|Year : 2022 | Volume
| Issue : 2 | Page : 107-112
Facial heights as predictors of occlusal vertical dimension in a Nigerian population: A pilot study
Tope Emmanuel Adeyemi1, Chikaodi Obinna Oguchi1, Paul Ikhodaro Idon2, Yewande Isabella Adeyemo3, Sabeer Muhammad Iya4, Oluwafeyisayo Francis Ikusika5
1 Senior Lecturer/Honorary Consultant Orthodontist, Bayero University Kano/Aminu Kano Teaching Hospital, Kano State, Nigeria
2 Lecturer/Honorary Consultant Restorative Dentist, University of Maiduguri/University of Maiduguri Teaching Hospital, Borno State, Nigeria
3 Senior Lecturer/Honorary Consultant Paedodontist, Bayero University Kano/Aminu Kano Teaching Hospital, Kano State, Nigeria
4 Lecturer II/Registrar in Maxillofacial Radiology, Bayero University Kano/Aminu Kano Teaching Hospital, Kano State, Nigeria
5 Senior Lecturer/Consultant Prosthodontist, Bayero University Kano/Aminu Kano Teaching Hospital, Kano State, Nigeria
|Date of Submission||28-Mar-2022|
|Date of Decision||14-Aug-2022|
|Date of Acceptance||27-Sep-2022|
|Date of Web Publication||23-Nov-2022|
Oluwafeyisayo Francis Ikusika
Senior Lecturer/Consultant Prosthodontist, Bayero University Kano/Aminu Kano Teaching Hospital, Kano State
Source of Support: None, Conflict of Interest: None
Context: Facial height measurements may aid in predicting occlusal vertical dimension (OVD). Aim: To compare facial third measurements among individuals with healthy occlusions for a predictive ratio for occlusal vertical dimension determination. Setting and Design: A cross-sectional prospective observational study at the Dental Clinic of Aminu Kano Teaching Hospital. Sampling was purposive. Materials and Methods: A digital caliper was used to measure the upper facial height (UFH), the midfacial height (MFH), and the lower facial height (LFH) of 103 participants. Statistical Analysis Used: The data collected were analyzed with IBM Statistical Package for the Social Sciences (SPSS) version 25. The level of statistical significance was set at P ≤ 0.05. Results: There were 69 male (67%) and 34 female (33%) members in the cohort analyzed. The ages of the participants ranged from 18 to 58 years, with a mean age of 27.3 ± 6.8 years. The UFH ranged from 60 to 110 mm with a mean value of 82.2 ± 9.8 mm. The MFH ranged from 55 to 100 mm with mean value of 74.6 ± 9.9 mm. The LFH ranged from 60 to 90 mm with a mean of 73.2 ± 7.4 mm. There was a significantly positive correlation between UFH and LFH (r = 0.22). This was similar to that of MFH and LFH (r = 0.61). The best fit model equation for the prediction of LFH was found to be LFH = 31.495 + (0.442 × MFH). Conclusions: This study found MFH to be a predictable factor for LFH estimation which can be used for OVD determination.
Keywords: Facial height (FH), lower facial height (LFH), midfacial height (MFH), occlusal vertical dimension (OVD), upper facial height (UFH)
|How to cite this article:|
Adeyemi TE, Oguchi CO, Idon PI, Adeyemo YI, Iya SM, Ikusika OF. Facial heights as predictors of occlusal vertical dimension in a Nigerian population: A pilot study. Niger J Basic Clin Sci 2022;19:107-12
|How to cite this URL:|
Adeyemi TE, Oguchi CO, Idon PI, Adeyemo YI, Iya SM, Ikusika OF. Facial heights as predictors of occlusal vertical dimension in a Nigerian population: A pilot study. Niger J Basic Clin Sci [serial online] 2022 [cited 2023 Mar 21];19:107-12. Available from: https://www.njbcs.net/text.asp?2022/19/2/107/361890
| Introduction|| |
Occlusal vertical dimension (OVD) is a measure of the amount of separation of the jaws with the teeth in occlusion., The OVD is equal to the lower facial height with the teeth in occlusion for a dentate individual without significant occlusal wear., It is usually a straightforward distance to record in a fully dentate occlusion that does not require rehabilitation. However, its determination is a painstaking and cumbersome endeavor when rehabilitating fully edentulous individuals or individuals with severely worn dentition following extensive attrition of the occluding surfaces of the teeth., The determination of the OVD may however prove critical to the success of efforts to rehabilitate such individuals.,
The individuals who are most likely to require OVD determination are also most likely to be elderly., The elderly have been documented to be better managed in a timely and less frustrating manner. Long cumbersome procedures present a significant challenge to them and are best avoided., The current options for OVD determination within the Nigerian clinical space are unfortunately long intricate procedures. The development of techniques to shorten the duration of these efforts are a salutary development in the continuing efforts to refine clinical service delivery.,
