Fractionalized Jeffrey fluid model for predicting magnetic nanoparticles trajectory: A physiological aspects of drug targeting

Nanotechnology based drug delivery is a recent and effective proceedure for the treatment of cancer and other diseases related to cardiovascular system. During drug delivery, it is very important to explore the skills to direct the medication at the diseased area. In this sense, magnetic drug targeting is one of the most noticeable drug delivery with bio-compatibility and non-invasive nature. This model aims to estimate the trajectories of the drug-based particles towards the diseased area in a permeable blood vessel by bearing in mind blood as Jeffrey fluid. Further, the problem deals with the Caputo fractional order time derivative, which gives the impact of the memory effect on the system. The system of governing equations are written in non-dimensional form. The velocity profile solve analytically by using Laplace and Hankel transform. An algorthim is developed with the forth order Range-Kutta method to find thesignificant trajectories of the drug carrier in both directions. It observed that short memory effect support the carrier particle trajectories towards the target location. Relaxation parameter slow down the motion of the drug carrier towards target cells, while an opposite phenomenan appears for retardation parameter. Magnetization and nanoparticle volume fractions enhance the capture efficiency. Darcy number slow down the motion of the drug carrier. Governing parameters shows a meaningful impact on the path of the drug-based carrier particle. The results of this model will help to understand the capture efficiency and trajectories of the drug carrier. Further it will help to develop the tools related to drug delivery and understand the phenomena.