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. 2024 Jun 22;245(4):551–559. doi: 10.1111/joa.14103

Charting facial growth and development for Bantu Africans: Central tendencies, variational properties and sexual dimorphisms

Yu Jie Zhong 1, Dan Cui 2, Patrick Yi Feng Wen 3,✉, Hai Ming Wong 1,✉
PMCID: PMC11424821  PMID: 38922713

Abstract

Current studies on facial growth and development have been largely based on European populations. Less studied are African populations, who because of their distinct genetic makeup and environmental conditions, provide deeper insights into patterns of facial development. Patterns of facial shape development in African populations remain largely uncharacterised. Our study aimed to establish facial growth and development trajectories based on a cohort of 2874 Bantu Africans from Tanzania aged 6–18 years, with particular focus on identifying morphogenetic processes that lead to observed developmental shape changes. Procrustes ANCOVA suggested sexually dimorphic patterns of facial shape development (p = 0.0036). The forehead was relatively contracted during development in both sexes. The glabella region was more anteriorly displaced in females due to expansion in the region laterosuperior to the eyes. Nasal protrusion increased with development, which was found to arise from local expansion in the nasal alae and columella. Local expansion in the upper and lower labial regions resulted in forward displaced lips in both sexes, with the effect more pronounced in males. The mentum was displaced more anteriorly in females due to comparatively more expanded mental regions with development. The lateral facial region corresponding to the underlying body of the mandible were developmentally expanded but were posteriorly positioned due to protrusive growth of surrounding structures. Generalised additive modelling of Procrustes variance suggested that facial variation decreased non‐linearly with age (p < 0.05). Relative principal component analysis suggested that variations in facial outline shape were developmentally constrained, whereas nasolabial and mental regions, where developmental changes were significant, became morphologically diversified with development. In contrast to simple descriptive illustration of facial shape development, we gained transformative insights into patterns of facial shape development by analysing morphogenetic processes and variational properties. Our analytical framework is broadly applicable to morphometric studies on ontogenetic shape changes.

Keywords: Africans, face, geometric morphometrics, growth, Procrustes variance

Patterns of facial growth and development of Bantu Africans were comprehensively evaluated. Variance of facial shape decreased overall with age but specific facial features demonstrated increased shape variance with age.

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1. INTRODUCTION

The human face is remarkable in its high degree of morphological variation among populations (Wen et al., 2015). Developmental processes shaping facial diversity result from the complex interplay between genetic and environmental factors. In particular, African populations harbour the richest genetic diversity among all modern human populations and are genetically distinct from other populations (Tishkoff et al., 2009). Despite their unique facial morphology, the pattern of facial growth and development in African populations remains largely uncharacterised (Larson et al., 2019). [Correction added on 23 September 2024 after first online publication: Larson et al. reference has been added.] Characterising facial shape development in African populations has important implications for a variety of fields such as delivering effective dental and medical treatments, improving accuracy of forensic facial reconstruction, and further understanding of the evolutionary history of modern populations.

Geometric morphometrics is a powerful statistical approach to characterising facial morphology. This approach has been applied in numerous facial growth studies (Liang et al., 2023; Matthews et al., 2018). With geometric morphometrics, all landmarks are analysed jointly, and as a result, the approach interrogates developmental changes of global shape formed by the entire constellation of facial landmarks. Evaluating local shape changes giving rise to observed shape differences is essential in unravelling the underlying morphogenetic processes shaping the human face (Klingenberg, 2021). Local shape changes can be evaluated by quantifying deformation of tissues surrounding landmarks (Piras et al., 2020). Despite its importance in unravelling facial morphogenetic processes, local shape changes during development have not been well studied.

A thorough understanding of facial shape development requires moving from current practices focusing on changes of mean shape to incorporating shape variation within the analytical framework. In addition to quantifying changes in shape variation, particular interest must be directed towards investigating developmentally constrained and diversified shape features (Le Maître & Mitteroecker, 2019). Changing patterns of variation and covariation of shape features can provide deeper insights into mechanisms that regulate the expression of facial shape variation during development.

