Water and solute active transport through model epidermis: Contribution of electrodiffusion

As part of a research program focusing on the role of human skin as a transport barrier, we formulate a coarse-grained model of the epidermis consisting of free extracellular water, live cells, and inert extracellular matrix subject to the coupling between molecular diffusive flux and electrokinetic flux (or electrodiffusion, as expressed by the Nernst-Planck equation). This polyphasic mathematical model accounts for active transport of physiologically-relevant solutes across the membrane of the live cells (keratinocytes), diffusion in the extracellular matrix and redistribution of water. The volume of the cell phase is regulated by the fluxes of water and Na⁺, K⁺ and Cl^- ions across the cell membrane and is controlled according to the time-delay scheme introduced in the model of Hemandez & Cristina (1998). Computing the transient response of a 100 μm-thick viable epidermis layer exposed to a hyposmotic shock reveals that accounting for the electrokinetic flux in the extracellular domain has negligible effect on the results. This result suggests that a significant simplification of the model can be made in terms of decoupling the extracellular variation of the electrostatic field from the diffusion problem during the study of complex transepidermal transport.