Utilizing multiple scale models to improve predictions of extra-axial hemorrhage in the immature piglet

Traumatic brain injury (TBI) is a leading cause of death and disability in the USA. To help understand and better predict TBI, researchers have developed complex finite element (FE) models of the head which incorporate many biological structures such as scalp, skull, meninges, brain (with gray/white matter differentiation), and vasculature. However, most models drastically simplify the membranes and substructures between the pia and arachnoid membranes. We hypothesize that substructures in the pia–arachnoid complex (PAC) contribute substantially to brain deformation following head rotation, and that when included in FE models accuracy of extra-axial hemorrhage prediction improves. To test these hypotheses, microscale FE models of the PAC were developed to span the variability of PAC substructure anatomy and regional density. The constitutive response of these models were then integrated into an existing macroscale FE model of the immature piglet brain to identify changes in cortical stress distribution and predictions of extra-axial hemorrhage (EAH). Incorporating regional variability of PAC substructures substantially altered the distribution of principal stress on the cortical surface of the brain compared to a uniform representation of the PAC. Simulations of 24 non-impact rapid head rotations in an immature piglet animal model resulted in improved accuracy of EAH prediction (to 94 % sensitivity, 100 % specificity), as well as a high accuracy in regional hemorrhage prediction (to 82–100 % sensitivity, 100 % specificity). We conclude that including a biofidelic PAC substructure variability in FE models of the head is essential for improved predictions of hemorrhage at the brain/skull interface.     

Global/local head models to analyse cerebral blood vessel rupture leading to ASDH and SAH

Blunt and rotational head impacts due to vehicular collisions, falls and contact sports cause relative motion between the brain and skull. This increases the normal and shear stresses in the (skull/brain) interface region consisting of cerebrospinal fluid (CSF) and subarachnoid space (SAS) trabeculae. The relative motion between the brain and skull can explain many types of traumatic brain injuries (TBI) including acute subdural hematomas (ASDH) and subarachnoid hemorrhage (SAH) which is caused by the rupture of bridging veins that transverse from the deep brain tissue to the superficial meningeal coverings. The complicated geometry of the SAS trabeculae makes it impossible to model all the details of the region. Investigators have compromised this layer with solid elements, which may lead to inaccurate results. In this paper, the failure of the cerebral blood vessels due to the head impacts have been investigated. This is accomplished through a global/local modelling approach. Two global models, namely a global solid model (GSM) of the skull/brain and a global fluid model (GFM) of the SAS/CSF, were constructed and were validated. The global models were subjected to two sets of impact loads (head injury criterion, HIC = 740 and 1044). The relative displacements between the brain and skull were determined from GSM. The CSF equivalent fluid pressure due to the impact loads were determined by the GFM. To locally study the mechanism of the injury, the relative displacement between the brain and skull along with the equivalent fluid pressure were implemented into a new local solid model (LSM). The strains of the cerebral blood vessels were determined from LSM. These values were compared with their relevant experimental ultimate strain values. The results showed an agreement with the experimental values indicating that the second impact (HIC = 1044) was strong enough to lead to severe injury. The global/local approach provides a reliable tool to study the cerebral blood vessel ruptures leading to ASDH and/or SAH.     

Prediction of brain deformations and risk of traumatic brain injury due to closed-head impact: quantitative analysis of the effects of boundary conditions and brain tissue constitutive model

