Parameter estimation in a mathematical model fur substrate diffusion in a metabolically active cutaneous tissue

K. Schittkowski: Progress in Optimization, X. Yang et al. eds., Kluwer Academic Publishers, 329 - 342 (2000)
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 is outlined in detail, that describes the diffusion of a substrate through cutaneous tissue. Metabolic reactions are included in form of Michaelis-Menten kinetics. The goal is to model transdermal drug delivery, where it is supposed that experimental data are available for substrate and metabolic fluxes. Some numerical results are included to show the efficiency of the implemented algorithms.

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