Traumatic brain injury represents one of the largest health crises worldwide. In the United States alone, the Centers for Disease Control and Prevention (CDC) indicates 2.87 million traumatic brain injuries resulting in emergency room visits, hospitalization, or death were recorded in 2014. The World Health Organization (WHO) places traumatic brain injury as the leading cause of death and disability for children and young adults, and estimates it to be involved in approximately half of all trauma-related deaths. The brain is likely one of the most mechanically complex materials known and, even after decades of study, robust estimates of material properties remain elusive. In order to predict brain response, develop tolerance curves, and apply injury criteria, the use of macroscopic computational brain models has become ubiquitous in the biomechanics community. There is growing concern that these models may not be sufficiently accurate across the range of scenarios for which they are often employed, and recent research across several groups has sought to quantify the variability both within and across computational brain models.

This dissertation identified deficiencies in current brain models across geometry, material formulation, numerical scheme, and experimental validation. In order to provide a tractable path forward for the biomechanics community, several of these deficiencies are addressed. In particular, the presence and propagation of shear nonlinearity has been underappreciated within the literature, despite wide acknowledgement of the importance of shear response in the brain for predicting and modeling injury. Recently it was experimentally demonstrated that the brain is capable of developing and propagating shear shock waves within physiological distances and kinematic inputs. This dissertation developed an optical method for visualizing and quantifying the propagation of nonlinear shear waves in spacetime. This study demonstrated the coalescence of shear waves during loading, a necessary precursor to shock formation. Furthermore, this dissertation presents and derives a numerical method for Eulerian nonlinear elasticity based on the conservation element solution element method, including a corresponding Mach-insensitive scheme, and eliminates several common deficiencies of traditional finite element –based brain models including large deformation instability, excessive hourglass energy, and locking phenomenon. Additionally, this dissertation demonstrated deficiencies with several common techniques used to scale responses to and from generic finite element brain models. This study recommended the cautious use of moment of inertia scaling or, preferably, subject-specific models and kinematic inputs.

The contributions in this dissertation further call into question many of the assumptions present across the mechanical computational brain modeling community. The present work both informs and supports future research with the goal of developing biofidelic brain injury models. These contributions improve the recognition of deficiencies in these models and their use to both understand and mitigate traumatic brain injury throughout the population. The presented recommendations and avenues for future work will aid researchers in obtaining accurate and robust solutions for the continued study of injurious brain mechanics.