In this study, we investigate the effects of modelling choices for the brain–skull interface (layers of tissues between the brain and skull that determine boundary conditions for the brain) and the constitutive model of brain parenchyma on the brain responses under violent impact as predicted using computational biomechanics model. We used the head/brain model from Total HUman Model for Safety (THUMS)—extensively validated finite element model of the human body that has been applied in numerous injury biomechanics studies. The computations were conducted using a well-established nonlinear explicit dynamics finite element code LS-DYNA. We employed four approaches for modelling the brain–skull interface and four constitutive models for the brain tissue in the numerical simulations of the experiments on post-mortem human subjects exposed to violent impacts reported in the literature. The brain–skull interface models included direct representation of the brain meninges and cerebrospinal fluid, outer brain surface rigidly attached to the skull, frictionless sliding contact between the brain and skull, and a layer of spring-type cohesive elements between the brain and skull. We considered Ogden hyperviscoelastic, Mooney–Rivlin hyperviscoelastic, neo–Hookean hyperviscoelastic and linear viscoelastic constitutive models of the brain tissue. Our study indicates that the predicted deformations within the brain and related brain injury criteria are strongly affected by both the approach of modelling the brain–skull interface and the constitutive model of the brain parenchyma tissues. The results suggest that accurate prediction of deformations within the brain and risk of brain injury due to violent impact using computational biomechanics models may require representation of the meninges and subarachnoidal space with cerebrospinal fluid in the model and application of hyperviscoelastic (preferably Ogden-type) constitutive model for the brain tissue.     

Influence of the lateral ventricles and irregular skull base on brain kinematics due to sagittal plane head rotation

Two-dimensional physical models of the human head were used to investigate how the lateral ventricles and irregular skull base influence kinematics in the medial brain during sagittal angular head dynamics. Silicone gel simulated the brain and was separatedfrom the surrounding skull vessel by paraffin that provided a slip interface between the gel and vessel. A humanlike skull base model (HSB) included a surrogate skull base mimicking the irregular geometry of the human. An HSBV model added an elliptical inclusion filled with liquid paraffin simulating the lateral ventricles to the HSB model. A simplified skull base model (SSBV) included ventricle substitute but approximated the anterior and middle cranial fossae by a flat and slightly angled surface. The models were exposed to 7600 rad/s2 peak angular acceleration with 6 ms pulse duration and 5 deg forced rotation. After 90 deg free rotation, the models were decelerated during 30 ms. Rigid body displacement, shear strain and principal strains were determined from high-speed video recorded trajectories of grid markers in the surrogate brains. Peak values of inferior brain surface displacement and strains were up to 10.9X (times) and 3.3X higher in SSBV than in HSBV. Peak strain was up to 2.7X higher in HSB than in HSBV. The results indicate that the irregular skull base protects nerves and vessels passing through the cranial floor by reducing brain displacement and that the intraventricular cerebrospinal fluid relieves strain in regions inferior and superior to the ventricles. The ventricles and irregular skull base are necessary in modeling head impact and understanding brain injury mechanisms.     

Temporal development of hippocampal cell death is dependent on tissue strain but not strain rate

Deformation of brain tissue in response to mechanical loading of the head is the root-cause of traumatic brain injury (TBI). Even below ultimate failure limits, deformation activates pathophysiological cascades resulting in delayed cell death. Injury response of soft tissues, such as the chest and spinal cord, is dependent on the product of deformation and velocity, a parameter termed the viscous criterion. We set out to test if hippocampal cell death could be predicted by a similar combination of strain and strain rate and if the viscous criterion was valid for hippocampus. Quantitative prediction of the brain's biological response to mechanical stimuli is difficult to achieve in animal models of TBI, so we utilized an in vitro model of TBI based on hippocampal slice cultures. We quantified the temporal development of cell death after precisely controlled deformations for 30 combinations of strain (0.05-0.50) and strain rate (0.1-50s(-1)) relevant to TBI. Loading conditions for a subset of cultures were verified by analysis of high-speed video. Cell death was found to be significantly dependent on time-post injury, on strain magnitude, and to a lesser extent, on anatomical region by a repeated-measures, three-way ANOVA. The responses of the CA1 and CA3 regions of the hippocampus were not statistically different in contrast to some in vivo TBI studies. Surprisingly, cell death was not dependent on strain rate leading us to conclude that the viscous criterion is not a valid predictor for hippocampal tissue injury. Given the large data set and extensive combinations of biomechanical parameters, predictive mathematical functions relating independent variables (strain, region, and time post-injury) to the resultant cell death were defined. These functions can be used as tolerance criteria to equip finite element models of TBI with the added capability to predict biological consequences.     

