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The mechanism of movement of the molecules during the percutaneous application of a finite dose of a drug to the surface of the skin and across the skin has been modeled by using diffusion equations, such as Fick's second law of diffusion (Kubota et al., 2002, Simon and Loney, 2003). This process is shown diagrammatically on Fig. 8.26. The drug first diffuses through the medium of delivery of thickness, L_{m}. The concentration of the drug, C_{m}, through the medium of delivery may be modeled by:
Subsequently, the drug enters and diffuses through the skin membrane of thickness, L_{s}. The concentration, C_{s}, in the skin is modeled by
where D_{m} is the effective drug diffusivity in the medium of delivery, and D~ is the diffusivity in the skin. These two equations are coupled at the boundary between the medium of delivery and the skin. The drug is finally absorbed in the receptor cell.
Solve the above equations simultaneously, with the following initial and boundary conditions:
where K_{m} is the medium-skin partition coefficient, and K_{cl} is the clearance per unit area of the drug per unit concentration excess at skin-receptor boundary. The constants to be used in this problem are:
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