Transport of nanoparticles in magnetic targeting: Comparison of magnetic, diffusive and convective forces and fluxes in the microvasculature, through vascular pores and across the interstitium.

Magnetic nanoparticle targeting in tumor areas is examined by an integrated consideration of the transport steps from the microcirculation to the vascular walls, through their pores and into the interstitium. Brownian, flow- and magnetically induced forces and fluxes are compared on the basis of order-of-magnitude estimates and numerical simulations. The main resistance to nanoparticle transport is found to be within the interstitium, since fluxes there are much smaller than the extravasation fluxes, and the latter are much smaller than the convective-diffusive ones within the microvasculature. For typical nanoparticle sizes, magnetic properties and strengths of magnetic fields as in MRI equipment, magnetic targeting is rather unlikely to play a significant role in directing nanoparticles towards vascular walls or through vascular pores. However, magnetic drift can have an effect within the interstitium and a tangible overall outcome, despite the fact that typical magnetic forces are smaller than Brownian ones or interstitial flow convective forces. The reason behind such an effect has to do with the much larger length scales involved in interstitial transport. Magnetic drift creates a front of large nanoparticle concentrations, flooding the inadequately perfused and poorly accessible tumor area. On the basis of time-scale estimates, it is suggested that sequential cycles of magnetic nanoparticle dosage may help in more efficient access of cell layers ever closer to the tumor center. The present results may assist in the quest for optimal parameters and conditions, given the conflicting requirements for particles small enough to evade hydrodynamic and steric hindrances in vascular pores and the interstitium, yet large enough to bear a substantial magnetic load.