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A physical modeling and theoretical simulation aspect for the simultaneous transport and metabolism of prodrug in viable skin were described to understand the influence of enzyme distribution and diffusion. The physical model was formulated assuming that the viable epidermis and dermis have distinct diffusional and metabolic characteristics and that the metabolic reaction in each layer follows a first-order kinetics. The differential equations were analytically solved, and the steady-state flux of prodrug into receiver and that of metabolite into receiver and donor and the total flux in forward (epidermis to dermis) and backward (dermis to epidermis) directions were derived. The flux of prodrug in the forward direction always equals that in the backward direction. The metabolite flux into receiver became transport direction-dependent when the diffusional characteristic of epidermis was different from that of dermis regardless of enzyme distribution. The metabolite flux into donor in the backward direction relative to that in the forward direction increased with increase of dermis/epidermis ratio of any parameters among metabolic rate constant, partition coefficient and diffusion coefficient of prodrug and metabolite. The difference of total flux between the 2 transport directions was caused by the difference in metabolic rate constant, partition coefficient and diffusion coefficient of prodrug between epidermis and dermis. The higher any parameters were for dermis, the higher was total flux in the backward direction.

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Influence of Enzyme Distribution and Diffusion on Permeation Profile of Prodrug through Viable Skin: Theoretical Aspects for Several Steady-State Fluxes in Two Transport Directions.