Golden ratio for the foramen magnum on CT images: a morphological and morphometrical study / Proporción áurea para el foramen magnum en imágenes de TC: un estudio morfológico y morfométrico

SUMMARY: The foramen magnum (FM) is a transition zone between the spine and skull. There is a study in the literature showing the golden ratio (4.62) and harmony between both FM and the anteroposterior and transverse diameters of the skull. The aim of this study is to examine the existence of this ratio on CT images and to investigate whether this ratio changes according to the FM shape types. In this study, 402 adult CT images belonging to the Turkish population were examined. Maximum cranial length (MCL), maximum cranial width (MCW) and the FM length (FML) and FM width (FMW) were measured. The different shapes of the FM were macroscopically classified. The number and incidence of each type in the studied skull was registered. In the 402 CT images used in the study, 12 FM shapes were detected. Three of the shape types observed in our study have not been reported in the literature until now, and were found in our study for the first time. In addition, our data supported that by using the ratio of 4.62, there was a great harmony between the skull and FM. The results obtained from the research show that there is a ratio of 4.62 between the basic cranial measurements and FM dimensions in all shapes except triangular shape. It is thought that repeating the calculated coefficients over more different FM shapes will contribute to the effectiveness of the proposed golden ratio.

RESUMEN: El foramen magno (FM) es una zona de transición entre la columna y el cráneo. Existe un estudio en la literatura que muestra la proporción áurea (4,62) y la armonía entre el FM y los diámetros anteroposterior y transversal del cráneo. El objetivo de este estudio fue examinar la existencia de esta relación en las imágenes de TC e investigar si esta relación cambia según los tipos de forma del FM. Se examinaron 402 imágenes de TC de adultos pertenecientes a la población turca. Se midieron la longitud craneal máxima, el ancho craneal máximo y la longitud del FM y la anchura del FM. Las diferentes formas del FM se clasificaron macroscópicamente. Se registró el número e incidencia de cada tipo en el cráneo estudiado. En las 402 imágenes de TC utilizadas en el estudio, se detectaron 12 formas de FM. Tres de los tipos de formas observados en nuestro estudio no se han reportado en la literatura consultada describiéndose por primera vez. Además, nuestros datos respaldaron que al usar la proporción de 4,62, había una armonía importante entre el cráneo y el FM. Los resultados obtenidos de la investigación muestran que existe una relación de 4,62 entre las medidas craneales básicas y las dimensiones de la FM en todas las formas excepto en la triangular. Se cree que la repetición de los coeficientes calculados en más formas de FM diferentes contribuirá a la eficacia de la proporción áurea propuesta.

The Face Shape and Golden Ratio Classification In Turkish Healthy Population.

Beauty indicates a specific proportion system. It comprises facial height, width, and symmetry. A beautiful and an attractive face or facial morphology, which is affected by many factors such as social, cultural, ethnic, racial, climate, gender, age, socio-economic, nutritional, and genetic is a subjective concept. We wanted to determine the facial morphology, golden ratio, and classify the face shape, in Turkish healthy adults. METHODSThis is a descriptive study conducted among two hundred twenty-eight (139 females; 89 males) subjects aged between 18 and 25 years. Physiognomic facial height, the width of face, face golden ratio, morphological facial height, facial index were measured. Based on the face index, the face shape was classified as hypereuryprosopic, euryprosopic, mesoprosopic, leptoprosopic, and hyperleptoprosopic. Also, the face shape was determined according to the golden ratio. Statistical analysis was done by SPSS Ver. 22. Chi-Square Test was used to determine the differences between gender and face measurements. A p value of <0.05 value was considered as significant.RESULTSOut of 228 subjects, face shape according to golden ratio was normal in 11 female subjects, short in 128 female subjects. Also, in males, the same parameter was normal in 10 subjects, short in 72, and long in 7 subjects. On the other hand, significant differences were found between the genders. Hypereuroprosopic face type was the least observed in males but not in females.CONCLUSİONSThe facial shape data may be valuable for evaluating various disorders and variations for plastic surgeons and orthodontists and other clinicians

A three-dimensional photogrammetric analysis of the facial esthetics of the Miss Korea pageant contestants / 대한치과교정학회지

OBJECTIVE: The aims of this study were to measure and compare the facial dimensions of the Miss Korea pageant contestants and a selected group of women from the general population by using three-dimensional (3D) image analysis, as well as to compare various facial ratios to the golden ratio within each group. METHODS: Three-dimensional images of 52 Miss Korea pageant contestants (MK group) and 41 young female adults selected from the general population (GP group) were acquired. Fifty-four variables and ratios were measured and calculated. Intergroup comparisons were performed using multivariate analysis of variance. RESULTS: Compared to the GP group, the MK group showed greater total facial height and eye width, lesser lower-facial height, and lesser facial, lower-facial, and nasal widths. Moreover, compared to the GP group, the MK group had more protruded noses with greater nasolabial angle, greater vertical curvature of the foreheads, lesser horizontal curvature of the cheek, and lesser lower-lip-and-chin volume. CONCLUSIONS: The MK group had longer faces but smaller lower lips and chins than did the GP group. The golden ratio was not matching the current facial esthetic standards. These data might be beneficial for treatment planning of patients undergoing orthognathic and plastic surgeries.

