Journal of Dentistry Defence Section

ORIGINAL ARTICLE
Year
: 2021  |  Volume : 15  |  Issue : 2  |  Page : 111--116

Validation of mathematical relationship for anterior teeth in the Indian population


Pushkar Andhare, Sanjeev Datana, Shiv Shankar Agarwal, SK Bhandari 
 Department of Dental Surgery and OHS, AFMC, Pune, Maharashtra, India

Correspondence Address:
Sanjeev Datana
Department of Dental Surgery & Oral Health Sciences, AFMC, Pune, Maharashtra
India

Abstract

Introduction: Smile is an important part of facial esthetics. Various authors have established a mathematical correlation between maxillary and mandibular teeth dimensions and dwelled upon its importance in smile designing. The present study aims to validate one such mathematical relation in the Indian population with an objective to identify the tooth exhibiting maximum variation. Materials and Methods: The present study was conducted by using 225 study models. Mesiodistal dimensions of the maxillary and mandibular anterior teeth were recorded and applied to the mathematical relation for assessing the validation. Results: 37.8% of the study models showed complete validation of mathematical relation. Females showed significantly higher validation compared to males (P < 0.01). However, validation did not differ significantly in relation to malocclusion. 15.6% of the study models of the patients exhibited mandibular canine with increased mesiodistal dimension, 13.3% of the study models showed maxillary central incisor, while 8.9% of the study models sample showed maxillary lateral incisor with decreased mesiodistal dimension, responsible for invalidation. Conclusions: Mathematical relation under validation was found to be completely validated in 37.8% of the study sample of the Indian population. Validation was observed to be more in females than in males. Mandibular canine followed by maxillary central incisor was most commonly involved for the invalidation of mathematical relation.



How to cite this article:
Andhare P, Datana S, Agarwal SS, Bhandari S K. Validation of mathematical relationship for anterior teeth in the Indian population.J Dent Def Sect. 2021;15:111-116


How to cite this URL:
Andhare P, Datana S, Agarwal SS, Bhandari S K. Validation of mathematical relationship for anterior teeth in the Indian population. J Dent Def Sect. [serial online] 2021 [cited 2021 Nov 30 ];15:111-116
Available from: http://www.journaldds.org/text.asp?2021/15/2/111/326218


Full Text



 Introduction



Background

The smile is an important part of facial esthetics.[1] It is pertinent for an orthodontist to diagnose all functional and esthetic components of the smile.[2] Various studies have mentioned several factors that contribute to smile esthetics: buccal corridors, midlines, gingival architecture, tooth and gingival display during smiling and repose, and smile arc. Proper tooth proportions are necessary for achieving optimal occlusion, ideal alignment, and complete space closure.[3] Variations of ideal tooth anatomy are undoubtedly prevalent in every population as it is affected by various factors such as race and ethnicity. It is therefore critical to understand the ideal tooth sizes, shapes, and proportions in a particular population. The golden proportion forms one such means to calculate the ideal size of the teeth. However, this concept has been questioned in several studies that conclude the low acceptance in smile design ratios by both clinicians and patients.[4],[5],[6],[7],[8],[9],[10] Various authors such as Ballard,[11] Black,[12] and Chu[13],[14],[15] have therefore attempted to find a suitable alternative so as to determine the mean dimensions of maxillary and mandibular incisors and used the same for establishing the ideal maxillomandibular incisor ratio. Furthermore, Chu showed a significant correlation between the widths of the central incisors, lateral incisors, and canines. Based on these findings, German et al.[16] determined a mathematical correlation between dimensions of the maxillary and mandibular anterior teeth in the American population [Figure 1], which was expressed using the following formulae: If mesiodistal dimension of the maxillary central incisor is considered as “Y” mm, then the mesiodistal dimension of the maxillary lateral incisor becomes “Y – 2” mm and that of the maxillary canine becomes “Y – 1” mm. If mesiodistal dimension of the mandibular central incisor is considered as “X” mm, then mesiodistal dimension of the mandibular lateral incisor becomes “X + 0.5” mm and that of the mandibular canine becomes “X + 1” mm. Furthermore, the relationship between mesiodistal dimensions of the maxillary and mandibular central incisor was established as “Y = X + 3” mm. Using such correlations, one can determine and achieve the optimal width of a missing or anomalous tooth which will ensure achievement of adequate smile esthetics. The above-mentioned formula is a simple, easy to understand, communicate, and easy to utilize so as to obtain the desired smile esthetics. Since the morphology, size, and shape of tooth are known to have racial and ethnic variation, there is a likely possibility that the above-mentioned mathematical relation may not hold valid for worldwide populations.{Figure 1}

Aim

The present study aims to validate these mathematical correlations and equations as observed by German et al. in the Indian population.

