Simulation of drug transport to a specific location to prevent the occurrence of a specific disease is a useful tool for improving the current methods of local delivery. If a patient suffers kidney failure, vascular grafts made from expanded polytetrafluoroethylene (ePTFE) can be surgically placed between an artery and a vein in order to provide high blood flow volumes for dialysis. However, such vascular accesses fail at a high rate typically due to neointimal hyperplasia formation at the venous anastamosis, where medial smooth muscle cells and/or adventitial fibroblasts grow uncontrollably and excessively. Delivery of antiproliferative drugs to this site from a perivascular drug depot has been suggested as a strategy to prevent neointimal hyperplasia from occurring. Challenges of this strategy include identifying effective drugs and determining their therapeutic/cytotoxic concentrations, as well as the availability of a suitable drug delivery vehicle. Previously the antiproliferative properties of dipyridamole and rapamycin have been examined using a porcine model of hemodialysis graft stenosis and a hydrogel delivery system in the vicinity of the graft anastomosis; some pharmacokinetic data also has been previously obtained, using in vitro experiments, on the diffusion of both drugs through ePTFE grafts and through arterial and venous tissues. Using the in vitro data, computational finite element methods and an idealized 3D mesh that approximates a graft –vessel anastomosis site, we have modeled diffusion without convection of both drugs delivered locally to the anastamoses of a hemodialysis vascular access graft. The simulation was carried out using COMSOL's multiphysics transient diffusion application in FEMLab, and the amount of drug present in each compartment calculated by the simulation was compared to the amount of drug present in tissues obtained from the porcine experiments. Our goal is to create a tissue-based pharmacokinetic and pharmacodynamic simulation that can help guide the development and optimization of the hydrogel delivery system to achieve a therapeutic goal in treating hemodialysis graft stenosis.