Feedback Control for 3D Needle Steering in Deformable Tissues

Kris Hauser, Nuttapong Chentanez, Noah Cowan, James O'Brien, Allison Okamura, and Ken Goldberg

Steerable needles are a new class of needles that can be steered along curved paths through soft tissue. The arc direction can be controlled by twisting the base of the needle, which allows the needle to travel in circular arcs and helical trajectories. In principle, these inputs can be used to correct for needle placement errors and deflections during insertion, which may enable more accurate targeting than standard straight needles. Motion planning techniques have been used to plan curved needle paths preoperatively, but during insertion the needle will deviate from a planned path due to deformations and modeling errors. We are investigating the use of feedback control for steerable needles through deformable tissue. A controller that combines imprecise planning with sensory feedback and rapid replanning can steer a needle tip to a desired target position under a variety of perturbations.

The control policy (Figure 1) consists of a single rule, which can be viewed as an imprecise planning step: it picks a constant twist rate such that its predicted helical trajectory minimizes the distance to the target. Then, the needle is inserted a short distance with the chosen twist rate, the needle tip pose is sensed using intraoperative imaging, and the process is repeated until the needle can get no closer. A fast branch and bound technique is used to find the closest point on a helix. This enables trajectory corrections to be computed at kilohertz rates, which greatly exceeds the refresh rate of currently available imaging (e.g. ultrasound).

We evaluated the controller on a wide variety of simulation experiments in both rigid tissue and in a finite element deformable tissue simulator (Figure 2). Our experiments suggest that the controller has a large basin of convergence in rigid tissue, attaining sub-millimeter accuracy for all targets sufficiently far from the insertion point (approximately twice the turning radius of the needle). It attains reasonable accuracy (less than 2.5mm) under a variety of simulated Markovian and non-Markovian perturbations, including imaging noise, needle deflection, and curvature estimation errors. In deformable tissue, the controller can compensate for deformation effects to achieve much higher accuracy than open-loop execution (an 88\% improvement in the example of Figure 2).

Figure 1. Left: overview of the feedback controller. (a) Out of a set P of predicted trajectories, the one closest to the goal is picked. (b) The needle is steered for a short distance with the twist velocity of the chosen trajectory. A disturbance may drive the needle off course. (c) The process repeats. Right: the controller uses the set of constant-twist-rate helices as the set of proposal trajectories P.

Figure 2. Simulation of the controller in highly deformable block of gelatin.