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.