

ORIGINAL ARTICLE 

Year : 2021  Volume
: 8
 Issue : 3  Page : 143148 

Evaluation of maxillary anterior tooth proportion using the novel TR proportion
Tarulatha R Shyagali^{1}, Ruchi Jha^{1}, Deepak Bhayya^{2}, Abhishek Gupta^{1}, Anil Tiwari^{1}, Rahul Patidar^{1}
^{1} Department of Orthodontics and Dentofacial Orthopedics, Hitkarini Dental College and Hospital, Jabalpur, Madhya Pradesh, India ^{2} Department of Pediatric and Preventive Dentistry, Hitkarini Dental College and Hospital, Jabalpur, Madhya Pradesh, India
Date of Submission  16Jan2021 
Date of Decision  01Feb2021 
Date of Acceptance  01Feb2021 
Date of Web Publication  23Aug2021 
Correspondence Address: Tarulatha R Shyagali Department of Orthodontics and Dentofacial Orthopedics, Hitkarini Dental College and Hospital, Jabalpur, Madhya Pradesh India
Source of Support: None, Conflict of Interest: None  Check 
DOI: 10.4103/jdrr.jdrr_6_21
Aim: The aim is to evaluate the maxillary anterior tooth proportion relationship using different calculations. Materials and Methods: Forty pleasing smile photographs were evaluated for the different calculations. Mesiodistal width of all the maxillary anterior teeth were measured and were subjected to different calculations like individual tooth width divided by the combined width of all the anterior teeth of one side and individual tooth width divided by the combined width of the remaining two teeth of one side. Calculated results were tabulated and were subjected to descriptive statistics. Results: Among the various formulas, the mesiodistal width of canine divided by the sum of mesiodistal width of central, lateral incisors, and canine showed the consistent quotient of 0.3 for all the subjects. Mesiodistal width individual teeth like central incisors when divided by the combined width of central incisor, lateral incisor and canine, also showed the constant quotient of 0.3 for all the patients. The sum of Mesiodistal width of central and lateral incisor when divided by combined width of central, lateral incisor and canine gave the constant value of 0.6. Conclusion: The consistent quotients obtained by the formulas like width of central incisors and the canine divided by the combined width of centrallateral incisorscanine and the other formulas can be used for building up of the missing teeth and the smile designing.
Keywords: Anterior teeth, canine, incisors, maxillary teeth, tooth proportion
How to cite this article: Shyagali TR, Jha R, Bhayya D, Gupta A, Tiwari A, Patidar R. Evaluation of maxillary anterior tooth proportion using the novel TR proportion. J Dent Res Rev 2021;8:1438 
How to cite this URL: Shyagali TR, Jha R, Bhayya D, Gupta A, Tiwari A, Patidar R. Evaluation of maxillary anterior tooth proportion using the novel TR proportion. J Dent Res Rev [serial online] 2021 [cited 2022 Oct 1];8:1438. Available from: https://www.jdrr.org/text.asp?2021/8/3/143/324420 
Introduction   
Smile is rightly said to be the first step toward communication and an attractive smile adds all the more value to the prospective of communication. Its age old sciences to correlate the beauty with the mathematical formula. Golden proportion is not only a mathematical formula, but also a valid tool to judge the attractiveness of the smile. Modern day smile designing tools also include golden proportion for construction of esthetic smile.^{[1]}
Leonardo da Vinci said “No human inquiry can be called science unless it pursues its path through mathematical exposition and demonstration.”^{[2]} Golden proportion has been studied since antiquity and since ages scientists have tried to rule out natures secret of beauty, many gave various proportions to justify the same. Some said it is genetically determined. Lombardi was the first to suggest the application of the golden proportion in dentistry.^{[3]}
Golden proportion is a constant ratio of 1.618:1. Literature on the golden proportion is explicit, giving it rather an oversimplified outlook. But in reality, the theoretical concepts which look simple to follow are practically very complex to apply. Apart from symmetry, deviations, the colorhue of teeth and the overall face also plays a major role in making smile attractive.^{[4],[5]}
Golden percentage even though widely used is inconsistent to judge the teeth width.^{[6],[7],[8],[9],[10]} However, few studies also have emphasized the its utility in difficult clinical conditions.^{[11]} Controversy still persists regarding the validity of golden proportion as a tool to evaluate the smile, thus the current study was undertaken with the aim to evaluate whether any other proportion is followed for tooth width in attractive smiles.
