Surgical Planning: a path planning approach with differentiable simulations and overdamped Langevin equation

Surgical planning based on medical images presents specific challenges. These include ambiguities in medical images, navigation in dynamically changing soft environments, penetrating obstacles, and the need to sample multiple paths. Additionally, simulations must account for various sources of uncertainty. These uncertainties may arise from the imaging process itself or from expected variances in a surgeon's movements. Furthermore, since planning is tailored to each patient, simulations should efficiently run on limited computing resources. They should also be adaptive to changes in the patient's condition or unforeseen changes during surgeries.

We introduce a streamlined method for quick path planning. This method utilizes differentiable simulations, eliminating the need to fully simulate all aspects of surgery. The issue is simplified to a random walk in an environment. In this environment, diffusion and forces are trained to pinpoint the optimal path under various constraints. Optimization is achieved by directly sampling paths based on the current fields and constraints, and differentiating the simulation. Non-local constraints can be incorporated to consider the mechanical limitations of surgical tools. Once the optimal path is found, our framework still offers the flexibility to sample multiple routes to the target by adjusting diffusion values. We showcase our method's effectiveness in navigating through the lungs, ear, and heart