Global facial soft tissue thicknesses for craniofacial identification (2023): a review of 140 years of data since Welcker's first study.

This year (2023) marks 140 years since the first publication of a facial soft tissue thickness (FSTT) study. Since 1883, a total of 139 studies have been published, collectively tallying > 220,000 tissue thickness measurements of > 19,500 adults. In just the last 5-years, 33 FSTT studies have been conducted. Herein, we add these data (plus an additional 20 studies) to the 2018 T-Table to provide an update of > 81,000 new datapoints to the global tallied facial soft tissue depths table. In contrast to the original 2008 T-Table, some notable changes are as follows: increased FSTTs by 3 mm at infra second molar (ecm2-iM2'), 2.5 mm at gonion (go-go'), 2 mm at mid-ramus (mr-mr'), and 1.5 mm at zygion (zy-zy'). Rolling grand means indicate that stable values have been attained for all nine median FSTT landmarks, while six out of nine bilateral landmarks continue to show ongoing fluctuations, indicating further data collection at these landmarks holds value. When used as point estimators for individuals with known values across 24 landmarks (i.e., C-Table data), the updated grand means produce slightly less estimation error than the 2018 T-Table means (3.5 mm versus 3.6 mm, respectively). Future efforts to produce less noisy datasets (i.e., reduce measurement and sampling errors as much as possible between studies) would be useful.

Facial soft tissue depth of a contemporary adult Greek population.

Facial approximation is a technique that involves constructing the facial muscles and applying a suitable facial soft tissue depth (FSTD) dataset. To date, several FSTD studies have been conducted for varying population groups. This study aims to establish a FSTD dataset of an adult Greek population sample for the first time. The facial depths of subjects were measured on 100 head CT scans of 50 male and 50 female subjects aged from 18 to 99. The 3D head and skull models of subjects were segmented in Amira 6.1 by using histogram method. FSTDs were measured at 22 cranial landmarks (5 mid-sagittal, 17 bilateral). The FSTD dataset was generated by considering the age and sex of subjects. The impact of age and sex on the FSTD was limited. Slight inter-population depth variations were reported. Facial asymmetry calculated between the bilateral landmarks was insignificant for both male and female subjects.

3D facial approximation and endocast analysis of the Mummy of Minirdis (Ancient Egypt, ca. 2,300 Before Present).

The present article offers the facial approximation of the mummy of the ancient Egyptian adolescent named Minirdis (ca. 2300 years BP) by means of anatomical analysis of video-images and through a facial approximation protocol implemented on more historical personages. An evaluation of the mummy's endocast is also offered. A potential diagnosis of Sotos syndrome is cautiously considered but its inherent limitations are detailed. Finally, the methodology is presented as a valuable tool both for bio-historical research and for further studies on normal and pathologic morphologies of the cranio-facial district.

A computerized facial approximation method for Homo sapiens based on facial soft tissue thickness depths and geometric morphometrics.

Facial approximation (FA) provides a promising means of generating the possible facial appearance of a deceased person. It facilitates exploration of the evolutionary forces driving anatomical changes in ancestral humans and can capture public attention. Despite the recent progress made toward improving the performance of FA methods, a limited understanding of detailed quantitative craniofacial relationships between facial bone and soft tissue morphology may hinder their accuracy, and hence subjective experience and artistic interpretation are required. In this study, we explored craniofacial relationships among human populations based upon average facial soft tissue thickness depths (FSTDs) and covariations between hard and soft tissues of the nose and mouth using geometric morphometrics. Furthermore, we proposed a computerized method to assign the learned craniofacial relationships to generate a probable facial appearance of Homo sapiens, reducing human intervention. A smaller resemblance comparison (an average Procrustes distance was 0.0258 and an average Euclidean distance was 1.79 mm) between approximated and actual faces and a greater recognition rate (91.67%) tested by a face pool indicated that average dense FSTDs contributed to raising the accuracy of approximated faces. Results of partial least squares (PLS) analysis showed that nasal and oral hard tissues have an effect on their soft tissues separately. However, relatively weaker RV correlations (<0.4) and greater approximation errors suggested that we need to be cautious about the accuracy of the approximated nose and mouth soft tissue shapes from bony structures. Overall, the proposed method can facilitate investigations of craniofacial relationships and potentially improve the reliability of the approximated faces for use in numerous applications in forensic science, archaeology, and anthropology.

