Fluidity and Geometry 1 | Fluidity and Geometry 2
Similarly as during the sideways rotational head deceleration, the character of the Kelvin-Voigt (K-V) solutions with and without the falx cerebri remains alike when the head is translated sideways. Specifically, during the head deceleration, the velocity vector field mirrors the direction of the force, and the brain matter oscillations, which begin just before the head rests, reflect the shape of each subdomain (top panels). To the contrary, the brain geometry and topology impact the translational solutions of the nonlinear fluid TBI model in a different way than the rotational solutions. First, in the translational case, the turbulent flow associated with the nonlinear TBI model appears in the cross-section's interior regardless of whether the falx cerebri is present or not. Second, the turbulent flow's intensity is overall smaller than in the rotational case. Third, the flow begins to appear at a time when the head comes to rest and not when the deceleration is the largest as it happens during a head rotation (bottom panels). Thus, during sideways head translational decelerations the falx cerebri seems to mitigate the turbulent flow in comparison to the rotational case. This prediction is consistent with medical and experimental data showing that Diffuse Axonal Injuries predominately occur as a consequence of traumatic head rotations.