The prevalent technique for OVD determination in our clinics at present is the Niswonger technique that depends on the subtraction of an estimate of freeway space (FWS) from the rest vertical dimension (RVD)., This technique is fraught with the risk of errors. These errors may occur while recording RVD or with the estimation of FWS., These errors can be overcome by the use of techniques that depend less on the ability of the patient to attain a position of rest, and reduce dependence on the application of a normative value of FWS. One technique that has been used to achieve this is the use of measurements of facial thirds in OVD estimation.,,
The use of facial measurements to determine OVD has been investigated among different populations, with significantly positive outcomes.[19–21] However such investigations are rare among Nigerian populations. This study therefore aimed to compare facial third measurements among individuals with healthy occlusions and without significant wear for a predictive ratio for lower facial height (LFH) determination. This ratio was expected to be obtained from a comparison of the upper and midfacial heights to lower facial heights in such individuals. This ratio is expected to guide OVD determination among individuals who require prosthetic rehabilitation.
| Methods|| |
Ethical approval (NHREC/28/01/2020/AKTH/EC/3095) was obtained from the Institutional Ethics Review Committee of the Teaching Hospital on the July 7, 2021. A sample size of 100 participants was chosen for inclusion in this observational pilot study. Inclusion in the study required participants to provide written and informed consent and to be 18 years or older in age. Participants were required to have Angle's class I static occlusion. Participants were required to have a full complement of their teeth and close with tight intercuspation of posterior teeth. Individuals with clinical evidence of occlusal attrition and those who had undergone any orthodontic treatment were excluded from the study. Individuals who had undergone significant restorative treatments were also excluded. Participants were recruited from the Dental Clinic of Aminu Kano Teaching Hospital.
Participants were seated comfortably with their heads upright and with their teeth in occlusion. Facial third heights were recorded with the use of digital calipers (TresnaR Guarig Province, China). Facial height recordings were done with the investigator facing the participant's right profile. The upper facial height (UFH) was recorded from the hairline to the nasion, the midfacial height (MFH) from the nasion to the junction of the lips, and the lower facial height (LFH) from the philtrum columella angle to the base of chin. The values obtained were entered into an electronic spreadsheet along with the participants' sociodemographic details. The sociodemographic data recorded were the participant's age, gender, and ethnicity.
Data handling and evaluation
The frequencies of participants' ages, gender, and ethnicities were recorded and means were derived for ages. The mean, standard deviation, and range of all facial height measurements were determined. UFH and MFH were categorized as predictor variables and the LFH was categorized as the outcome variable.
A preliminary test of data suitability for hierarchal multiple regression was performed and revealed collinearity between the predictor variables and the outcome variable. Data from two respondents were eliminated from the study prior to this preliminary test as their standard deviations lay outside acceptable limits. The presence of outliers was examined with Mahalanobis distance and Cook's distance.
Two regression models were developed. The first contained UFH and MFH as predictor variables while gender was introduced into the second regression model. A regression equation was derived and a best fit model determined for prediction of LFH. All data were analyzed with IBM's Statistical Package for the Social Sciences (SPSS) version 25. The level of statistical significance was set at P ≤ 0.05.
| Results|| |
Data from 103 participants were analyzed. There were 69 male (67%) and 34 female (33%) members in the cohort analyzed. The analyzed cohort was predominantly of Hausa ethnicity. There were 82 Hausas (79.6%), 8 Fulanis (7.8%), 5 Yorubas (4.9%), and 3 Igbos (2.9%) in the cohort. There were five participants who were not from one of the four major Nigerian ethnic groups. The ages of analyzed participants ranged from 18 to 58 years, with a mean age of 27.3 ± 6.8 years.
