Permeation of water through the stratum corneum. A mathematical model based on diffusion with memory

In this note, we describe the transport of water across the stratum corneum of human skin by means of the Fick diffusion equation, modified by the introduction of a memory formalism. We derive the expressions for the flux in the permeation and desorption processes and compare these predictions with some recent experimental results obtained by Anissimov and Roberts [J. Pharm. Sci., 2009]. The data can be accounted for with a good agreement with two parameters, the diffusion coefficient D and the exponent of the fractional derivative v. This approach can be easily generalized to other diffusion processes which occur in highly heterogeneous systems.