This paper presents an iterative Jacobian-based inverse kinematics method for a magnetic resonance imaging (MRI) guided magnetically actuated steerable intravascular catheter system. The catheter is directly actuated by magnetic torques generated on a set of current-carrying microcoils embedded on the catheter tip by the magnetic field of the 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 an 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.

Objective: This paper presents the 3-D kinematic modeling of a novel steerable robotic ablation catheter system. The catheter, embedded with a set of current-carrying microcoils, is actuated by the magnetic forces generated by the magnetic field of the magnetic resonance imaging (MRI) scanner. Methods: This paper develops a 3-D model of the MRI-actuated steerable catheter system by using finite differences approach. For each finite segment, a quasi-static torque-deflection equilibrium equation is calculated using beam theory. By using the deflection displacements and torsion angles, the kinematic model of the catheter system is derived. Results: The proposed models are validated by comparing the simulation results of the proposed model with the experimental results of a hardware prototype of the catheter design. The maximum tip deflection error is 4.70 mm and the maximum root-mean-square error of the shape estimation is 3.48 mm. Conclusion: The results demonstrate that the proposed model can successfully estimate the deflection motion of the catheter. Significance: The presented 3-D deflection model of the magnetically controlled catheter design paves the way to efficient control of the robotic catheter for the treatment of atrial fibrillation.