Numerical Simulation of Two Phase Mathematical Model for Transportation of Mass and Drug from Drug Eluting Stents

A two phase coupled mathematical model for investigating the drug release in drug eluting stents is developed in this study. The release of drug in coating is modeled by the convection-diffusion equation while drug delivery in arterial wall is modeled by diffusion equation. This research explores the impact of non-dimensional parameters on drug release and mass concentrations from coating and arterial tissue having different dimensions and properties. Moreover, it is noted that the drug release speed and the timing of peak bound drug concentrations can be controlled by varying the values of ratio of available volume fraction to solid fraction e(1) and solid-liquid mass transfer parameter gamma. The governing equations together with suitable initial and boundary conditions are numerically solved by finite element method. The obtained time dependent system of ordinary differential equations are solved by backward difference and Galerkin difference time marching schemes in order to calculate the results with desired degree of accuracy. This bilayer model is useful for providing better understanding of the mechanism of mass transfer in coating and tissue layers. Furthermore, for different times, the drug release profiles in both layers are presented graphically so as to verify the application of the considered model.