Magnetically Targeted Drug Transport Across a Tumor Cell Membrane Under Magnetic Field Gradients

Magnetic targeting of drug carriers is commonly studied at macroscopic scales, while its impact on drug transport across individual cell membranes remains poorly quantified. Here, we present a theoretical and numerical model of magnetically assisted drug transport across the membrane of a single tumor cell exposed to magnetic field gradients. Extracellular transport is described by an advection-diffusion equation that couples passive diffusion with magnetophoretic drift, whereas intracellular transport is governed by diffusion and first-order uptake kinetics. The cell membrane is modeled as a semi-permeable interface with finite permeability, providing explicit coupling between extracellular and intracellular domains. Assuming spherical symmetry, the coupled transport equations are solved using finite-difference schemes, with magnetic forcing represented through an effective drift velocity vmag and interpreted using the magnetic Peclet number. To enable a controlled comparison between healthy and tumor cells, identical geometric, diffusive, and magnetic parameters are used, while biological differences are introduced solely through membrane permeability and intracellular uptake rates. By separating cumulative membrane delivery from cumulative intracellular uptake, the model resolves ambiguities arising from heterogeneous uptake kinetics. The results show that magnetophoretic drift enhances near-membrane drug accumulation and effective transmembrane flux without modifying intrinsic membrane properties. Magnetic targeting therefore acts as a transport amplifier, magnifying pre-existing biological differences and producing a larger model-predicted delivery advantage in tumor cells. Overall, the framework identifies the magnetic Peclet number as the key parameter governing the transition from diffusion-dominated to drift-enhanced cellular drug transport.