Magnetic drug targeting during Casson blood flow in a microvessel: A Caputo fractional model

Abstract

A mathematical model on fractionalized axisymmetric Casson blood flow through a cylindrical shaped blood vessel is introduced to present the capture location of drug carrier particles at diseased regions during magnetic drug targeting (MDT). The Caputo fractional order time-derivative is introduced in the momentum equation to impose the time memory effect. The governing momentum equation is solved analytically in terms of Lorenzo – Hartley and Robotonov – Hartley special functions using Laplace transform (LT) and finite Hankel transform (FHT). The outcome solution for coupled force balance equations is solved using fourth order Runge – Kutta (RK) method, whereas the total volume fraction (TVF) of magnetic nanoparticles (MNPs) is obtained analytically. The present model introduced the effects of magnetic parameter, Darcy number, Reynolds number and pulsatile frequency with the impact of the memory effect in the form of the fractional parameters on the axial and radial trajectories of drug carrier particles (CPs) and on the volume fraction of MNPs. The impacts of tumor-magnet distance, Casson parameter, and Hematocrit parameter on the volume fraction of MNPs is also investigated. A comparison is made with the existing literature, and it shows a good agreement. Short time memory effect leads to a speedy move of the drug particles towards the disease region and the phenomenon is more significant with increase in the volume fraction of the MNPs, magnetization and permeable nature of the microvessel. The outcome of the present study will be helpful to the field of medical science to carry out further research to treat disease in specific locations by using MDT.