A Bayesian approach to selecting hyperelastic constitutive models of soft tissue

Abstract Hyperelastic constitutive models of soft tissue mechanical behavior are extensively used in applications like computer-aided surgery, injury modeling, etc. While numerous constitutive models have been proposed in the literature, an objective method is needed to select a parsimonious model that represents the experimental data well and has good predictive capability. This is an important problem given the large variability in the data inherent to soft tissue mechanical testing. In this work, we discuss a Bayesian approach to this problem based on Bayes factors. We propose a holistic framework for model selection, wherein we consider four different factors to reliably choose a parsimonious model from the candidate set of models. These are the qualitative fit of the model to the experimental data, evidence values, maximum likelihood values, and the landscape of the likelihood function. We consider three hyperelastic constitutive models that are widely used in soft tissue mechanics: Mooney–Rivlin, Ogden and exponential. Three sets of mechanical testing data from the literature for agarose hydrogel, bovine liver tissue, porcine brain tissue are used to calculate the model selection statistics. A nested sampling approach is used to evaluate the evidence integrals. In our results, we highlight the robustness of the proposed Bayesian approach to model selection compared to the likelihood ratio, and discuss the use of the four factors to draw a complete picture of the model selection problem.