Lip morphology estimation models based on three-dimensional images in a modern adult population from China.

Lips are the main part of the lower facial soft tissue and are vital to forensic facial approximation (FFA). Facial soft tissue thickness (FSTT) and linear measurements in three dimensions are used in the quantitative analysis of lip morphology. With most FSTT analysis methods, the surface of soft tissue is unexplicit. Our study aimed to determine FSTT and explore the relationship between the hard and soft tissues of lips in different skeletal occlusions based on cone-beam CT (CBCT) and 3dMD images in a Chinese population. The FSTT of 11 landmarks in CBCT and 29 lip measurements in CBCT and 3dMD of 180 healthy Chinese individuals (90 males, 90 females) between 18 and 30 years were analyzed. The subjects were randomly divided into two groups with different skeletal occlusions distributed equally: 156 subjects in the experimental group to establish the prediction regression formulae of lip morphology and 24 subjects in the test group to assess the accuracy of the formulae. The results indicated that FSTT in the lower lip region varied among different skeletal occlusions. Furthermore, sex discrepancy was noted in the FSTT in midline landmarks and linear measurements. Measurements showing the highest correlation between soft and hard tissues were between total upper lip height and Ns-Pr (0.563 in males, 0.651 in females). The stepwise multiple regression equations were verified to be reliable with an average error of 1.246 mm. The method of combining CBCT with 3dMD provides a new perspective in predicting lip morphology and expands the database for FFA.

Using Computed Tomography (CT) Data to Build 3D Resources for Forensic Craniofacial Identification.

Forensic craniofacial identification encompasses the practices of forensic facial approximation (aka facial reconstruction) and craniofacial superimposition within the field of forensic art in the United States. Training in forensic facial approximation methods historically has used plaster copies, high-cost commercially molded skulls, and photographs. Despite the increased accessibility of computed tomography (CT) and the numerous studies utilizing CT data to better inform facial approximation methods, 3D CT data have not yet been widely used to produce interactive resources or reference catalogs aimed at forensic art practitioner use or method standardization. There are many free, open-source 3D software packages that allow engagement in immersive studies of the relationships between the craniofacial skeleton and facial features and facilitate collaboration between researchers and practitioners. 3D CT software, in particular, allows the bone and soft tissue to be visualized simultaneously with tools such as transparency, clipping, and volume rendering of underlying tissues, allowing for more accurate analyses of bone to soft tissue relationships. Analyses and visualization of 3D CT data can not only facilitate basic research into facial variation and anatomical relationships relevant for reconstructions but can also lead to improved facial reconstruction guidelines. Further, skull and face surface models exported in digital 3D formats allow for 3D printing of custom reference models and novel training materials and modalities for practitioners. This chapter outlines the 3D resources that can be built from CT data for forensic craniofacial identification methods, including how to view 3D craniofacial CT data and modify surface models for 3D printing.

Open-Source Tools for Dense Facial Tissue Depth Mapping of Computed Tomography Models.

Computed tomography (CT) scans provide anthropologists with a resource to generate three-dimensional (3D) digital skeletal material to expand quantification methods and build more standardized reference collections. The ability to visualize and manipulate the bone and skin of the face simultaneously in a 3D digital environment introduces a new way for forensic facial approximation practitioners to access and study the face. Craniofacial relationships can be quantified with landmarks or with surface-processing software that can quantify the geometric properties of the entire 3D facial surface. This article describes tools for the generation of dense facial tissue depth maps (FTDMs) using deidentified head CT scans of modern Americans from the Cancer Imaging Archive public repository and the open-source program Meshlab. CT scans of 43 females and 63 males from the archive were segmented and converted to 3D skull and face models using Mimics and exported as stereolithography files. All subsequent processing steps were performed in Meshlab. Heads were transformed to a common orientation and coordinate system using the coordinates of nasion, left orbitale, and left and right porion. Dense FTDMs were generated on hollowed, cropped face shells using the Hausdorff sampling filter. Two new point clouds consisting of the 3D coordinates for both skull and face were colorized on an RGB (red-green-blue) scale from 0.0 (red) to 40.0-mm (blue) depth values and exported as polygon (PLY) file format models with tissue depth values saved in the "vertex quality" field. FTDMs were also split into 1.0-mm increments to facilitate viewing of common depths across all faces. In total, 112 FTDMs were generated for 106 individuals. Minimum depth values ranged from 1.2 mm to 3.4 mm, indicating a common range of starting depths for most faces regardless of weight, as well as common locations for these values over the nasal bones, lateral orbital margins, and forehead superior to the supraorbital border. Maximum depths were found in the buccal region and neck, excluding the nose. Individuals with multiple scans at visibly different weights presented the greatest differences within larger depth areas such as the cheeks and neck, with little to no difference in the thinnest areas. A few individuals with minimum tissue depths at the lateral orbital margins and thicker tissues over the nasal bones (>3.0 mm) suggested the potential influence of nasal bone morphology on tissue depths. This study produced visual quantitative representations of the face and skull for forensic facial approximation research and practice that can be further analyzed or interacted with using free software. The presented tools can be applied to preexisting CT scans, traditional or cone beam, adult or subadult individuals, with or without landmarks, and regardless of head orientation, for forensic applications as well as for studies of facial variation and facial growth. In contrast with other facial mapping studies, this method produced both skull and face points based on replicable geometric relationships, producing multiple data outputs that are easily readable with software that is openly accessible.

