The four series of MPEG movies, which can be downloaded below, illustrate the transitions of planar solutions of the linear Kelvin-Voigt (K-V) and the nonlinear fluid TBI models (with c=1m/s and v=0.01m²/s) when a horizontal or a vertical rotational axis is gradually moved from the head's center of mass to infinity (translation). The movies depict the 0.3s long temporal evolution of the brain matter velocity relative to the skull using Curved-Vector-Field plots. All solutions are obtained under the same load (lasting for 0.072s) with the following periodic average tangential acceleration/deceleration corresponding to the critical value of the universal Brain Injury Criterion (BIC): BIC₃₆=HIC₃₆=1000:

When the load is applied, rotational solutions in each series transition smoothly into the translational solution. This result supports our approach to use the transfer of the same amount of energy from the skull to the brain through a narrow region along a given brain cross-section to extend the translational HIC scale to arbitrary planar rotations. In all scenarios presented, the brain matter continues to oscillate after the head comes to rest. However, in the nonlinear model the oscillations are more pronounced and more randomly scattered in the brain compared to the linear model.

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Linear K-V TBI model

1. Downloadable MPEGs of solutions in a centrally located sagittal brain cross-section. Forward head rotation about a horizontal axis located at: the center of mass (MPEG 2.24MB) , the skull's base (MPEG 2.40MB), the neck (MPEG 2.24 MB), the abdomen (MPEG 2.12MB). Forward head translation (MPEG 1.92MB).

2. Downloadable MPEGs of solutions in a centrally located horizontal brain cross-section with the falx cerebri. Sideways counter-clockwise head rotation about a vertical axis located: at the center of mass (MPEG 1.63MB), at the left ear (MPEG 2.32MB), to the left of the ear at a distance equal to the head radius (MPEG 2.14MB), to the left of the ear at a distance equal to the head diameter (MPEG 2.10MB). Forward head translation (MPEG 2.04MB).

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Nonlinear fluid TBI model

3. Downloadable MPEGs of solutions in a centrally located sagittal brain cross-section. Forward head rotation about a horizontal axis located at: the center of mass (MPEG 5.50MB) , the skull's base (MPEG 2.93MB), the neck (MPEG 3.56MB), the abdomen (MPEG 3.55MB). Forward head translation (MPEG 3.19MB).

4. Downloadable MPEGs of solutions in a centrally located horizontal brain cross-section with the falx cerebri. Sideways counter-clockwise head rotation about a vertical axis located: at the center of mass (MPEG 5.88MB), at the left ear (MPEG 6.52MB), to the left of the ear at a distance equal to the head radius (MPEG 5.83MB), to the left of the ear at a distance equal to the head diameter (MPEG 6.55MB). Forward head translation (MPEG 7.71MB).

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MPEG viewing suggestion