Global sensitivity analysis based on Gaussian-process metamodelling for complex biomechanical problems

Barbara Wirthl, Sebastian Brandstaeter, Jonas Nitzler, Bernhard A. Schrefler, Wolfgang A. Wall

Research output: Contribution to journalArticlepeer-review

4 Scopus citations


Biomechanical models often need to describe very complex systems, organs or diseases, and hence also include a large number of parameters. One of the attractive features of physics-based models is that in those models (most) parameters have a clear physical meaning. Nevertheless, the determination of these parameters is often very elaborate and costly and shows a large scatter within the population. Hence, it is essential to identify the most important parameters (worth the effort) for a particular problem at hand. In order to distinguish parameters which have a significant influence on a specific model output from non-influential parameters, we use sensitivity analysis, in particular the Sobol method as a global variance-based method. However, the Sobol method requires a large number of model evaluations, which is prohibitive for computationally expensive models. We therefore employ Gaussian processes as a metamodel for the underlying full model. Metamodelling introduces further uncertainty, which we also quantify. We demonstrate the approach by applying it to two different problems: nanoparticle-mediated drug delivery in a complex, multiphase tumour-growth model, and arterial growth and remodelling. Even relatively small numbers of evaluations of the full model suffice to identify the influential parameters in both cases and to separate them from non-influential parameters. The approach also allows the quantification of higher-order interaction effects. We thus show that a variance-based global sensitivity analysis is feasible for complex, computationally expensive biomechanical models. Different aspects of sensitivity analysis are covered including a transparent declaration of the uncertainties involved in the estimation process. Such a global sensitivity analysis not only helps to massively reduce costs for experimental determination of parameters but is also highly beneficial for inverse analysis of such complex models.

Original languageEnglish (US)
Article numbere3675
JournalInternational Journal for Numerical Methods in Biomedical Engineering
Issue number3
StatePublished - Mar 2023


  • Gaussian-process metamodel
  • Sobol method
  • global sensitivity analysis
  • growth and remodelling
  • tumour growth
  • Models, Theoretical
  • Biomechanical Phenomena

ASJC Scopus subject areas

  • Software
  • Applied Mathematics
  • Molecular Biology
  • Biomedical Engineering
  • Computational Theory and Mathematics
  • Modeling and Simulation


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