A Belief-State World Model for Catheter Navigation under Sparse Fluoroscopy: A Planar Proof of Concept

Endovascular catheter navigation relies on continuous fluoroscopy, exposing patients and clinical staff to ionizing radiation throughout the procedure. We investigate whether a physics-based world model can sustain the navigation task between deliberately sparse X-ray acquisitions, and whether the model can signal when its internal state estimate is no longer reliable. We formulate sparse-fluoroscopy navigation as a partially observable Markov decision process where a Cosserat rod simulator supplies transition dynamics, sparse noisy projections provide observations, and a particle filter maintains a belief over the device state, reduced in this implementation to a tip state with a geometric contact proxy. We evaluate this formulation in a deliberately simplified setting: a synthetic planar vessel phantom with a quasi-static rod model and simulated projections, without clinical or animal data. In this setting, the belief-state model tracks the simulated tip with a root mean square error of 1.30 mm while acquiring observations at one fifteenth of the continuous rate (0.97 mm at every frame, 1.51 mm at one thirtieth), reported 90 percent credible intervals achieve 0.92 empirical coverage, and the belief-derived contact risk estimate discriminates unsafe contact events with an AUROC of 0.68. These results constitute a proof of concept on a simplified simulation rather than a demonstration of clinical readiness; their purpose is to establish that calibrated belief, rather than point-estimate accuracy alone, is the essential property a sparse-imaging world model must deliver.