrupu-lously and the molars will spon-taneously seat themselves inaccordance with this optimalcompromise of and Andrewskey to occlusion.

5 - CONCLUSION

This study emphasizes the impor-tance of posterior arch length dis-crepancy and pro poses ameasurement tool, the posteriorlower to upper relationshipRp=6LP/6UP(reference value: 1.062).

Lack of posterior harmony isresponsible for instances of non-con-cordance of the Class I relationshipsof the canines and the molars.

Confronted with this clinical situa-tion, our therapeutic choice isunequivocally to aim at achieving aperfect anterior guidance:

– either by accepting a slightimperfection in the posteriorrelationships as would beexpected by the Rp reading;

– or by changing the shape andsize of selected posterior teeth.

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1. Bolton W.A. Disharmony in tooth size and its relation to the analysis and treatment ofmalocclusion. Am J Orthod 1958;28:113-30.

2. Bolton W.A. The clinical application of tooth size analysis. Am. J Orthod 1952;48:504-29.3. Faure J, Baron P. Troubles morphologiques du bloc incisif supérieur. J Edge

1997;36:78-88.4. Freeman J.E, Maskeroni A.J, Lorton L. Frequency of Bolton tooth size discrepancy

among orthodontic patients. Am. J Orthod 1996;110:24-7.5. Grosby D.R, Alexander C.G. The occurrence of tooth size discrepancy among different

malocclusion groups. Am. J Orthod 1989;95:186-9.6. Lorette M.A. Dysharmonies dento-basales et dento-dentaires. Orthod. Fr 1975;46:177-84.7. Marseiller E. Les dents humaines: morphologie. Gauthier-Villars éditeur. 1969.8. Nabbout F, Faure J, Baron P, Braga J, Treil J. Anatomie dentaire et orthodontie. L’apport

du scanner 3D/Dental anatomy and orthodontics. The benefit of the 3D scanner. RevOrthop Dento Faciale 2003;37:59-73.

9. Nabbout F, Faure J, Baron P, Braga J, Treil J. L’ancrage dentaire en orthodontie: les don-nées du scanner/Tooth anchorage in orthodontics: scanner generated data.International Orthod 2004;2:241-56.

10. Pujol A. Contribution à l’étude des dysharmonies dento-dentaires. Thèse 3° cycle Sci.Odontol. Bordeaux. 1977; n°43047708.

11. Romorovski J, Bresson G. Morphologie dentaire de l’adulte. EMC Editions tech-niques. Stomatologie 1994;22003(A-10):34 pages.

REFERENCES

Abbreviations employed in this study:6LA: sum of the mesio-distal widths of the lower incisor-canine group (43;42; 41; 31; 32; 33)

6UA: sum of the mesio-distal widths of the upper incisor-canine group (13;12; 11; 21; 22; 23)

12L: sum of the mesio-distal widths of the teeth between the two lower firstmolars (46; 45; 44; 43; 42; 41; 31; 32; 33; 34; 35; 36)

12U: sum of the mesio-distal widths of the teeth between the two upperfirst molars (16; 15; 14; 13; 12; 11; 21; 22; 23; 24; 25; 26)

6LP: sum of the mesio-distal widths of the lower premolar-molar group (46;45; 44; 34; 35; 36)

6UP: sum of the mesio-distal widths of the lower premolar-molar group (16;15; 14; 24; 25; 26)

Ra: 6LA/6UA

Rt: 12L/12U

Rp :6LP/6UP

RatU: 6UA/12U

RatL: 6LA/12L