Contribution of rational design and fractional rheology on magnetic nanoparticle-based drug targeting in a microvessel with Saffman force

Abstract

Magnetic nanoparticles based drug targeting is one of the prominent drug targeting methods due to non-invasive treatments, and recovery efficiency. The aim of the present problem is to analyze the trajectories of drug carrier particles and the total volume fraction of magnetic nanoparticles required for capturing purposes close to the tumor region. Due to the complex nature of blood, the viscoelastic Maxwell fluid relation is used to describe blood, and the flow of nanoparticles is investigated using momentum equations with the time-variant Caputo-Fabrizio fractional order expression to capture memory effects. The rational design of the nanoparticles such as size and shape with different aspect ratio along particle-particle interaction, Saffman force and external magnetic force are incorporated in the governing equation. The velocity profile of the fluid is represented in the form of the inverse of Laplace and Hankel transform. The velocity profile is solved by numerical integration and trajectories of the drug carrier particles analyzed by using the fourth order Runge-Kutta method by developing an algorithm. The conclusion drawn from the study shows that drug carriers lead towards the tumor region with long term memory effects, and it is easily captured at the tumor region. Viscoelastic rheology capture possibly opposes the drugs carrying magnetic nanoparticles to capture at tumor regions following a similar phenomenon by Saffman force. Spherical shaped drugs carrying magnetic nanoparticles are more prominent to be targeted to the tumor region than other shaped drugs carrying magnetic nanoparticles. The present study will help biomedical engineers and nanomedicine researchers develop magnetic devices and the next generation of drug carrier particles to treat cancerous tumors.