Objectives

The study was conducted keeping in mind the following objectives:

To assess the percentage of validation in the Indian populationTo quantify the validation in relation to gender and type of malocclusionTo identify the tooth responsible for invalidation of the mathematical relationTo identify whether the invalidation is because of excess or deficient mesiodistal dimension of the involved tooth/teeth.

 Materials and Methods



Study design

The study is a cross-sectional study.

Setting

The study was carried out at the Department of Orthodontics and Dentofacial Orthopaedics of a tertiary care teaching institute of Western India.

Participants

After taking necessary ethical clearance, the pretreatment records (diagnostic study models) of the patients in permanent dentition stage with full complement of teeth present, who reported for orthodontic treatment, as available from the undertreatment cases and archives of the department, were examined for mesiodistal dimensions of the maxillary and mandibular anterior teeth.

Inclusion criteria

Patients in the permanent dentition stage with fully erupted maxillary and mandibular anterior teeth.

Exclusion criteria

Patient records showing a history of trauma resulting in fracture of anterior teeth, diagnosed syndromic case that affects dimensions of dentition, history of restorations of the anterior teeth, signs of abnormal size and shape of anterior teeth owing to attrition, erosion or any other cause, and improper records such as defective dental casts were excluded from the study.

Variables

The variables studied include mesiodistal dimensions of the maxillary and mandibular anterior teeth, type of anterior teeth, gender of the individual, and type of malocclusion.

Data source and measurements

Diagnostic study models of undertreatment cases and records from the departmental achieves of patients who reported for orthodontic treatment were assessed. After assessing the study models for any defects, the mesiodistal tooth dimensions of six maxillary and six mandibular anterior teeth were recorded using a digital caliper, sensitive up to the first decimal point. The data thus collected were subjected to mathematical relation using the formula as described by German et al.[16] [Figure 1]; any deviation from the formula was recorded and tabulated using excel sheets.

Study size

As determined by the inclusion and exclusion criteria, 225 diagnostic study models were selected for the study.

Bias

The possibility of intra- and inter-examiner bias was anticipated. To overcome the same, randomly selected 100 study models were reassessed by the same examiner (PA) and also reviewed by a senior orthodontist (SD) at interval of 1 week.

Quantitative variables

The mesiodistal dimensions of six maxillary and six mandibular anterior teeth were recorded using a digital caliper, sensitive up to first decimal point. The data were divided into different groups depending upon gender, type of malocclusion (based on Angle's classification), and tooth type to assess the extent of validation in different groups and also to identify the tooth responsible for the invalidation of mathematical relation. Moreover, an attempt was also made to identify whether the invalidation is because of excess or deficient dimensions of the responsible tooth.

Statistical methods

The data on categorical variables are shown as n (percentage of cases). The statistical comparison of distribution of categorical variables was tested using Chi-square test.[17],[18],[19] All results are shown in the tabular as well as graphical format to visualize the statistically significant difference. In the entire study, the P < 0.05 was considered to be statistically significant. All study hypotheses were formulated using two-tailed alternatives against each null hypothesis (hypothesis of no difference). The entire data were statistically analyzed using Statistical Package for the Social Sciences (SPSS version 22.0, IBM Corporation, USA) for MS Windows.

 Results



Descriptive data

The inter-examiner recordings did not show any significant difference (kappa value = 0.8). On complete evaluation of the study sample, it was observed that, out of 225 study models, 100 (44.5%) were pertaining to female patients and 125 (55.5%) were pertaining to male patients, with age group ranging from 14 to 28 years. It was also observed that there were 105 (46.7%) patients exhibiting Class I malocclusion, 110 (48.9%) patients showing Class II malocclusion, and 10 (4.4%) patients showing Class III malocclusion among the sample selected for the study.

Main results

On analysis of the study sample, it was found that of the sample of 225, 85 (37.8%) study models showed 100% validation which means that mesiodistal dimensions of all the teeth were in accordance with the mathematical relation; 100 (44.4%) study models exhibited 83% validation which implies that 2 teeth out of 12 anterior teeth did not follow the mathematical relation and 40 (17.8%) study models showed 66% validation which means that 4 teeth out of 12 anterior teeth did not follow the mathematical relation [Table 1] and [Figure 2]. On evaluating the validation in relation to gender, significantly higher validation was observed in female cases compared to male cases in the study sample (P < 0.01) [Table 2] and [Figure 3]. The validation in respect to malocclusion did not differ significantly with the type of malocclusion (P > 0.05) [Table 3] and [Figure 4].{Table 1}{Figure 2}{Table 2}{Figure 3}{Table 3}{Figure 4}