The Bantu people are a major ethnic group constituting approximately 30% of the African population (Pereira et al., 2021). Our study aimed to establish the facial growth and development trajectories based on a cohort of Bantu Africans from Tanzania, unravelling morphogenetic processes giving rise to observed morphological changes. Our in‐depth characterisation of facial development in Africans can provide a unique perspective and understanding of craniofacial development in humans, thereby benefitting research and clinical practice in African and African diaspora populations.

2. MATERIALS AND METHODS

2.1. Study sample

This study is based on a cohort of 3605 Bantu Africans based in Tanzania between 3 and 21 years of age (Hallgrimsson et al., 2015, Samuels et al., 2020). [Correction added on 23 September 2024 after first online publication: Hallgrimsson et al. and Samuels et al. references have been added.] Details of the study population have been described elsewhere (Cole et al., 2016, 2018). [Correction added on 23 September 2024 after first online publication: Cole et al., 2016, reference has been added.] Individuals with birth defects, history of facial surgical operations, or personal or first‐degree relatives with craniofacial anomalies were excluded from the study. Only participants 18 years of age and below were included in our study due to a limited and unbalanced sample beyond 18 years of age (three females and 11 males). Individuals were further removed from the study based on unsatisfactory image quality and missing demographic information. Height, weight and BMI z‐scores of the study participants were calculated using the anthroplus (Schumacher et al., 2021) R package based on the WHO growth reference data for 5–19 years (WHO, 2007). Individuals with z‐scores for either height, weight or BMI greater than 1.96 (absolute value) were removed.

2.2. Quantification of facial morphology

3D facial images were obtained for each participant using MegaCapturor digitiser. A template mesh of 7160 facial landmarks was warped to the 3D facial mesh of each participant using the MeshMonk toolbox in MATLAB to then derive 7160 homologous landmarks (White et al., 2019). Centroid size (CS), the square root of sum of squared distance between each landmark and the centroid, was used to reflect the overall facial size (Zelditch et al., 2012). Facial landmarks of all participants were jointly submitted to generalised Procrustes analysis to remove non‐shape information regarding position, scale and orientation (Rohlf & Slice, 1990). Since facial asymmetry is not of interest in our study, symmetrisation was performed to investigate the growth and development of the symmetric component of facial shape. Principal component analysis (PCA) suggested that the top 305 eigenvectors jointly accounted for over 99% of shape variation in the study sample. Principal component (PC) scores along these 305 eigenvectors were used as shape variables for further analysis. Generalised Procrustes analysis and symmetrisation was performed using the procSym function in Morpho package (Version 2.1.1) in R 4.3.1 (Schlager, 2017).

2.3. Establishing facial growth trajectories

Gaussian kernel‐weighted partial least squares regression (wPLS) was applied to establish non‐linear trajectories of facial CS following methods by Matthews et al. (2018). Bandwidth of the Gaussian kernel determined the weights of observations when predicting CS. Larger bandwidth allowed distant observations to have larger modelling weights, and as a result the model became more linear. Repeated grid search suggested an optimal bandwidth of 1.15 for females and 0.50 for males. Bandwidth of 1.15 was chosen for modelling of both sexes to be conservative about the non‐linear trends and to ensure comparability of both sexes. To ensure stable predictions of facial CS, predictions were restricted to 8 to 15 years of age so that the summed weights for individuals aged above and below any age at prediction are comparable (ratio not less than 0.4).

