Fluidity and Geometry
The role of the brain fluidity during traumatic head rotations and translations
The linear Kelvin-Voigt (K-V) TBI model, which treats the brain as a viscoelastic solid, predicts
that during rotational or translational head accelerations and decelerations, the velocity vector field initially 'reacts to'
the rotational or translational character of the force. However, after a few milliseconds, the brain elasticity triggers brain matter
oscillations whose multi-vortex circular patterns adjust to the skull's shape. In particular, during the forward head deceleration,
the oscillatory patterns accommodate to the shape of the sagittal cross-sections (top panels). The dark to light
shading of the curved velocity vectors indicates the oscillation direction.
The introduction of the nonlinear material temporal derivative into the K-V PDEs, which reflects
the brain fluidity, leads to much more complex turbulent oscillatory patterns whose vortices are
randomly scattered (bottom panels). The turbulent flow
usually results in high values of the strain norm. Thus, the brain
fluidity may be one of the reasons why Diffuse Axonal Injuries are scattered.
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