Unsteady transport and two-phase binding of a drug in an atherosclerotic artery

Abstract

To quantify the biology and physical understanding of endovascular drug delivery, a mathematical model that accounts for the two-phase binding of drug molecules in a diseased patient-specific artery has been developed. Using an image segmentation technique, the edges of the computational domain have been successfully extracted from an asymmetric intravascular ultrasound longitudinal image. The flow inside the porous tissue is described by the Brinkman model, and the luminal flow is Newtonian. At the lumen–tissue interface, an irreversible uptake kinetics for the injected drug from the luminal side into the tissue is taken into account. Furthermore, the drug's two-phase binding process, namely, the nonspecific binding caused by the drug's trapping in the extracellular medium (ECM-bound) and the specific binding caused by the interaction between drug molecules and receptors (REC-bound), has been considered. The Marker and Cell method has been leveraged to solve the governing equations numerically. Spatiotemporal variations of free drug, ECM-bound drug, and REC-bound drug are examined thoroughly for varying absorption parameter. Simulated results reveal that the interstitial flow amplifies drug distribution, retention, and delivery effectiveness, but flow separation downstream of the constriction reduces transmural flux. Concomitantly, the larger the absorption parameter, the higher the tissue content and effectiveness; nevertheless, significantly, larger absorption parameter values do not necessarily suggest improved delivery effectiveness. A thorough sensitivity analysis was carried out to predict the effects of some of the parameters involved.