Shear induced fractionalized dispersion during Magnetic Drug Targeting in a permeable microvessel

Solute dispersion is a significant phenomenon during drug targeting to estimate the accumulation of drug particles at the tumour region with the capture efficiency. In this present study, we aim to predict the effective dispersion and saturated concentration of drug carriers during magnetic drug targeting in a microvessel with a time fractional derivative based dispersion model. The magnetic nanoparticles are bound with the non-magnetic materials/microgels with the therapeutic agents to prepare the drug carriers. A magnetic field is created outside the body to control and accelerate the trajectories of the drug carriers. The nature of the blood flow into the vessel is considered as Casson fluid. The velocity of the drug carriers is solved analytically, while the fractional-order dispersion equation is computed numerically using the finite difference technique with the forward time and central space discretization. The influence of fractional-order parameter and model biological parameters such as rheological parameter, permeability parameter related to hydraulic conductivity, magnetization, volume fraction of nanoparticles, tumour-magnet distance, nanoparticle radius, drug elimination, and source term on the relative effective dispersion are discussed. The outcomes showed that both rheological parameters and volume fraction increase drug carrier particle concentration, and that saturating occurs at a later time as they increase. Higher magnetization, permeability parameter related to the hydraulic conductivity, and source term are associated with faster transportation of drug carriers to the tumour site. In addition, we note that by using small particle sizes, a high concentration of the drug-coated nanoparticles will be expected in the tumour area, and this slows the rate at which it reaches the saturation point.