Inclusion of magnetic dipole–dipole and hydrodynamic interactions in implant-assisted magnetic drug targeting

Mathematical modelling of the implant-assisted magnetic drug targeting system of Avilés, Ebner and Ritter is performed. In order to model the agglomeration of particles known to occur in this system, the magnetic dipole–dipole and hydrodynamic interactions are included. Such interactions were calculated previously by Mikkelsen et al. under low magnetic fields (~0.05 T) in microfluidic systems. Here, a higher magnetic field (0.7 T) is considered and the effect of interactions on two nanoparticles with a seed implant is calculated. The calculations were performed with the open-source software OpenFOAM. Different initial positions are considered and the system performance is assessed in terms of capture cross section. Inclusion of both interactions was seen to alter the capture cross section of the system by up to 7% in absolute terms.