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Publisher DOI: 10.1002/cnm.3675
Title: Global sensitivity analysis based on Gaussian-process metamodelling for complex biomechanical problems
Language: English
Authors: Wirthl, Barbara 
Brandstäter, Sebastian 
Nitzler, Jonas 
Schrefler, Bernhard A. 
Wall, Wolfgang A. 
Keywords: Gaussian-process metamodel; global sensitivity analysis; growth and remodelling; Sobol method; tumour growth
Issue Date: 22-Dec-2022
Publisher: Wiley
Source: International Journal for Numerical Methods in Biomedical Engineering 39 (3): e3675 (2023-03)
Abstract (english): 
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.
DOI: 10.15480/882.4847
ISSN: 2040-7939
Journal: International journal for numerical methods in biomedical engineering 
Institute: Kontinuums- und Werkstoffmechanik M-15 
Document Type: Article
Project: Vaskuläre Wachstums- und Umbildungsprozesse in Aneurysmen 
Experimentelle Untersuchung und mathematische Modellierung mechanisch gesteuerter Wachstums- und Umbauprozesse in postpubertären Schweineharnblasen 
License: CC BY 4.0 (Attribution) CC BY 4.0 (Attribution)
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