Adaptive Approach for Modelling Variability in Pharmacokinetics

Andrea Y. Weiße, Illia Horenko, Wilhelm Huisinga

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

We present an improved adaptive approach for studying systems of ODEs affected by parameter variability and state space uncertainty. Our approach is based on a reformulation of the ODE problem as a transport problem of a probability density describing the evolution of the ensemble of systems in time. The resulting multidimensional problem is solved by representing the probability density w.r.t. an adaptively chosen Galerkin ansatz space of Gaussian densities. Due to our improvements in adaptivity control, we substantially improved the overall performance of the original algorithm and moreover inherited to the numerical scheme the theoretical property that the number of Gaussian distributions remains constant for linear ODEs. We illustrate the approach in application to dynamical systems describing the pharmacokinetics of drugs and xenobiotics, where variability in physiological parameters is important to be considered.
Original languageEnglish
Title of host publicationComputational Life Sciences II
Subtitle of host publicationSecond International Symposium, CompLife 2006, Cambridge, UK, September 27-29, 2006, Proceedings
PublisherSpringer Berlin Heidelberg
Pages194-204
Number of pages11
Volume4216
ISBN (Electronic)978-3-540-45768-8
ISBN (Print)978-3-540-45767-1
DOIs
Publication statusPublished - 2006

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