期刊
APPLIED MATHEMATICAL MODELLING
卷 62, 期 -, 页码 86-102出版社
ELSEVIER SCIENCE INC
DOI: 10.1016/j.apm.2018.04.021
关键词
Monte Carlo; Uncertainty quantification; Sensitivity analysis; Hyperelastic models; Brain deformation; UFL expressions
资金
- European Research Council Starting Independent Research Grant (ERC Stg grant) [279578]
- Luxembourg
- Marie Curie Actions of the European Commission (FP7-COFUND) [6693582]
- Luxembourg National Research Fund [INTER/MOBILITY/14/8813215/CBM/Bordas]
- internal MOMENTUM project at the University of Luxembourg
We present a simple open-source semi-intrusive computational method to propagate uncertainties through hyperelastic models of soft tissues. The proposed method is up to two orders of magnitude faster than the standard Monte Carlo method. The material model of interest can be altered by adjusting few lines of (FEniCS) code. The method is able to (1) provide the user with statistical confidence intervals on quantities of practical interest, such as the displacement of a tumour or target site in an organ; (2) quantify the sensitivity of the response of the organ to the associated parameters of the material model. We exercise the approach on the determination of a confidence interval on the motion of a target in the brain. We also show that for the boundary conditions under consideration five parameters of the Ogden-Holzapfel-like model have negligible influence on the displacement of the target zone compared to the three most influential parameters. The benchmark problems and all associated data are made available as supplementary material. (C) 2018 Elsevier Inc. All rights reserved.
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