Inertia effects on characterization of dynamic response of brain tissue

Modeling and simulation of traumatic brain injury (TBI) resulted from collision or blast loading requires characterization of mechanical response over a wide range of loading rates under valid testing conditions. In this study, mechanical response of fresh bovine brain tissue was studied using the two modified Kolsky bar techniques. Radial deformation behavior of annular specimens, which are typically used to characterize the dynamic uniaxial compressive response of biological tissues, was examined using a modified Kolsky bar and a high speed camera to collect images while the specimen deforms at an axial strain rate of 2000s(-1). The high-speed images revealed inhomogeneous specimen deformation possibly brought about by radial inertia and causing a multi-axial stress state. To acquire valid stress-strain results that can be used to produce constitutive behavior of the soft materials, a novel torsion technique was developed to obtain pure shear response at dynamic loading rates. Experimental results show clear differences in the material response using the two methods. These results indicate that the previously demonstrated annular specimen geometry aimed at reducing inertia induced stress components for high rate soft materials uniaxial-compressive testing may still possess a significant component of radial inertia induced radial stress which consequently caused the observed inhomogeneous deformation in brain tissue test samples.     

A multi-body dynamics study on a weight-drop test of rat brain injury

Traumatic brain injury (TBI), induced by impact of an object with the head, is a major health problem worldwide. Rats are a well-established animal analogue for study of TBI and the weight-drop impact-acceleration (WDIA) method is a well-established model in rats for creating diffuse TBI, the most common form of TBI seen in humans. However, little is known of the biomechanics of the WDIA method and, to address this, we have developed a four-degrees-of-freedom multi-body mass-spring-damper model for the WDIA test in rats. An analytical expression of the maximum skull acceleration, one of the important head injury predictor, was derived and it shows that the maximum skull acceleration is proportional to the impact velocity but independent of the impactor mass. Furthermore, a dimensional analysis disclosed that the maximum force on the brain and maximum relative displacement between brain and skull are also linearly proportional to impact velocity. Additionally, the effects of the impactor mass were examined through a parametric study from the developed multi-body dynamics model. It was found that increasing impactor mass increased these two brain injury predictors.     

High rate shear strain of three-dimensional neural cell cultures: a new in vitro traumatic brain injury model

The fidelity of cell culture simulations of traumatic brain injury (TBI) that yield tolerance and mechanistic information relies on both the cellular models and mechanical insult parameters. We have designed and characterized an electro-mechanical cell shearing device in order to produce a controlled high strain rate injury (up to 0.50 strain, 30 s(-1) strain rate) that deforms three-dimensional (3-D) neural cultures (neurons or astrocytes in an extracellular matrix scaffold). Theoretical analysis revealed that these parameters generate a heterogeneous 3-D strain field throughout the cultures that is dependent on initial cell orientation within the matrix, resulting in various combinations of normal and shear strain. The ability to create a linear shear strain field over a range of input parameters was verified by tracking fluorescent microbeads in an acellular matrix during maximal displacement for a range of strains and strain rates. In addition, cell death was demonstrated in rat cortical astrocytes and neurons in response to high rate, high magnitude shear strain. Furthermore, cell response within the 3-D neuronal cultures depended on orientation, with higher predicted shear strain correlating with an increased loss of neurites, indicating that culture configuration may be an important factor in the mechanical, and hence cellular, response to traumatic insults. Collectively, these results suggest that differential responses exist within a 3-D culture subjected to mechanical insult, perhaps mimicking the in vivo environment, and that this new model can be used to investigate the complex cellular mechanisms associated with TBI.     

