Kinetics of finite dose absorption through skin 2: volatile compounds

A diffusion model to account for the disposition of an arbitrary dose of a (potentially) volatile compound applied to skin from a volatile vehicle is presented. In its most general form, the model allows for variable diffusivity of the permeant in the stratum corneum (SC) and must be solved numerically. However, for permeants having a constant diffusivity, absorption, and evaporation is characterized in terms of four dimensionless parameters-a reduced time tau, a fractional deposition depth in the SC f, a ratio of membrane capacity for the permeant to the applied dose beta, and a ratio of evaporative mass transfer coefficient to diffusive permeability chi. An important combination of these parameters arises as the reduced dose M(r) = (fbeta)(-1). Two cases are distinguished. In Case 1, corresponding to M(r) < or = 1, the dose is less than that required to saturate the upper layers of the SC, and the shape of the absorption and evaporation profiles is independent of the dose. Analytical solutions to Case 1 may be derived for arbitrary initial distributions of the permeant; the solution for a square wave is presented. In Case 2, corresponding to M(r) > 1, absorption and evaporation approach steady-state values as the dose is increased. Numerical evaluations of this behavior are shown. Limiting behavior for the case of a highly volatile solvent applied to skin is discussed. A companion paper discusses the application of the model to the absorption and evaporation of benzyl alcohol from human skin in vitro.