Past Event: Oden Institute Seminar

A Bayesian Approach to Model Calibration, Selection & Surrogate Modeling: Application to Traumatic Brain Injury

Kumar Vemaganti, Department of Mechanical & Materials Engineering, University of Cincinnati

Abstract

Computational models of the head and brain are extensively used to study traumatic brain injuries (TBI). Simulations of TBI are complex and computationally challenging because of (a) the large uncertainty in the material testing data and the resulting uncertainty in the constitutive model parameters, (b) high strain rates and the short time scales of the impact loading, and (c) the complex geometry of the human brain model.We propose a Bayesian framework for parameter estimation and constitutive model selection based on the parallel nested Monte Carlo sampling algorithm MULTINEST. Four different factors are used 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. This approach provides a robust and efficient alternative to Markov chain Monte Carlo methods to sample from multi-modal distributions and to efficiently calculate the evidence integral. Brain tissue in general has a non-linear visco-hyperelastic constitutive response. In this study, the long-term viscoelasticity, the short-term viscoelasticity, and hyperelasticity contributions to the mechanical response of the brain tissue are modeled separately. The distributions of the corresponding parameters are obtained using the nested sampling-based Bayesian framework. This constitutive model is then implemented into the finite element code LS-DYNA. Traumatic brain injury caused by impact loading from a vehicle crash is simulated using the SIMon finite element model of the human head. A maximum principal strain-based injury criterion is used to assess the severity of the brain injury. The uncertainty in the material model parameters is non-intrusively propagated to the injury criterion using a Bayesian Gaussian process surrogate of the finite element model to avoid computationally expensive simulations. This enables us to calculate the probability that an injury tolerance is reached for a given impact loading. This probabilistic method can be used to further simulate injuries and calculate various injury criteria with high fidelity.