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.

中文翻译：

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基于迭代雅可比行列式的逆运动学和 MRI 引导磁驱动可转向导管系统的开环控制

本文提出了一种基于迭代雅可比行列式的逆运动学方法，用于磁共振成像（MRI）引导的磁驱动可操纵血管内导管系统。导管由 MRI 扫描仪的磁场嵌入导管尖端的一组载流微线圈产生的磁扭矩直接驱动。使用导管偏转的三维运动学模型导出将通过线圈的电流的变化与尖端位置的变化相关联的雅可比矩阵。逆运动学是通过迭代应用雅可比矩阵的逆来进行数值计算的。采用阻尼最小二乘法是为了避免雅可比矩阵逆计算过程中存在的数值不稳定问题。通过将通过开环控制获得的导管尖端的实际轨迹与所需轨迹进行比较，使用机器人导管原型验证了所提出的逆运动学方法的性能。再现性和准确性评估的结果表明，所提出的基于雅可比行列式的逆运动学方法可用于在开环中驱动导管，以成功执行房颤消融手术所需的复杂消融轨迹。这项研究为后续研究中通过 MRI 引导的实时反馈对机器人导管进行有效、准确的闭环控制铺平了道路。