Membrane permeability based on mesh analysis

The main function of a membrane is to control the exchange of matter between the surrounding regions. As such, accurate modeling of membranes is important to properly describe their properties. In many cases in both biological systems and technical applications, the membranes are composite structures where transport properties may vary between the different sub-regions of the membrane. In this work we develop a method based on Mesh analysis that is asymptotically exact and can describe diffusion in composite membrane structures. We do this by first reformulating a generalized Fick's law to include the effects from activity coefficient, diffusion coefficient, and solubility using a single condensed parameter. We then use the derived theory and Mesh analysis to, in essence, retrieve a finite element method approach. The calculated examples are based on a membrane structure that reassembles that of the brick and mortar structure of stratum corneum, the upper layer of our skin. Resulting concentration profiles from this procedure are then compared to experimental results for the distribution of different probes within intact stratum corneum, showing good agreement. Based on the derived approach we further investigate the impact from a gradient in the fluidity of the stratum corneum mortar lipids across the membrane, and find that it is substantial. We also show that anisotropic organisation of the lipid mortar can have large impact on the effective permeability compared to isotropic mortar lipids. Finally, we examine the effects of corneocyte swelling, and their lateral arrangement in the membrane on the overall membrane permeability.