Traumatic Brain Injury (TBI) Research

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

Stress-strain Relation 1  |  Stress-strain Relation 2

The role of a nonlinear stress-strain relation during traumatic head rotations

The linear Kelvin-Voigt (K-V) TBI model, which assumes a constant shear wave velocity, predicts that a forward rotational deceleration of the head about its center of mass triggers brain matter oscillations whose patterns reflect the shape of the skull's sagittal cross-section. Consequently, the strain norm is smoothly distributed in the cross-section's interior and assumes very high maximal values at the boundary and in the middle of the cross-section (top panels). The introduction of a shear wave velocity that exponentially depends on the strain norm, which reflects the stiffening of the brain matter under strain implied by experiments, leads to smaller velocity magnitudes and much more complex oscillatory patterns. As a result, the norm maxima assume more realistic values and their distribution becomes more random (bottom panels). Thus, a nonlinear stress-strain relation may also be one of the reasons why Diffuse Axonal Injuries are scattered.

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Strain norm N(x,t), 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 characteristics and average tangential load values at a centrally located sagittal cross-section

Strain norm

Velocity vector field

Velocity magnitude

Linear K-V TBI model

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Nonlinear stress-strain TBI model

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