Modeling Magneto-Active Soft Robots in Vessels Based on Discrete Differential Geometry of Framed Curves

Cardiac arrhythmias, such as atrial fibrillation, pose significant health risks and are often treated using minimally invasive cardiac ablation. However, the limited maneuverability of mechanically driven catheters can undermine both the success and efficiency of the procedure. In contrast, magnetic soft continuum robots (MSCRs) offer a promising alternative by utilizing external magnetic fields to directly steer the catheter tip. This approach allows for precise control, simplifying navigation through intricate vascular systems, ensuring stable contact with lesions, and minimizing manual manipulation. To optimize the use of MSCRs in magnetically assisted cardiac ablation, it is crucial to model their behavior, focusing on contact with the vascular environment. This article establishes a theoretical model of MSCRs based on Cosserat beam theory and discrete differential geometry (DDG). The model is validated and subsequently used to simulate three scenarios: partially magnetized MSCRs, MSCRs with point contacts, and MSCRs with line contacts. The results reveal significant nonlinear behavior upon contact. By applying our model, we demonstrate how adjustments of the magnetic field's direction, magnitude, and MSCR length can guide navigation through bifurcated vessels and achieve precise contact with a lesion. These findings provide valuable insights into the design and control of MSCRs, enabling more efficient, simulation-driven guidance for minimally invasive procedures and advancing digital health care in endovascular applications.