Adaptive Approach for Modelling Variability in Pharmacokinetics

  • Andrea Y. Weiße
  • Illia Horenko
  • Wilhelm Huisinga
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4216)

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.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Andrea Y. Weiße
    • 1
    • 2
  • Illia Horenko
    • 2
  • Wilhelm Huisinga
    • 1
    • 2
  1. 1.DFG Research Center MATHEON, and Department of Mathematics 
  2. 2.Informatics, Free University BerlinBerlinGermany

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