Computational Study of Kinematics of Capture of Magnetic Particles by Stent: 2-D Model

Abstract

This paper presents a simple 2-D model to study the kinematics of capture of 1 $\mu \text{m}$ diameter magnetic particles (MPs) by a periodic array of magnetic wires, which are aligned perpendicularly to Poiseuille flow in a rectangular 2-D channel in order to suggest improvements in the design of stent-assisted drug-targeting systems. The model examines the following: 1) the kinematics of particles near the wires; 2) the distribution of captured particles across the array of wires; and 3) the final position of particles that are not captured. An external homogenous magnetic field is applied perpendicularly to the axis of the wires and either perpendicular to or along the flow in order to magnetize the particles and the wires to saturation. The trajectories of MPs are determined using the first-order stiff ordinary differential equations that are solved numerically using MATLAB. These trajectories reveal that regardless of the orientation of external magnetizing field, it is always the first wire that captures the MPs. In addition, the particles that are not captured are found to be repelled to the center of the channel when compared with their starting position. This is an unexpected phenomenon indicating that the repulsive effect of the magnetic stent is stronger than the attractive effect, and the simplicity of our model allowed us to expose this previously undiscovered effect.