Traumatic Brain Injury (TBI) Research

Brain Fluidity  |  Fluidity and Geometry  |  Stress-strain Relation  |  Resonance Effect  | Grey/White Boundary  

Grey/White Boundary 1  |  Grey/White Boundary 2

The role of the gray/white matter boundary during traumatic head rotations

Diffuse Axonal Injuries (DAI) are usually a consequence of a rapid head rotation. They are scattered in a point-wise manner mostly in the white matter, predominantly along its boundary with the gray matter. In the absence of strain, the velocity in the white matter cw equals approximately 1m/s whereas in the gray matter cg is up to four times larger. The linear viscoelastic Kelvin-Voigt (K-V) TBI model with identical shear wave velocities in the gray and the white matter, predicts that a sideways rotational acceleration of the head about its center of mass followed by the head's deceleration triggers smooth brain matter oscillations (left panels). If cg > cw the gray matter tends to oscillate in the opposite direction than the white matter shortly after the forcing stops (center panels). The rapid localized changes of the velocity’s direction and magnitude appearing in this case at the gray/white matter boundary are indicative of high strain values and hence of possible localizations of brain injuries. Thus, the linear K-V model can explain the DAI localization at the gray/white matter boundary but cannot replicate the scattered character of the injuries. The introduction of a shear wave velocity that exponentially depends on the strain norm, i.e., using the nonlinear stress-strain model without the material derivative, leads to a similar result. The main difference is that the ‘opposite’ oscillation in the gray matter appears earlier and the velocity magnitude is larger (right panels).

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Velocity vector field relative to the skull V(x,t), and velocity magnitude |V(x,t)| in a centrally located sagittal brain cross-section during the forward rotational deceleration of a head about its center of mass with BIC15=700

Brain matter viscosity and average tangential load values at a centrally located sagittal cross-section


Linear K-V model

cg = cw = 1m/s

Linear K-V model

cg = 3m/s, cw = 1m/s

Nonlinear stress-strain model

cg = 3m/s, cw = 1m/s, r =1.5





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