Magnetic nanodrug delivery in non-Newtonian blood flows

Abstract

With the goal of determining strategies to maximise drug delivery to a specific site in the body, we developed a mathematical model for the transport of drug nanocarriers (nanoparticles) in the bloodstream under the influence of an external magnetic field. Under the assumption of long (compared to the radius) blood vessels the Navier-Stokes equations are reduced, to a simpler model consistently with lubrication theory. Under these assumptions, analytical results are compared for Newtonian, power-law, Carreau and Ellis fluids, and these clearly demonstrate the importance of shear thinning effects when modelling blood flow. Incorporating nanoparticles and a magnetic field to the model we develop a numerical scheme and study the particle motion for different field strengths. We demonstrate the importance of the non-Newtonian behaviour: for the flow regimes investigated in this work, consistent with those in blood micro vessels, we find that the field strength needed to absorb a certain amount of particles in a non-Newtonian fluid has to be larger than the one needed in a Newtonian fluid. Specifically, for one case examined, a two times larger magnetic force had to be applied in the Ellis fluid than in the Newtonian fluid for the same number of particles to be absorbed through the vessel wall. Consequently, models based on a Newtonian fluid can drastically overestimate the effect of a magnetic field. Finally, we evaluate the particle concentration at the vessel wall and compute the evolution of the particle flux through the wall for different permeability values, as that is important when assessing the efficacy of drug delivery applications. The insights from our work bring us a step closer to successfully transferring magnetic nanoparticle drug delivery to the clinic.

How the Magnetization Angle of a Linear Halbach Array Influences Particle Steering in Magnetic Drug Targeting—A Systematic Evaluation and Optimization

“…For the sake of simplicity, in this paper, the medium of the background flow is assumed to be water since the flow properties of blood are much more complex. The interested reader can find detailed information regarding the mathematical modeling of magnetic nanoparticles in a blood flow for MDT in the work of Fanelli et al [67].…”

“…The interested reader can find a review on how to model the pressure and flow properties in vessels in the work of Zhou et al [118]. Modeling of magnetic nanoparticles in blood flow was investigated numerically by Fanelli et al [67], and the magnetic accumulation of SPIONs under arterial flow conditions in blood was measured by Hennig et al [59].…”

Effect of Particle–Particle and RBC–Particle Interactions on Capture Efficiency of Magnetic Nanocarriers Under the Influence of a Nonuniform Magnetic Field

“…It was also found that by reducing the length of constriction in the vessel, the CE of nanoparticles increases. Fanelli et al (2021) mathematically simulated targeted drug delivery in a vessel under the influence of an external magnetic field. The Newtonian and three different non-Newtonian models were used to model the blood.…”

Analysis of Nanodrug Delivery in Blood Flowing through Blood Vessels Using Machine Learning Models

“…Asha and Neetu [18] studied the stenosis geometry and the effect of blood flowing through an artery under various conditions. Claudia et al [19] investigated the effect of nanodrug delivery with magnetic effect in non-Newtonian blood flow. They analyzed the effect of shear thinning with Newtonian power-law, Ellis, and Carreau fluids.…”