A two-fiber anisotropic constitutive model of human brain with intravoxel heterogeneity of fiber orientation using diffusion spectrum imaging (DSI)

Sports-related concussion is a major public health problem in the United States that is estimated to occur in 1.6-3.8 million individuals annually, and is particularly common in football. Despite the significance and growing concerns about the potential long-term consequences of concussion, its biomechanical mechanisms are not fully understood. Since 1970's computational head modeling has proved to be an efficient tool for establishment of health injury criteria and studies on head injury mitigation. One important step in the computational modeling of the human head is to develop the mathematical material models (constitutive models) for the tissue. There have been many attempts to develop an accurate constitutive model for brain tissue. Recent experimental studies have highlighted the significant influence of axonal fibers on the non-linear and anisotropic behavior of brain tissue. Tractography based on diffusion tensor imaging (DTI) has been used in various previous studies to develop a constitutive model for human brain by including the anisotropic properties. Though DTI provides a macro scale information about the axonal fibers in the brain, it cannot directly describe multiple fiber orientations within a single voxel. To address this limitation within the DTI tractography, Diffusion Spectrum imaging (DSI), a variant of Diffusion Weighted Imaging, is used. DSI is generally used in deriving connectome sets and is sensitive to intravoxel heterogeneities of fiber orientation in diffusion direction caused by crossing fiber tracts and thus allowing for more accurate mapping of axonal trajectories than other diffusion methods. Thus more accurate constitutive models can be developed from the structural information about the human brain using DSI. This paper extends, the anisotropic constitutive models developed previously, for two family of fibers which will be useful in the computational modeling of the human brain using DSI.