Materials and Methods   
A crosssectional study was done on a sample of 40 smile photographs. Ethical clearance was obtained from the institutional ethical committee. Dental under graduate students and interns were asked to rate the most pleasing smile in the order of 1–10 of their classmates, where rating 1 represented most attractive smile. All the students who were having an attractive smile were enlisted and were asked to report to the department of orthodontics and dentofacial orthopedics. Assembled students were explained about the purpose of the study and an informed consent was obtained for their willing participation in the current research. Each student was scanned for the following selection criteria such as presence of all maxillary and mandibular teeth, healthy gingival and periodontal condition, absence of spacing and crowding, and no previous history of orthodontics and anterior restoration. After the selection scanning, 30 students met the said criteria and data related to golden proportion was collected from this final sample.
Smiling (social smile) front photographs of each patient [Figure 1] was taken with a digital singlelens reflex camera (Canon, Tokiyo, Japan) with 1/125 shutter speed, F1/5.6 aperture, and ISO 200 sensitivity.
All the subjects were made to stand in natural head position with 11 inch of gap from the background screen and the distance between the triploid and the patient was fixed to 5 feet. Mesiodistal width of the maxillary central incisors and lateral incisors and canine were measured bilaterally on the smiling photographs [Figure 2] indirectly using adobe photo shop application 7 (Adobe Inc., for Windows and macOS).
To check whether the tooth follow any pattern of association various equations were tried. Following which the frequency calculation was done. Equation tried for the current study is represented in the [Table 1].
All the measurements were done by a single examiner and to know the intraexaminer variability the 10 consecutive photographs were measured twice within the gap of a week and the obtained data were subjected to kappa statistics (95%).
Obtained data were tabulated and descriptive statistics was performed to know the frequency of distribution of the different calculations using Microsoft excel office (Microsoft office 2010).
Results   
[Table 2] shows the various calculations for all the subjects. The formula which showed consistency was seen in relation to the mesiodistal width of lateral incisor was divided by the sum of mesiodistal width of central and lateral incisors and we obtained a proportionality constant (coefficient of proportionality) of 0.4. Moreover, if we assign the parameter to this constant with central as X, Y, and Z as lateral incisor and canine measurement, respectively, then we have the formula;
Y = 0.4 (X + Y)
Similarly, formulas like mesiodistal width of central incisor divided by the combined width of central incisor, lateral incisor and canine, showed the constant quotient of 0.3 as a proportionality constant. Again if we assign the parameters, then we have the formula.
X = 0.3(X + Y + Z)
Mesiodistal width of canine divided by the combined mesiodistal width of the central, lateral incisor and canine fetched the proportionality constant of 0.3 for all the patients.
Z = 0.3(X + Y + Z)
The sum of mesiodistal width of central and lateral incisor when divided by combined width of central, lateral incisor, and canine gave the constant proportionality value of 0.6.
