The Case for Interpretable Geometry: Statistical Shape Models vs. Curvature-Based Descriptors in Aortic Disease Classification.

Purpose: Quantifying aortic morphology is central to surgical planning for thoracic endovascular aortic repair (TEVAR), yet no consensus exists on how best to represent three-dimensional aortic shape for outcome prediction. Two broad strategies have emerged: statistical shape analysis (SSA), which relies on statistical methods and dimensionality reduction to capture the most significant shape modes, and geometrically-informed approaches that extract descriptors grounded in differential geometry. Here, we directly compare these paradigms on a cohort of 290 CTA scans classified by surgical outcome (non-pathological, successful TEVAR, failed TEVAR). Methods: For the geometrically-informed approach, we use a two-dimensional feature space using normalized fluctuation in integrated Gaussian curvature Results: SSA's leading principal components encode variations in global aortic size and are statistically redundant with Conclusion: These results demonstrate that geometrically-informed descriptors offer a more interpretable, robust, and clinically translatable framework for aortic disease classification than data-driven statistical shape representations.