Concentric Tube Robots for Transurethral Prostate Surgery: Matching the Workspace to the Endoscopic Field of View

INTRODUCTION Transurethral laser surgery using a flexible multibackbone robot was recently demonstrated by Simaan et al. for bladder resection [1]. For transurethral prostate resection, thinner flexible manipulators are desirable. We have developed a hand-held system that transurethrally deploys two concentric tube robots through an 8.3 mm diameter rigid endoscope [2], as shown in Figs. 1 and 2. The purpose of this system is to facilitate Holmium Laser Enucleation of the Prostate (HoLEP), a surgery that is rarely used despite its demonstrated clinical benefits, because it is so challenging for the surgeon to perform [3]. The objective of the surgery is to remove prostate tissue transurethrally with a laser, and the challenge arises from the need to angulate the entire endoscope (impeded by a great deal of soft tissue) to aim the laser. Our system assists by providing one manipulator to aim the laser and a second to retract tissue, exposing desired targets to the laser. The purpose of this paper is to explore optimal design of the concentric tube manipulators. We define an optimal design as one in which there is maximal overlap between the workspace of the manipulator and the space viewable by the endoscope. Here, we restrict our attention to the special case in which the concentric tube robot consists of two tubes, where the outer tube is straight and the inner tube is circularly curved. We note that more complex concentric tube manipulators are possible, such as the three tube robot shown in Fig. 2, but leave more complex cases to future work. Based on this, our objective is to choose (1) the curvature of the inner tube, and (2) the distance behind the camera lens inside the endoscope where the base of the workspace should occur.