Blood flow through a deformable artery and magnetically targeted drug delivery

Drug targeting with magnetic nanoparticles to a diseased location is of greater interest in medicine for controlling tumor growth, removing blood clots, managing infections, and treating cardiovascular diseases like atherosclerosis and aneurysm. This article aims to develop a mathematical model for blood flow with injected drug carrier particles into the bloodstream. We assume that carrier particles are loaded with both drug molecules and magnetic nanoparticles, enabling targeted drug delivery to specific locations within the bloodstream by applying an external magnetic field. The arterial wall is assumed to be a linearly elastic solid, undergoing deformation as pressure waves propagate along the blood vessel, driven by the periodic pumping action of the heart. We obtain analytical solutions in two dimensions, considering certain limitations on the nonlinearity of the governing equations. We present solutions based on the Young wave mode (radial deformation) and Lamb wave mode (axial deformation) to observe the impact of wall deformation on the motion of the carrier particles and blood flow. The capturing efficiency of the carrier particles increases with either an increase in the radius or volume fraction of the carriers. The velocity of the carrier particles decreases as the distance from the source of an external magnetic field increases. The trajectory of the carrier particles clearly shows the capturing efficiency, which leads to a greater influence on magnetic particle imaging (MPI).