A two-phase two-layer model for transdermal drug delivery and percutaneous absorption

One of the 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 two-phase mathematical model describing the dynamics of a substance between two coupled media of different properties and dimensions is presented. A system of partial differential equations describes the diffusion and the binding/unbinding processes in both layers. Additional flux continuity at the interface and clearance conditions into systemic circulation are imposed. An eigenvalue problem with discontinuous coefficients 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 masses are given and their dependence on the physical parameters is discussed.