Biological Cybernetics

, Volume 113, Issue 1–2, pp 121–138 | Cite as

Parameter subset selection techniques for problems in mathematical biology

  • Christian Haargaard Olsen
  • Johnny T. Ottesen
  • Ralph C. Smith
  • Mette S. OlufsenEmail author
Original Article


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.


Parameter identifiability Parameter subset selection Parameter estimation Modeling 



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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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  • Christian Haargaard Olsen
    • 1
  • Johnny T. Ottesen
    • 2
  • Ralph C. Smith
    • 1
  • Mette S. Olufsen
    • 1
    Email author
  1. 1.Department of MathematicsNC State UniversityRaleighUSA
  2. 2.Department of Science and EnvironmentRoskilde UniversityRoskildeDenmark

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