3-D MDT with spherical targets by bilinear interpolation for determining blood velocity profiles including the vessel wall effect

A numerical simulation of three-dimensional (3-D) implant assisted-magnetic drug targeting (IA-MDT) using ferromagnetic spherical targets, including the effect from the vessel wall on the blood flow, is presented. The targets were implanted within arterioles and subjected to an externally uniform applied magnetic field in order to increase the effectiveness of targeting magnetic drug carrier particles (MDCPs). The capture area (As) of the MDCPs was determined by inspection of the particle trajectories simulated from the particle equations of motion. The blood flow velocities at any particle position around the target were obtained by applying bilinear interpolation to the numerical blood velocity data. The effects on As of the type of ferromagnetic materials in the targets and MDCPs, average blood flow rates, mass fraction of the ferromagnetic material in the MDCPs, average radii of MDCPs (Rp) and the externally applied magnetic field strength (μ0H0) were evaluated. Furthermore, the appropriate μ0H0 and Rp for the IA-MDT design is suggested. In the case of the SS409 target and magnetite MDCPs, dimensionless capture areas ranging from 4.1- to 12.4 and corresponding to particle capture efficiencies of 31-94% were obtained with Rp ranging from 100- to 500 nm, weight fraction of 80%, μ0H0 of 0.6 T and an average blood flow rate of 0.01 ms−1. In addition, the more general 3-D modelling of IA-MDT in this work is applicable to IA-MDT using spherical targets implanted within blood vessels for both laminar and potential blood flows including the wall effect.