Topological analysis of bladder filling.

Bladder function is assessed through pressure-volume relations, compliance indices and flow measurements, while structural evaluation relies primarily on qualitative imaging descriptors. These approaches do not formally quantify how bladder geometry evolves during filling. To distinguish structural reorganization from pure mechanical stiffness, we developed a simulation-based topological analysis of bladder filling grounded in mechanical parameters derived from the literature. Progressive filling was modeled under quasi-static conditions, generating multi-volume geometries from which spatial descriptors were computed. Inspired by the Freudenthal suspension theorem, filling was interpreted as a dimensional expansion process, while structural stability was evaluated by examining whether geometric invariants remain preserved across increasing volumes. Simulated smooth expansion and controlled structural perturbations were compared under identical loading conditions. We found that pressure trajectories and wall stress estimates were similar across configurations when compliance was matched, whereas geometric descriptors exhibited divergent volume-indexed stability profiles in the presence of remodeling. Computable instability measures detected progressive spatial heterogeneity despite preserved global pressure behavior. Providing quantitative measure of geometric continuity across successive filling states, our approach suggests that structural remodeling becomes detectable before conventional functional impairment is apparent. Progressive surface irregularity can emerge even when compliance, detrusor pressure and flow parameters remain within reference limits. In addition, serial imaging over time may reveal increasing instability in shape organization across filling cycles, allowing identification of individuals at higher risk of diverticula formation, functional decompensation or structural complications despite stable pressure measurements.