Parameter Estimation and Model Verification in Systems of Partial Differential Equations Applied to Transdermal Drug Delivery

K. Schittkowski: Report, Department of Mathematics, University of Bayreuth (1999)
Abstract: A numerical approach is described to determine parameters in a system of one-dimensional partial differential equations and coupled ordinary differential equations. The model allows arbitrary transition conditions between separate integration areas for functions and derivatives. The minimum least squares distance of the measured data from the solution of a system of differential equations at designated space values is computed. A special application model serves as a case study and is outlined in detail. We consider the diffusion of a substrate through cutaneous tissue, where metabolic reactions are included in form of Michaelis-Menten kinetics. The goal is to simulate transdermal drug delivery, where it is supposed that experimental data are available for substrate and metabolic fluxes. Numerical results are included to show a typical validation procedure, e.g., the identifiability of parameters, the satisfaction of a mass balance equation, and the stability of discretization procedure.


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