Mathematical Modeling of Patch Transdermal Drug Delivery Systems

Abstract

We detail two different mathematical solution techniques for a system of first-order differential equations used to model the diffusion of a drug in a transdermal drug delivery system. We include derivation of the mathematical model from first principles involving conservation of mass and the differential form of the continuity equation, along with a description of patch delivery systems. The mathematical solution using eigenvalues and eigenvectors matches results using the Laplace transform method. A main contribution of this work is that an application of the model is presented using experimentally-obtained data associated with nicotine-patch delivery systems, and we obtain excellent agreement between the model and empirical data.