Planning for Steerable Bevel-tip Needle Insertion Through 2D Soft Tissue with Obstacles

We explore motion planning for a new class of highly flexible bevel-tip medical needles that can be steered to previously unreachable targets in soft tissue. Planning for these procedures is difficult because the needles bend during insertion and cause the surrounding soft tissues to displace and deform. In this paper, we develop a planning algorithm for insertion of highly flexible bevel-tip needles into soft tissues with obstacles in a 2D imaging plane. Given an initial needle insertion plan specifying location, orientation, bevel rotation, and insertion distance, the planner combines soft tissue modeling and numerical optimization to generate a needle insertion plan that compensates for simulated tissue de formations, locally avoids polygonal obstacles, and minimizes needle insertion distance. The simulator computes soft tissue deformations using a finite element model that incorporates the effects of needle tip and frictional forces using a 2D mesh. We formulate the planning problem as a constrained nonlinear optimization problem that is locally minimized using a penalty method that converts the formulation to a sequence of unconstrained optimization problems. We apply the planner to bevel-right and bevel-left needles and generate plans for targets that are unreachable by rigid needles.