Coupled vehicle–skin models for drug release

Percutaneous absorption of a drug delivered by a vehicle source is usually modeled by using diffusion Fick’s law. In this case, the model consists in a system of partial differential equations of diffusion type with a compatibility condition on the transition boundary between the vehicle and the skin. Using this model, the fractional drug release in both components – vehicle and skin – is proportional to the square root of the release time. Often experimental results show that the predicted drug concentration distribution in the vehicle and in the skin by the Fick’s model does not agree with experimental data. In this paper, we present a non-Fickian mathematical model for the introduced percutaneous absorption problem. In this new model, the Fick’s law for the flux is modified by introducing a non-Fickian contribution defined with a relaxation parameter related to the properties of the components. Combining the flux equation with the mass conservation law, a system of integro-differential equations is established with a compatibility condition on the boundary between the two components of the physical model. The stability analysis is presented. In order to simulate the mathematical model, its discrete version is introduced. The stability and convergence properties of the discrete system are studied. Numerical experiments are also included.