title: On mathematical modeling of dermal and transdermal drug delivery.
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.
authors.affiliation: the Department of Mathematics and Computer Sciences, University of Halle, D-06099 Halle, Germany.
authors.forename: R
authors.initials: R
authors.lastname: Manitz
authors.forename: W
authors.initials: W
authors.lastname: Lucht
authors.forename: K
authors.initials: K
authors.lastname: Strehmel
authors.forename: R
authors.initials: R
authors.lastname: Weiner
authors.forename: R
authors.initials: R
authors.lastname: Neubert
mesh_terms: D000279:Administration, Cutaneous; D003198:Computer Simulation; D006801:Humans; D008432:Mathematical Computing; D008954:Models, Biological; D010599:Pharmacokinetics; D012867:Skin / Q000033:anatomy & histology / Q000378:metabolism; D012869:Skin Absorption