Applicability of the polynomial chaos expansion method for personalization of a cardiovascular pulse wave propagation model

Huberts, Wouter; Donders, Wouter P.; Delhaas, Tammo; Vosse, F.N. van de

doi:10.1002/cnm.2720

Cited by 17 publications

(41 citation statements)

References 50 publications

(70 reference statements)

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“…In the first step non-important model parameters are identified by using a Morris screening. In the second step the generalized polynomial chaos expansion method is applied to the reduced input space, resulting in a metamodel from which the sensitivity indices can be calculated straightforwardly [37]. …”

Section: Morris Screening and General Polynomial Chaos Expansionmentioning

confidence: 99%

Modeling regulation of vascular tone following muscle contraction: Model development, validation and global sensitivity analysis

Keijsers

Leguy

Narracott

et al. 2018

Journal of Computational Science

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Section: Morris Screening and General Polynomial Chaos Expansionmentioning

confidence: 99%

Modeling regulation of vascular tone following muscle contraction: Model development, validation and global sensitivity analysis

Keijsers

Leguy

Narracott

et al. 2018

Journal of Computational Science

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“…It estimates the coefficients for known orthogonal polynomial functions based on a response metric of interest according to a set of simulations. Thus, it creates a meta-model by encompassing the results space (Huberts et al, 2015). The response coefficients of the expansion can be computed by (1) spectral projection, which employs inner products and polynomial orthogonality properties, or (2) linear regression, called also point collocation, which extracts the coefficients that best match a set of output spaces by linear least square (Xiu, 2007; Eldred and Burkardt, 2009; Huberts et al, 2015).…”

Section: Uncertainty and Variability In Computational Models: Propagamentioning

confidence: 99%

“…Thus, it creates a meta-model by encompassing the results space (Huberts et al, 2015). The response coefficients of the expansion can be computed by (1) spectral projection, which employs inner products and polynomial orthogonality properties, or (2) linear regression, called also point collocation, which extracts the coefficients that best match a set of output spaces by linear least square (Xiu, 2007; Eldred and Burkardt, 2009; Huberts et al, 2015). In order to estimate its coefficients, spectral projection can use a simple sampling approach – known as non-intrusive spectral projection (Loeven et al, 2008; Abgrall et al, 2010).…”

Section: Uncertainty and Variability In Computational Models: Propagamentioning

confidence: 99%

“…The idea is to sample a discrete parameter space where the deterministic simulation is computed obtaining a set of responses (Abgrall et al, 2010), and the variable solution is reconstructed as a polynomial expansion. Huberts et al (2015) reported a better performance of the least-squares regression approach, compared to the spectral projection, in a cardiovascular pulse wave propagation model (Huberts et al, 2015). PC expansion can be also employed together with surrogate models, previously introduced as response surface method, to reduce the computational cost, for instance, creating the surrogate model in the form of the Hermite polynomials (Isukapalli et al, 1998).…”

Section: Uncertainty and Variability In Computational Models: Propagamentioning

confidence: 99%

“…Concretely, Eck et al (2015) evaluated how arterial stiffness influenced on backward-propagating pressure waves, using a previously developed model that employs PC expansion in order to set the parameters of the model to create a patient-specific predictive model (Huberts et al, 2015). Later, Eck et al (2016) provided a guideline for the uncertainty analysis in cardiovascular applications.…”

Section: Uncertainty and Variability In Computational Models: Propagamentioning

confidence: 99%

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Analysis of Uncertainty and Variability in Finite Element Computational Models for Biomedical Engineering: Characterization and Propagation

Mangado

Piella

Noailly

et al. 2016

Front. Bioeng. Biotechnol.

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Computational modeling has become a powerful tool in biomedical engineering thanks to its potential to simulate coupled systems. However, real parameters are usually not accurately known, and variability is inherent in living organisms. To cope with this, probabilistic tools, statistical analysis and stochastic approaches have been used. This article aims to review the analysis of uncertainty and variability in the context of finite element modeling in biomedical engineering. Characterization techniques and propagation methods are presented, as well as examples of their applications in biomedical finite element simulations. Uncertainty propagation methods, both non-intrusive and intrusive, are described. Finally, pros and cons of the different approaches and their use in the scientific community are presented. This leads us to identify future directions for research and methodological development of uncertainty modeling in biomedical engineering.

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Personalization of models with many model parameters: an efficient sensitivity analysis approach

Donders

Huberts

Vosse

et al. 2015

Numer Methods Biomed Eng

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Uncertainty quantification and global sensitivity analysis are indispensable for patient-specific applications of models that enhance diagnosis or aid decision-making. Variance-based sensitivity analysis methods, which apportion each fraction of the output uncertainty (variance) to the effects of individual input parameters or their interactions, are considered the gold standard. The variance portions are called the Sobol sensitivity indices and can be estimated by a Monte Carlo (MC) approach (e.g., Saltelli's method [1]) or by employing a metamodel (e.g., the (generalized) polynomial chaos expansion (gPCE) [2, 3]). All these methods require a large number of model evaluations when estimating the Sobol sensitivity indices for models with many parameters [4]. To reduce the computational cost, we introduce a two-step approach. In the first step, a subset of important parameters is identified for each output of interest using the screening method of Morris [5]. In the second step, a quantitative variance-based sensitivity analysis is performed using gPCE. Efficient sampling strategies are introduced to minimize the number of model runs required to obtain the sensitivity indices for models considering multiple outputs. The approach is tested using a model that was developed for predicting post-operative flows after creation of a vascular access for renal failure patients. We compare the sensitivity indices obtained with the novel two-step approach with those obtained from a reference analysis that applies Saltelli's MC method. The two-step approach was found to yield accurate estimates of the sensitivity indices at two orders of magnitude lower computational cost.

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Applicability of the polynomial chaos expansion method for personalization of a cardiovascular pulse wave propagation model

Cited by 17 publications

References 50 publications

Modeling regulation of vascular tone following muscle contraction: Model development, validation and global sensitivity analysis

Modeling regulation of vascular tone following muscle contraction: Model development, validation and global sensitivity analysis

Analysis of Uncertainty and Variability in Finite Element Computational Models for Biomedical Engineering: Characterization and Propagation

Personalization of models with many model parameters: an efficient sensitivity analysis approach

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