The UFH ranged from 60 to 110 mm with a mean value of 82.2 ± 9.8 mm. The MFH ranged from 55 to 100 mm with mean value of 74.6 ± 9.9 mm. The LFH ranged from 60 to 90 mm with a mean of 73.2 ± 7.4 mm. The boxplot in [Figure 1] illustrates values obtained with facial height measurements.
|Figure 1: Boxplot of upper, middle, and lower facial heights in a Nigerian population|
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The UFH and MFH correlated positively with LFH (r = 0.22 and r = 0.61 respectively), and both relationships achieved statistical significance. However, there was poor correlation between UFH and MFH [Table 1].
|Table 1: Correlations among upper, middle, and lower facial heights among participants|
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Tolerance was >0.9, and the variance inflation factor (VIF) was 1.015–1.059 for all variables. Normality of residuals was assessed from the normal P-P plot and revealed a lack of major deviations, as shown in [Figure 2]. Mahalanobis and Cook's distances were 9.99 and 0.09, respectively (Mahalanobis distance >16.27, and Cook's distance >1 show evidence of potential outliers).
|Figure 2: Normal P-P plot of regression standardized residual of the dependent variable (LFH in millimeters)|
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Hierarchical regression [Table 2] of predictor and outcome variables revealed statistically significant relations. The outcome variable was the LFH. Model 1 regression with UFH and MFH as predictor variables revealed F (2, 100) = 32.94, P < 0.001, adjusted R2 = 39%. Regression model 2 with UFH, MFH, and gender as predictor variables exhibited reduction in model fit F (3, 99), P < 0.001, adjusted R2 = 38%. Model 2 regression revealed MFH as the strongest and only significant predictor of LFH (B = 0.442, t = 7.416, P < 0.001). The regression model (equation) for predicting LFH was found to be the following: LFH = 31.495 + (0.442 × MFH) + (0.105 × UFH) + (0.366 × Gender). The best fit model equation for the prediction of LFH from the regression models was found to be LFH = 31.495 + (0.442 × MFH).
|Table 2: Hierarchical multiple linear regression for variables predicting lower facial heights among study participants|
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| Discussion|| |
The study cohort was predominantly male and of Hausa ethnicity. The male preponderance did not seem to affect our results as gender was not found to be a strong predictive factor of facial height proportions. This finding is also supported by the findings of Fang et al. The ages of the cohort ranged from early adulthood to late middle age. This wide range was utilized to accommodate any variations that age may impact on our findings. Our predominant consideration for inclusion in the study was the presence of the desired occlusal characteristics without significant wear in our study participants.
The stomatognathic system functions optimally within narrow physiological and anatomical boundaries. These boundaries must be respected when providing prosthetic rehabilitation to the edentulous individual. The OVD is a major determinant of the equilibrium that exists between the structures in the stomatognathic system., The estimation of the OVD therefore becomes integral to comfortable function in many complete denture patients. There is some dissension among practitioners as to the level of accuracy needed with this estimation, but there is a general acceptance of the need for its determination.,
The determination of OVD has traditionally been done by the application of the Niswonger method in the Nigerian dental community. This technique has been effectively deployed in the provision of complete dentures but has the drawback of making the registration of occlusion a tedious, time-consuming, and often frustrating experience for the dentist and the patient alike. The success of this technique is also intimately linked with the ability to obtain a true record of RVD and a proper estimation of FWS.
There have been several attempts made toward developing a predictive model for determination of OVD.,,, These models were conceived to remove the generalization inherent in the use of the Niswonger technique. They attempt to make OVD determination subject-specific or at least develop a predictive formula applicable to the general population. These predictive models rely on the use of the subject's pre-extraction records or on the use of anthropometrics. These methods have been investigated extensively among different ethnic groups. Unfortunately, such investigations are sparse among dark-skinned individuals of African descent and are particularly rare among Nigerians.
The use of pre-extraction records individualizes OVD determination., However, these records may be unavailable in environments with poor record-keeping practices like Nigeria. There is the added challenge of individuals changing service providers and a lack of synergy between such providers. This will make reliance on such records unrealistic and unattainable.
The use of anthropometrics as a predictor of OVD developed as a consequence of the observation of proportionality between different body parts in different populations. There are proponents of a direct 1:1 proportionality between comparable regions on the face. There are those who propose a “golden ratio” relationship between such segments. The proponents of a golden ratio relationship have been said to belong to a neoclassical school of thought due to propositions ascribed to philosophers in classical antiquity. However, it must be emphasized that anthropometric studies have shown relationships between distances measured on the face, and in some instances, on other parts of the body.