Facial soft tissue thicknesses in Bulgarian adults: relation to sex, body mass index and bilateral asymmetry.

BACKGROUND: The aim of the study is to measure the facial soft tissue thicknesses (STTs) in Bulgarians, to evaluate the relation of the STTs to the nutritional status, sex and bilateral asymmetry, and to examine the correlations between the separate STTs as well as between the STTs and body weight, height, and body mass index (BMI). In the present study, the facial STTs were measured on computed tomography scans of the head of Bulgarian adults. MATERIALS AND METHODS: The STTs were measured at 7 midline and 9 bilateral landmarks. The measurements were performed in the free software InVesalius in the axial and sagittal planes. The mean, standard deviation, minimum and maximum values, median and coefficient of variation were reported for the STT at each landmark according to the sex and BMI category. The BMI, sex and bilateral differences were assessed for statistical significance. Pearson correlation analysis was applied to assess the strength and direction of the relationships between the STTs and body height, weight and BMI, as well as between separate STTs. RESULTS AND CONCLUSIONS: The facial soft tissues in Bulgarian adults changed in accordance with the nutritional status of the individual and in both sexes all STTs augmented with the increasing BMI. For both normal and overweight BMI categories, males had more soft tissue at the majority of facial points than females, as the only exceptions were observed in the cheek zone, where STTs were thicker in females. Significant bilateral differences were observed in either sex and BMI category. Stronger correlations were established for the STTs in the jaw region and between the cheek and jaw soft tissues. Besides, the correlations between the homologous bilateral landmarks were among the strongest ones.

Recognition of computerized facial approximations by familiar assessors.

Studies testing the effectiveness of facial approximations typically involve groups of participants who are unfamiliar with the approximated individual(s). This limitation requires the use of photograph arrays including a picture of the subject for comparison to the facial approximation. While this practice is often necessary due to the difficulty in obtaining a group of assessors who are familiar with the approximated subject, it may not accurately simulate the thought process of the target audience (friends and family members) in comparing a mental image of the approximated subject to the facial approximation. As part of a larger process to evaluate the effectiveness and best implementation of the ReFace facial approximation software program, the rare opportunity arose to conduct a recognition study using assessors who were personally acquainted with the subjects of the approximations. ReFace facial approximations were generated based on preexisting medical scans, and co-workers of the scan donors were tested on whether they could accurately pick out the approximation of their colleague from arrays of facial approximations. Results from the study demonstrated an overall poor recognition performance (i.e., where a single choice within a pool is not enforced) for individuals who were familiar with the approximated subjects. Out of 220 recognition tests only 10.5% resulted in the assessor selecting the correct approximation (or correctly choosing not to make a selection when the array consisted only of foils), an outcome that was not significantly different from the 9% random chance rate. When allowed to select multiple approximations the assessors felt resembled the target individual, the overall sensitivity for ReFace approximations was 16.0% and the overall specificity was 81.8%. These results differ markedly from the results of a previous study using assessors who were unfamiliar with the approximated subjects. Some possible explanations for this disparity in performance were examined, and it was ultimately concluded that ReFace facial approximations may have limited effectiveness if used in the traditional way. However, some promising alternative uses are explored that may expand the utility of facial approximations for aiding in the identification of unknown human remains.