Mechanical Effects of Dynamic Binding between Tau Proteins on Microtubules during Axonal Injury

The viscoelastic nature of axons plays a key role in their selective vulnerability to damage in traumatic brain injury (TBI). Experimental studies have shown that although axons can tolerate 100% strain under slow loading rates, even strain as small as 5% can rupture microtubules (MTs) during the fast loading velocities relevant to TBI. Here, we developed a computational model to examine rate-dependent behavior related to dynamic interactions between MTs and the MT-associated protein tau under varying strains and strain rates. In the model, inverted pairs of tau proteins can dynamically cross-link parallel MTs via the respective MT-binding domain of each tau. The model also incorporates realistic thermodynamic breaking and reformation of the bonds between the connected tau proteins as they respond to mechanical stretch. With simulated stretch of the axon, the model shows that despite the highly dynamic nature of binding and unbinding events, under fast loading rates relevant to TBI, large tensile forces can be transmitted to the MTs that can lead to mechanical rupture of the MT cylinder, in agreement with experimental observations and as inferred in human TBI. In contrast, at slow loading rates, the progressive breaking and reformation of the bonds between the tau proteins facilitate the extension of axons up to ∼100% strain without any microstructural damage. The model also predicts that under fast loading rates, individual MTs detach from MT bundles via sequential breaking of the tau-tau bonds. Finally, the model demonstrates that longer MTs are more susceptible to mechanical rupture, whereas short MTs are more prone to detachment from the MT bundle, leading to disintegration of the axonal MT ultrastructure. Notably, the predictions from the model are in excellent agreement with the findings of the recent in vitro mechanical testing of micropatterned neuronal cultures.     

Infant skull and suture properties: measurements and implications for mechanisms of pediatric brain injury

The mechanical properties of the adult human skull are well documented, but little information is available for the infant skull. To determine the age-dependent changes in skull properties, we tested human and porcine infant cranial bone in three-point bending. The measurement of elastic modulus in the human and porcine infant cranial bone agrees with and extends previous published data [McPherson, G. K., and Kriewall, T. J. (1980), J. Biomech., 13, pp. 9-16] for human infant cranial bone. After confirming that the porcine and human cranial bone properties were comparable, additional tensile and three-point bending studies were conducted on porcine cranial bone and suture. Comparisons of the porcine infant data with previously published adult human data demonstrate that the elastic modulus, ultimate stress, and energy absorbed to failure increase, and the ultimate strain decreases with age for cranial bone. Likewise, we conclude that the elastic modulus, ultimate stress, and energy absorbed to failure increase with age for sutures. We constructed two finite element models of an idealized one-month old infant head, one with pediatric and the other adult skull properties, and subjected them to impact loading to investigate the contribution of the cranial bone properties on the intracranial tissue deformation pattern. The computational simulations demonstrate that the comparatively compliant skull and membranous suture properties of the infant brain case are associated with large cranial shape changes, and a more diffuse pattern of brain distortion than when the skull takes on adult properties. These studies are a fundamental initial step in predicting the unique mechanical response of the pediatric skull to traumatic loads associated with head injury and, thus, for defining head injury thresholds for children.     

Construction of a risk model through the fusion of experimental data and finite element modeling: Application to car crash-induced TBI

This article introduces a new approach for the construction of a risk model for the prediction of Traumatic Brain Injury (TBI) as a result of a car crash. The probability of TBI is assessed through the fusion of an experiment-based logistic regression risk model and a finite element (FE) simulation-based risk model. The proposed approach uses a multilevel framework which includes FE simulations of vehicle crashes with dummy and FE simulations of the human brain. The loading conditions derived from the crash simulations are transferred to the brain model thus allowing the calculation of injury metrics such as the Cumulative Strain Damage Measure (CSDM). The framework is used to propagate uncertainties and obtain probabilities of TBI based on the CSDM injury metric. The risk model from FE simulations is constructed from a support vector machine classifier, adaptive sampling, and Monte-Carlo simulations. An approach to compute the total probability of TBI, which combines the FE-based risk assessment as well as the risk prediction from the experiment-based logistic regression model is proposed. In contrast to previous published work, the proposed methodology includes the uncertainty of explicit parameters such as impact conditions (e.g., velocity, impact angle), and material properties of the brain model. This risk model can provide, for instance, the probability of TBI for a given assumed crash impact velocity.     

