Mathematical Modeling and Numerical Approximations for Intravascular Drug Release from Arterial Stents and Transport in Arterial Tissues

This dissertation focuses on mathematical modeling and analysis, as well as numerical approximations for intravascular drug release from arterial stents and transport in arterial tissues. The first model presented is a case study of an existing one-dimensional, multi-physics, coupled model. The model is shown to be well-posed using the Galerkin construction alongside a compactness argument. Optimal-order numerical error estimates are also derived, and numerical simulation results are computed. The one-dimensional model is then extended to two different two-dimensional models. The first is a direct extension, while the second is further coupled with Darcy's Law to model porous media flow. For both two-dimensional models, the well-posedness of the model and the optimal-order error estimates are established. Simulations are also conducted for these models to illustrate the drug-transport dynamics.