An improved diffusion/compartmental model for transdermal drug delivery from a matrix-type device

Predicting Viable Skin Concentration: Modelling the Subpapillary Plexus

The skin concentration of a substance after a topical application or exposure determines both local treatment outcomes and the dermal toxicity assessment of various products. However, quantifying the time course of those concentrations at skin effect sites, such as the viable epidermal, superficial dermis and appendages in humans is especially problematic in vivo, making physiologically based mathematical modelling an essential tool to meet this need. This work further develops our published physiologically based pharmacokinetic and COMSOL based dermal transport modelling by considering the impact of the superficial subpapillary dermal plexus, which we represent as two well stirred compartments. The work also studied the impact on dermal concentrations of subpapillary plexus size, depth, blood velocity and density of subpapillary plexus vessels. Sensitivity analyses are used to define the most important transport determinants of skin concentrations after topical application of a substance, with previously published results used to validate the resulting analyses. This resulting model describes the available experimental data better than previous models, especially at deeper dermal depths.

On mathematical modeling of dermal and transdermal drug delivery

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.