A combined theoretical and in vitro modeling approach for predicting the magnetic capture and retention of magnetic nanoparticles in vivo.

Magnetic nanoparticles (MNP) continue to draw considerable attention as potential diagnostic and therapeutic tools in the fight against cancer. Although many interacting forces present themselves during magnetic targeting of MNP to tumors, most theoretical considerations of this process ignore all except for the magnetic and drag forces. Our validation of a simple in vitro model against in vivo data, and subsequent reproduction of the in vitro results with a theoretical model indicated that these two forces do indeed dominate the magnetic capture of MNP. However, because nanoparticles can be subject to aggregation, and large MNP experience an increased magnetic force, the effects of surface forces on MNP stability cannot be ignored. We accounted for the aggregating surface forces simply by measuring the size of MNP retained from flow by magnetic fields, and utilized this size in the mathematical model. This presumably accounted for all particle-particle interactions, including those between magnetic dipoles. Thus, our "corrected" mathematical model provided a reasonable estimate of not only fractional MNP retention, but also predicted the regions of accumulation in a simulated capillary. Furthermore, the model was also utilized to calculate the effects of MNP size and spatial location, relative to the magnet, on targeting of MNPs to tumors. This combination of an in vitro model with a theoretical model could potentially assist with parametric evaluations of magnetic targeting, and enable rapid enhancement and optimization of magnetic targeting methodologies.