2.4. Establishing facial shape developmental trajectories

The multivariate linear regression model Shape = Age + Sex + Age  ×  Sex was applied to establish facial shape developmental trajectories (Text S1), where Shape represents individuals' PC scores along the 305 eigenvectors, and Age  ×  Sex represents the interaction between participants' age and sex. Procrustes analysis of covariance (ANCOVA) was performed to investigate statistical significance involving the interaction effect based on Procrustes distances among observations (Goodall, 1991) through 10,000 permutation iterations of residual randomisation. Sex differences in the rate of facial shape development, a high‐dimensional vector characterised by magnitude and direction, were investigated using the Procrustes ANCOVA model. The analysis was performed using the lm.rrpp and pairwise function in RRPP (version 1.3.1) in R. The developmental trajectory of the magnitude of sex difference in model‐predicted facial shape, quantified through Procrustes distance, was modelled using a generalised additive model (GAM) with penalised thin plate regression splines.

2.5. Developmental changes of facial shape variation

Procrustes variance, the sum of squared Procrustes distance of individuals from the model‐predicted mean shape divided by group size, was used to quantify the magnitude of facial shape variation. Individuals were binned into 1‐year age groups of from 6 to 18 years of age for estimation and pairwise comparison of Procrustes variance. The pairwise function in RRPP was used for analysis with 10,000 permutations for statistical evaluation. GAM was used to model the developmental trajectories of Procrustes variance.

Developmental trajectories of facial phenotypic covariance matrix were established in order to investigate changes in facial shape covariance structure. Individuals were categorised into age‐by‐sex groups based on age intervals (6 to 8, 9 to 12, 13 to 14 and 15 to 18 years of age). The matrix of pairwise squared Riemannian distance of covariance matrices across groups was ordinated using principal coordinate analysis (PCoA) to establish developmental facial phenotypic covariance matrix trajectories. Relative PCA was performed based on the phenotypic covariance matrix of 6 to 8 and 15 to 18 year age groups in order to identify developmentally constrained and diversified facial features. The vcvComp R package (version 1.0.2) was used for analysis. The RElative STrength of Relative Eigenvectors (RESTORE) was developed to evaluate the proportion of shape variation described by relative eigenvectors. Low RESTORE score indicates that relative eigenvectors trivially explain shape variation. Details on establishing trajectories of facial phenotypic covariance matrix, relative PCA and the RESTORE metrics are available in Text S2 and S3 and Figure S1. For visualisations in this study, colour mesh of local deformations and superimposed facial meshes illustrating relative landmark displacement are used to denote the magnitude of local deformations and their morphological effects. Local deformations were calculated using the localmeshdiff function in the Arothron package (version 2.0.5) in R.

3. RESULTS

A total of 2874 individuals (Females: 1630; Males: 1244) between 6 and 18 years of age were retained for analysis. Individual age distribution is shown in Figure S2.

3.1. Growth changes of facial CS

Facial CS increased monotonically from 8 to 15 years of age (Figure 1a). Facial size growth rate peaked at 12 years of age for females and 14 to 15 years of age for males (Figure 1b).

FIGURE 1.

FIGURE 1

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Growth trajectories of facial CS. (a) Growth trajectories of facial CS stratified by sex. (b) Trajectories of the instantaneous rate of changes of facial CS stratified by sex. Shadings around the lines represent 95% confidence bands of the estimates.

3.2. Developmental changes of facial shape

Procrustes ANCOVA (Table S1) suggested significant differences in facial shape developmental patterns between sexes (p = 0.0036). The shape developmental trajectories for both sexes differed in direction by 22.8° in shape space. The magnitude of shape change per year quantified through Procrustes distance was 0.0024 and 0.0025 in females and males, respectively, and was not significantly different (p = 0.4978). Facial shapes predicted from the linear model from 6 to 18 years of age were projected to the first two PCs from the PCA of the entire sample to establish facial shape developmental trajectories (Figure 2). PC1 of the sample was generally aligned with facial shape development and PC2 differentiated sex. Permutation analysis suggested significant differences (p < 0.001) in model‐predicted female and male facial shape throughout development (Table S2). GAM suggested significant age effects on facial sexual dimorphism (p < 0.001), where Procrustes distance between‐model predicted female and male facial shape decreased before 9 years age and increased afterwards (Figure S3).

FIGURE 2.

