Using the method of homogenization to calculate the effective diffusivity of the stratum corneum with permeable corneocytes

The stratum corneum is the outermost layer of the skin, which acts as a barrier membrane against the penetration of molecules into and out of the body. It has a biphasic structure consisting of keratinized cells (corneocytes) that are embedded in a lipid matrix. The macroscopic transport properties of the stratum corneum are functions of its microstructure and the transport properties of the corneocytes and the lipid matrix, and are of considerable interest in the context of transdermal drug delivery and quantifying exposure to toxins, as well as for determining the relation of skin disorders to disruption of the stratum corneum barrier. Due to the complexity of the tissue and the difference in length scales involved in its microstructure, a direct analysis of the mass transport properties of the stratum corneum is not feasible. In this study, we undertake an approach where the macroscopic diffusion tensor of the stratum corneum is obtained through homogenization using the method of asymptotic expansions. The biphasic structure of the stratum corneum is fully accounted for by allowing the corneocytes to be permeable and considering the partitioning between the corneocytes and the lipid phases. By systematically exploring the effect of permeable corneocytes on the macroscopic transport properties of the stratum corneum, we show that solute properties such as lipophilicity and relative permeabilities in the two phases have large effects on its transdermal diffusion behavior.