Steady-state flux and lag time in the stratum corneum lipid pathway: results from finite element models

Finite element model (FEM) solutions of the diffusion through two-dimensional representations of the stratum corneum (SC) lipid pathway are presented. Both simplified, regular "brick and mortar" models and a more complex, irregular model are analyzed. It is assumed that diffusion occurs only within the SC lipids and the lipids are isotropic. The steady-state flux and lag time are solved and compared with the corresponding values for a homogeneous membrane of the same thickness consisting of lipid material. Results confirm that the heterogeneous SC model behaves like a homogeneous membrane, meaning that FEM diffusion simulations are well approximated by an appropriate solution of the diffusion equation for a homogeneous membrane. Additionally, both steady-state flux and lag time (relative to these values in a homogeneous membrane) can be predicted from algebraic equations based on simple dimensionless descriptors of SC geometry. However, values for diffusivity derived from homogeneous membrane approximations to the FEM solutions (effective diffusivity, D*) are not equal to the intrinsic diffusivity of the chemical in lipid. Furthermore, the pathlength derived from homogeneous membrane approximations to FEM solutions (effective pathlength, l*) is not equal to the lipid pathlength and is not dependent on SC tortuosity. Whereas l* is not a function of corneocyte overlap, D* is. These model results suggest that diffusion properties of the SC lipid pathway can be correlated to SC geometry, but intrinsic diffusion coefficients and SC tortuosity cannot be derived from common diffusion cell experiments. Use of the model equations to predict permeability and lag time of lipophilic solutes is described.