BASIC MATHEMATICAL PRINCIPLES IN SKIN PERMEATION

Abstract

Sound knowledge of the underlying mathematical principles of membrane transport is essential if we are to expand our understanding of how membrane barriers fulfill their function and how we can alter their properties to our advantage. The subject of the mathematics of diffusion are enough to fill entire books, but in this chapter we have attempted to pick out those mathematical solutions and descriptions that are both commonly used and most appropriate in the field of percutaneous absorption. It is the purpose of this work to attempt to present these equations in a manner that will enable readers to apply them to real numbers generated in their laboratories. At its simplest and most ideal a membrane can be described as a homogeneous slab of an inert material, with a finite and uniform thickness. This is a convenient theoretical picture and, although it is somewhat removed from the reality of such complex biological membranes as the stratum corneum, it is a logical model with which to begin when attempting to construct any sort of mathematical treatise of the process of membrane permeation.