Mass diffusion through two-layer media: an application to the drug-eluting stent

A mathematical model for the diffusion-transport of a substance between two porous homogeneous media of different properties and dimensions is presented. A strong analogy with the one-dimensional transient heat conduction process across two-layered slabs is shown and a similar methodology of solution is proposed. Separation of variables leads to a Sturm-Liouville problem with discontinuous coefficients and an exact analytical solution is given in the form of an infinite series expansion. The model points out the role of four non-dimensional parameters which control the diffusion mechanism across the two porous layers. The drug-eluting stent constitutes the main application of the present model. Drug concentration profiles at various times are given and analyzed. Also, qualitative considerations and a quantitative description to evaluate feasibility of new drug delivery strategies are provided, and some indicators, such as the emptying time, useful to optimize the drug-eluting stent design are discussed.