| Abstract|| |
Objectives: Even though the constant relation of golden proportion and inner canthal distance (ICD) with the width of the maxillary central incisor (CIW) has been found in European population, it may not be applied to Indian population as we differ from Europeans racially and genetically. Hence, this study was carried out with the objectives of determining if these parameters are applicable to our population also.
Materials and Methods: Three hundred south Indian subjects between 18 and 26 years of age, free from facial and dental deformities were examined. Inner canthus of each eye was used as soft tissue landmark. The maxillary central incisors were measured at the contact point area with the help of digital vernier caliper. The CIW was also calculated using golden proportion ratio to obtain the calculated central incisor width. A comparison was made with measured width. Statistical analyses were done to identify any significant difference using "Z" tests. Pearson's Correlation Coefficient test was used to evaluate the measured and the calculated width of the central incisor.
Results: ICD and the width of two maxillary incisors were in golden proportion in south Indian population. Also, ICD when multiplied by a decreasing function value of the golden proportion and divided by 2 is a reliable predictor of determining CIW.
Conclusion: As in the European population, the ICD and the golden proportion are reliable predictors for determining the width of the maxillary central incisors in the south Indian population also.
Keywords: Golden proportion, inner canthal distance, maxillary central incisor, south Indian population
|How to cite this article:|
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;21:491-5
Facial appearance is of great concern to everyone as it is a significant part of self-image. The pursuit of beauty is based on numerous subjective factors, the concept of which arises from the custom, education and civilization. Maxillary central incisors play a significant role in contributing to the factors responsible for the pleasing appearance. For a completely edentulous patient, when pre-extraction records are not available, it is extremely difficult to select these teeth to bring out harmony with the facial appearance. ,,,,
|How to cite this URL:|
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 [serial online] 2010 [cited 2015 Jan 31];21:491-5. Available from: http://www.ijdr.in/text.asp?2010/21/4/491/74214
No efforts have been spared to evaluate the relationship between various landmarks of the face with maxillary central incisor width (CIW). ,,, The earlier anthropometric studies included many facial landmarks like bizygomatic width, inter commissural width, inter alar width, etc. ,, These measurements were not evaluated with geometric progression to determine proportionality between them and maxillary CIW.  Another landmark that has been studied to a lesser extent is the inner canthal distance (ICD). This is the distance between the medial angles of the palpebral fissures of the eyes. Only one study has been carried out, that too, in the Saudi Arabian population who belong to Semitic ethnic group. As there could be racial and genetic differences in facial growth, the reliability of the relation of ICD to CIW should be confirmed in other populations also. ,,
Main aim of the present study was to determine the relationship of this distance with the existing golden proportion and its reliability in selecting maxillary CIW for the south Indian population. Objectives were:
- to analyze if ICD and CIW were in golden proportion in south Indians,
- to compare the measured and calculated maxillary CIWs,
- to compare the mean CIW and ICD between males and females of this population, and
- to compare the values between south Indian and Saudi Arabian population.
| Materials and Methods|| |
Three hundred south Indian adults, 144 males and 156 females, between the age of 18 and 26 years, with no facial or dental deformity were selected. All the subjects had full complement of teeth with no history of orthodontic treatment, crowding, diastema, morphological deformity or any form of restorations. Informed consent was obtained from each subject. The subject was seated in a relaxed, upright position during examination to ensure selection criteria mentioned above.
Central incisor width
Maxillary central incisors were measured mesiodistally at their contact point with the adjacent central incisor, with the help of a divider. This divider could be fixed in position with a screw thread and it had finely pointed ends that fitted interdentally accurately. Measurements were made in a straight line, with the pointed members held parallel to the incisal edges and vertical to the facial surface of the tooth. After the measuring procedure, the pointed members of the divider were placed on a white paper that was placed on a cork board. Gentle pressure is applied over the divider so that the pointed members perforated the paper and the cork board. The perforations were joined by a straight line, and it was measured with a digital vernier caliper. The instrumental error of -0.02 mm was subtracted. Each tooth was measured three times by the same operator and the average was taken as measured central incisor width (MCIW). This was done to ensure observational reliability of the procedure.
