Surrogate‐based Bayesian calibration of biomechanical models with isotropic material behavior. (4th March 2022)

• Record Type: Journal Article
• Authors: Römer, Ulrich; Liu, Jintian; Böl, Markus
• Is Part Of: International journal for numerical methods in biomedical engineering. Volume 38:Number 4(2022)
• Page Start: n/a
• Page End: n/a
• Publication Date: 2022-03-04
• Subjects: Bayesian calibration -- biomechanical models -- global sensitivity analysis -- iterative model error -- Karhunen‐Loève expansion -- surrogate models -- uncertainty quantification; Biomedical engineering -- Periodicals; Imaging systems in medicine -- Periodicals; Numerical analysis -- Periodicals; Engineering mathematics -- Periodicals; 610.28
• DOI: 10.1002/cnm.3575
• Languages: English
• ISSNs: 2040-7939

Abstract

Abstract: This work introduces a computational methodology to calibrate material models in biomechanical applications under uncertainty. We adopt a Bayesian approach, which estimates the probability distributions of hyperelastic material parameters, based on force‐strain measurements. We approximate the parametric biomechanical model by combining a reduced order representation of the force response with a Polynomial Chaos expansion. The surrogate model allows to employ sampling‐intensive Markov chain Monte Carlo methods and provides an efficient way to estimate (generalized) Sobol coefficients. We use a Sobol sensitivity analysis to assess the influence of material parameters and present an iterative procedure to quantify the accuracy of the surrogate model as additional uncertainty during Bayesian updating. The methodology is illustrated with three cases, tensile experiments on heat‐induced whey protein gel, indentation experiments for oocytes and a manufactured example. Real experimental data are used for the calibration. Abstract : This work introduces a computational method to calibrate isotropic biomechanical material models with Bayesian inference, surrogate modeling and the Karhunen‐Loève expansion. A reduction of the parameter number is achieved by ranking parameters with generalized Sobol coefficients. Surrogate modeling errors are quantified and corrected within the calibration framework.