INTRODUCTION
The presence of sports related concussions and minor traumatic brain injuries has increase in frequency over the past decade. Where a possible reason for the increase is improved diagnosis methods and general awareness, the overall improvement in helmet safety technology has seemingly not had a significant effect on reducing these concussion symptoms. Short term effects of traumatic brain injuries are known to lead to impairment in cognitive functions. This study looks to provide a quantitative predictor for how the direction of head impact leads to a biomechanical response in the deep brain, more specifically the corpus callosum (CC) and how it affects cognitive aptitude. The CC contains the greatest density of fibril tract connections between the cerebral hemispheres of the brain making it the primary neural connector and an important factor for human cognitive function. The existence of previous literature with defined diffuse axonal injury (DAI) thresholds allows for a comparative study and the ability to use a mathematical approach as a preliminary predictor of injury.
METHODS
Using Diffusion Tensor Imaging (DTI) a computed tractography finite element model of the fibril network (Essen et al 2013) was created and inserted into the Global Human Body Model Consortium (GHBMC) head and brain model. Different impact loading cases (n= 4) were simulated with similar time-history impact curves (5k rad/s^2 at 10 ms) to recreate artificial rotational impact scenarios. The four cases presented in this study are: flexion, extension, rotation and lateral bend. The results of these mathematical simulations were then analyzed quantitatively for both magnitude and location of greatest maximum principal strain (MPS) as well as largest Cumulative Strain Damage Measure (CSDM). 
RESULTS
The GHBMC and DTI fibril network of the CC finite element model showed that the peak MPS was largest in the lateral bend (0.256) that was followed by extension (0.221) and flexion (0.206) and finally rotation (0.192). The Fibril networks had opposing rankings with flexion and extension having an MPS of 0.475 followed by lateral bend at 0.31 and rotation at 0.225. These results were then further analyzed using CSDM to determine more in depth, the extent of the injury. 
DISCUSSION AND CONCLUSION
These results help set up the quantitative assessment of the cognitive effects of brain injury, based on previous literature thresholds. The use of computer simulation to both diagnose and identify areas of the brain injured through reverse processing the qualitative symptoms of cognitive tests is a novel approach with many clinical and industry advantages. The future goal of this study is to provide the link between current cognitive tests and the areas affected by traumatic brain trauma while providing a new tool for safety manufactures to quantify the effectiveness of safety equipment designed to protect the brain.

Predicting cognitive impairment following traumatic brain injury: A mathematical approach