Surrogate-based Bayesian calibration of biomechanical models with isotropic material behavior

Area of Science:

• Biomechanics
• Computational Modeling
• Materials Science

Background:

• Accurate material models are crucial for biomechanical simulations.
• Uncertainty quantification is essential for reliable predictions in biological systems.
• Traditional calibration methods can be computationally expensive.

Purpose of the Study:

• To develop a computational methodology for calibrating biomechanical material models under uncertainty.
• To efficiently estimate probability distributions of hyperelastic material parameters.
• To assess the influence of material parameters and quantify surrogate model accuracy.

Main Methods:

• Bayesian approach for parameter estimation.
• Reduced order modeling combined with Polynomial Chaos expansion for surrogate model creation.
• Markov chain Monte Carlo (MCMC) methods for sampling-intensive computations.
• Sobol sensitivity analysis for parameter influence assessment.

Main Results:

• A surrogate model approximating the parametric biomechanical model was developed.
• Efficient estimation of (generalized) Sobol coefficients was achieved.
• An iterative procedure for quantifying surrogate model accuracy was presented.
• The methodology was successfully illustrated using tensile tests on protein gel, oocyte indentation, and a manufactured example.

Conclusions:

• The proposed computational methodology enables robust calibration of biomechanical material models under uncertainty.
• The integration of surrogate modeling with Bayesian inference offers an efficient approach for parameter estimation and sensitivity analysis.
• The study demonstrates the practical applicability of the method using real experimental data.