BIOINSPIRED MATHEMATICAL MODELING OF CHEMICAL DISPERSION IN NARROW AND CURVED ARTERIES: A COMPUTATIONAL APPROACH

Abstract

This study investigated the dispersion kinetics of pharmaceutical agents within blood flow characterized by the rheological properties of Herschel-Bulkley (H-B) fluids, occurring in arteries afflicted with cosine and sine-shaped stenosis, while concurrently considering the influence of chemical reactions. Stenosis, resulting from the accumulation of atherosclerotic plaques comprising cholesterol, lipids, and fats along arterial walls, instigates arterial constriction, thereby modulating drug dispersion dynamics. The geometrical configuration of stenosis and chemical reaction kinetics exert substantial influences on the efficacy of drug dispersion within the bloodstream. To elucidate these intricate phenomena, the study employs analytical solutions to the nonlinear differential equations governing momentum and constitutive behavior to derive the blood velocity profile. The dispersion function, a critical metric for characterizing drug dispersion patterns, is obtained by solving the convective-diffusion equation utilizing a generalized dispersion model. Notably, the attained results demonstrate concordance with scenarios devoid of chemical reactions or stenosis, affirming the robustness of the analytical framework. Furthermore, the investigation reveals distinctive trends in drug dispersion kinetics in arteries with cosine-shaped stenosis compared to those with sine-shaped stenosis. Specifically, the steady dispersion function is observed to be attenuated in cosine-shaped stenosed arteries relative to their sine-shaped counterparts, whereas the opposite trend is evident for unsteady dispersion dynamics. Additionally, escalating levels of chemical reaction and stenosis height correlate with augmented steady dispersion rates at the arterial center, while conversely impacting unsteady dispersion kinetics. This research underscores the biomedical significance of comprehensively understanding drug dispersion dynamics within blood flow, offering theoretical insights that can inform predictive modeling of drug behavior and facilitate the design of next-generation medical interventions aimed at optimizing drug delivery efficacy in cardiovascular therapies.