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Magnetic nanoparticles have emerged as a promising approach to improvingcancer treatment. However, many novel nanoparticle designs fail in clinicaltrials due to a lack of understanding of how to overcome the in vivo transportbarriers. To address this shortcoming, we develop a novel computational modelaimed at the study of magnetic nanoparticles in vitro and in vivo. In thispaper, we present an important building block for this overall goal, namely anefficient computational model of the in-flow capture of magnetic nanoparticlesby a cylindrical permanent magnet in an idealised test setup. We use acontinuum approach based on the Smoluchowski advection-diffusion equation,combined with a simple approach to consider the capture at an impenetrableboundary, and derive an analytical expression for the magnetic force of acylindrical magnet of finite length on the nanoparticles. This provides asimple and numerically efficient way to study different magnet configurationsand their influence on the nanoparticle distribution in three dimensions. Suchan in silico model can increase insight into the underlying physics, help todesign novel prototypes and serve as a precursor to more complex systems invivo and in silico.

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