Concentration-flux relations for a multicellular biological membrane with metabolism

A mathematical model is described for the simultaneous diffusion and metabolism of a chemical penetrating a multicellular biological membrane such as skin. Metabolism is assumed to follow saturable Michaelis-Menten kinetics, which leads to nonlinear relationships between the applied concentration and the metabolic and diffusive fluxes through the membrane. Approximate concentration-flux relations are derived under limiting conditions, and a computational method is described for the general case. The major barrier to dermal penetration of very lipophilic molecules is thought to be the viable tissues (viable epidermis and some of the dermis) underlying the stratum corneum, and some molecules are known to be metabolized by enzymes within these tissues. It is proposed to use the model to describe penetration and metabolism of such lipophilic molecules within the viable tissues of the skin.