Optimizing Clearance of Bézier Spline Trajectories for Minimally-Invasive Surgery

Abstract

Preoperative planning of nonlinear trajectories is a key element in minimally-invasive surgery. Interpolating between start and goal of an intervention while circumnavigating risk structures provides the necessary feasible solutions for such procedure. While recent research shows that Rapidly-exploring Random Trees (RRT) on Bézier Splines efficiently solve this task, access paths computed by this method do not provide optimal clearance to surrounding anatomy. We propose an approach based on sequential convex optimization that rearranges Bézier Splines computed by an RRT-connect, thereby achieving locally optimal clearance to risk structures. Experiments on real CT data of patients demonstrate the applicability of our approach on two scenarios: catheter insertion through the aorta and temporal bone surgery. We compare distances to risk structures along computed trajectories with the state of the art solution and show that our method results in clinically safer paths.