## Parameter Identification in Transdermal Systems (in German)

M. Dobmann, K. Schittkowski, M. Wolf: Report, Dept. of Mathematics, University of Bayreuth (1996)

**Abstract:**
A numerical approach is described to determine parameters in a
system of one-dimensional parabolic 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.
The numerical method of lines is used to discretize the partial differential
equation with respect to polynomials of arbitrary even order, and
to transform the original system into a sequence of ordinary
differential equations, that can be solved then by any available
ODE-solver. A special application model is outlined, i.e. the
identification of parameters in a system describing
the diffusion of a substance through human skin.
The model simulates the generation of a metabolite by
a Michaelis-Menten-kinetic.
Some numerical results are included to show the efficiency of the
implemented algorithm.