Parameter subset selection techniques for problems in mathematical biology

Christian Haargaard-Olsen, Johnny T. Ottesen, Ralf Smith, Mette Olufsen

Research output: Contribution to journalJournal articleResearch

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.
Original languageEnglish
JournalBiological Cybernetics
Volume113
Issue number1-2
Pages (from-to)121-138
ISSN0340-1200
DOIs
Publication statusPublished - 2019

Keywords

  • Modeling
  • Parameter estimation
  • Parameter identifiability
  • Parameter subset selection

Cite this

Haargaard-Olsen, Christian ; Ottesen, Johnny T. ; Smith, Ralf ; Olufsen, Mette. / Parameter subset selection techniques for problems in mathematical biology. In: Biological Cybernetics. 2019 ; Vol. 113, No. 1-2. pp. 121-138.
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Parameter subset selection techniques for problems in mathematical biology. / Haargaard-Olsen, Christian; Ottesen, Johnny T.; Smith, Ralf; Olufsen, Mette.

In: Biological Cybernetics, Vol. 113, No. 1-2, 2019, p. 121-138.

Research output: Contribution to journalJournal articleResearch

TY - JOUR

T1 - Parameter subset selection techniques for problems in mathematical biology

AU - Haargaard-Olsen, Christian

AU - Ottesen, Johnny T.

AU - Smith, Ralf

AU - Olufsen, Mette

PY - 2019

Y1 - 2019

N2 - 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.

AB - 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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