Modeling of mass dynamics in arterial drug-eluting stents

A mathematical model describing the advection-diffusion reaction 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 evidenced and a similar methodology is proposed. The model incorporates not only drug diffusive effects, but also convection phenomena and metabolic processes in the wall. Transformation and 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 the nondimensional parameters, which control the complex transfer mechanism across the two layers. In particular, the drug diffusivity in the wall is shown to greatly influence the residence time. Drug concentration profiles at various times are given and discussed.