Virtopsy shows a high status funerary treatment in an early 18th Dynasty non-royal individual.

This work presents the multidisciplinary investigation of the head of Nebiri (Museo Egizio, Turin S_5109), Chief of Stables, a high status elite person from the 18th Dynasty involving MDCT, 3D brain surface and facial reconstructions accompanied by a consideration of previously presented chemical analysis of the embalming materials found in fragments of bandages used on the head and viscera (lung) found in one of the four canopic jars. Comparison of the techniques used for the cosmetic treatment of Nebiri with those used in other elite and high status non-royal persons confirms the validity of the use of the term "high status elite" in the case of Nebiri. This case highlights the importance of using modern forensic techniques both to enhance new technologies of retrospective diagnosis on altered human remains and to increase knowledge of past populations.

Turning the tables of sex distinction in craniofacial identification: Why females possess thicker facial soft tissues than males, not vice versa.

Males are universally reported to possess larger facial soft-tissue thickness (FSTT) than females, however, this observation oversimplifies the raw data yielding an underpowered assessment of FSTT sex-patterning where: differences are small (η(2) < 5%) and inconsistent (females are routinely larger than males at the cheeks). Here we investigate body-size normalized data to assess whether more general and improved understanding of FSTT sex-variation in humans is possible. FSTTs were measured in 52 healthy living Australians aged 18 to 30 years using B-mode ultrasound. Participants' stature and body mass were also measured. Sex differences were calculated before and after normalization by the aforementioned body-composition variables. Methods were repeated in three other independent samples to evaluate reproducibility: 100 American Whites and 60 American Blacks measured by B-mode ultrasound; and 50 Turkish residents measured by regular supine CT. Compared to raw mean differences (F < M, by -6%), females displayed much thicker FSTTs than males when normalized for body mass (F > M, by +16%). Consequently, while the sexes share similar raw values, females possess much larger FSTTs for their relatively lighter bodies. The relative FSTT difference was 2.7× larger than the raw mean difference. Sex differences in FSTT are of larger magnitude and reversed direction in mass normalized data. Contrary to popular thought, females possess much larger FSTTs than males owing to their generically lighter bodies (-18 kg). These data patterns help explain why the pooling of sex-categorized FSTT does not jeopardize the sex-difference-it is encoded more strongly in terms relative to body mass.

Automated reconstruction: Predictive models based on facial morphology matrices.

Forensic Facial Approximation (FFA) has evolved, with techniques advancing to refine the intercorrelation between the soft-tissue facial profile and the underlying skull. FFA has become essential for identifying unknown persons in South Africa, where the high number of migrant and illegal labourers and many unidentified remains make the identification process challenging. However, existing FFA methods are based on American or European standards, rendering them inapplicable in a South African context. We addressed this issue by conducting a study to create prediction models based on the relationships between facial morphology and known factors, such as population affinity, sex, and age, in white South African and French samples. We retrospectively collected 184 adult cone beam computed tomography (CBCT) scans representing 76 white South Africans (29 males and 47 females) and 108 French nationals (54 males and 54 females) to develop predictive statistical models using a projection onto latent structures regression algorithm (PLSR). On training and untrained datasets, the accuracy of the estimated soft-tissue shape of the ears, eyes, nose, and mouth was measured using metric deviations. The predictive models were optimized by integrating additional variables such as sex and age. Based on trained data, the prediction errors for the ears, eyes, nose, and mouth ranged between 1.6 mm and 4.1 mm for white South Africans; for the French group, they ranged between 1.9 mm and 4.2 mm. Prediction errors on non-trained data ranged between 1.6 mm and 4.3 mm for white South Africans, whereas prediction errors ranging between 1.8 mm and 4.3 mm were observed for the French. Ultimately, our study provided promising predictive models. Although the statistical models can be improved, the inherent variability among individuals restricts the accuracy of FFA. The predictive validity of the models was improved by including sex and age variables and considering population affinity. By integrating these factors, more customized and accurate predictive models can be developed, ultimately strengthening the effectiveness of forensic analysis in the South African region.

Recognizability of Demographically Altered Computerized Facial Approximations in an Automated Facial Recognition Context for Potential Application in Unidentified Persons Data Repositories.

