Magnetic nanodrug delivery in non-Newtonian blood flows

With the goal of determining strategies to maximise drug delivery to a specific site in the body, a mathematical model for the transport of drug nanocarriers (nanoparticles) in the bloodstream under the influence of an external magnetic field is presented. Under the assumption of long (compared to the radius) blood vessels the Navier-Stokes equations are reduced, consistent with lubrication theory. Within these restrictions analytical results are compared for Newtonian, power-law, Carreau and Ellis fluids, which clearly demonstrate the importance of shear thinning effects when modelling blood flow. Incorporating nanoparticles and a magnetic field to the model we develop a numerical scheme and study the particle motion for different field strengths. In particular, we demonstrate the importance of the non-Newtonian behaviour: for certain field strengths a Newtonian model predicts that all particles are absorbed into the vessel wall, whilst the non-Newtonian models predict that a small number of particles are absorbed into the wall while the rest flow along with the blood and leave the vessel at the outlet. Consequently, models based on a Newtonian fluid can drastically overpredict the effect of a magnetic field. Finally, we evaluate the particle concentration at the vessel wall and compute the evolution of the particle flux through the wall for different permeability values, which is important when assessing the efficacy of drug delivery applications. The insights from our work bring us a step closer to successfully transferring magnetic nanoparticle delivery to the clinic.