FIGURE 2

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Developmental changes and sexual dimorphism of facial shape. (a) Developmental trajectories of female and male facial shape projected onto the first two PCs. Facial meshes along the trajectories illustrate the predicted facial shapes at key developmental stages. Numbers in parentheses are the percentage of shape variance accounted for by the respective PC. Grey facial meshes along the PC axes illustrate predicted facial shapes two standard deviations (SD) below and above the mean shape along the respective PC. Colour facial meshes illustrate the deformation from two SD below to two SD above the mean shape along the respective PC. The colour coding represents the percentage changes of the surface area of the meshes' triangular facets. Warm colour denotes expansion and cold colour denotes contraction. (b) Sexual dimorphism of predicted facial shape at key developmental stages. The colours represent deformation from predicted female facial shape to predicted male facial shape. Principles of the colour coding is as described in the legend for panel A, which is adopted through this paper.

Patterns of facial shape development were similar in both sexes, characterised by relative contraction in the forehead, mentum and along the nasolabial fold and local expansion in the nasal alae, columella, labial and zygomatic regions, as well as the lateral facial region corresponding to the underlying body of the mandible (Figure 3a,b). These local deformations resulted in protrusive displacement of the nasolabial and zygomatic regions with development (Figure S4).

FIGURE 3.

FIGURE 3

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Rate of facial shape development and its sexual dimorphism. Morphological effect of the rate of development of facial shape from age 6 to 18 years visualised through coloured meshes. (a) Deformation from predicted female facial shape at age 6 years to the target shape, which is the sum of the predicted shape and the matrix representing rate of female facial shape development. (b) Deformation from predicted male facial shape at age 6 years to the target shape, which is the sum of the predicted shape and the matrix representing rate of male facial shape development. (c) Sexual dimorphism of the morphological effect of the rate of changes of facial shape. This is evaluated as the deformation from the reference shape (The sum of predicted female facial shape at age 6 years and the matrix representing rate of female facial shape development) to the target shape (The sum of predicted female facial shape at age 6 years and the matrix representing rate of male facial shape development). While results are presented using predicted female face to construct the reference and target shape, highly similar patterns are obtained when predicted male face are used instead.

Males had less developmental contraction in the glabella (~1%), less expansion in the lateral orbital region (~1%), columella (~0.5%) and nasal alare (~0.5%), more labial expansion (~0.5%) and more developmental contraction in the mentum (~1%) compared with female shape development (Figure 3c). The different local deformations led to the glabella, nasal tip and mental region becoming progressively more anteriorly positioned in females (Figure S5).

3.3. Developmental changes of variation of facial shape

Procrustes variance of facial shape decreased non‐linearly with age (pFemale = 0.0006, pMale = 0.0010, pPooled < 0.0001; Figure 4a). Pairwise comparison suggested Procrustes variance was significantly larger in 6 to 8 years of age compared to other age groups (Figure 4b).

FIGURE 4.

FIGURE 4

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Variation of facial shape with development. (a) Developmental trajectory of Procrustes variance of facial shape. The non‐linear relationship was modelled using generalised additive model. Shadings around the lines represent 95% confidence bands of the estimates. (b) Pairwise differences in Procrustes variance between age groups from 6 to 18 years. The absolute values of the differences are displayed in the right triangle and corresponding p‐values are displayed in the left triangle. Significant differences are indicated by asterisks and are bordered in yellow. (c) Age trajectories of sex‐specific phenotypic covariance structure along the first two principal coordinates. (d) Sex‐specific relative eigenvalues of the covariance matrix of shape variables for individuals aged 6–8 years relative to that of individuals aged 15–18 years.