(X + Y) = 0.6 (X + Y + Z)
Discussion   
The golden proportion (phi) (1.618:1.0) describes the ratio between the dimensions of a larger and a smaller length. Nowadays, for all patient dental esthetics have become a major consideration and to achieve an excellent esthetics various authors have provided valuable guidelines.^{[5]}
The golden proportion is said to be a reliable predictor for determining the width of the maxillary central incisors.^{[6]} on the other hand Gillen et al., 1994, Rosenstiel et al., 2000 and Ward, 2001 found that anterior teeth widths did not follow golden proportion.^{[12],[13],[14]}
The result of the current study for tooth proportion showed that many of the measurements were not consistent for various calculations except for the four formulas which showed constant value for all the subjects. Lateral incisor width showed a proportionality constant of 0.4 for the formula width of lateral incisor divided by the combined width of central and lateral incisor. The most common congenital missing teeth are maxillary laterals incisors^{[15]} and this formula can be used for building up or for the replacement of lateral incisors in such cases. We are proposing these particular proportions as, TR proportion as an acronym on the name of authors (TarulathaRuchi Proportion). The same proportion formulas were used to build up the missing lateral incisors with satisfactory results [Figure 3] and [Figure 4].  Figure 3: Building up of peg lateral. (a) Pretreatment. (b) Post build up
Click here to view 
Combined width of the maxillary central, lateral incisors and canines when used as a divisor to the individual teeth such as central incisors, lateral incisor, and canines, there was a consistent value obtained for central incisor and canine. These relationships can be used to design the esthetic smile for the required patients.
Most of the literature so far gave lots of importance to the golden proportion, however, there are very few studies which give consistent results.^{[16]} There are other proportion measuring tools such as recurring esthetic dental, the Chu's gauge and preston propotion.^{[2],[17]} Among these, golden percentage and Chu's gauges are considered good for clinical practice.^{[2],[18]}
The current study is one of its kinds as none of the previous studies have explored the different proportions proposed here. Similar study of same nature was proposed by German et al. (2015), where they advised various measurements like maxillary lateral incisor is 2 mm less than the central incisors and maxillary canine was 1 mm less than the maxillary central incisor.^{[19]}
The proportion relationship was consistent for all the subjects studied the measured width of maxillary lateral was more than the ideal value. Similar results were also found in the earlier study on South Indian population by Subhashini et a.^{[20]}
However, we did notice the repetition of a particular pattern for the different proportion involving the combined width of central incisor, lateral incisor and canine to the individual width of either canine, lateral, or central. One important point to be noted is that most of the dentist preferred building their patients smile based on the overall smile balance than based on any of these proportion.^{[21]} However, considering the ease of the formulas used here, most of the dentist can take advantage of the simplicity of these calculations.
The study carries the scope to explore the results further on the larger population.
Conclusion   
The divine proportion of the tooth cannot be emphasized as a sole criterion to judge an attractive smile. Within the limitation of this study, it can be concluded that the consistent quotients obtained by the formulas like width of central incisors and the canine divided by the combined width of centrallateral incisorscanine and the other formula like width of lateral incisors divided by the combined width of centrallateral incisors can be used successfully to design the smile esthetics. These values can be applied for building up of the missing teeth and the smile designing.
Ethical clearance
HDCH/IEC/2019/521. (HDCH: Hitkarini Dental College and Hospital).
Financial support and sponsorship
Nil.
Conflicts of interest
There are no conflicts of interest.
References   
1.  Jafri Z, Ahmad N, Sawai M, Sultan N, Bhardwaj A. Digital smile design – An innovative tool in aesthetic dentistry. J Oral Biol Craniofac Res 2020;10:1948. 
2.  Murthy BV, Ramani N. Evaluation of natural smile: Golden proportion, RED or Golden percentage. J Conserv Dent 2008;11:1621. 
3.  Singh R, Datta K. The golden proportionGod's building block for the world. J Indian Prosthodont Soc 2008;8:69. [Full text] 
4.  Chander NG, Kumar VV, Rangarajan V. Golden proportion assessment between maxillary and mandibular teeth on Indian population. J Adv Prosthodont 2012;4:725. 
5.  Aldegheishem A, Azam A, AlMadi E, AbuKhalaf L, Bani Ali B, Anweigi L. Golden proportion evaluation in maxillary anterior teeth amongst Saudi population in Riyadh. Saudi Dent J 2019;31:3229. 