Inner canthal distance measurement
Subjects were seated with their heads supported in an upright position and they looked straight. The sterilized caliper was placed against the forehead and lowered toward the eyes. The arms of the calipers were adjusted so that they were in gentle contact with the medial angle of the palpebral fissures of the eyes. Utmost care was taken not to compress the soft tissues. The distance between these two anatomical landmarks was recorded as ICD to an accuracy of 0.01 mm and the instrumental error of -0.02 mm was subtracted. ICD was measured three times for each subject by the same operator. Average value was taken to avoid intraoperator observational errors.
Application of golden proportion to calculate central incisor width
Golden proportion is 1.618:1 and its reciprocal 0.618 in geometry.  The common ratios of the geometric progression are 0.618 and 1.618. , Any decreasing function is multiplied by 0.618 and any increasing function by 1.618 to get the next result.  The ICD was found to be greater than the combined widths of the maxillary central incisors. Hence, the ICD of each subject was multiplied by a decreasing function value of the geometric progression term (0.618) to provide the combined width of two central incisors. The product was then divided by 2 to obtain the width of a single maxillary central incisor. The formula can be expressed as follows:
combined width of central incisors = ICDΧ0.618
calculated central incisor width (CCIW) = (ICDΧ0.618)/2.
The observed measurements were subjected to statistical analysis. The CCIW was compared with the MCIW for each subject. Agreement between measured and calculated widths of central incisor was evaluated with Pearson's Correlation Coefficient (Pearson r).
A Z-test at 5% level of significance was used to find the statistical significance between measured and calculated values of CIW for male and female subjects separately (48% of the sample were males and 52% were female subjects).
| Results|| |
[Table 1] and [Table 2] show the observations and statistical calculations done for Pearson's Correlation Coefficient (r) and the Z value significance between male and female subjects.
|Table 1: Descriptive statistics, Z-test, Pearson's correlation coefficient and its critical values for the measured and calculated values of CIW by gender|
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|Table 2: Descriptive statistics, Z value, 95% confidence interval (CI) for mean ICD and CIW values|
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From [Table 1], the correlation between the measured and calculated values of CIW was found to be positively very high for both males and females [Pearson's r 0.95 (males= 0.949 and females=0.952]. The Pearson's r is the correlation coefficient which measures the strength of relationship between the two values. A high value for this coefficient is indicative of positively high correlation between the two values. Here, the CCIW was the product of golden proportion with ICD divided by 2. That is, they are in golden proportion. The critical value for Pearson's r at 5% was found to be insignificant.
From [Table 2] it is seen that the mean of CIW and ICD measurements were significantly higher for males (Z 144 = 7.25) than for females (Z 156 =9.9291). Since it was a large sample size study, Z-test was used (P<0.05).
Type I error-α=0.05 (only in the 5% interval)
Type II error-β=0.01 negligible by the sample size (Z 300 )
Sensitivity of the study was calculated to find out the sampling error. Type I error-α was calculated at 0.05, showing that the error was only in 5% interval. This means that for rejecting the hypothesis, the type I error was in 5% interval. Type II error-β was made to 0.01 (negligible) by increasing the sample size. This means, for accepting the hypothesis type II error-β was negligible. Power of the test I-β was calculated. For males it was 2.8429 and for females 2.3666. So, this can be applied to any number of samples. The Pearson's r=0.95 showed that the sample size (Z 300 ) was sufficient enough to apply in the population study.
| Discussion|| |
The golden proportion, used in ancient Greek architecture to design the Parthenon,  long considered among the most beautiful architectural creations in history, has all of its parts laid out in proportion of 1.618:1. This ratio is found in nature, in shells, and plants.
It is also the one which mind registers at the subconscious level as beauty. It mathematically describes the ratio between a larger and smaller length, and the larger and the total length as being equal to phi. The mathematical relation of 1.618 to 1 is called the golden section. A golden divider was constructed in 1954 by taking phi relationship, which maintains it, even when it is expanded.  The golden divider can be readily used to measure the proportion of the teeth, face, mouth, and jaws.  The width of the maxillary central incisor is in golden proportion to the width of lateral incisor and the laterals are in golden proportion to canine, when viewed from frontal aspect. 