Trajectories of facial phenotypic covariance matrix from PCoA suggested that the covariance structure of facial shape is under continuous change and is generally aligned with the first principal coordinate (Figure 4c). Tests of proportionality suggested an overall difference in relative eigenvalues from relative PCA (pFemales < 0.001, pMales < 0.001). Generalised variance of facial shape among individuals 6 to 8 years of age was 29.6 and 57.8 times the generalised variance among those 15 to 18 years of age for females and males, respectively. Facial features captured by each relative eigenvector were visualised in Figures S6 and S7. The first 12 and 11 relative eigenvectors in females and males captured developmentally constrained shape features (Figure 4d). Variations in facial outline shape (proportionally longer or wider face) were key features that were developmentally constrained (Figure S8a,c). Variations in the relative protrusion of the nasolabial and mental regions were key facial features that were developmentally diversified (Figure S8b,d). Local deformations associated with these facial features were illustrated in Figure 5. Caveats on interpreting shape features captured by relative eigenvectors are provided in Text S4. The RESTORE metric revealed that relative eigenspace captured 42.8% of shape variance for both females and males. Our results support the use of relative PCA to explore shape variation as shape features encoded by relative eigenvectors contributed non‐trivially to overall shape variation.

FIGURE 5.

FIGURE 5

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Visualisation of key developmentally constrained and diversified facial features. Joined morphological effects of the top five relative eigenvectors on females (a) and males (c), which respectively explain 70.4% and 74.0% of variance of developmentally constrained facial features. Joined morphological effects of the last four relative eigenvectors on females (b) and males (d), which respectively explain 81.0% and 73.8% of variance of all developmentally diversified facial features.

4. DISCUSSION

Based on a large sample of Bantu Africans from Tanzania, our study comprehensively characterised facial shape development among this population from 6 to 18 years of age, a major but under‐represented population in facial developmental research. These characterisations within our study included trajectories of facial shape development, sexual dimorphism of facial shape, Procrustes variance and phenotypic covariance structure. Facial shape developmental changes were interpreted beyond simple description towards analysing the underlying morphogenetic processes that result in observed shape changes. Facial shape was found overall to be developmentally constrained. Further investigation revealed certain facial features which were developmentally constrained and diversified.

To the best of our knowledge, our study is the first to investigate developmental changes of soft tissue facial structures in an African population. A previous study based on approximately 200 CT scans of South Africans from birth to 18 years of age investigated growth of the viscerocranium using linear measurements (Niemann et al., 2021). Growth was faster during 0 to 5 years of age than in later periods, whereas consistent growth was noted in the nasal region. Our results likewise suggest a high degree of changes in nasal shape prior to 18 years of age.

In Europeans, facial size of females has been suggested to be larger than males at around age 5 years but smaller at 20 years (Smith et al., 2021). In the present Bantu African sample, male facial size was found larger than females before age 10 years, whereas no difference was observed beyond 10 years. The increase in facial size is linked to growth of the underlying facial skeleton to accommodate increasing functional needs, such as respiration and mastication. Our findings also suggest that females reach facial growth peak at age 12 years, whereas males at around 14.5 years. These findings suggest that females reach pubertal facial growth spurt over 2 years earlier than males, which is consistent with the earlier pubertal growth spurt in somatic growth.

Studies based on the European population consistently suggested significant sexual dimorphism in facial shape at age 10 years and beyond (Matthews et al., 2018; Smith et al., 2021). Reports on the presence of sexual dimorphism at earlier developmental stages have been inconclusive due to limitations in sample size for younger individuals. In Bantu Africans, our findings suggest facial sexual dimorphism to have emerged as early as age 6 years, and the amount of the difference increased monotonically up to the end of the observation period.

A previous geometric morphometric study involving adult crania of Bantu southern Africans suggested a more protrusive glabella and sloping forehead in males (Franklin et al., 2006). Our findings suggested that the glabella region was indeed, relatively expanded at 18 years of age in males compared with females. However, our findings suggest this did not translate into a more protrusive glabella in males since the relative developmental expansion in the region laterosuperior to the eyes in females pushed the female inter‐orbital, nasal root and glabella regions altogether to more protrusive positions. The discrepancy may result from the fact that Franklin and colleagues reported forehead shape difference along PC1 while our findings were based on comparisons of overall facial shapes. In addition, the difference between facial and skeletal shape and the omission of the mandibles in the cranial study may also account for the discrepant research findings. In our study, the forehead was found relatively contracted with development in both sexes, resulting from a more rapid mid‐ and lower‐facial growth to accommodate the increasing respiratory and masticatory capacities which surpass absolute growth in the forehead (Enlow & Hans, 1996). In addition, the forehead was found posteriorly displaced resulting from a more significant protrusive development of the nasolabial region.

