Study on Worst-Case Gradient Forces on Untethered Magnetic Devices Using Two Synchronized Rotating Magnetic Dipoles

Untethered magnetic devices (UMDs) hold significant clinical potential for removing blood clots. However, in the complex intravascular environment, their locomotion may be disturbed. Such disturbances can lead to variations in the magnetic gradient force exerted on the UMD, increasing the risk of vascular damage. Therefore, evaluating the magnetic gradient force acting on the UMD under worst-case conditions is essential for risk mitigation. In this letter, we a novel method to estimate the upper and lower bounds of the worst-case magnetic gradient force acting on the UMD, with actuation provided by two synchronized rotating magnetic dipoles. To assess the robustness of the algorithm, we conducted a Monte Carlo simulation in which the dipole directions of the two synchronized rotating magnetic dipoles and the dipole direction of the UMD were randomly varied 1 000 000 times in the three-dimensional space to simulate all possible scenarios that may be encountered by the UMD in intravascular environments. The simulation results indicate that the worst-case magnetic gradient force remains below the upper bound predicted by the algorithm, thereby validating its effectiveness.