Unsteady nano-magnetic drug dispersion for pulsatile Darcy flow through microvessel with drug elimination phenomena

Abstract

Drug delivery by nano-drug carriers in magnetic drug targeting has shown a promising future in various cancer tumor treatments. The distinguishing properties of nanocarriers, such as small size, selective targeting, controlled release, and others, have made them more effective than the existing conventional treatments. However, several factors affect its delivery. In the present problem, we study the unsteady dispersion of drug-loaded magnetic nanocarriers in microvessels driven by a pulsatile pressure gradient derived from the unsteady Darcy law. Both fluid flow rate and mean velocity are computed analytically. The finite difference method is used to obtain the numerical solution of the solute transport equation, and the results are presented in graphs. Our results show that not only does the Womersley number influence the pulsatility dispersion of nanocarrier particles but also the microvessel permeability, magnetic-tumor distance, magnetization number, and volume fraction of magnetic nanoparticles. We found a drop in drug-loaded magnetic nanocarriers' concentration at the targeted site with decreasing blood pulsatility in the microvessel as portrayed by the Womersley parameter. In contrast, the descending magnetic tumor distance promotes nanoparticle concentration in the tumor tissue. Furthermore, the effects of other parameters, such as permeability, magnetization, volume fraction of magnetic nanoparticles, source term, elimination parameter, and nanocarrier radius, are discussed. To sum up, based on the Womersley frequency parameter coefficient used to describe blood pulsatility resulting from forceful heartbeat, flow pulsatility and nanocarrier particle dispersion are positively correlated, while magnetic-tumor distance is negatively correlated with both pulsatility and nanoparticle concentration.