The models cited above are concerned with two-dimensional idealizations. More geometrically complex humanlike models require three-dimensional finite element simulations. Ward and Thompson's model (1975) was one of the first finite element models that approximated the three-dimensional anatomy of the brain, including the falx cerebri and tentorium. The discretized mesh of the brain had 877 degrees of freedom. However, the skull was assumed to be rigid. The model results included the natural frequencies from the first to the sixth mode with and without the interior membrane present in the model. Subsequent models by Ward and others (Ward et al., 1980; Nahum et al., 1977, 1980) predicted the pattern of pressure variation in the brain and showed that the dura, falx cerebri, and tentorium were important structures affecting brain response. Model responses were compared with experimental cadaver data.
Later, Ward et al. (1978) proposed two brain models representing the baboon and the small primate (rhesus or cynomolgus monkey) brains in addition to the early human brain model (Ward and Thompson, 1975). The models included the internal folds of the falx and tentorium. Each model was subjected to the same skull acceleration in an attempt to establish response relationships between species. Model responses were compared with experimentally derived head injury data and correlated well with test results. It showed that the location and magnitude of the maximum stresses were different in humans and animals. This finding led to a conclusion that scaling the response between specimens is inadvisable.
Shugar (1977) developed a 3-D model that closely approximated the geometry of the human skull and brain. A three-layered skull and a homogeneous brain were modeled. His results included shell strain near the impact site and around the foramen magnum at the base of the skull. A nearly linear pressure gradient in the brain was predicted. No experimental data comparison was given by this model. A 3-D monkey brain model was also developed in the same study.
The model proposed by Hosey and Liu (1982) simulated a layered skull, dura, cerebrospinal fluid (CSF), brain, spinal cord, cervical column, and cerebral membranes: falx and tentorium. The model predicted that there were pressure differences across the membranes. However, because of the geometric complexity of the model, a detailed parametric study was not provided at the time the model was developed. Also, no model comparisons with experimental data were made although such data were available at that time.
With the development of faster computers and explicit, nonlinear, large deformation finite element techniques, several three-dimensional models have been reported. Tong et al. (1989) simulated the physical model tests conducted at the University of Pennsylvania. The physical model was a simple half-cylinder containing a brainlike gel and was designed to study diffuse axonal injury (DAI). The model was used to estimate the material properties of brainlike gel used in the physical model. A comparison of mesh deformation between the finite element model and physical model was given. Strain contours induced in the model with sliding boundary interface between the brain and skull and with friction levels of 0.07, 0.22, and 0.7 were given. The model showed significantly higher strains at the tip of the anatomic partition (presumably the falx).
More recently, DiMasi et al. (1991) developed a 3-D brain model to study diffuse axonal injury by assuming that DAI is related to brain strains. The model predicted shear and normal strains in the brain in response to head impact with an automotive A-pillar. Only a portion of the brain was modeled. It included the upper cerebral cortex with longitudinal fissure, which provided the distinctive sagittal and coronal geometric features and the surrounding dura including the falx. The dura and cortex were enclosed by a rigid skull to simulate direct-impact events with a padded and an unpadded A-pillar. Although the model could estimate brain strains in an impact event, it was insufficient to evaluate directional loading effects through simulated impacts simply because the skull was not modeled.
Mendis (1992) developed 3-D models of a baboon and a human head in an attempt to extrapolate animal data to the human.
A three-dimensional human head model simulating three-layer skull, cerebrospinal fluid, and brain was developed by Ruan et al. (1991b, 1992, 1994) to study in more detail the coup/contrecoup response in the brain. This model was validated against cadaveric intracranial pressure reported by Nahum et al. (1976, 1977). The model predicted higher skull stresses and negative intracranial pressures at the contrecoup site from occipital impacts than from frontal impacts. This finding afforded a biomechanical explanation of the clinical observation that occipital impacts cause more severe contrecoup injury than frontal impacts.
Also, the viscoelastic response of the human brain to impact has been investigated by Ruan et al. (1993a) using a 3-D finite element human head model. The model was developed based on their previous model (Ruan et al., 1992, 1994) by the addition of the scalp, dura mater, and falx partition. Model meshes were also refined in order to improve model accuracy. The viscoelastic behavior of the brain in shear was characterized by a short- and long-term shear modulus and a time decay factor. The values of these parameters were scaled from the literature (Galford and McElhaney, 1970). The study showed that the viscoelasticity of the brain had an insignificant effect on intracranial pressure. It also showed a complicated shear stress distribution in the brain. Unlike pressure, the shear stress time history did not follow that of the impact force. When the impact force was reduced to zero at the end of the pulse, the shear stress was not reduced. Using the same model, Ruan et al. (1993b) studied the human head response to different impacts (impact locations, impactor mass, and velocity) by having a rigid cylinder impact the head model directly. The study demonstrated the variation of human head response to different impacts, and the HIC (head injury criterion) was found to be generally proportional to the impact force, intrac-ranial pressure, linear acceleration, and skull stress. The authors pointed out that the HIC appeared to be a reasonable index of injury severity in a direct-impact situation.
Zhou et al. (1994) developed a 3-D porcine finite element model and compared the dynamic response of this model with Ruan et al.'s human model. The porcine model showed a similar pressure and shear response to that of the human. A three-dimensional human head model including the skull, brain (white and gray matter), CSF, ventricles, falx cerebri, tentorium cerebelli, and bridging veins was proposed by Zhou et al. (1995). The new features of this model include differentiation of the white and gray matter of the brain and the modeling of the bridging veins. The authors found that higher shear stresses were produced in the white matter and hence DAI can occur in areas of high shear.
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