Mathematical models of skin permeability: An overview

Abstract

Mathematical models of skin permeability play an important role in various fields including prediction of transdermal drug delivery and assessment of dermal exposure to industrial chemicals. Extensive research has been performed over the last several decades to yield predictions of skin permeability to various molecules. These efforts include the development of empirical approaches such as quantitative structure-permeability relationships and porous pathway theories as well as the establishment of rigorous structure-based models. In addition to establishing the necessary mathematical framework to describe these models, efforts have also been dedicated to determining the key parameters that are required to use these models. This article provides an overview of various modeling approaches with respect to their advantages, limitations and future prospects.

Transdermal drug delivery: 30 + years of war and still fighting!

“…However, at least in theory, Equation (2) should be valid for any vehicle, which does not alter the SC barrier, or change the drug's solubility therein [11]. Assuming that water satisfies these criteria, the corresponding permeability coefficient (k p,w ) and aqueous solubility (C w,sat ) can then be used to estimate J max using Equation (2).…”

Dermic diffusion and stratum corneum: A state of the art review of mathematical models

“…Whereby, the maximum flux, Jmax, is given when the maximum solubility Ss of a solute in the stratum corneum is achieved, and the equation can be written as [30,36].…”

“…Traditionally, the skin, the SC and the diffusion phenomena have been studied associated with pure mathematical models, especially based on the Fick Equation [24][25][26][27][28][29][30][31][32]. A systematic analysis of these models implies a division based upon the particular approach and use of the Fick Law.…”

“…However, nonlinearity can arise as a result of solute-skin and solute-vehicle non-ideal interactions [30,37]. It is (Cv) more convenient to express concentrations in terms of the solute concentration in the vehicle and a partition coefficient, K, of the solute between the skin and the vehicle as follows:…”

“…Furthermore, mathematical models provide means to assess the likelihood of systemic exposure upon dermal contact with toxic chemicals. Mitragotri and collaborators have been applied of mathematical modelling to dermal risk assessment, privileging the use of permeability coefficients (Kp) and their model-based estimation [30].…”