Immediate, but not delayed, microsurgical skull reconstruction exacerbates brain damage in experimental traumatic brain injury model

Moderate to severe traumatic brain injury (TBI) often results in malformations to the skull. Aesthetic surgical maneuvers may offer normalized skull structure, but inconsistent surgical closure of the skull area accompanies TBI. We examined whether wound closure by replacement of skull flap and bone wax would allow aesthetic reconstruction of the TBI-induced skull damage without causing any detrimental effects to the cortical tissue. Adult male Sprague-Dawley rats were subjected to TBI using the controlled cortical impact (CCI) injury model. Immediately after the TBI surgery, animals were randomly assigned to skull flap replacement with or without bone wax or no bone reconstruction, then were euthanized at five days post-TBI for pathological analyses. The skull reconstruction provided normalized gross bone architecture, but 2,3,5-triphenyltetrazolium chloride and hematoxylin and eosin staining results revealed larger cortical damage in these animals compared to those that underwent no surgical maneuver at all. Brain swelling accompanied TBI, especially the severe model, that could have relieved the intracranial pressure in those animals with no skull reconstruction. In contrast, the immediate skull reconstruction produced an upregulation of the edema marker aquaporin-4 staining, which likely prevented the therapeutic benefits of brain swelling and resulted in larger cortical infarcts. Interestingly, TBI animals introduced to a delay in skull reconstruction (i.e., 2 days post-TBI) showed significantly reduced edema and infarcts compared to those exposed to immediate skull reconstruction. That immediate, but not delayed, skull reconstruction may exacerbate TBI-induced cortical tissue damage warrants a careful consideration of aesthetic repair of the skull in TBI.     

Parametric analysis of the biomechanical response of head subjected to the primary blast loading – a data mining approach

Traumatic brain injury due to primary blast loading has become a signature injury in recent military conflicts and terrorist activities. Extensive experimental and computational investigations have been conducted to study the interrelationships between intracranial pressure response and intrinsic or ‘input’ parameters such as the head geometry and loading conditions. However, these relationships are very complicated and are usually implicit and ‘hidden’ in a large amount of simulation/test data. In this study, a data mining method is proposed to explore such underlying information from the numerical simulation results. The heads of different species are described as a highly simplified two-part (skull and brain) finite element model with varying geometric parameters. The parameters considered include peak incident pressure, skull thickness, brain radius and snout length. Their interrelationship and coupling effect are discovered by developing a decision tree based on the large simulation data-set. The results show that the proposed data-driven method is superior to the conventional linear regression method and is comparable to the nonlinear regression method. Considering its capability of exploring implicit information and the relatively simple relationships between response and input variables, the data mining method is considered to be a good tool for an in-depth understanding of the mechanisms of blast-induced brain injury. As a general method, this approach can also be applied to other nonlinear complex biomechanical systems.     

Physical model simulations of brain injury in the primate

Diffuse brain injuries resulting from non-impact rotational acceleration are investigated with the aid of physical models of the skull-brain structure. These models provide a unique insight into the relationship between the kinematics of head motion and the associated deformation of the surrogate brain material. Human and baboon skulls filled with optically transparent surrogate brain tissue are subjected to lateral rotations like those shown to produce diffuse injury to the deep white matter in the brain of the baboon. High-speed cinematography captures the deformations of the grids embedded within the surrogate brain tissue during the applied load. The overall deformation pattern is compared to the pathological portrait of diffuse brain injury as determined from animal studies and autopsy reports. Shear strain and pathology spatial distributions mirror each other. Load levels and resulting surrogate brain tissue deformations are related from one species to the other. Increased primate brain mass magnified the strain amplified without significantly altering the spatial distribution. An empirically-derived value for a critical shear strain associated with the onset of severe diffuse axonal injury in primates is determined, assuming constitutive similarity between baboon and human brain tissue. The primate skull physical model data and the critical shear strain associated with the threshold for severe diffuse axonal injury were used to scale data obtained from previous studies to man, and thus derive a diffuse axonal injury tolerance for rotational acceleration for humans.     