On assessing the tooth responsible for making the mathematical relation invalid, it was found that in 100 study models, only one tooth type was responsible for the invalidation of the mathematical relation, while in 40 study models, two types of teeth were responsible for making the mathematical relation invalid in the study group. Mandibular canine was most commonly involved in the invalidation of the mathematical relation, followed by maxillary central incisor and maxillary lateral incisor. Mandibular lateral incisor was in tandem with the mathematical relation in all the study models; therefore, no study model exhibited invalidation of the mathematical relation because of mandibular lateral incisor [Table 4] and [Figure 5].{Table 4}{Figure 5}

Considering the mathematical relation and values derived from its formula as standard, it was found that most commonly the study models exhibited increased mesiodistal dimensions of the mandibular canine. In the study models showing maxillary central or lateral incisor involved for invalidation, decrease in the mesiodistal dimension was evident [Table 5] and [Figure 6].{Table 5}{Figure 6}

 Discussion



Key results

The mathematical relation was completely validated in 37.8% of the study sample of Indian population. The validation was significantly more in females as compared to males. No significant correlation of malocclusion and validation of mathematical relation could be established. Most common tooth responsible for invalidation was mandibular canine, followed by maxillary central incisor, maxillary canine, and finally maxillary lateral incisor. Mandibular and maxillary canine exhibited increased mesiodistal dimension, whereas maxillary central and lateral incisor exhibited decreased mesiodistal dimensions in the study sample.

Limitations

The study sample did not have equal distribution in terms of malocclusion, therefore resulting in unproductive result in relation to malocclusion and invalidation of mathematical relation. The study is a record-based study conducted on diagnostic plaster model of the patients; hence, the possibility of dimensional changes in the plaster models due to time lapse in fabrication of diagnostic models cannot be ruled out.

Interpretation

Mandibular central incisor was found to have the least variations in terms of morphology and dimensions and hence was considered as basis for deriving the mathematical relation between maxillary and mandibular anterior teeth. This mathematical relation gives a guiding reference for anticipating the tooth dimensions of missing or morphologically defective tooth, therefore assisting in achieving ideal relation between maxillary and mandibular anterior teeth so as to yield a better esthetic outcome.[3]

The disparity of tooth size in maxillary and mandibular teeth can be a potential factor for minor malocclusions and may interfere in achievement of correct occlusion. This can be treated by selective mesiodistal resizing of the concerned tooth and minor tooth movement. It is therefore essential to analyze and isolate the tooth responsible for the discrepancy, taking into consideration the acceptable relative proportions between maxillary and mandibular teeth.[20] Bolton's analysis is used in Orthodontics for identification and calculation of the discrepancy in size of maxillary and mandibular teeth. However, there are limitations to the use of this analysis: it was estimated for the Class I cases only and variations in other type of malocclusions were not considered, the analysis did not identify the tooth responsible for discrepancy and further did not highlight the excessiveness or deficiency of the tooth size.[21],[22] Hence, the mathematical relation suggested by German et al. proves to be beneficial. Various authors have tried to establish the existence of golden proportion in the Indian population but found golden proportion to be an inappropriate method to relate tooth dimensions.[23] Literature search however does not yield any study that validates the mathematical relation illustrated by German et al. in the Indian population. The present study therefore aims to validate this relation in the Indian population. It is evident from the previously conducted studies that gender dimorphism is persistent[24],[25],[26] which was also seen in the present study. It is also proven that the upper canines and upper central incisors show the greatest gender differences,[24] whereas the upper lateral incisor and lower central incisor are the most homogenous,[25],[26] which substantiate the basis of the mathematical relation in making the mandibular central incisor as a reference to calculate dimensions of other teeth in the maxillary and mandibular anterior segment. The maxillary lateral incisor has been proven to be the most common tooth responsible for morphological variation and dimensional abnormalities with reduced tooth dimensions.[27] However, in the present study, the most common tooth responsible for invalidation was found to be mandibular canine with increased mesiodistal dimensions followed by maxillary central incisors with reduced mesiodistal dimensions. The inconsistency of the result with the previous conducted studies might be because of small sample size and uneven distribution in terms of type of malocclusion in the study sample.

 Conclusions



The present study observed that the mathematical relation under verification was found to be completely validated in 37.8% of the study sample of the Indian population. The mathematical relation holds true, more in female patients as compared to males. No significant correlation between types of malocclusion could be established, probably owing to uneven distribution of type of malocclusion in the study sample. Most commonly involved tooth for invalidation was observed to be the mandibular canine which exhibited increased mesiodistal dimensions, followed by maxillary central incisors, which mainly showed decreased dimensions. It is recommended that more such studies with larger sample size and better distribution of type of malocclusion be carried out, which will establish a more efficient and effective mathematical relation between maxillary and mandibular teeth in esthetic zone and also identify the tooth showing maximum variation. Such research data will certainly assist a clinician in space management during the treatment and establish ideal tooth size in relation to obtain esthetically pleasing and balanced outcome.

