Quantifying the uncertainty in a hyperelastic soft tissue model with stochastic parameters

Abstract

• A general approach for the stochastic finite element analysis of soft tissue deformation is presented. • Sensitivity derivative Monte Carlo method to propagate uncertainty through hyperelastic models with stochastic parameters. • The proposed method is up to two orders of magnitude faster than the standard Monte Carlo approach. • The method is able to provide the user with statistical results on quantities of practical interest. • We applied the approach to a simple academic example and to the stochastic deformation of a brain. 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.