Magnetic nanoparticle transport within flowing blood and into surrounding tissue

Magnetic drug delivery refers to the physical confinement of therapeutic magnetic nanoparticles to regions of disease, tumors, infections and blood clots. Predicting the effectiveness of magnetic focusing in vivo is critical for the design and use of magnetic drug delivery systems. However, current simple back-of-the-envelope estimates have proven insufficient for this task. In this article, we present an analysis of nanoparticle distribution, in and around a single blood vessel (a Krogh tissue cylinder), located at any depth in the body, with any physiologically relevant blood flow velocity, diffusion and extravasation properties, and with any applied magnetic force on the particles. For any such blood vessel our analysis predicts one of three distinct types of particle behavior (velocity dominated, magnetic dominated or boundary-layer formation), which can be uniquely determined by looking up the values of three nondimensional numbers we define. We compare our predictions to previously published magnetic-focusing in vitro and in vivo studies. Not only do we find agreement between our predictions and prior observations, but we are also able to quantitatively explain behavior that was not understood previously.