Mathematical and numerical analysis for PDE systems modeling intravascular drug release from arterial stents and transport in arterial tissue

Abstract

This paper is concerned with the PDE (partial differential equation) and numerical analysis of a modified one-dimensional intravascular stent model. It is proved that the modified model has a unique weak solution by using the Galerkin method combined with a compactness argument. A semi-discrete finite-element method and a fully discrete scheme using the Euler time-stepping have been formulated for the PDE model. Optimal order error estimates in the energy norm are proved for both schemes. Numerical results are presented, along with comparisons between different decoupling strategies and time-stepping schemes. Lastly, extensions of the model and its PDE and numerical analysis results to the two-dimensional case are also briefly discussed.

Keywords

• intravascular stent
• drug release
• diffusion-advection-reaction equation
• well-posedness
• galerkin finite-element method
• error estimates
• pharmacokinetics