Dynamic Modeling of Abdominal Aortic Aneurysms 1: Anatomic Features and Equation Discovery

Endovascular aneurysm repair (EVAR) alters abdominal aortic aneurysm (AAA) sacs in ways not captured by size alone. We construct a low-dimensional, anatomically grounded state space using two physically interpretable variables derived from CT images: sac surface area A (size) and the fluctuation of integrated Gaussian curvature δK (shape). Longitudinal clinical scans (74 patients, 164 time points) are embedded as trajectories in A--δK, then upsampled with an FEA-informed resampling procedure to mitigate sparse, irregular follow-up. We fit class-specific ordinary differential equations via Z-SINDy (a sparse system-identification model with uncertainty quantification) to cohorts clinically defined as regressing versus stable. The learned vector fields reproduce empirical flow structure and yield interpretable fixed points: regressing sacs are attracted toward a low-size/low-shape state on a 5-year timescale, while stable sacs exhibit elevated δK over long time-scales. Eigenanalysis of the mean ODEs provides characteristic time scales and principal directions of remodeling. Population flow maps, fixed-point locations, and uncertainty bands from posterior-predictive simulations close the loop between data and model. This talk focuses on (i) the geometric/biophysical motivation for A and δK; (ii) pipeline details for derivative estimation under clinical sampling constraints; and (iii) how parsimony in the Z-SINDy library preserves interpretability without sacrificing fidelity.