Anatomically Parameterized Statistical Shape Model: Explaining Morphometry through Statistical Learning

<italic>Objective:</italic> Statistical shape models (SSMs) are a popular tool to conduct morphological analysis of anatomical structures which is a crucial step in clinical practices. However, shape representations through SSMs are based on shape coefficients and lack an explicit one-to-one relationship with anatomical measures of clinical relevance. While a shape coefficient embeds a combination of anatomical measures, a formalized approach to find the relationship between them remains elusive in the literature. This limits the use of SSMs to subjective evaluations in clinical practices. We propose a novel SSM controlled by anatomical parameters derived from morphometric analysis. <italic>Methods:</italic> The proposed anatomically parameterized SSM (ANAT<inline-formula><tex-math notation="LaTeX">$_{\text{SSM}}$</tex-math></inline-formula>) is based on learning a linear mapping between shape coefficients (latent space) and selected anatomical parameters (anatomical space). This mapping is learned from a synthetic population generated by the standard SSM. Determining the pseudo-inverse of the mapping allows us to build the ANAT<inline-formula><tex-math notation="LaTeX">$_{\text{SSM}}$</tex-math></inline-formula>. We further impose orthogonality constraints to the anatomical parameterization (OC-ANAT<inline-formula><tex-math notation="LaTeX">$_{\text{SSM}}$</tex-math></inline-formula>) to obtain independent shape variation patterns. The proposed contribution was evaluated on two skeletal databases of femoral and scapular bone shapes using clinically relevant anatomical parameters within each (five for femoral and six for scapular bone). <italic>Results:</italic> Anatomical measures of the synthetically generated shapes exhibited realistic statistics. The learned matrices corroborated well with the obtained statistical relationship, while the two SSMs achieved moderate to excellent performance in predicting anatomical parameters on unseen shapes. <italic>Conclusion:</italic> This study demonstrates the use of anatomical representation for creating anatomically parameterized SSMs and as a result, removes the limited clinical interpretability of standard SSMs. <italic>Significance:</italic> The proposed models could help analyze differences in relevant bone morphometry between populations, and be integrated in patient-specific pre-surgery planning or in-surgery assessment.