Mass diffusion through two-layer porous 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 nondimensional 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.