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 and falx cerebri during traumatic head rotations

Similarly as in forward rotational head decelerations, the linear Kelvin-Voigt (K-V) TBI model predicts that sideways rotational decelerations of the head about its center of mass trigger brain matter oscillations whose patterns reflect the shape of each of the horizontal cross-section's subdomains separated by the falx cerebri. Consequently, the strain norm is smoothly distributed in the subdomains' interiors, and assumes very high maximal values at the boundary (including the falx cerebri) and in the middle of each subdomain. However, in this case, the maximal strain norm and velocity values are approximately half as large as in a sagittal cross-section under a similar load (top panels). As in forward head rotations, the introduction of a variable shear wave velocity exponentially depending on the strain norm leads to complex oscillatory patterns with randomly distributed realistic maximal strain norm values (bottom panels). Thus, the impact of a nonlinear stress-strain relation on the scattered character of Diffuse Axonal Injuries seems to be independent of the position of the rotational axis. However, contrary to the nonlinearity reflecting the brain fluidity, a nonlinear stress-strain relation does not lead to asymmetric oscillatory patterns in the brain hemispheres.

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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 horizontal brain cross-section with the falx cerebri during the sideways counter-clockwise 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 horizontal cross-section

Strain norm

Velocity vector field

Velocity's magnitude

  Linear K-V TBI model

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Nonlinear stress-strain TBI model

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