Fluidity and Geometry 1 | Fluidity and Geometry 2
In the nonlinear fluid TBI model, the brain geometry and topology impact the character of the solutions to a much greater extent than in the Kelvin-Voigt (K-V) linear solid body model. For instance, during the sideways rotational deceleration of a head about its center of mass, both models predict that the corresponding vector fields reflect the elliptic shape of the skull's horizontal cross-section without the falx cerebri, and the turbulent flow characteristic for the solutions of the nonlinear model appears only near the minor imperfections of the elliptical shape of the cross-section (left panels). The introduction of the falx cerebri leads to dramatic differences between the predictions of both models (right panels). The nonlinear model predicts not only more turbulent flow but also quite a different distribution of the vector field in each part of the disconnected domain. The latter indicates that its solutions are very sensitive to the asymmetry of the domain's boundary. In fact, the extensive turbulent flow appearing in the front of the sagittal cross-section during a forward head rotation is due to the concave shape of this cross-section. Thus, the specific localization of Diffuse Axonal Injuries may strongly depend on the traumatic motion's characteristics.