A Bayesian method with nonlinear noise model to calibrate constitutive parameters of soft tissue

The measured mechanical responses of soft tissue exhibit large variability and errors, especially for the softest brain tissue, while calibrating its constitutive parameters in a deterministic way remains a common practice. Here we implement a Bayesian method considering the nonlinear noise model to calibrate constitutive parameters of brain tissue. A probability model is first developed based on the measured experimental data, likelihood function, and prior function, from which the posterior distributions of model parameters are formulated. The likelihood function considers the nonlinear behaviors of the constitutive response and noise distribution of the experimentally measured data. Meanwhile, the prior predictive distribution is computed to check the probability model preliminarily. Secondly, the Markov Chain Monte Carlo (MCMC) method is used to compute the posterior distributions of model parameters, enabling assessment of parameter uncertainty, correlation, and model calibration error. Finally, the posterior predictive distributions of the overall response, constitutive response, and noise response are computed to validate the probabilistic model, all of which are consistent with the corresponding data. Furthermore, the effect of the prior distribution, experimental data, and noise model on posterior distribution is studied. Our study provides a general approach to calibrating constitutive parameters of soft tissue despite errors and large variability in experimental data.