In females and males, the nose becomes proportionally larger and relatively more protrusive with development, arising from local expansion in the nasal alae and columella. Both these features were more pronounced in females. The more expanded female columella resulted in a gradually more protrusive nasal tip from 6 to 18 years of age. Although nasal alae expansion was also more pronounced in females, a proportionally wider nasal alae was found in males from 6 to 18 years of age. The wider nasal alae resulted from a larger developmental expansion in the area where the nasal alae merged into the nasal dorsum, pushing the entire nasal alae laterally to a greater degree in males.

The labial region was developmentally expanded in both sexes, resulting in increasingly protrusive lips with development. The stronger expansion in the upper lip and lower vermillion in males resulted in structures that were progressively anteriorly displaced relative to females. The stronger cutaneous lower lip expansion in males resulted in its displacement from a relatively posterior position at 6 years of age and assumed a more protrusive position at 18 years of age compared with females.

The cranial base angle (the angle formed by nasion, top of dorsum sellae and posterior sphenoid plane) is larger in African populations than other populations (Botelho et al., 2020; Enlow & Hans, 1996), resulting in a downward and posterior movement of the mandible. However, this mandibular retrusion is compensated for by a characteristic major broadening of the ramus, and results in mandibular protrusion (Enlow & Hans, 1996). The maxillary incisors correspondingly tip labially, finally leading to the bimaxillary protrusion commonly observed among African populations (Yemitan et al., 2022). This accounts for the labial protrusion and developmental contraction along the nasolabial fold region that was identified in this study.

The developmental pattern in the mental region presented as sexually dimorphic, characterised by greater relative contraction in males. This pattern also resulted in displacement of the female mental region from a relatively posterior position at 6 years of age to a more anterior position at 18 years of age when compared with males. The zygomatic region was developmentally expanded in both sexes, resulting in more anteriorly positioned zygoma from 6 to 18 years of age. The lateral facial region corresponding to the underlying body of the mandible underwent expansion during the age period under investigation, however, protrusive growth of the nasal, labiomental and zygomatic region resulted in the lateral facial region corresponding to the underlying body of the mandible positioned posteriorly with development.

Our findings revealed that facial variation decreased overall from 6 to 18 years of age, with significantly higher variance among individuals 6–8 years of age. The relative proportion of the forehead, relative midfacial width and lower facial robustness variations, which collectively result in varying facial outline shape, were identified as primary facial features leading to developmentally constrained facial shape. While requiring further investigation, these shape features hint at the possibility of requirements to accommodate increasing respiratory and masticatory functional demands as potential drivers of constrained African facial development. The larger genetic variation in African populations may have led to a more diversified facial shape at an early age, causing the effect of the developmental constraint comparatively more conspicuous in the present sample. Developmentally diversified facial features were concentrated in the nasolabial and mental regions, where developmental changes in mean shape were also significant and suggesting that facial regions with faster developmental changes are developmentally diversified. However, this effect is counteracted by the developmentally constrained facial outline shape, resulting in an overall reduction in facial variance with development.

This study addressed three key limitations of current studies on human facial growth and development: lack of detailed analysis of local morphological changes, a mere focus on changes in mean facial shape and a restriction of analysis largely to European populations. By quantifying localised facial changes through deformation, this study provides a series of transformative insights into detailed patterns of facial development. This allows the present study to move beyond simple description of the observed changes to unveil the underlying morphogenetic processes shaping such differences. In addition, this study exploits state‐of‐the‐art morphometric methods to comprehensively characterise changes in mean, variation and sexual dimorphism of facial shape. Finally, we leveraged a uniquely large sample of Bantu Africans to characterise facial development in an important but previously neglected population.

