We study the problem of drug delivery in a catheterized artery in the presence of atherosclerosis. The problem is modeled in the context of a two-phase flow system which consists of red blood cells and blood plasma. The coupled differential equations for fluid (plasma) and particles (red cells) are solved for the relevant quantities in the reasonable limits. The drug delivery problem is modeled with a partial differential equation that is developed in terms of the drug concentration, blood plasma velocity, hematocrit value and the diffusion coefficient of the drug/fluid. A conservative-implicit finite difference scheme is develop in order to numerically solve the drug concentration model with an atherosclerosis region. We find that the evolution of the drug concentration varies in magnitude depending on the roles played by the convection and diffusion effects. For the cases where the diffusion coefficient is not too small, then convection effect is not strong enough and drug was delivered mostly in the central part of the blood flow region and could not reach effectively the atherosclerosis zone. However, for sufficiently small values of the diffusion coefficient, the convective effect dominates over the diffusion effect and the drug was delivered effectively over the blood flow region and on the atherosclerosis zone.
Orizaga, Saulo, Daniel N. Riahi, and José R. Soto. 2020. “Drug Delivery in Catheterized Arterial Blood Flow with Atherosclerosis.” Results in Applied Mathematics 7 (August): 100117. https://doi.org/10.1016/j.rinam.2020.100117.
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Results in Applied Mathematics