This study examined the recognizability of demographically altered facial approximations for potential utility in unidentified persons tracking systems. Five computer-generated approximations were generated for each of 26 African male participants using the following demographic parameters: (i) African male (true demographics), (ii) African female, (iii) Caucasian male, (iv) Asian male, and (v) Hispanic male. Overall, 62% of the true demographic facial approximations for the 26 African male participants examined were matched to a corresponding life photo within the top 50 images of a candidate list generated from an automated blind search of an optimally standardized gallery of 6159 photographs. When the African male participants were processed as African females, the identification rate was 50%. In contrast, less congruent identification rates were observed when the African male participants were processed as Caucasian (42%), Asian (35%), and Hispanic (27%) males. The observed results suggest that approximations generated using the opposite sex may be operationally informative if sex is unknown. The performance of approximations generated using alternative ancestry assignments, however, was less congruent with the performance of the true demographic approximation (African male) and may not yield as operationally constructive data as sex-altered approximations.

Facial reconstruction using 3-D computerized method: A scoping review of Methods, current Status, and future developments.

Facial reconstruction (otherwise known as facial approximation) is an alternative method that has been widely accepted in forensic anthropological and archaeological circumstances. This method is considered useful for creating the virtual face of a person based on skull remain. Three-dimensional (3-D) traditional facial reconstruction (known as sculpture or manual method) has been recognized for more than a century; however, it was declared to be subjective and required anthropological training. Until recently, with the progression of computational technologies, many studies attempted to develop a more appropriate method, so-called the 3-D computerized facial reconstruction. This method also relied on anatomical knowledge of the face-skull relationship, divided into semi- and automated based computational method. The 3-D computerized facial reconstruction makes it more rapid, more flexible, and more realistic to generate multiple representations of faces. Moreover, new tools and technology are continuously generating fascinating and sound research as well as encouraging multidisciplinary collaboration. This has led to a paradigm shift in the 3-D computerized facial reconstruction to a new finding and new technique based on artificial intelligence in academia. Based on the last 10-years scientific-published documents, this article aims to explain the overview of the 3-D computerized facial reconstruction and progression as well as an issue relating to future directions to encourage further improvement.

Cranial and facial inter-landmark distances and tissue depth dataset from computed tomography scans of 388 living persons.

Computed tomography (CT) scans of 388 living adults of both sexes were collected from four self-identified ancestry groups from the United States (African, Asian, European, and Hispanic). Scans were acquired from multiple institutions and under a variety of scanning protocols. Scans were used to produce 3D bone and soft tissue models, from which were derived cranial and facial inter-landmark distances (ILDs) and soft tissue depth measurements. Similar measurements were made on 3D facial approximations produced by ReFace software. 3D models and all measurements were obtained using MimicsR software. These measurements are useful for facial approximations of unidentified decedents and for investigations into human variation between and among ancestry groups and sexes.

Soft-tissue thickness values using cone beam computed tomography: A literature review.

When human remains are found, with no evidence of identity, facial approximation can be a useful technique to employ. The reconstruction of the ante-mortem appearance can reproduce the likely features of the face, starting from the skull, based on the overlying soft-tissue thickness. Over the years, many techniques have been developed to achieve soft-tissue thickness measurements, one of which is based on the use of cone beam computed tomography. This study aimed to review the status of this technique and to evaluate heterogeneity among studies undertaken in this field, with particular regard to determination of landmarks, sex and body mass index.

Facial soft tissue depth measurements in cone-beam computed tomography: A study of a Brazilian sample.

Forensic facial reconstruction (approximation) (FFR) is an aid to human identification when no presumed identity is available. It is based on average soft tissue thickness (STT) applied onto a skull. These averages vary at each landmark according to sex, ancestry, and Facial Growth Patterns (FGP). To obtain the reference, there are different protocols and conditions, such as needles in cadavers, ultrasound, magnetic resonance, and computer tomography. Using cone-beam computed tomography (CBCT), landmark placement and direction of measurement are critical. The purpose of this article is to detailly describe a method for STT measurement in CBCT DICOM files and to test it in the analysis of a multi-ancestral Brazilian sample, subdivided into sex, age and FGP. A sample of 100 (50 male and 50 female) CBCT exams were selected and the volume was primarily been repositioned to cephalometric standards. A detailed description of the location and measurement direction of 32 landmarks was provided and granted good reproducibility of the measurements. The averages were assessed by sex, age, and FGP. There were significant differences between males and females. The CBCT measuring protocol provided standardization of measurements and is a method to be used in future researches. Advantages of CBCT, such as the subject's upright position and adjustable volume positioning, also justify its usage. Limited differences of STT were related to age and FGP. The updated Brazilian soft tissue thickness chart is a reliable source of data for forensic and clinical purposes.