6.  George S, Bhat V. Inner canthal distance and golden proportion as predictors of maxillary central incisor width in south Indian population. Indian J Dent Res 2010;21:4915. [ PUBMED] [Full text] 
7.  Marwan S, Amal A, Mohammed A. Evaluation of the golden proportion and golden standard of maxillary anterior teeth in relation to smile attractiveness. Braz Dent Sci 2019;22:17889. 
8.  Ali Fayyad M, Jamani KD, Agrabawi J. Geometric and mathematical proportions and their relations to maxillary anterior teeth. J Contemp Dent Pract 2006;7:6270. 
9.  Shahnawaz D, Akhtar H, Choudry Z, Naz F, Hasan A, Khan JA. Golden proportion and golden standard assessment of maxillary anterior teeth among undergraduate students. J Pak Dent Assoc 2019;28:747. 
10.  Sandeep N, Satwalekar P, Srinivas S, Reddy CS, Reddy GR, Reddy BA. An analysis of maxillary anterior teeth dimensions for the existence of golden proportion: Clinical study. J Int Oral Health 2015;7:1821. 
11.  Pini NP, deMarchi LM, Gribel BF, Ubaldini AL, Pascotto RC. Analysis of the golden proportion and width/height ratios of maxillary anterior dentition in patients with lateral incisor agenesis. J Esthet Restor Dent 2012;24:40214. 
12.  Gillen RJ, Schwartz RS, Hilton TJ, Evans DB. An analysis of selected normative tooth proportions. Int J Prosthodont 1994;7:4107. 
13.  Rosenstiel SF, Ward DH, Rashid RG. Dentists' preferences of anterior tooth proportion – A webbased study. J Prosthodont 2000;9:12336. 
14.  Ward DH. Proportional smile design: Using the recurring esthetic dental proportion to correlate the widths and lengths of the maxillary anterior teeth with the size of the face. Dent Clin North Am 2015;59:62338. 
15.  Rakhshan V. Congenitally missing teeth (hypodontia): A review of the literature concerning the etiology, prevalence, risk factors, patterns and treatment. Dent Res J (Isfahan) 2015;12:13. 
16.  Parnia F, Hafezeqoran A, Mahboub F, Moslehifard E, Koodaryan R, Moteyagheni R, et al. Proportions of maxillary anterior teeth relative to each other and to golden standard in Tabriz dental faculty students. J Dent Res Dent Clin Dent Prospects 2010;4:836. 
17.  Navon D. The sisters of the golden section. Perception 2011;40:70524. 
18.  Nautiyal A, Gujjari S, Kumar V. Aesthetic crown lengthening using Chu aesthetic gauges and evaluation of biologic width healing. J Clin Diagn Res 2016;10:ZC515. 
19.  German DS, Chu SJ, Furlong ML, Patel A. Simplifying optimal toothsize calculations and communications between practitioners. Am J Orthod Dentofacial Orthop 2016;150:10515. 
20.  Subhashini MH, Venkat Prasad MK, Ashish RJ. Incidence of golden proportion among a target South Indian population. J Pharm Res 2018;12:203. 
21.  Dalaie K, Behnaz M, Mirmohamadsadeghi H, Dashti M. Maxillary anterior teeth width proportion a literature review. EC Dent Sci 2017;16.5:197206. 
[Figure 1], [Figure 2], [Figure 3], [Figure 4]
[Table 1], [Table 2]
This article has been cited by  1 
Recommended clinical practice guidelines of aesthetic dentistry for Indians: An expert consensus 

 Dibyendu Majumder, MithraN Hegde, Shishir Singh, Ashu Gupta, ShashiRashmi Acharya, P Karunakar, RS Mohan Kumar, B Mrinalini, Shazeena Qaiser, UrvashiBhimjibhai Sodvadia, HonapManjiri Nagesh   Journal of Conservative Dentistry. 2022; 25(2): 110   [Pubmed]  [DOI]  