A comparison of the relationship between the golden ratio and anatomical characteristics of the supraorbital foramen in bare skulls belonging to the Byzantine era and modern era / Comparación de la relación entre la proporción áurea y las características anatómicas del foramen supraorbitario en cráneos de la época bizantina y la edad moderna

The aim of the present study is to determine the frequency of the occurrence of supraorbital foramen/notch (SOF/N) in the skulls of the people who lived in the modern era and the late Byzantine era, to determine the symmetry and the asymmetry between the two halves of the skulls by measuring the linear distance to various landmarks, to check the consistency between the location of the SOF/N and the golden ratio by calculating the ratio between linear distances and to evaluate the differences between the skulls from both historical periods. In the study, the frequency of the occurrence of the supraorbital notch in the skulls from the Byzantine era was found to be 26.60 % on the right and 13.30 % on the left while it was 14.30 % on the right and 9.52 % on the left in the skulls belonging to modern humans. In the skulls belonging to the Byzantine era, the average distance between SOF/N and the sagittal axis passing along the lateral orbital wall was found to be 34.81±2.51 mm and 32.99±2.81 mm respectively on the right and the left while it was 33.14±2.19 mm and 33.39±2.06 mm in the skulls belonging to modern era. The average distance between the SOF/N and the sagittal plane passing along the midline of the skull was found to be 24.55±2.79 mm and 21.57±2.44 mm on the right and the left respectively in the skulls belonging to the Byzantine era while it was 0.04±3.30 mm and 20.96±2.37 mm in the skulls belonging to the modern era. The average distance between the SOF/N and sagittal plane passing along the medial orbital wall was found to be 23.78±3.60 mm and 23.81±3.20 mm on the right and the left respectively in the skulls belonging to the Byzantine era while it was found to be 22.23±3.29 mm and 23.97±1.93 mm in the skulls belonging to the modern era. The average value of the distance between the sagittal planes passing along the lateral and medial sides of the orbit and the ratios between the distance from SOF/N to the sagittal plane passing along the lateral side of the orbit was found to be 1.47±0.21 mm and 1.60±0.08 mm respectively in the skulls belonging to the Byzantine era and the modern era. No significant difference was found between this ratio and the golden ratio; the average value of the ratios between the distance from the SOF/N to the sagittal plane passing along the midline of the skull and the distance from the SOF/N to the sagittal plane passing along the lateral side of the orbit was found to be 0.98±0.26 mm and 1.04±0.36 mm respectively in the skulls belonging to the Byzantine era and the modern era. A significant difference was found between this ratio and the golden ratio for both historical periods (modern society and late Byzantine period) (p <0.005). The comparison of the relevant anatomic characteristics of the SOF/N is very important for anthropologists while a broad knowledge on proportional calculations regarding morphometric values and the location are important for reconstructive surgeons and the experts in forensics and pain control.

