Facial surface morphology predicts variation in internal skeletal shape

Abstract

Introduction: The regular collection of 3-dimensional (3D) imaging data is critical to the development and implementation of accurate predictive models of facial skeletal growth. However, repeated exposure to x-ray-based modalities such as cone-beam computed tomography has unknown risks that outweigh many potential benefits, especially in pediatric patients. One solution is to make inferences about the facial skeleton from external 3D surface morphology captured using safe nonionizing imaging modalities alone. However, the degree to which external 3D facial shape is an accurate proxy of skeletal morphology has not been previously quantified. As a first step in validating this approach, we tested the hypothesis that population-level variation in the 3D shape of the face and skeleton significantly covaries.

Methods: We retrospectively analyzed 3D surface and skeletal morphology from a previously collected cross-sectional cone-beam computed tomography database of nonsurgical orthodontics patients and used geometric morphometrics and multivariate statistics to test the hypothesis that shape variation in external face and internal skeleton covaries.

Results: External facial morphology is highly predictive of variation in internal skeletal shape ([Rv] = 0.56, P <0.0001; partial least squares [PLS] 1-13 = 98.7% covariance, P <0.001) and asymmetry (Rv = 0.34, P <0.0001; PLS 1-5 = 90.2% covariance, P <0.001), whereas age-related (r(2) = 0.84, P <0.001) and size-related (r(2) = 0.67, P <0.001) shape variation was also highly correlated.

Conclusions: Surface morphology is a reliable source of proxy data for the characterization of skeletal shape variation and thus is particularly valuable in research designs where reducing potential long-term risks associated with radiologic imaging methods is warranted. We propose that longitudinal surface morphology from early childhood through late adolescence can be a valuable source of data that will facilitate the development of personalized craniodental and treatment plans and reduce exposure levels to as low as reasonably achievable.

FIGURE 1. Partial Least Squares (PLS) analysis of external surface and internal skeletal shape covariation

Variation in facial morphology and internal skeletal shape exhibit significant covariation (PLS [Face-Skeleton]: R_v=0.56, p<0.0001; PLS1-13=98.7% covariance, p<0.001). (A) PLS1 (45.7% covariance, r=0.92, p<0.0001) describes depth and anterior projection of the lower jaw, which tracks size and forward location of the mandible as well as location of the zygomatics in the skeleton. (B) PLS2 (25.3% covariance, r=0.83, p<0.0001) describes relative coordination of prognathism of the upper and lower jaw, which in the skeleton is associated with a more convex or concave facial profile. (C) PLS3 (13.1% covariance, p=0.82, p<0.0001) describes location of the eyes as a proportion of the upper jaw plus width of the face, which in the skeleton manifests as orbital location and robusticity of the jaws. Facial and skeletal transformations show shapes associated with the extremes of each PLS applied to a representative cranium or face (note: the shape of the cranial vault is unconstrained by landmarks). Purple = female, blue = male. Red points represent the mean landmark configurations of skeleton and face, lines represent the direction and magnitude of a positive vector displacement along each associated axis.

FIGURE 2. Partial Least Squares (PLS) analysis of external surface and internal skeletal asymmetry covariation

Variation in facial asymmetry and internal skeletal asymmetry exhibit significant covariation (PLS [Face-Skeleton]: R_v=0.34, p<0.0001; PLS1-5=90.2% covariance, p<0.001). (A) PLS1 (52.4% covariance, r=0.73, p<0.0001) describes left-right asymmetries of the anterior lower jaw and height of the eyes, which in the skeleton manifests as a corresponding deviation of the anterior mandible and clockwise-counterclockwise rotation of the orbits, all independent of the upper jaw. (B) PLS2 (24.3% covariance, r=0.73, p<0.0001) describes asymmetry of the mouth and nose, which corresponds to asymmetry in the anterior upper jaw and zygomatics, in this case independent of the lower jaw and orbits. Color coding and landmark descriptions as in Figure 1.

FIGURE 3. Comparison of external surface and internal skeletal shape covariation associated with population-level age/size related changes

Size and age-associated shape variation from late childhood to adult (age=7–21+ years) is correlated between internal and external datasets. Internal shape scores from multivariate regressions of shape on age (A) and size (B) predict the majority of variation in external shape scores (84% and 67% total variation, respectively). External faces and internal skeletons reflect shape changes at early, middle and late ages or sizes calculated by applying associated growth vectors to the mean configuration and visualized on a representative face or cranium. Color coding and landmark descriptions as in Figure 1.