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Parameter subset selection techniques for problems in mathematical biology

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Abstract

Patient-specific models for diagnostics and treatment planning require reliable parameter estimation and model predictions. Mathematical models of physiological systems are often formulated as systems of nonlinear ordinary differential equations with many parameters and few options for measuring all state variables. Consequently, it can be difficult to determine which parameters can reliably be estimated from available data. This investigation highlights pitfalls associated with practical parameter identifiability and subset selection. The latter refer to the process associated with selecting a subset of parameters that can be identified uniquely by parameter estimation protocols. The methods will be demonstrated using five examples of increasing complexity, as well as with patient-specific model predicting arterial blood pressure. This study demonstrates that methods based on local sensitivities are preferable in terms of computational cost and model fit when good initial parameter values are available, but that global methods should be considered when initial parameter value is not known or poorly understood. For global sensitivity analysis, Morris screening provides results in terms of parameter sensitivity ranking at a much lower computational cost.

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Acknowledgements

Olsen and Olufsen was supported in part by the National Science Foundation (Grant NSF-DMS 1022688 and NSF-DMS 1557761) as well as the Virtual Physiological Rat Project funded by the National Institute of General Medical Sciences (NIH-NIGMS P50 GM094503).

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Authors and Affiliations

  1. Department of Mathematics, NC State University, Raleigh, NC, 27695, USA

    Christian Haargaard Olsen, Ralph C. Smith & Mette S. Olufsen

  2. Department of Science and Environment, Roskilde University, 4000, Roskilde, Denmark

    Johnny T. Ottesen

Authors
  1. Christian Haargaard Olsen
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  2. Johnny T. Ottesen
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  3. Ralph C. Smith
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  4. Mette S. Olufsen
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Corresponding author

Correspondence to Mette S. Olufsen.

Additional information

Communicated by Peter J. Thomas.

This article belongs to the Special Issue on Control Theory in Biology and Medicine. It derived from a workshop at the Mathematical Biosciences Institute, Ohio State University, Columbus, OH, USA.

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Olsen, C.H., Ottesen, J.T., Smith, R.C. et al. Parameter subset selection techniques for problems in mathematical biology. Biol Cybern 113, 121–138 (2019). https://doi.org/10.1007/s00422-018-0784-8

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  • DOI: https://doi.org/10.1007/s00422-018-0784-8

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