# Does 3-dimensional facial attractiveness relate to golden ratio, neoclassical canons, ‘ideal’ ratios and ‘ideal’ angles? – Maxillofacial Plastic and Reconstructive Surgery

#### ByRoger A. Zwahlen, Alexander T. H. Tang, Wai Keung Leung and Su Keng Tan

Sep 7, 2022

The ethical approval for this study was granted by the local authority (Institutional Review Board no.: UW 12–066). The study was conducted at Prince Philip Dental Hospital, The University of Hong Kong. Prior written informed consent was obtained from all the model volunteers and judges.

### 3-D photograph

Ninety Chinese dental students ranging in age from 20 to 27 years old (mean = 22.8) have volunteered and been recruited as 3-dimensional (3-D) photograph models in this study. These 90 volunteers consisted of 30 individuals presenting dento-skeletal classes 1, 2, and 3 each. Each model obtained a 3-dimensional photograph in a neutral facial expression using the 3dMDface stereophotography system (3dMD, Atlanta, USA). To reduce potentially extraneous aesthetic factors during the photo-shooting session, their hair was covered. The make-up and jewellery were also removed.

The 3-D photos of the models were imported into the 3dMDVultus software (3dMD LLC, Atlanta, GA, USA). Five models each for three different dento-skeletal patterns (classes 1, 2, and 3) of both genders were then selected randomly using the random number generator function of Microsoft Excel (Microsoft Office Professional Plus 2016, Microsoft Corporation). This resulted in 15 male and 15 female 3-D photographs with diverse dental and skeletal patterns. A 10-s video was generated for each 3-D facial photograph rotating around its y-axis, starting from left to right face (Fig. 1). All videos were converted into black and white to reduce potential bias caused by skin colour and complexion.

### Judges

Judges for this study were recruited from the pool of consecutive patients attending the oral and maxillofacial discipline seeking orthognathic treatment, as well as from those patients who have attended the Reception and Primary Care Clinic of the same hospital for reasons other than potential orthognathic treatment. Only Hong Kong Chinese between 18 to 40 years old were included.

The judges were instructed to evaluate 30 videos based on a 100 mm visual analogue scale (VAS) from 0 (very unattractive) to 100 (very attractive). No time limit was set for the evaluation of the 3-D photographs. The consecutive videos were played only after the score for the previous video was recorded by the judges. The mean VAS score of each judging panel represented the final facial aesthetic score for each 3-D photograph.

The soft tissue landmarks for each 3-D photograph were plotted using the 3dMDVultus software (3dMD LLC, Atlanta, GA, USA). The landmarks normally identified in the profile view of 2-D photographs were plotted in the midline of the frontal 3-D photograph view to prevent measurement errors due to horizontal deviations. The soft tissue landmarks used in this study are shown in Fig. 2.

According to already established methodologies [4, 5, 13,14,15,16], the golden ratio, neoclassical canons, ‘ideal’ ratios and ‘ideal’ angles were applied in this study (Figs. 3, 4, 5 and 6). The differences between the measured parameters and the ‘ideal’ reference values were calculated.

All 3-D photos were remeasured 2 weeks after the first measurement, and the technical error measurement (TEM) was calculated with the Dahlberg formula as follows [17]:

$$mathrm{D }=sqrt{sum_{i=1}^{N}frac{{d}_{i}^{2}}{2N}}$$

where ({d}_{i}) is the difference between the first and the second measurements and N is the sample size that was remeasured. Subsequently, the relative TEM (% TEM) was calculated as follows:

$$%;mathrm{TEM}=frac{mathrm{TEM}}{overline{mathrm x}}times100%$$

where (overline{mathrm{x}}) is the sample mean. The acceptable range for intra-examiner % TEM is < 1.5% [18].

### Statistical analysis

Descriptive statistics were used to analyse the demographic parameters of the judges. Paired t-test was performed to examine any differences between the mean VAS scores of orthognathic versus non-orthognathic judges.

One-sample Wilcoxon signed-rank test was used to examine to differences between attractive faces with the ideal value of recommended parameters. Five female and male models with the highest VAS scores were selected for this analysis. Subsequently, the Pearson correlations test was used to examine the association between the mean VAS scores with all the measured independent variables.

A p-value of < 0.05 was considered significant for all statistical tests. All data unless specified were analysed using the SPSS Statistics software version 23.0 (Armonk, NY: IBM Corp, USA).