El objetivo fue determinar la frecuencia del foramen y incisura supraorbitaria (FSO/E) en cráneos de individuos de la era moderna y aquellos de la era bizantina, para determinar la simetría y asimetría entre las dos mitades de cráneos, mediante la medición de la distancia lineal a varios puntos de referencia, para comprobar la coherencia entre la ubicación del FSO/ y la proporción áurea, a través del cálculo de la relación entre las distancias lineales. Además, se evaluaron las diferencias entre los cráneos de periodos históricos. En el estudio, se determinó que la frecuencia registrada de la incisura supraorbitaria en los cráneos de la época bizantina fue del 26,60% en el lado derecho y 13,30 % en el izquierdo; mientras que en cráneos humanos modernos fue de 14,30% en el lado derecho y 9,52 % en el izquierdo. En los cráneos pertenecientes a la época bizantina, la distancia media entre FSO/E y el eje sagital a lo largo de la pared lateral de la órbita fue de 34,81±2,51 mm y 32,99±2,81 mm, a la derecha e izquierda, respectivamente; mientras que en cráneos de la era moderna fue de 33,14±2,19 mm y 33,39±2,06 mm, a la derecha e izquierda, respectivamente. La distancia media entre la FSO/E y el plano sagital que pasa a lo largo de la línea mediana del cráneo, en los cráneos de la época bizantina, fue de 24,55±2,79 mm y 21,57±2,44 mm a la derecha e izquierda, respectivamente; mientras que fue de 0,04±3,30 mm y 20,96±2,37 mm en los cráneos de la era moderna. La distancia media entre la FSO/E y el plano sagital que pasa a lo largo de la pared medial de la órbita, en los cráneos pertenecientes a la época bizantina fue de 23,78±3,60 mm y 23,81±3,20 mm, a la derecha e izquierda, respectivamente; mientras que en los cráneos pertenecientes a la era moderna fue de 22,23±3,29 mm y 23,97±1,93 mm, a la derecha e izquierda, respectivamente. Se determinó que el valor medio de la distancia entre los planos sagitales a lo largo de los márgenes lateral y medial de la órbita y las proporciones entre la distancia desde FSO/E al plano sagital a lo largo del lado lateral de la órbita fueron de 1,47±0,21 mm y 1,60±0,08, respectivamente, en los cráneos pertenecientes a la época bizantina y la era moderna. No encontramos diferencias significativas entre esta relación y la proporción áurea. El valor medio de las relaciones entre la distancia de la FSO/E al plano a lo largo de la línea mediana del cráneo y la distancia de la FSO/E al plano sagital a lo largo de la pared lateral de la órbita fueron de 0,98±0,26 mm y 1,04±0,36 mm, respectivamente, en los cráneos pertenecientes a la era bizantina y la era moderna. No se encontró una diferencia significativa entre esta relación y la proporción áurea en ambos períodos históricos (la sociedad moderna y el periodo bizantino tardío) (p <0,005). La comparación de características anatómicas relevantes para el FSO/E son importantes para los antropólogos, donde un conocimiento integro de cálculos proporcionales con respecto a los valores morfométricos, mientras que para los cirujanos reconstructivos y los expertos en medicina forense es importante su ubicación.

A comparison of anatomical measurements of the infraorbital foramen of skulls of the modern and late Byzantine periods and the golden ratio / Comparación de las medidas anatómicas del foramen infraorbitario en cráneos de la época bizantina tardía, edad moderna y la proporción áurea

The aim of this study was to examine the morphometric characteristics of the infraorbital foramen of skulls of people living in modern society and in the late Byzantine period, to ascertain the symmetry or asymmetry of the two halves of the skulls by measuring the linear distance between various landmarks, to evaluate at the conformity between the infraorbital foramen and the golden ratio by calculating the ratios between these linear distances, and to set out the differences or similarities between the skulls of these different periods. It was found in the study that the morphometric characteristics of the infraorbital foramen in skulls of the modern period were 47.05 % circular, 41.17 % oval and 11.76 % atypical (semilunar and triangular) on the right, and 70.58 % circular and 29.41 % oval on the left, while those of the Byzantine period were 46.06 % circular and 53.3% oval on the right, and 50% circular and 50 % oval on the left. It was found that the measurements across the infraorbital foramen of the Byzantine skulls averaged 2.93±1.05 mm and 3.15±1.03 mm on the right side and 2.62±0.97 mm and 3.16±0.68 mm on the left vertically and horizontally respectively, and those of the modern period measured 2.32±0.50 mm and 3.00±0.92 mm on the right and 2.48±0.45 mm and 2.76±0.65 mm on the left vertically and horizontally respectively. The ratio between the distances from the outer orbital wall of the IOF to the sagittal plane and the piriform aperture were 1.46±0.25 mm and 1.40±0.21 mm for left and right respectively for the Byzantine skulls, and 1.24±0.24 mm and 1.29±0.42 mm for the modern skulls. A significant difference was found between the ratio obtained and the golden ratio for each of the periods (modern and Byzantine) (p<0.005). A comparison of anatomical characteristics of the infraorbital foramen of people living at different historical periods is important for anthropologists and knowing morphological types and amassing knowledge on the proportional calculation of location is important for dentistry, maxillofacial surgery and algology.

