Modelling Transdermal Drug Delivery through a Two-layered System

One of the most promising frontiers of bioengineering is the controlled release of a therapeutic drug from a vehicle across the skin (transdermal drug delivery). In order to study the complete process, a multiphase mathematical model describing the dynamics of a substance between two porous coupled media of different properties and extents is presented. A system of partial differential equation describes the diffusion and the reversible binding and unbinding processes in both layers. Additional flux continuity at the interface and clearance conditions into systemic circulation are imposed. A Sturm-Liouville problem is solved and an analytical solution is given in the form of an infinite series expansion. The model points out the role of the diffusion and reaction parameters, which control the complex transfer mechanism and the drug kinetics across the two layers. Drug mass are given and their dependence on the physical parameters are discussed.