Modeling of Diffusion and Concurrent Metabolism in Cutaneous Tissue

Clearance by cutaneous metabolism can shield the body from penetration of environmental and therapeutic xenobiotics. Here we report on a physical model to relate Fickian diffusion and concurrent Michaelis–Menten metabolism of drugs in the viable epidermis of human skin. For this purpose, we numerically generated substrate concentration profiles within the metabolizing tissue and the resulting donor-to-receiver substrate fluxes through the tissue for various mass transport and metabolism parameters. To validate the model, permeation and concurrent metabolism of a peptidomimetic compound, L -Ala-4-methoxy-2-naphthylamide (Ala-MNA), across both stripped human skin and HaCaT cell culture sheets were compared to numerical simulations. Parameter estimates for those calculations were extracted from independent experiments. Experimental data and numerical predictions were in excellent agreement. Also, numerical fits and independently validated parameters correlated closely, indicating the principal validity of the physical model. Numerical simulations and theoretical derivations illustrate the kinetic impact of the factors involved, i.e. the diffusion coefficient D, substrate donor concentration CS,D, substrate partition coefficient P, tissue thickness L and maximum metabolic rate Vmax, on drug permeation, with L having the strongest effect. In the steady state, the coefficient 2 α, i.e. the dimensionless ratio of the residence time term (L2/D) of a substrate in the tissue to the metabolic half-life term (CS,DP/2 Vmax), allows to estimate concentration gradients within the tissue and the extent of metabolism. High 2 α values represent practically complete metabolic cleavage upon penetration. Epidermis (∼40 μm thick) of stripped human skin and HaCaT sheets (∼10 μm) had 2α values of 43 and 2.7, respectively, indicating that intact Ala-MNA could only permeate HaCaT sheets, but not skin. Independent permeation experiments confirmed this outcome. This physical model may be applicable to other metabolizing tissues as well.