Several two-dimensional finite element models have been reported to simulate the human brain, animal brain, and physical surrogates. The model geometry ranged from midsagittal to coronal sections of the human and animal brains. Both elastic and viscoelastic materials have been considered to simulate the brain tissues. The loading conditions included direct and indirect or rotational impacts. Brain pressures and strains have been used as parameters for injury-potential assessment.
Shugar and Katona (1975) developed a plane strain model of a midsagittal section of the human head represented by a shell and fluid. They predicted a quadratic pressure gradient with the contrecoup pressure about twice as large as the coup pressure. Pressure contours were provided to visualize the pressure distribution in the brain. Khalil and Hubbard (1977) used the finite element method to model the head as an axisymmetric spherical fluid-filled shell. The model simulated the scalp, skull, and brain, including a multilayered skull. They found a linear pressure gradient in the fluid, with compression near the point of impact (coup) and tension on the opposite side (contrecoup). Pluche et al. (1985) proposed a two-dimensional finite element model to simulate a midsagittal section of the human head. The model included the skull, cerebrospinal fluid, and brain. After many computer runs were made by this model, the authors concluded that the neck restraint and skull deformation were important in head injury simulation.
A two-dimensional finite element model of a rhesus monkey head was proposed by Lee et al. (1987) to study the mechanism of traumatic subdural hematoma. The model was a rigid shell containing an elastic material that simulated the brain. The model predicted higher shear stress (hence strain) at the vertex where the parasagittal bridging veins were located. The authors deduced from the model prediction that subdural hematoma might have occurred. They concluded that for a Poisson's ratio of 0.475 for the brain material, both rotational and translational acceleration contributed equally to the deformation of the bridging vein (vertex in the model), and for a Poisson's ratio of 0.49, angular acceleration contributed more to the deformation of the bridging vein than translational acceleration.
Ueno et al. (1989) used a 2-D finite element model of a human brain based on a photograph of a sagittal section of the brain in conjunction with Lee et al.'s rhesus monkey model to scale experimental animal data (Abel et al., 1978) to the human level by a scaling law based on the mass of two models. Ueno et al. (1991) developed a 2-D ferret brain model subjected to a direct impact to the brain at a controlled velocity and stroke. A fairly good agreement between simulated and experimental pressure-time histories was reported.
Cheng et al. (1990) developed a two-dimensional finite element model representing a coronal section of the brain to study the diffuse axonal injury (DAI) problem. Model results were compared with experiments that were carried out at the University of Pennsylvania (Margulies, 1987). The effects of the skull/brain interface boundary, partitioning by a falxlike partition, load magnitude, brain size, and pulse duration on the levels of shear strain were studied by parametric variations. It was shown that the skull/brain interface and the geometry and partition of the brain had considerable influence on brain response to inertial loading.
In simulating the physical model of Margulies (1987), Lee (1990) developed two-dimensional full-cylinder and half-cylinder models. The models were subjected to an angular acceleration. The relationship between shear strains in the gel material that represented the brain and the linearly elastic properties of the brain was studied parametrically. The no-slip boundary condition at skull-brain interface was also investigated.
Ruan et al. (1991a) formulated three finite element models, an axisymmetric model, and a plane strain model of the coronal section of the human head, with and without the falx and cerebral tentorium, respectively, to study the side impact response of the head. The responses of the models were compared with previously published data and were found to be in good agreement. A parametric study addressed the effects of brain material properties on pressure response and the effects of the interior membrane on side impact response. The model prediction indicated that the cerebral membrane played an important role in the stresses produced in the brain.
A finite element model of the human head in the sagittal plane was devolved by Willinger et al. (1992) to perform a modal analysis. Based on the vibration mode of head model, the author concluded that a global vibration motion of the brain within the skull was responsible for the contrecoup injury mechanism.
A plane strain model of a parasagittal section of an average human head was created by Chu et al. (1994) to study the mechanisms of cerebral contusion. The model response was compared with previous experimental cadaver data (Nahum et al., 1977). The investigators found that the presence of a foramen magnum had only minor effects on the calculated pressure and believed that cerebral contusion was due to shear stress rather than pressure gradients in the brain.
Zhou et al. (1994) analyzed a 2-D porcine model to study the DAI problem. The model was used to simulate the porcine test performed at the University of Pennsylvanian (Ross et al., 1994). It was found that locations of high-shear strains predicted by the model matched the sites in the brain where DAI was found.
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