A Bayesian model calibration framework to evaluate brain tissue characterization experiments

Abstract

A Bayesian model calibration framework is implemented to determine the posterior parameter distributions of a hyper-viscoelastic constitutive model using mechanical testing data of brain tissue. Despite the fact that brain tissue exhibits large property variability and uncertainty, least squares model calibration remains common practice. It is shown that through Bayesian calibration, the capability of an experimental design to identify parameter values can be quantitatively evaluated. A large range of experimental designs (i.e., loading modes) are considered, including rate dependent, cyclic loading through compression, shear, and tension, as well as shear and compression relaxation loading. An implementation of the nested sampling algorithm is utilized to compute the joint posterior probability distributions of the constitutive parameters based on the data considered. The joint probability distribution of the parameters enables assessment of parameter sensitivity, uncertainty, correlation, and model calibration error as a function of experimental design. By calibrating simultaneously to numerous combinations of loading modes, redundancy in loading mode as well as parameter convergence can be evaluated based on model calibration error and parameter variability. The results of this study verify that the inclusion of more loading modes in the calibration increases the accuracy of parameter identification, while only one or two loading modes may provide almost no information for identifying certain parameters.