5. CONCLUSIONS

We comprehensively characterised facial growth and development based on a large Bantu African sample, a population with distinct facial developmental patterns that may have important implications for various disciplines but which remains largely absent in facial growth studies. Investigating facial morphogenetic processes and variational properties expands the scope of current facial developmental research and our findings result in transformative insights into facial growth and development. The analytical framework of this study is broadly applicable to morphometric investigations of ontogenies of shape in general.

AUTHOR CONTRIBUTIONS

YJZ: Data curation, Formal analysis, Methodology, Visualisation, Writing—original draft; DC: Formal analysis, Methodology; PYFW: Conceptualisation, Formal analysis, Methodology, Project administration, Writing—review and editing; HMW: Conceptualisation, Funding acquisition, Project administration, Resources, Supervision, Writing—review and editing. All authors gave final approval for publication and agreed to be held accountable for the work performed therein.

FUNDING INFORMATION

The work described in this paper was fully supported by a grant from the Research Grants Council of the Hong Kong Special Administrative Region, China (Project No. 17102620), URL: http://www.ugc.edu.hk/eng/rgc/. The funding recipient was Hai Ming Wong. The funders had no role in the study design; in the collection, analysis and interpretation of data; in the writing of the report; and in the decision to submit the article for publication.

CONFLICT OF INTEREST STATEMENT

We declare we have no competing interests.

ETHICS STATEMENT

The study protocol was approved by the Institutional Review Board of the University of Hong Kong/Hospital Authority Hong Kong West Cluster (IRB reference number: UW 19–591).

Supporting information

Appendix S1.

JOA-245-551-s001.docx (10.6MB, docx)

ACKNOWLEDGEMENTS

None.

Zhong, Y.J. , Cui, D. , Wen, P.Y.F. & Wong, H.M. (2024) Charting facial growth and development for Bantu Africans: Central tendencies, variational properties and sexual dimorphisms. Journal of Anatomy, 245, 551–559. Available from: 10.1111/joa.14103

Contributor Information

Patrick Yi Feng Wen, Email: wyf320@connect.hku.hk.

Hai Ming Wong, Email: wonghmg@hku.hk.

DATA AVAILABILITY STATEMENT

All 3D facial images are available through the FaceBase Consortium controlled access repository. Template facial mesh and MeshMonk toolbox for landmark digitisation are available: https://gitlab.kuleuven.be/mirc/meshmonk. Scripts to establish facial growth trajectories through the weighted partial least squares regression model are available: https://github.com/harrymatthews50/Modelling_Craniofacial_Growth_Trajectories. The custom routine for RESTORE score estimation is publicly available: https://github.com/Patrick‐Wen/RESTORE. The script is fully annotated with further guidance in Text S3. Example script to run the custom function is provided in the GitHub repository along with the source code. All other analyses are based on publicly available packages in R software as described in the main text.

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Associated Data

This section collects any data citations, data availability statements, or supplementary materials included in this article.

Supplementary Materials

Appendix S1.

JOA-245-551-s001.docx (10.6MB, docx)

Data Availability Statement

All 3D facial images are available through the FaceBase Consortium controlled access repository. Template facial mesh and MeshMonk toolbox for landmark digitisation are available: https://gitlab.kuleuven.be/mirc/meshmonk. Scripts to establish facial growth trajectories through the weighted partial least squares regression model are available: https://github.com/harrymatthews50/Modelling_Craniofacial_Growth_Trajectories. The custom routine for RESTORE score estimation is publicly available: https://github.com/Patrick‐Wen/RESTORE. The script is fully annotated with further guidance in Text S3. Example script to run the custom function is provided in the GitHub repository along with the source code. All other analyses are based on publicly available packages in R software as described in the main text.

Articles from Journal of Anatomy are provided here courtesy of Anatomical Society of Great Britain and Ireland

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