Estimation of the mandibular dimensions from linear cranial measurements for use in craniofacial reconstruction: A preliminary study.

BACKGROUND: A missing mandible is a common problem in facial identification cases requiring forensic facial approximation or reconstruction. The Sassouni and Sassouni-Plus methods which are currently used to predict the missing mandible from the cranium produce low levels of accuracy. AIMS: This study proposes a new method for the estimation of the overall dimensions of the mandible based upon linear cranial measurements, the proposed method has the potential to be utilised in the facial reconstruction of a range of adult skulls with dentition. SAMPLE AND METHOD: 21 measurements were taken from a sample of 90 skulls, 44 male, 43 female and three juvenile, originating from 9 different geographical areas. Ordinary least-squares regression, hierarchical cluster analysis and analysis of variance (ANOVA) were used to investigate trends in the data and to produce equations for the estimation of condylar height, corpus length and anterior height. CONCLUSION: When tested the equations produced an overall mean error of 0.09 mm with a standard deviation of ±4.84. The proposed method offers an improvement upon the currently used methods. It can be used to estimate the overall mandibular dimensions with a good level of accuracy.

Facial soft tissue thickness in Yangtze River delta Han population: Accurate assessment and comparative analysis utilizing Cone-Beam CT.

Facial approximation plays a vital role in personal identification when other methods cannot be applied, and the study on facial soft tissue thickness (FSTT) is important to allow more accurate facial approximation. The Cone-Beam CT (CBCT) is considered to be an accurate approach in assessing FSTT, however only few studies have assessed the FSTT norms by CBCT in Chinese populations. The aim of this study was to (1) establish forensic measurement approach on a 3D model reconstructed by CBCT image; (2) obtain FSTT norms from the adults of Yangtze River delta Han population; (3) determine the impacts of sex, age, BMI as well as malocclusion type on FSTT and (4) form a FSTT database through CBCT. A total of 60 facial landmarks were primarily established from 3D reconstructed models from CBCT images of 424 healthy Han adults (130 males and 294 females) aged from 21 to 50 years in Yangtze River delta region and measurements were carried out. The multivariate analysis of variance test and multiple linear regressions test showed that the FSTT values on most landmarks were significantly different between sexes and BMI, and males showed greater values, expect for the landmarks distributed in malarzygomatic areas. Simultaneously, BMI mostly affected the landmarks located in zygomatic region. Besides, only a few landmarks were influenced by age. Interestingly, several periodontal landmarks were influenced by malocclusion types, thus the impact of malocclusion types on FSTT requires attention. Finally, the validation analysis suggested that measurement approach is an important factor for FSTT.

Three-Dimensional Prediction of the Nose for Facial Approximation in a Thai Population.

Most of the previous studies about nose prediction were concentrated only some landmarks of the nose. This study aimed to generate prediction equations for ten landmarks of the nose in the midline and alar regions for forensic facial approximation. The six midline landmarks were the sellion, nasion-pronasale posterior, nasion-pronasale anterior, pronasale, nasal drop, and subnasale. The four landmarks of the alar region were the alare, superior alar groove, posterior alar groove, and inferior alar groove. We used the skull landmarks in the nasal, zygomatic, and maxillary bone to predict the landmarks of the nose. Cone-beam computed tomography scans of 108 Thai subjects with normal BMI and age ranging from 21.0 to 50.9 years were obtained in a sitting position. The data were converted into three-dimensional (3-D) images of the skull and face. The Cartesian coordinates of the landmarks of the skull and nose were used to formulate the multiple regression equations. The formulated equations were tested in 24 new subjects. The mean differences in the predicted midline landmarks varied between -0.4 mm and 0.5 mm, whereas those for bilateral landmarks varied between -1.0 mm and 1.4 mm. In conclusion, the prediction equations formulated here will be beneficial for facial approximation of the nose in a Thai population.