Mathematical model to predict skin concentration after topical application of drugs

Skin permeation experiments have been broadly done since 1970s to 1980s as an evaluation method for transdermal drug delivery systems. In topically applied drug and cosmetic formulations, skin concentration of chemical compounds is more important than their skin permeations, because primary target site of the chemical compounds is skin surface or skin tissues. Furthermore, the direct pharmacological reaction of a metabolically stable drug that binds with specific receptors of known expression levels in an organ can be determined by Hill's equation. Nevertheless, little investigation was carried out on the test method of skin concentration after topically application of chemical compounds. Recently we investigated an estimating method of skin concentration of the chemical compounds from their skin permeation profiles. In the study, we took care of "3Rs" issues for animal experiments. We have proposed an equation which was capable to estimate animal skin concentration from permeation profile through the artificial membrane (silicone membrane) and animal skin. This new approach may allow the skin concentration of a drug to be predicted using Fick's second law of diffusion. The silicone membrane was found to be useful as an alternative membrane to animal skin for predicting skin concentration of chemical compounds, because an extremely excellent extrapolation to animal skin concentration was attained by calculation using the silicone membrane permeation data. In this chapter, we aimed to establish an accurate and convenient method for predicting the concentration profiles of drugs in the skin based on the skin permeation parameters of topically active drugs derived from steady-state skin permeation experiments.