Iterative Jacobian-Based Inverse Kinematics and Open-Loop Control of an MRI-Guided Magnetically Actuated Steerable Catheter System

Abstract

This paper presents an iterative Jacobian-based inverse kinematics method for an MRI-guided magnetically-actuated steerable intravascular catheter system. The catheter is directly actuated by magnetic torques generated on a set of current-carrying micro-coils embedded on the catheter tip, by the magnetic field of the magnetic resonance imaging (MRI) scanner. The Jacobian matrix relating changes of the currents through the coils to changes of the tip position is derived using a three dimensional kinematic model of the catheter deflection. The inverse kinematics is numerically computed by iteratively applying the inverse of the Jacobian matrix. The damped least square method is implemented to avoid numerical instability issues that exist during the computation of the inverse of the Jacobian matrix. The performance of the proposed inverse kinematics approach is validated using a prototype of the robotic catheter by comparing the actual trajectories of the catheter tip obtained via open-loop control with the desired trajectories. The results of reproducibility and accuracy evaluations demonstrate that the proposed Jacobian-based inverse kinematics method can be used to actuate the catheter in open-loop to successfully perform complex ablation trajectories required in atrial fibrillation ablation procedures. This study paves the way for effective and accurate closed-loop control of the robotic catheter with real-time feedback from MRI guidance in subsequent research.

Keywords: Continuum Robots; Inverse Kinematics; Magnetically Actuated Catheter; Robotic Catheter.

Fig. 1

(a) Illustration of catheter ablation procedure [3]. (b) Illustration of a proof-of-concept catheter prototype in a magnetic field, including a set of embedded current-carrying coils [3].

Fig. 2

Diagram of a catheter with one set of current-carrying coils, which is divided into N finite segments [3]. The coil is located at the tip.

Fig. 3

An illustration of the iterative inverse kinematics method.

Fig. 4

(a) Experiment setup inside a clinical MRI scanner. (b) Front view of the experimental setup. The catheter prototype is immersed in a phantom (aquarium tank, left in the picture) filled with distilled water doped with a gadolinium-based contrast agent. It is clamped vertically at its base. The mirror next to the tank (right in the figure) displays the side view of the actuated catheter. The catheter is marked in orange at three spots (base, coils, tip) for measuring the deflections of the catheter prototype using a camera.

Fig. 5

(a) A proof-of-concept catheter prototype used in the validation experiments. The unit of the dimensions is in mm. (b) Diagram of the catheter prototype with one coil set. Each coil set is composed of two orthogonal side coils and one axial coil.

Fig. 6

Trajectories used for parameter estimations. The blue and black circles show the actual locations of the tip and coil on the catheter. The red stars denote the estimated locations of the end points on each segment of the catheter from the model. (a) Trajectory of the catheter with the axial coil actuated. (b) Trajectory of the catheter with one side coil actuated for twisting motion. (c) Trajectory of the catheter with the other side coil actuated for bending motion.

Fig. 7

Catheter trajectories as measured using the camera-based vision system. The red diamonds represent the given trajectories. The blue, green, and yellow squares represent the observed positions of the labeled markers on the tip, coils and base, respectively. The unit in all these plots is mm.

Fig. 8

Shape comparisons between the given desired trajectory and the observed trajectories which are transformed without scaling. The red diamonds represent the desired trajectories. The blue markers represent the observed positions of the labeled markers on the tip. Each kind of trajectory has been collected 7 times. The unit in all these plots is mm.

Fig. 9

Reproducibility of trajectory shapes among the observed tip trajectories. The black circle markers represent the reference trajectory collected from experiments. The blue markers represent the other observed trajectories of the labeled markers on the tip. Each kind of trajectory has been collected 7 times. The unit in all these plots is mm.