Numerical Simulation of Local Pharmacokinetics of a Drug after Intravascular Delivery with an Eluting Stent

We use mathematical modelling to delineate the influence of two important factors on local pharmacokinetics of a drug delivered via an eluting stent, namely: (1) diffusional resistance of a stent coating, and (2) reversible binding of a drug to the vascular tissue. A system of differential equations that describes diffusion of the drug out of the polymeric coating of the stent into the vascular tissue and into the bloodstream, as well as reversible binding of the drug within the vascular tissue, was solved numerically and the spatial profiles of the concentration of the drug at various points of time were produced and analysed. Also, kinetic curves of the spatial average concentration of the drug within the wall were constructed, and the areas under those curves (AUC) were calculated. The simulations showed that AUC might be enhanced, if the stent is coated with a continuous layer of a drug-releasing medium with a high diffusional resistance. Both the residence time and the average concentration of the drug within the vascular wall increase in this case mainly because the coating imposes a diffusional barrier between the vascular tissue and the bloodstream, thereby reducing the wash-out. If the drug reversibly binds to the tissue, the residence time increases greatly, but the AUC for the free (unbound) drug remains unchanged, implying that the presence of the drug in the vessel is prolonged at the expense of a proportional reduction in concentration of a free drug within the tissue. These findings justify the design of eluting stents with continuous coatings with enhanced diffusional resistance and the engineering of drugs with enhanced affinity to the vascular matrix. Reversible binding to tissue may be beneficial for prolonging the presence of the drug in the target tissue, and for avoiding potential toxic peak effects of high concentrations of the free (unbound) drug.