Mechanics of blast loading on the head models in the study of traumatic brain injury using experimental and computational approaches

Blast waves generated by improvised explosive devices can cause mild, moderate to severe traumatic brain injury in soldiers and civilians. To understand the interactions of blast waves on the head and brain and to identify the mechanisms of injury, compression-driven air shock tubes are extensively used in laboratory settings to simulate the field conditions. The overall goal of this effort is to understand the mechanics of blast wave–head interactions as the blast wave traverses the head/brain continuum. Toward this goal, surrogate head model is subjected to well-controlled blast wave profile in the shock tube environment, and the results are analyzed using combined experimental and numerical approaches. The validated numerical models are then used to investigate the spatiotemporal distribution of stresses and pressure in the human skull and brain. By detailing the results from a series of careful experiments and numerical simulations, this paper demonstrates that: (1) Geometry of the head governs the flow dynamics around the head which in turn determines the net mechanical load on the head. (2) Biomechanical loading of the brain is governed by direct wave transmission, structural deformations, and wave reflections from tissue–material interfaces. (3) Deformation and stress analysis of the skull and brain show that skull flexure and tissue cavitation are possible mechanisms of blast-induced traumatic brain injury.     

Ghrelin attenuates brain injury after traumatic brain injury and uncontrolled hemorrhagic shock in rats

Traumatic brain injury (TBI) and hemorrhagic shock often occur concomitantly due to multiple injuries. Gastrointestinal dysfunction occurs frequently in patients with TBI. However, whether alterations in the gastrointestinal system are involved in modulating neuronal damage and recovery after TBI is largely neglected. Ghrelin is a "gut-brain" hormone with multiple functions including antiinflammation and antiapoptosis. The purpose of this study was to determine whether ghrelin attenuates brain injury in a rat model of TBI and uncontrolled hemorrhage (UH). To study this, brain injury was induced by dropping a 450-g weight from 1.5 m onto a steel helmet attached to the skull of male adult rats. Immediately after TBI, a midline laparotomy was performed and both lumbar veins were isolated and severed at the junction with the vena cava. At 45 min after TBI/UH, ghrelin (4, 8 or 16 nmol/rat) or 1 mL normal saline (vehicle) was intravenously administered. Brain levels of TNF-α and IL-6, and cleaved PARP-1 levels in the cortex were measured at 4 h after TBI/UH. Beam balance test, forelimb placing test and hindlimb placing test were used to assess sensorimotor and reflex function. In additional groups of animals, ghrelin (16 nmol/rat) or vehicle was subcutaneously (s.c.) administered daily for 10 d after TBI/UH. The animals were monitored for 28 d to record body weight changes, neurological severity scale and survival. Our results showed that ghrelin downregulated brain levels of TNF-α and IL-6, reduced cortical levels of cleaved PARP-1, improved sensorimotor and reflex functions, and decreased mortality after TBI/UH. Thus, ghrelin has a great potential to be further developed as an effective resuscitation approach for the trauma victims with brain injury and severe blood loss.     

Deformation of the human brain induced by mild angular head acceleration

Deformation of the human brain was measured in tagged magnetic resonance images (MRI) obtained dynamically during angular acceleration of the head. This study was undertaken to provide quantitative experimental data to illuminate the mechanics of traumatic brain injury (TBI). Mild angular acceleration was imparted to the skull of a human volunteer inside an MR scanner, using a custom MR-compatible device to constrain motion. A grid of MR "tag" lines was applied to the MR images via spatial modulation of magnetization (SPAMM) in a fast gradient echo imaging sequence. Images of the moving brain were obtained dynamically by synchronizing the imaging process with the motion of the head. Deformation of the brain was characterized quantitatively via Lagrangian strain. Consistent patterns of radial-circumferential shear strain occur in the brain, similar to those observed in models of a viscoelastic gel cylinder subjected to angular acceleration. Strain fields in the brain, however, are clearly mediated by the effects of heterogeneity, divisions between regions of the brain (such as the central fissure and central sulcus) and the brain's tethering and suspension system, including the dura mater, falx cerebri, and tentorium membranes.     

