An evaluation of mathematical models for predicting skin permeability

A number of mathematical models have been proposed for predicting skin permeability, mostly empirical and very few are deterministic. Early empirical models use simple lipophilicity parameters. The recent trend is to use more complicated molecular structure descriptors. There has been much debate on which models best predict skin permeability. This article evaluates various mathematical models using a comprehensive experimental dataset of skin permeability for 124 chemical compounds compiled from various sources. Of the seven models compared, the deterministic model of Mitragotri gives the best prediction. The simple quantitative structure permeability relationships (QSPR) model of Potts and Guy gives the second best prediction. The two models have many features in common. Both assume the lipid matrix as the pathway of transdermal permeation. Both use octanol-water partition coefficient and molecular size. Even the mathematical formulae are similar. All other empirical QSPR models that use more complicated molecular structure descriptors fail to provide satisfactory prediction. The molecular structure descriptors in the more complicated QSPR models are empirically related to skin permeation. The mechanism on how these descriptors affect transdermal permeation is not clear. Mathematically it is an ill-defined approach to use many colinearly related parameters rather than fewer independent parameters in multi-linear regression. (C) 2007 Wiley-Liss, Inc. and the American Pharmacists Association J Pharm Sci 97:584-598, 2008.