Mathematical Model for Estimating Skin Permeation Parameters

Mathematical modelling of drug transport to the skin is useful to gain fundamental understanding on the drug permeation mechanism for formulation design. For this purpose, the diffusion equation from Fick’s law of diffusion is commonly used to model the transport of drug through the skin. In this paper, this diffusion equation was solved using Laplace transform with appropriate initial and boundary conditions representing infinite dosing. The solution was then inverted numerically using the Weeks method and used to fit drug experimental data for the estimation of the apparent partition coefficient, P1 and apparent diffusion coefficient, P2. To test this model, particularly on the best curve fitting algorithm to use, the estimated P1 and P2 values were compared to those reported in literature. Three curve fitting methods, namely simple loop, particle swarm optimization (PSO) and non-linear least squares (NLS), were evaluated. The result suggests that PSO and NLS can provide P1 and P2 estimates that are comparable to those reported in the literature.