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Parameter Selection Methods in Inverse Problem Formulation

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Mathematical Modeling and Validation in Physiology

Part of the book series: Lecture Notes in Mathematics ((LNMBIOS,volume 2064))

Abstract

We discuss methods for a priori selection of parameters to be estimated in inverse problem formulations (such as Maximum Likelihood, Ordinary and Generalized Least Squares) for dynamical systems with numerous state variables and an even larger number of parameters. We illustrate the ideas with an in-host model for HIV dynamics which has been successfully validated with clinical data and used for prediction and a model for the reaction of the cardiovascular system to an ergometric workload.

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Acknowledgements

This research was supported in part by Grant Number R01AI071915-07 from the National Institute of Allergy and Infectious Diseases and in part by the Air Force Office of Scientific Research under grant number FA9550-09-1-0226. The content is solely the responsibility of the authors and does not necessarily represent the official views of the NIAID, the NIH or the AFOSR.

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Authors and Affiliations

  1. Center for Research in Scientific Computation and Center for Quantitative Sciences in Biomedicine, Department of Mathematics, North Carolina State University, Raleigh, NC, 27695-8212, USA

    H. T. Banks, Ariel CintrĂ³n-Arias & Franz Kappel

  2. Department of Mathematics and Statistics, East Tennessee State University, Johnson City, TN, 37614-0663, USA

    Ariel CintrĂ³n-Arias

  3. Institute for Mathematics and Scientific Computation, University of Graz, A8010, Graz, Austria

    Franz Kappel

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  1. H. T. Banks
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  2. Ariel CintrĂ³n-Arias
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  3. Franz Kappel
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Correspondence to H. T. Banks .

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Editors and Affiliations

  1. Mathematics and Scientific Computing, University of Graz, Heinrichstrasse 36, Graz, 8010, Austria

    Jerry J. Batzel

  2. College of Sciences, Department of Mathematics, King Saud University, King Khalid Road, Diriyah Campus, Riyadh, 11451, Saudi Arabia

    Mostafa Bachar

  3. Institute for Mathematics, and Scientific Computing, University of Graz, Heinrichstrasse 36, Graz, 8010, Austria

    Franz Kappel

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Banks, H.T., CintrĂ³n-Arias, A., Kappel, F. (2013). Parameter Selection Methods in Inverse Problem Formulation. In: Batzel, J., Bachar, M., Kappel, F. (eds) Mathematical Modeling and Validation in Physiology. Lecture Notes in Mathematics(), vol 2064. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-32882-4_3

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