Olusanya et al. found no correlations between facial thirds and neoclassical canons in a Nigerian population. Akinbami and Nsirim found gender differences in LFH among their cohort. They found males with generally longer LFHs than females. The results from our study also show an influence of gender on facial heights, but this did not have as strong a predictive value on LFH as MFH values. This suggests that the proportionality between facial height and not-absolute facial height values hold predictive usefulness in determining LFHs. This would seem to be diametrically opposed to the submissions of Olusanya et al. A proportional relationship between facial heights leans more toward the neoclassical canon, even if that proportionality does not strictly adhere to the principle of the golden ratio.
The study by Olusanya et al. and that by Akinbami and Nsirim were conducted from an oral surgical perspective and may not have put into consideration restorative dental needs. However, a study by Yemitan et al., though with an orthodontic lens, provides some support to our findings with regards to the influence of gender on facial heights. They found no significant differences between the genders and facial height measurements. Unfortunately, we could only find descriptive studies on OVD among Nigerian restorative dentists. We did not find any studies that sought to define a predictive factor for OVD determination among Nigerian dentists. Although the study by Dosumu and Ikusika highlighted differences in FWS values among the genders and static occlusal classes, it did not attempt to develop a predictive factor for OVD determination. While Esan et al. studied facial anthropometrics for aiding complete denture fabrication, they paid less attention to vertical facial heights. We are of the opinion that this lukewarm attitude toward a critical analysis of OVD-determining factors may have been due to the prevalent adoption of the Niswonger method by the Nigerian restorative dental community.
There are variations in facial height proportions among different ethnic groups.,,, This emphasizes the need for different localities to study peculiarities of their populations. Baral et al. found significant differences in facial proportions between the Brahmin, Rai, Lumbu, and Chhetri ethnic communities in Sunsari district in Nepal. Fang et al. in their systematic review found no significant difference in facial proportions between genders, but a significant difference in the height of the forehead between different ethnic groups. This result further validates our finding that gender is not significantly predictive of facial height proportions. De Freitas et al. found increased UFH among Caucasian Brazilians and increased LFH among Brazilians of Black African descent. Conversely, Mizumoto et al. did not find significant differences in facial proportions between Japanese and Caucasian women.
Our choice of MFH for use in our best fit model equation was informed by the insignificance we observed with UFH and gender as independent predictors of LFH and hence OVD. While UFH correlated positively with LFH and hence OVD, it accounted for only 2% of its variability. Gender did not also serve as an independent predictor of LFH and did not have a major confounding influence on the three facial heights measured. It did not cause any major changes in the regression coefficient when introduced in the model 2 regression, as seen in [Figure 2].
The findings of our pilot study may significantly affect patient management if validated by larger studies with a greater variability of ethnicities. The development of a simple predictive equation for estimating OVD may significantly shorten the registration of occlusion appointment during complete denture fabrication. This would give clinicians a specific target instead of the range of targets available with the Niswonger method. The opportunities for rational post-treatment follow-up will also be increased. The patients will also benefit from a more efficient and precise treatment protocol that may reduce the number of review appointments they may need to undergo.
This pilot study also opens up channels for possible future investigations. It will be interesting to know if the findings among a predominantly Hausa population of northern Nigeria can be replicated among other ethnic communities in the country. A combination of clinical and radiological studies may enable knowledge of the relationship of condylar head positions to OVD to be unearthed. Studies utilizing the ratio determined from this pilot study may be used to design standardized investigations into occlusal schemes for complete denture patients, as well as those undergoing occlusal rehabilitation.
A major limitation of this study is our finding that UFH and MFH account for at most 39% of the variability of LFH values. This may indicate that there are other factors that may affect LFH measurements. The study is also limited by the lack of a like-for-like study in the same or similar study populations for comparison. This study potentially provides baseline figures to which future larger studies can be compared. These future studies may also seek to investigate other factors that may contribute to LFH variability.
| Conclusions|| |
This pilot study, within its limitations found MFH to be a predictive factor for LFH estimation. The relationship between MFH and LFH can be represented mathematically. This relationship can be used for OVD determination in patients requiring complete dentures or occlusal rehabilitation because the value of LFH determined by the equation will rationally guide the prosthodontist in the adjustment of the record blocks during bite-registration.
The authors recommend a large multi-center study to test the results of this pilot study.