El objetivo fue examinar las características morfométricas de los forámenes infraorbitarios en cráneos de personas que viven en la sociedad moderna y aquellas que vivieron en el periodo bizantino tardío, para determinar la simetría o asimetría de las dos mitades de los cráneos. Se realizó la medición de la distancia lineal entre varios puntos de referencia, para evaluar la conformidad entre el foramen infraorbitario (FO) y la proporción áurea, mediante el cálculo de la relación entre esas distancias lineales, así como las diferencias y similitudes entre los cráneos de estos períodos. En relación a las características morfométricas, se encontraron en cráneos de la época moderna FO circulares (47,05%), ovalados (41,17 %) y atípicos (semilunar y triangular) en un 11,76 %, del lado derecha, y en el lado izquierdo estos porcentajes correspondieron a circulares (70,58 %) y ovalados (29,41%). Por su parte, los cráneos del período bizantino presentaron FO circulares (46,06 %) y ovalados (53,3 %) del lado derecho, mientras que del lado izquierdo fueron circulares (50 %) y ovalados (50 %). Se encontró que las medidas del FO de los cráneos bizantino tuvo un promedio de 2,93±1,05 mm y 3,15±1,03 mm en el lado derecho, y 2,62±0,97 mm y 3,16±0,68 mm a la izquierda, vertical y horizontal, respectivamente; y en el período moderno midieron 2,32±0,50 mm y 3,00±0,92 mm a la derecha y 2,48±0,45 mm y 2,76±0,65 mm a la izquierda, en medidas verticales y horizontales respectivamente. La relación entre las distancias de la pared orbitaria exterior del FO al plano sagital y la apertura piriforme fue de 1,46±0,25 mm y 1,40±0,21 mm, a izquierda y derecha respectivamente, para los cráneos bizantinos; y 1,24±0,24 mm y 1,29±0,42 mm para los cráneos modernos. Se encontró una diferencia significativa entre la proporción obtenida y la proporción áurea para cada uno de los períodos (moderno y bizantino) (p <0,005). La comparación de las características anatómicas del FO de individuos que vivieron en diferentes períodos históricos es valioso para los antropólogos y los conocimientos sobre el cálculo proporcional de la ubicación del FO son importantes en la odontología, cirugía maxilofacial y el estudio del dolor.

Vertical and horizontal facial proportions of Indian American men / 대한해부학회지

The importance of understanding all gender facial differences is critical in providing a successful cosmetic outcome. Men are a growing segment of the cosmetic industry. Understanding of the male face and its appropriate treatment with minimally invasive cosmetic procedures are essential. The aim was to investigate various facial ratios in Indian American men and to compare them with the Indian and Caucasian norms. Additionally, we wanted to evaluate whether these values satisfy golden and silver ratios. Direct facial anthropometric measurements were made using a digital caliper in 100 Indian American men students (18-30 years) at the American University of Antigua (AUA), Antigua. A set of facial ratios were calculated and compared with coefficients of variation (CV). Most of the facial ratios had small CV thus making them highly reliable due to reduced intra-sample variability. The upper face to face height and mandibulo upper face height indices were close to golden ratios whereas mandibulo lower face height, upper face height biocular width, and nasal indices were close to silver ratios. There was significant difference in most of the values when compared with previous studies. The present facial ratios data can be used as a reference value for Indian American men.

A Study for the Anatomic Feature of Asian Tribes: In View Point of the Golden Ratio and Beauty / 체질인류학회지

We observed and measured the structures showing the golden ratio in human body. Southeast Asian tribes, Aka and Lahu who live in Thailand, Miyanmar and China mountain areas and Koreans were examined by means of facial photography. The pictures of lateral facial view were taken by the fixed method. Then the length and width of auricles were measured by Phi-matrix software (version 1.1) on the scanned images. Helix ratio were also obtained by the same method. As a results, the ratio of the ear of Southeast Asian tribes showed the golden ratio and the racial and the individual differences were noticed a little.

Golden proportion assessment between maxillary and mandibular teeth on Indian population

PURPOSE: This study evaluated the existence of golden proportion between the widths of the maxillary and mandibular anterior teeth in Indian population. MATERIALS AND METHODS: The clinical tooth width measurements were recorded with the digital vernier calipers on 576 patients of both sexes in the age group of 21 - 30 years. Flexible ruler was used to determine the width of maxillary and mandibular anterior teeth on the patients by the same operator. The data obtained was statistically analyzed using paired student t-test (alpha=.05). RESULTS: The golden proportion was not found between the width of the right central and lateral incisors in 53% of women and 47% of men. The results revealed the golden percentage was rather inconstant in terms of relative tooth width. CONCLUSION: The golden proportion is an inappropriate method to relate the successive widths of the maxillary anterior teeth in Indian population.

Easy Facial Analysis Using Facial Golden Mask

For over two thousand years, many artists and scientists have tried to understand or quantify the form of the perfect, ideal, or the most beautiful face both in art and in vivo(life). However, this mathematical relationship has been consistently and repeatedly reported to be present in beautiful things. This particular relationship is referred to as the golden ratio. It is a mathematical ratio of 1.618:1 that seems to appear recurrently in beautiful things in nature as well as in other things that are seen as beautiful. Dr. Marquardt made the facial golden mask that contains and includes all of the 1-dimensional and 2-dimensional geometric golden element formed from the golden ratio. The purpose of this study is to evaluate the usefulness of the golden facial mask. In our cases(n=40), the authors applied the facial golden mask to the preoperative and postoperative photographs, and scored each photograph. Compared with the average scores of the facial mask applied photographs and none applied photographs using non-parametric test, statistical significance was not checked (p>0.05). It means that the facial golden mask can be used for facial analysis. The facial golden mask is easy to apply, cheap and relatively objective. So, the authors introduce the one of useful facial analyses.