Traumatic brain injury (TBI) is a debilitating injury that affects more than 1.4 million people in the United States each year. Of the incidences of TBI, diffuse axonal injury (DAI) accounts for the second largest percentage of deaths. DAI is caused by inertial loads to the head, and it is characterized by damage to neurons. Despite the extensive research on DAI, the injury mechanisms associated with the pathology are still poorly understood. The crucial link between the inertial forces to the head at the macroscale and the resulting damage at the cellular level has yet to be explained. An integral step to understanding this coupling between mechanical forces and the functional damage of neurons is the development of an analytical model that accurately represents the mechanics of brain deformation under inertial loads. It has been noted in clinical and experimental studies that the most common injury location of DAI is within the deep white matter of the brain. Structures such as the splenium of the corpus callosum are cited as being highly susceptible to damage [1]. Although numerous brain tissue models have been proposed, few models account for the anisotropic nature of white matter in the brain. As a first step in developing an anisotropic model for white matter, the effect of the invariant terms in a strain energy function for white matter is analyzed.

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