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

TL;DR

This paper analyzes a PDE model for intravascular drug release from arterial stents, proving existence, uniqueness, and error estimates for numerical schemes, and discusses extensions to 2D cases.

Contribution

It provides the first rigorous mathematical and numerical analysis of a modified PDE model for drug release from arterial stents, including error estimates and extensions.

Findings

Proved existence and uniqueness of the weak solution.

Established optimal error estimates for finite element schemes.

Presented numerical results comparing different computational strategies.

Abstract

This paper is concerned with the PDE and numerical analysis of a modified one-dimensional intravascular stent model originally proposed in [4]. It is proved that the modified model has a unique weak solution 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 are 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.