Efficient computational model of the in-flow capturing of magnetic nanoparticles by a cylindrical magnet for cancer nanomedicine

Magnetic nanoparticles have emerged as a promising approach to improving cancer treatment. However, many nanoparticle designs fail in clinical trials due to a lack of understanding of how to overcome the in vivo transport barriers. To address this shortcoming, we develop a computational model aimed at the study of magnetic nanoparticles in vitro and in vivo. In this paper, we present an important building block for this overall goal, namely an efficient computational model of the in-flow capture of magnetic nanoparticles by a cylindrical permanent magnet in an idealized test setup. We use a continuum approach based on the Smoluchowski advection-diffusion equation, combined with a simple approach to consider the capture at an impenetrable boundary, and derive an analytical expression for the magnetic force of a cylindrical magnet of finite length on the nanoparticles. This provides a simple and numerically efficient way to study different magnet configurations and their influence on the nanoparticle distribution in three dimensions. Such an in silico model can increase insight into the underlying physics, help to design prototypes, and serve as a precursor to more complex systems in vivo and in silico.