Numerical simulation of superparamagnetic nanoparticle motion in blood vessels for magnetic drug delivery

A numerical model is developed for the motion of superparamagnetic nanoparticles in a non-Newtonian blood flow under the influence of a magnetic field. The rheological properties of blood are modeled by the Carreau flow and viscosity, and the stochastic effects of Brownian motion and red blood cell collisions are considered. The model is validated with existing data and good agreement with experimental results is shown. The effectiveness of magnetic drug delivery in various blood vessels is assessed and found to be most successful in arterioles and capillaries. A range of magnetic field strengths are modeled using equations for both a bar magnet and a point dipole: it is shown that the bar magnet is effective at capturing nanoparticles in limited cases, while the point dipole is highly effective across a range of conditions. A parameter study is conducted to show the effects of changing the dipole moment, the distance from the magnet to the blood vessel, and the initial release point of the nanoparticles. The distance from the magnet to the blood vessel is shown to play a significant role in determining nanoparticle capture rate. The optimal initial release position is found to be located within the tumor radius in capillaries and arterioles to prevent rapid diffusion to the edges of the blood vessel prior to arriving at the tumor and near the edge of the magnet when a bar magnet is used.