Piecewise-rigid 2D-3D registration for pose estimation of snake-like manipulator using an intraoperative x-ray projection

Background: Snake-like dexterous manipulators may offer significant advantages in minimally-invasive surgery in areas not reachable with conventional tools. Precise control of a wire-driven manipulator is challenging due to factors such as cable deformation, unknown internal (cable friction) and external forces, thus requiring correcting the calibration intraoperatively by determining the actual pose of the manipulator. Method: A method for simultaneously estimating pose and kinematic configuration of a piecewise-rigid object such as a snake-like manipulator from a single x-ray projection is presented. The method parameterizes kinematics using a small number of variables (e.g., 5), and optimizes them simultaneously with the 6 degree-of-freedom pose parameter of the base link using an image similarity between digitally reconstructed radiographs (DRRs) of the manipulatora's attenuation model and the real x-ray projection. Result: Simulation studies assumed various geometric magnifications (1.2-2.6) and out-of-plane angulations (0°-90°) in a scenario of hip osteolysis treatment, which demonstrated the median joint angle error was 0.04° (for 2.0 magnification, ±10° out-of-plane rotation). Average computation time was 57.6 sec with 82,953 function evaluations on a mid-range GPU. The joint angle error remained lower than 0.07°while out-of-plane rotation was 0°-60°. An experiment using video images of a real manipulator demonstrated a similar trend as the simulation study except for slightly larger error around the tip attributed to accumulation of errors induced by deformation around each joint not modeled with a simple pin joint. Conclusions: The proposed approach enables high precision tracking of a piecewise-rigid object (i.e., a series of connected rigid structures) using a single projection image by incorporating prior knowledge about the shape and kinematic behavior of the object (e.g., each rigid structure connected by a pin joint parameterized by a low degree polynomial basis). Potential applications of the proposed approach include pose estimation of vertebrae in spine and a series of electrodes in coronary sinus catheter. Improvement of GPU performance is expected to further augment computational speed.