Models
Due to the geometric and constitutive complexities of the problem, early models of brain concussion consisted of simple spheres or oval shells filled with some fluid, whose mechanical properties were close to that of the brain (Ruan et al., 1991). One of the problems that all models of brain concussion face is the lack of accurate data about the brain mechanical properties. Some authors have found that the dynamic bulk modulus of the human brain is approximately that of water. This may be due to the high water content of the brain. Therefore, employing water as the fluid model of the brain tissue seems a reasonable approach (Huang et al., 2000).
The absence of accurate experimental methods to measure brain strain and stress during sudden accelerations of the head, as during an impact, has promoted the use of numerical tools to improve the understanding of the subjacent physics of the phenomenon. In particular, finite element models have been used recently to perform biomechanical analysis and provide data that otherwise cannot be measured experimentally. This approach allows one to consider more complex and realistic geometries of the human head. Conditions where the head was directly impacted have been investigated (e.g., Ruan et al., 1991; Voo et al., 1996; Kumaresan and Radhakrishnan, 1996) as well as conditions where no impact was present and the head was suddenly accelerated (e.g., Huang et al., 2000). Ruan et al. (1991) investigated the influence of the effects of the membranes and the mechanical properties of the skull, brain, and membrane on the dynamic response of the brain during a side impact by using several two-dimensional finite elements models. Kumaresan et al. (1996) investigated the influence of the partitioning membranes of the brain and the neck in head injury by using three-dimensional finite element analysis. Huang et al. (2000) concluded that, in the absence of impact when the head rotates forward and backward, a negative pressure develops in the countercoup region. However, the pressure is not low enough to form bubbles and the posterior cavitations. On the other hand, their results point to the shear strain theory as the more suitable theory to describe the concussion phenomenon in the absence of direct impact. Recent finite element efforts include those of Zhang et al. (2001a) and Takhounts et al. (2003). In the first one, a finite element model of the head has been developed to study direct and indirect impacts. This model includes facial bone details and the damage properties of materials, which enables simulation of bone fracture.
Hong et al. (2007) have studied the mechanism of brain contusion by separating the problem into rigid body and brain deformation dynamics. The authors concluded that for low-speed impacts, the mechanisms of brain injury are governed by the rigid-body displacement within the skull. Conversely, at higher impact speeds, it is the deformation of the brain, which plays a primary role.
King et al. (2003) investigated the relative importance of angular and translational accelerations in the development of brain injury. They employed a helmeted model that was subjected to different head collisions. It was established that although the translational acceleration was reduced by the use of the helmet, the angular acceleration was not. Since helmets have been shown to be a factor in reducing brain injuries, their results may suggest that it is actually the translational acceleration of the brain that may be the main cause of brain damage.