Financial support and sponsorship
The study was entirely self-funded by the investigators.
Conflicts of interest
There are no conflicts of interest.
| References|| |
Dosumu OO, Ikusika OF. An assessment of interocclusal space in a dentate Nigerian population. Niger Postgrad Med J 2013;20:315-8. [Full text]
Goldstein G, Goodcare C, MacGregor K. Occlusal vertical dimension: Best evidence consensus statement. J Prosthodont 2021;30:12-9.
Alhajj MN, Khalifa N, Abdou J, Amran AG, Ismail IA. Determination of occlusal vertical dimension for complete denture patients: An updated review. J Oral Rehabil 2017;44:896-907.
Basuktar N, Borham AM, AlGhamdi S, Aldera EW, AlShammari MM, Sheik KH. Reliability of anthropological measurements in determining vertical dimension of occlusion in Saudi population: A cross sectional study. Saudi Dent J 2021;33:568-73.
Moreno-Hay I, Okeson P. Does altering the occlusal vertical dimension produce temporomandibular disorders? A literature review. J Oral Rehabil 2015;42:875-82.
Calamita M, Coachman C, Sesma N, Kois J. Occlusal vertical dimension: Treatment planning decisions and management considerations. Int J Esthet Dent 2019;14:166-81.
Ogunrinde TJ, Olawale OF. The prevalence of denture related mucosa lesions among patients managed in a Nigerian teaching hospital. Pan Afr Med J 2020;37:358.
Eregie UJ, Omo JO, Sede MA, Esan TA. Impact of conventional removable complete dentures on the oral health-related quality if life of completely edentulous patients in a tertiary health institution in Nigeria, Niger J Dent Res 2021;6:18-25.
Koczorowski R, Jundzill-Bieniek E, Galczynska-Rusin M. The usefulness of psychometric tests in dental treatment of patients aged above 65. Acta Odontol Scand 2014;72:209-15.
Gil-Montaya JA, de Mello AL, Barrios R, Gonzalez-Moles MA, Bravo M. Oral health in the elderly patient and its impact on general well-being: A nonsystematic review. Clin Interv Aging 2015;10:461-7.
Preston AJ. Dental management of the elderly patient. Dent Update 2012;39:141-3.
Akinyinka MR, Oluwole EO, Odusanya OO. Predictors of client satisfaction among recent users of health services in Lagos, Nigeria. Health Services Insight 2020. doi: 10.1177/117863292034499.
Welsh JS, Patel RR, Ritter MA, Harari PM, Mackie TR, Mehta MP. Helical tomotherapy: An innovative technology and approach to radiation therapy. Technol Cancer Res Treat 2002;1:311-6.
Olusile AO, Ogunbodede EO, Oginni AO. Prosthetic parameters among dental patients in Ile-Ife, Nigeria. Nig Postgrad Med J 2003;10:88-91.
Brar A, Mattoo KA, Singh Y, Khurana PRS, Singh M. Clinical reliability of different facial measurements in determining vertical dimension of occlusion in dentulous and edentulous subjects. Int J Prosthodont Restorat Dent 2014;4:68-77.
Mosier M, Barmak BA, Gomez-Polo M, Zandinejad A, Revilla-Leon M. Digital and analog vertical dimension measurements: A clinical observational study. Int J Prosthodont 2021;34:419-27.
Watarai Y, Mizuhashi F, Sato T, Koide K. Highly producible method for determination of occlusal vertical dimension: Relationship between measurement of lip contact position with the closed mouth and area of upper prolabium. J Prosthodont Res 2018;62:485-9.
Singh DK, Subhas S, Gupta A, Kesari M, Kumar A, Nayak L. Facial measurements: A guide for vertical dimension. J Family Med Prim Care 2020;9:2056-60. [Full text]
Basnet BB, Singh RK, Parajuli PK, Shrestha P. Correlation between facial measurements and occlusal vertical dimension: An anthropometric study in two ethnic groups in Nepal. Int J Dent Sci Res 2014;2:171-4.
Majeed MI, Haralur SB, Khan MF, Ahmari MA, Al Sharani NF, Shaik S. An anthropometric study of cranio-facial measurements and their correlation with vertical dimension of occlusion among Saudi Arabian sub-populations. Open Access Maced J Med Sci 2018;6:680-6.
