Modeling of diffusion and concurrent metabolism in cutaneous tissue
P. Boderke, K. Schittkowski, M. Wolf, H.P. Merkle: Journal of Theoretical Biology, Vol. 204, No. 3, 393-407 (2000)
In this study a mathematical model has been derived, which describes the complex
interplay of mass transfer and saturable metabolism in living tissue.
It considers diffusion and simultaneous non-linear Michaelis-Menten metabolism
of a drug within the metabolizing layer. Numerically generated substrate concentration
profiles within the tissue and resulting substrate fluxes through the tissue are
presented for various values of the diffusion coefficient, substrate partition
coefficient, tissue thickness and maximum metabolic rate to illustrate
their relative effect on the overall kinetics of drug permeation. The results of the numerical computations and theoretical derivations demonstrate
that all of the parameters have an influence on the permeation and concurrent
metabolism of intact substrate, tissue thickness having the strongest effect.
The ratio of the Michaelis constant Km to the drug concentration in the first
layer of the tissue will also influence the extent of metabolism.
To verify the model, permeation experiments with the peptidomimetic model
compound Alanine-4-methoxy-naphtylamine through HaCaT cell sheets, a
substitute for the viable human epidermis, are performed and compared to
numerically generated data. Parameters used for those calculations were
validated in independent experiments. Experimental data are in good
agreement with the numerical predictions. It is shown theoretically
and experimentally that the viable epidermis can represent an effective
metabolic barrier to block the permeation of labile drugs.
The physical model may be helpful to understand this barrier and the
complex processes involved. It also provides a rational basis for
implications to dermal and transdermal drug delivery.
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