A Deep Learning-Based Pipeline for Developing Multi-Rib Shape Generative Model with Populational Percentiles or Anthropometrics As Predictors

Rib cross-sectional shapes (characterized by the outer contour and cortical bone thickness) affect the rib mechanical response under impact loading, thereby influence the rib injury pattern and risk. A statistical description of the rib shapes or their correlations to anthropometrics is a prerequisite to the development of numerical human body models representing target demographics. Variational autoencoders (VAE) as anatomical shape generators remain to be explored in terms of utilizing the latent vectors to control or interpret the representativeness of the generated results. In this paper, we propose a pipeline for developing a multi-rib cross-sectional shape generative model from CT images, which consists of the achievement of rib cross-sectional shape data from CT images using an anatomical indexing system and regular grids, and a unified framework to fit shape distributions and associate shapes to anthropometrics for different rib categories. Specifically, we collected CT images including 3193 ribs, surface regular grid is generated for each rib based on anatomical coordinates, the rib cross-sectional shapes are characterized by nodal coordinates and cortical bone thickness. The tensor structure of shape data based on regular grids enable the implementation of CNNs in the conditional variational autoencoder (CVAE). The CVAE is trained against an auxiliary classifier to decouple the low-dimensional representations of the inter- and intra- variations and fit each intra-variation by a Gaussian distribution simultaneously. Random tree regressors are further leveraged to associate each continuous intra-class space with the corresponding anthropometrics of the subjects, i.e., age, height and weight. As a result, with the rib class labels and the latent vectors sampled from Gaussian distributions or predicted from anthropometrics as the inputs, the decoder can generate valid rib cross-sectional shapes of given class labels (male/female, 2nd to 11th ribs) for arbitrary populational percentiles or specific age, height and weight, which paves the road for future biomedical and biomechanical studies considering the diversity of rib shapes across the population.