Design and Optimization of Concentric Tube Robots Based on Surgical Tasks, Anatomical Constraints and Follow-the-Leader Deployment

Many neurological disorders are characterized by the focal and anatomically definable lesions within the brain parenchyma. Traditional treatment may introduce major trauma in neurosurgery and conventional medical devices can only trace straight trajectories. To overcome these problems, a design and optimization method for a patient-specific concentric tube robot (CTR) satisfying the constraints of anatomy, surgical tasks and follow-the-leader (FTL) deployment is proposed in this paper. CTR is a tentacle like continuum robot that can work inside confined and complex biological chambers with the ability of tracking complex 3D trajectories. It consists of pre-curved superplastic tubes with hollow cavities to accommodate the surgical tools. These merits make the CTR well suitable for minimally invasive surgeries. This paper introduces a design framework that utilizes preoperative MRI data to configure patient-specific CTR for single and multiple tasks with the minimum number of tubes. A constant curvature circular arc model is built to solve the problem of inverse kinematics. Two iterative optimization methods for single and multiple tasks are proposed to optimize the parameters of the CTR. Initial waypoints of the CTR are produced based on the FTL deployment. The waypoints are then refined using a Follow Shape Rapidly-exploring Random Tree algorithm (FSRRT) for cases that the initial configurations of the CTR cannot completely satisfy the FTL deployment. Simulations and experiments are carried out on a human brain model to validate the proposed methods. The parameters of CTR including the entire length, curvature, radius angle, number, diameter, arc length and the waypoints are obtained. The errors of the FTL deployment are found to be within 2.1mm.