Needle Steerability Measures: Definition and Application for Optimized Steering of the Programmable Bevel-Tip Needle

Minimally invasive surgical techniques, such as percutaneous intervention, have been shown to improve clinical outcomes. Therefore over the last decade, several novel mechanisms for steering needles in soft tissue have been developed. One such design is the Programmable Bevel-tip Needle (PBN), which uses a biologically inspired multi-segment approach to control steering during soft tissue traversal. Important for control of these needles is the understanding of the relationship between the needle inputs and the resultant steering. In this paper we explore the properties of this relationship by considering the concept of needle `steerability'. Two measures, the steerability index and steering condition number, are proposed and compared. A solution is then presented which optimizes these measures to solve the inverse problem for PBNs: generating the required segment offsets to follow a desired 3D trajectory. We then demonstrate the proposed inverse solution for a desired needle trajectory in simulation, and show that it is able to generate a smooth, optimized input profile for the PBN.