The use of mathematical modeling and simulation tools to study transdermal drug delivery systems

A closed-form mathematical solution was obtained for in vitro skin permeation of a drug dissolved in a vehicle. The solution to the mathematical model, which was described by Fickian diffusion equations and appropriate boundary conditions, was derived using Laplace transform methods. The Residue Theorem was applied to invert the equations from the Laplace domain into the time domain. The closed-form solution, obtained for the present percutaneous drug-delivery model, can be readily applied to many drug/vehicle systems to predict drug-release profiles, reducing the cost associated with extensive experimental procedures. Results showed that both axial and temporal variations in the concentration were significant in the skin. The time required for all of the drug to penetrate through the skin is less for a small dose than for a large dose.