title: Mathematical models for dermal drug absorption.
abstract: BACKGROUND
  Mathematical models of dermal transport offer the advantages of being much faster and less expensive than in vitro or in vivo studies. The number of methods used to create such models has been increasing rapidly, probably due to the steady rise in computational power. Although each of the various approaches has its own virtues and limitations, it may be difficult to decide which approach is best suited to address a given problem.
  
  
  METHODS
  Here we outline the basic ideas, drawbacks and advantages of compartmental and quantitative structure-activity relationship models, as well as of analytical and numerical approaches for solving the diffusion equation. Examples of special applications of the different approaches are given.
  
  
  CONCLUSIONS
  Although some models are sophisticated and might be used in future to predict transport through damaged or diseased skin, the comparatively low availability of suitable and accurate experimental data limits extensive usage of these models and their predictive accuracy. Due to the lack of experimental data, the possibility of validating mathematical models is limited.
authors.affiliation: a 1 Saarland University, Biopharmaceutics and Pharmaceutical Technology , 66123 Saarbruecken, Germany.|b 2 Scientific Consilience GmbH, Saarland University , Bldg. 30, 66123 Saarbruecken, Germany +49 681 302 71230 ; +49 681 302 64956 ; d.neumann@scientific-consilience.com.
authors.forename: Dominik
authors.initials: D
authors.lastname: Selzer
authors.affiliation: a 1 Saarland University, Biopharmaceutics and Pharmaceutical Technology , 66123 Saarbruecken, Germany.|b 2 Scientific Consilience GmbH, Saarland University , Bldg. 30, 66123 Saarbruecken, Germany +49 681 302 71230 ; +49 681 302 64956 ; d.neumann@scientific-consilience.com.
authors.forename: Dirk
authors.initials: D
authors.lastname: Neumann
authors.affiliation: c 3 Saarland University, Biopharmaceutics and Pharmaceutical Technology , 66123 Saarbruecken, Germany.
authors.forename: Ulrich F
authors.initials: UF
authors.lastname: Schaefer
mesh_terms: D000279:Administration, Cutaneous; D000818:Animals; D001692:Biological Transport; D006801:Humans; D008962:Models, Theoretical; D004364:Pharmaceutical Preparations / Q000008:administration & dosage* / Q000378:metabolism; D021281:Quantitative Structure-Activity Relationship; D012867:Skin / Q000378:metabolism / Q000473:pathology; D012869:Skin Absorption
chemical_list: D004364:Pharmaceutical Preparations
keywords: QSAR; analytical solution; diffusion equation; finite dose; infinite dose; limitations; numerical solution; pharmakokinetic models; skin penetration; skin permeation