Esthetics is one of the important aspects of complete denture fabrication. ,,,,, In cases where there is no pre-extraction record for edentulous patients, selection of anterior teeth is more challenging. When anterior teeth are selected for edentulous patients, the mesiodistal width of maxillary central incisors is important because they are the most prominent teeth in the arch when viewed from the frontal aspect. ,,,
Certain anthropometric measurements of the face have been suggested to determine the mesiodistal width of the maxillary central incisor. ,,,, Scandrett et al.  studied the ratio between the maxillary CIW and certain anthropometric parameters including inter commissural width, bizygomatic width, sagittal cranial diameter, inter alar width, inter buccal frenum distance and philtrum width. They reported that more than one measurement is required to obtain the best predictable model for maxillary CIW.
Although earlier anthropometric studies included many facial landmarks, ICD has been studied to a lesser extent in relation to the CIW. , ICD is the distance between the medial angles of the palpebral fissure of each eye. Anthropometrically, it is endocanthion bilaterally (en-en). 
Laestadius  reported that in 78% of adults, the ICD is attained by the age of 1 year, after which the growth in this area is slow in contrast to outer orbital dimension. According to Epker and Fish,  these values are established by 6-8 years of age and do not change significantly after this time. This stable landmark can be identified, located and measured accurately.  It has not been investigated by the researchers to obtain width of the maxillary central incisors. ICD can be taken for obtaining the width of the central incisor, if they are found to be in golden proportion.
One study conducted by Md. Abdullah  compared the relation between ICD and maxillary CIW in the Saudi Arabian population. This study proved that ICD is a reliable guideline for selecting width of maxillary central incisor.  However, this study was conducted in Arabs who belong to Semitic ethnic group. Facial proportions can vary in different ethnic groups. , south Indian population belongs to Dravidian ethnic group. Dravidians are one of the non-Aryan races of Southeast Asia and are distributed mainly in South India and Ceylon. LeTT et al.  reported that facial profile can vary in different ethnic groups and that the dominant characteristics of the Asian faces were a wider ICD in relation to shorter palpebral fissures, compared to Caucasians.
Since ethnic differences exist between different populations, ,,, universal application of the previous research work is possible only when it is studied in all populations. ,,, The present study was an attempt to analyze this relation in south Indian population.
In this study, it was found that there was high positive correlation between the measured and calculated values of CIW. (Pearson's r=0.95). Since the CCIW is the product of golden proportion with ICD (ICDΧ0.618), the MCIW also should be in golden proportion to ICD. That is, ICD and CIW are in golden proportion.
Gender based difference in mesiodistal width of central incisor was reported by previous investigators like Lavellea,  Cesario et al.,  and Md. Abdullah.  So a Z-test was used to identify any significant difference in the CIW and the ICD by gender in the present study. It was observed that there was a gender based difference in ICD (males: 32.59±2.1 mm; females: 30.77±2.1 mm) and maxillary CIW (males 9.68±0.5mm and females 9.12±0.4 mm). Mean CIW recorded for south Indian Population was higher than that was recorded for Saudi Arabian population (males 8.87 mm and females 8.68 mm). The mean ICD recorded for south Indian Population was also greater than that was recorded for Saudi Arabian population (males 28.69 mm and females 27.68 mm).
Even though facial proportion varies in different ethnic groups, the present study conducted in south Indian population proved that the facial measurements were in golden proportion. However, implementation of this finding should be reserved till other such studies to include combined width of all the anterior teeth of maxilla are carried out.
Within the limitation of this study, it has been found that the ICD is a reliable predictor of mesiodistal width of the maxillary central incisors in the south Indian Population. Universal application of this interpretation should be done carefully after further research into other ethnic groups is completed.
| Conclusions|| |
- ICD and the width of the maxillary central incisors are in golden proportion in south Indian population.
- ICD when multiplied by a decreasing function value of the geometric progression term 0.618 and divided by 2 was a reliable predictor of maxillary CIW.
- Mean maxillary CIW and ICD were significantly higher for males than for females in south Indian population.
- Both ICD and CIW were higher in south Indian population as compared to the values in Saudi Arabian population.
- Further studies in other ethnic groups with combined maxillary anterior teeth width as a parameter are recommended, for global application of these observations.
| Acknowledgments|| |
The authors would like to thank Prof. R. Subramaniam and Prof. T V Padmanabhan for their constant support and encouragement throughout the study.
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Department of Prosthodontics & Implantology, A B Shetty Memorial Institute of Dental Sciences, Nitte University, Mangalore, Karnataka
[Table 1], [Table 2]