An estimated 3.8 million concussions are believed to occur annually in the United States, resulting in a serious concern for helmet and automotive safety manufacturers. Tissue-level deformation is believed to be the primary mechanism for concussion;​ however, existing dummies used in helmet and crash testing do not directly measure brain strain. Instead, brain injury assessments are made using head kinematics.

Kinematic brain injury criteria utilize a metric which relates head impact severity to a mathematical function of the velocity and/or acceleration components of translational and/or rotational head motion. Existing metrics used in helmet and crash testing are based on translational kinematics which were developed for skull fracture assessment;​ however, rotational motion of the head is believed to be the primary mechanism for brain strain. Although numerous rotational metrics have been proposed, many were developed using empirical methods based on limited datasets, and do not represent the mechanical principles that govern brain deformation. As a result, this renders most rotational brain injury criteria ineffective for application in a broad range of head impacts.

This dissertation presents the development of two new metrics for brain injury criteria. These metrics were developed through several steps:​ First, existing kinematicbased metrics were compared with finite element (FE) model brain strains from simulations of head kinematics from football impacts and car crash tests. Correlations between brain strain and rotational metrics were highest, while translational metrics were least correlative. The Brain Injury Criterion (BrIC), an angular velocity-based metric proposed for government crashworthiness assessments had the highest overall correlation with FE strains;​ however, its performance was limited in longer duration events. Results from this study suggest that brain injury metrics use only on rotational head kinematics.

Based on the correlation analysis, a parametric study was performed using idealized head motions and an FE model to study physics of brain deformation to rotational head motion. Results from this study revealed a resonance behavior of the brain, which was adequately described using a second order system:​ For short duration head motions, brain deformation was proportional to maximum angular velocity, for motions of long duration brain deformation was proportional to maximum angular acceleration. For head motions near system resonance (30 – 40) ms, where typical head impacts occur, brain deformations depended on both velocity and acceleration. These results explain limitations with existing rotational metrics, and were used as a basis for formulating improved metrics.

The first metric presented in this dissertation is the Universal Brain Injury Criterion (UBrIC). UBrIC was formulated based on deformation response from a second order system and uses the magnitudes of head angular velocity and acceleration to predict strainbased brain injury indicators (MPS and CSDM). Relative to existing metrics, UBrIC was a better predictor of brain strains using the football and crash test data;​ R² = 0.93 with MPS for UBrIC vs. 0.84 for BrIC. In addition to UBrIC, a MB model analog for was developed to predict brains strains under more complicated head motions. Relative to the BrIC and UBrIC, the MB model had higher correlation with MPS overall (R² = 0.97) and performed better in nearly every impact condition assessed. This dissertation provides metrics for improved prediction of brain strains in a broad range of head impact conditions including those in football and car crashes. These metrics can be used in helmet and crash safety evaluations, and can discriminate the efficacy of improved countermeasures.