Modelling 3D craniofacial growth trajectories for population comparison and classification illustrated using sex-differences

Abstract

Many disorders present with characteristic abnormalities of the craniofacial complex. Precise descriptions of how and when these abnormalities emerge and change during childhood and adolescence can inform our understanding of their underlying pathology and facilitate diagnosis from craniofacial shape. In this paper we develop a framework for analysing how anatomical differences between populations emerge and change over time, and for binary group classification that adapts to the age of each participant. As a proxy for a disease-control comparison we use a database of 3D photographs of normally developing boys and girls to examine emerging sex-differences. Essentially we define 3D craniofacial 'growth curves' for each sex. Differences in the forehead, upper lip, chin and nose emerge primarily from different growth rates between the groups, whereas differences in the buccal region involve different growth directions. Differences in the forehead, buccal region and chin are evident before puberty, challenging the view that sex differences result from pubertal hormone levels. Classification accuracy was best for older children. This paper represents a significant methodological advance for the study of facial differences between growing populations and comprehensively describes developing craniofacial sex differences.

Conflict of interest statement

The authors declare no competing interests.

Figures

Figure 1

Counts of boys and girls at each age.

Figure 2

Kernel regression and classification in shape space. In both figures the axes are the first and second principal components, which are two orthogonal directions through the shape space that explain the most and second-most variance. The aspects of facial variability the axes represent are illustrated by the large grey faces. The data points show simulated data. In a) each individual (indicated by the markers) can be thought of as a location in the space that codes their shape. Kernel regression (illustrated by the curved lines) chart a curve through this space that describes how shape changes as a function of age (indicated by marker colour). Locations on these lines correspond to expected ‘typical’ heads for each age, some of which are superimposed onto the line. b) illustrates calculating the score for classification. This is equivalent to interpolating heads between and beyond the two age appropriate expected heads (illustrated by the heads on the dotted line), then finding the one most similar to the test case.

Figure 3

Overall trends in growth and sexual dimorphism. a) describes the change in size of boys’ and girls’ heads. Size is calculated as the mean distance of each point on the head from the centroid of all points in mm. Lines are the kernel regression trend-lines for each group. b) describes the change in the size of sexual dimorphism (Procrustes distance). c) compares the rate of change in shape between males and females. In all plots the filled regions indicate the 95% confidence intervals of the estimate. These were calculated by resampling with replacement and recomputing the estimates 10 000 times.

Figure 4

Growth patterns and comparison of expected faces. The first three columns describe sexual dimorphism. The grey heads are the expected images. ‘Shape difference’ indicates how the expected images are different in the inward/outward direction. Blue indicates points are more inwards on the boys’ images than the girls’ images. Red indicates the points are more outwards. The last two columns illustrate the growth patterns of boys and girls. These indicate the amount of change occurring in the inward/outward direction at each point. Stronger colours indicate more change.

Figure 5

Comparison of growth patterns between boys and girls. ‘Rate Difference’ compares the growth rate of males and females at each point on the head. Red indicates males are changing faster, blue indicates females are changing faster. ‘Direction Difference’ compares the growth directions at each point on the head. Red indicates the growth vectors are pointing in the same direction, blue indicates they are pointing in the opposite direction.

Figure 6

Distributions of scores for the classification analysis for males and females.