An unsteady analysis of two-phase binding of drug in an asymmetric stenosed vessel

Abstract

In this paper, we investigate endovascular delivery to get a step ahead of the pharmacological limitations it has due to the complexity of dealing with a patient-specific vessel through a mathematical model. We divide the domain of computation into four sub-domains: the lumen, the lumen-tissue interface, the upper tissue and the lower tissue which are extracted from an asymmetric atherosclerotic image derived by the intravascular ultrasound (IVUS) technique. The injected drug at the luminal inlet is transported with the streaming blood which is considered Newtonian. An irreversible uptake kinetics of the injected drug at the lumen-tissue interface from the luminal side to the tissue domains is assumed. Subsequently, the drug is dispersed within the tissue followed by its retention in the extracellular matrix (ECM) and by receptor-mediated binding. The Marker and Cell (MAC) method has been leveraged to get a quantitative insight into the model considered. The effect of the wall absorption parameter on the concentration of all drug forms (free as well as two-phase bound) has been thoroughly investigated, and some other important factors, such as the averaged concentration, the tissue content, the fractional effect, the concentration variance and the effectiveness of drug have been graphically analyzed to gain a clear understanding of endovascular delivery. The simulated results predict that with increasing values of the absorption parameter, the averaged concentrations of all drug forms do decrease. An early saturation of binding sites takes place for smaller values of the absorption parameter, and also rapid saturation of ECM binding sites occurs as compared to receptor binding sites. Results also predict the influence of surface roughness as well as asymmetry of the domain about the centerline on the distribution and retention of drug. A thorough sensitivity analysis has been carried out to determine the influence of some parameters involved.