Parameter
Identification and Model Verification in Systems of
Partial Differential Equations Applied to Transdermal Drug Delivery
K. Schittkowski: Mathematics and Computers in Simulation, Vol. 79, 521-538
Abstract: The purpose of this paper is to present some numerical tools
which facilitate the interpretation of simulation or parameter estimation
results
and which allow to compute optimal experimental designs. They help to validate
mathematical models describing the dynamical behavior of a biological, chemical,
or pharmaceutical system, without requiring a priory knowledge about the
physical or chemical background. Although the ideas are quite general, we will
concentrate our attention to systems 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 sys\-tem of partial 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
based on laboratory data to show typical steps of a model validation procedure,
i.e., the interpretation of confidence intervals, the compliance with physical
laws, the identification and elimination of redundant model parameters, the
computation of optimum experimental designs and the determination of a minimum
set of experimental time values.
To download a preprint, click here: pe_valid.pdf