On Mathematical Modeling of Dermal and Transdermal Drug Delivery

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Abstract
This paper deals with two extensions of diffusion models for the drug delivery process into human skin in order to give a more realistic approach. As one extension several penetrating substances formulated within a vehicle are considered for modeling the case of an applied drug and some penetration modifiers (enhancers and reducers, respectively). A coupling via concentration-dependent diffusivities between the diffusion equations of the involved substances is used to model the dependencies between them. Furthermore, a moving boundary problem for the diffusion equation of the drug delivery process is developed to describe the time-dependent maximum penetration depth of each penetrant marked by a movingboundary. On this basis a model is developed that can predict both the concentration profile and the position of the penetration boundary depending on time. Both concepts are described on a two-dimensional multilayered domain representing a cross section through human skin. The model equations are solved by exploiting a suitable numerical discretization method.