Two-phase binding of drug in a three-layered arterial wall following stent implantation

The present study explores the distribution and the binding of drug eluted from an embedded drug-eluting stent (DES), having struts of the circular cross-section. The arterial tissue is composed of three distinct layers, namely, the intima, the media and the adventitia, with varying diffusivity, and at the interfaces between different layers, a jump condition is imposed. The transport of free drug is modelled by the convection-diffusion-reaction process while the binding of drug is modelled by a nonlinear saturable reversible chemical reaction only. This model incorporates two types of binding mechanisms, namely, the specific binding caused by the interaction of drug and receptors, and the non-specific binding due to the gripping of drug in the extracellular medium (ECM). Furthermore, a constant as well as time-dependent release kinetics have been considered. All the governing equations along with suitable initial, boundary and jump interface conditions in cylindrical polar coordinate system are solved successfully by using the finite difference method. In this study, several clinical key factors like the degree of strut embedment, inter-strut distance (ISD), release mechanism are examined thoroughly. The study reveals that the inclusion of different layers along with jump interface conditions has a remarkable impact on stent-based delivery. Simulated results predict that a higher concentration profile for free drug and rapid saturation of binding sites take place for a half-embedded stent as compared to a quarterly and well-apposed stent. An intriguing feature is to be noted that the inter-strut distance through which the transmural plasma filtration takes place, plays a pivotal role in the distribution and retention of drug in the therapeutic domain considered. Furthermore, the steady-state simulation predicts the influence of strut dimension on the distributions of all drug forms.