Bajunaid SO, Baras B, Alhathlol N, Al Ghamdi A. Evaluating the reliability of facial and hand measurements in determining the vertical dimension of occlusion. Int J Med Pharm 2017;5:1-11.
Oaucea L, Burlibasa M, Petre AE, Panaitescu E, Cristhache C. Predictive model for occlusal vertical dimension determination and preservation with three-dimensional facial scanning. Appl Sci 2020;10:7890.
Fang F, Clapham PJ, Chung KC. A systematic review of interethnic variability in facial proportions. Plat Reconstr Surg 2011;127:874-81.
Saratti CM, Rocca GT, Vaucher P, Awain L, Papini A, Zuber S, et al
. Functional assessment of the stomatognathic system. Part I: The role of static elements of analysis. Quintessence Int 2021;52:920-32.
Fayz F, Eslami A. Determination of occlusal vertical dimension: A literature review. J Prosthet Dent 1988;59:321-3.
Munshi MSM, Shah MU, Shaik MI, Shahnawaz S, Awais F, Yasser F, et al
. Role of anthropometric measurements in determining occlusal vertical dimension. Pak Oral Dent J 2020;40:103-6.
Hussain S, Yazdanie N. Correlation of the vertical dimension of occlusion with anthropometric measurement of index finger. J Pak Dent Assoc 2019;28:108-12.
Morata C, Pizarro A, Gonzalez H, Frugone-Zambra R. A craniometry-based predictive model to determine occlusal vertical dimension. J Prosthet Dent 2020;123:611-7.
Ladda R, Bhandari AJ, Kasat VO, Angadi GS. A new technique to determine vertical dimension of occlusion from anthropometric measurements of fingers. Indian J Dent Res 2013;24:316-20.
] [Full text]
Fayz F, Eslami A, Graser GN. Use of anterior teeth measurement in determining occlusal vertical dimension. J Prosthet Dent 1987;58:317-22.
Garadawa HI, Isa A, Nggada HA, Sandabe MB, Samdi MT, Sambo UG, et al
. Oropharyngeal cancers in Maiduguri, Nigeria: A ten-year review of clinical profile. Online J Med Med Sci Res 2012;1:116-21.
Padilla CJ, Ferreyro FA, Arnold WD. Anthropometry as a readily accessible health assessment of older adults. Exp Gerontol 2021;153:111464.
Prokopakis EP, Vlastos IM, Picavert VA, Nolst Trenite G, Thomas R, Cingi C, et al
. The golden ratio in facial symmetry. Rhinology 2013;51:18-21.
Fan J, Chau KP, Wan X, Zhai L, Lau E. Prediction of facial attractiveness from facial proportions. Pattern Recognit 2012;45:2326-34.
Ahila SC, Vaishnavi P, Muthu Kumar B. Comparative evaluation of maxillary and mandibular anterior tooth width with the length of index and little finger. J Indian Prosthodont Soc 2014;14:215-8.
Olusanya AA, Aladelusi TO, Adedokun B. Anthropometric analysis of the Nigerian face: Any conformity to the neo-classical canons? J Craniofac Surg 2018;29:1978-82.
Akinbami BO, Nsirim PE. Analysis of occlusal vertical dimension and mandibular basal bone height in a Nigerian population. Anat Res Int 2014;2014:584508.
Yemitan TA, Oludare YS, Ogunbanjo BO. Vertical facial height and it's correlation with skeletal pattern among young Nigerian orthodontic patients. Int J Dent Oral Sci 2018;5:661-6.
Esan TA, Ozeigbe OE, Onapokya HO. Facial approximations: Evaluation of dental and facial proportions and height. Afr Health Sci 2012;12:63-8.
Baral P, Lobo SW, Menezes RG, Kanchan T, Krishan K, Bhattacharya S, et al
. An anthropometric study of four endogamous communities in Sunsari district of Nepal. Singapore Med J 2010;51:212-5.
de Freitas LMA, Pinzan A, Janson G, Freitas KMS, de Freitas MR, Henriques JFC. Facial height comparison in young white and black Brazilian subjects with normal occlusion. Am J Orthod Dentofacial Orthop 2007;131:706.e1-6.
Mizumoto Y, Deguchi T Sr, Fong KW. Assessment of facial golden proportions among young Japanese women. Am J Orthod Dentofacial Orthop 2009;136:168-74.
[Figure 1], [Figure 2]
[Table 1], [Table 2]