Mathematical modeling of transdermal drug-delivery systems: Analysis and applications

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. In this work, the developed solution was used to assess the relative impact of different physicochemical parameters on the drug-release profiles. Such parameters include the vehicle-skin partition coefficient for the drug k_m, the thickness of applied medicament l_a and the diffusion through the vehicle D₁. Results showed that the rate of drug delivery decreased with an increase in the vehicle-skin partition coefficient. The time required for all of the drug to penetrate through the skin is less for a small dose than for a large dose.