Financial support and sponsorship

Nil.

Conflicts of interest

There are no conflicts of interest.

References

1Naini FB, Gill DS. Smile aesthetics. In: Naini FB, editors. Facial Aesthetics Concept and Clinical Diagnosis. West Sussex, UK: Wiley-Blackwell; 2011. p. 370-86.
2Fields HW. Orthodontic-restorative treatment for relative mandibular anterior excess tooth-size problems. Am J Orthod 1981;79:176-83.
3Bolton WA. Disharmony in tooth size and its relation to the analysis and treatment of malocclusion. Angle Orthod 1958;28:113-30.
4Levin EI. Dental esthetics and the golden proportion. J Prosthet Dent 1978;40:244-52.
5Lombardi RA. The principles of visual perception and their clinical application to denture esthetics. J Prosthet Dent 1973;29:358-82.
6Kokich VO Jr., Kiyak HA, Shapiro PA. Comparing the perception of dentists and lay people to altered dental esthetics. J Esthet Dent 1999;11:311-24.
7Kokich VO, Kokich VG, Kiyak HA. Perceptions of dental professionals and laypersons to altered dental esthetics: Asymmetric and symmetric situations. Am J Orthod Dentofacial Orthop 2006;130:141-51.
8Rosenstiel SF, Rashid RG. Public preferences for anterior tooth variations: A web-based study. J Esthet Restor Dent 2002;14:97-106.
9Rosenstiel SF, Ward DH, Rashid RG. Dentists' preferences of anterior tooth proportion-a web-based study. J Prosthodont 2000;9:123-36.
10Witt M, Flores-Mir C. Laypeople's preferences regarding frontal dentofacial esthetics: Periodontal factors. J Am Dent Assoc 2011;142:925-37.
11Ballard ML. Asymmetry in tooth size: A factor in the etiology, diagnosis and treatment of malocclusion. Angle Orthod 1944;14:67-70.
12Black GV. Descriptive Anatomy of the Human Teeth. 4th ed. Philadelphia: SS White Dental Mfg. Co.; 1902.
13Chu SJ. Range and mean distribution frequency of individual tooth width of the maxillary anterior dentition. Pract Proced Aesthet Dent 2007;19:209-15.
14Chu SJ, Okubo S. Range and mean discordance of individual tooth width of the mandibular anterior dentition. Pract Proced Aesthet Dent 2008;20:313-20.
15Chu SJ. A biometric approach to predictable treatment of clinical crown discrepancies. Pract Proced Aesthet Dent 2007;19:401-9; quiz 410.
16German DS, Chu SJ, Furlong ML, Patel A. Simplifying optimal tooth-size calculations and communications between practitioners. Am J Orthod Dentofacial Orthop 2016;150:1051-5.
17Rosner B. Fundamentals of Biostatistics. 5th ed. Duxbury: Thomson Book; 2000. p. 80-240.
18Riffenburg RH. Statistics in Medicine. 2nd ed. Cambridge: Academic Press; 2005. p. 85-125.
19Rao PS, Richard J. An Introduction to Biostatistics: A Manual for Students in Health Sciences. 4th ed. New Delhi: Prentice Hall of India; 2006. p. 86-160.
20Sanin C, Savara BS. An analysis of permanent mesiodistal crown size. Am J Orthod 1971;59:488-500.
21Lavelle CL. Maxillary and mandibular tooth size in different racial groups and in different occlusal categories. Am J Orthod 1972;61:29-37.
22Arya BS, Savara BS, Thomas D, Clarkson Q. Relation of sex and occlusion to mesiodistal tooth size. Am J Orthod 1974;66:479-86.
23Chander GN, Kumar VV, Rangarajan V. Golden proportion assessment between maxillary and mandibular teeth on Indian population. J Adv Prosthodont 2012;4:72-5.
24Doris JM, Bernard BW, Kuftinec MM, Stom D. A biometric study of tooth size and dental crowding. Am J Orthod 1981;79:326-36.
25Araujo E, Souki M. Bolton anterior tooth size discrepancies among different malocclusion groups. Angle Orthod 2003;73:307-13.
26Potter RH. Univariate versus multivariate differences in tooth size according to sex. J Dent Res 1972;51:716-22.
27McArthur DR. Determination of approximate size of maxillary anterior denture teeth when mandibular anterior teeth are present. Part III: Relationship of maxillary to mandibular central incisor width. J Prosthet Dent 1985;53:540-2.