Biomechanical analysis of fluid percussion model of brain injury

Fluid percussion injury (FPI) is a widely used experimental model for studying traumatic brain injury (TBI). However, little is known about how the brain mechanically responds to fluid impacts and how the mechanical pressures/strains of the brain correlate to subsequent brain damage for rodents during FPI. Hence, we developed a numerical approach to simulate FPI experiments on rats and characterize rat brain pressure/strain responses at a high resolution. A previous rat brain model was improved with a new hexahedral elements-based skull model and a new cerebrospinal fluid (CSF) layer. We validated the numerical model against experimentally measured pressures from FPI. Our results indicated that brain tissues under FPI experienced high pressures, which were slightly lower (10–20%) than input saline pressure. Interestingly, FPI was a mixed focus- and diffuse-type injury model with highest strains (12%) being concentrated in the ipsilateral cortex under the fluid-impact site and diffuse strains (5–10%) being spread to the entire brain, which was different from controlled cortical impact in which high strains decreased gradually away from the impact site.     

A finite element analysis of masticatory stress hypotheses

Understanding how the skull transmits and dissipates forces during feeding provides insights into the selective pressures that may have driven the evolution of primate skull morphology. Traditionally, researchers have interpreted masticatory biomechanics in terms of simple global loading regimes applied to simple shapes (i.e., bending in sagittal and frontal planes, dorsoventral shear, and torsion of beams and cylinders). This study uses finite element analysis to examine the extent to which these geometric models provide accurate strain predictions in the face and evaluate whether simple global loading regimes predict strains that approximate the craniofacial deformation pattern observed during mastication. Loading regimes, including those simulating peak loads during molar chewing and those approximating the global loading regimes, were applied to a previously validated finite element model (FEM) of a macaque (Macaca fascicularis) skull, and the resulting strain patterns were compared. When simple global loading regimes are applied to the FEM, the resulting strains do not match those predicted by simple geometric models, suggesting that these models fail to generate accurate predictions of facial strain. Of the four loading regimes tested, bending in the frontal plane most closely approximates strain patterns in the circumorbital region and lateral face, apparently due to masseter muscle forces acting on the zygomatic arches. However, these results indicate that no single simple global loading regime satisfactorily accounts for the strain pattern found in the validated FEM. Instead, we propose that FE models replace simple cranial models when interpreting bone strain data and formulating hypotheses about craniofacial biomechanics.     

The mechanical behaviour of brain tissue: large strain response and constitutive modelling

The non-linear mechanical behaviour of porcine brain tissue in large shear deformations is determined. An improved method for rotational shear experiments is used, producing an approximately homogeneous strain field and leading to an enhanced accuracy. Results from oscillatory shear experiments with a strain amplitude of 0.01 and frequencies ranging from 0.04 to 16 Hz are given. The immediate loss of structural integrity, due to large deformations, influencing the mechanical behaviour of brain tissue, at the time scale of loading, is investigated. No significant immediate mechanical damage is observed for these shear deformations up to strains of 0.45. Moreover, the material behaviour during complex loading histories (loading-unloading) is investigated. Stress relaxation experiments for strains up to 0.2 and constant strain rate experiments for shear rates from 0.01 to 1 s(-1) and strains up to 0.15 are presented. A new differential viscoelastic model is used to describe the mechanical response of brain tissue. The model is formulated in terms of a large strain viscoelastic framework and considers non-linear viscous deformations in combination with non-linear elastic behaviour. This constitutive model is readily applicable in three-dimensional head models in order to predict the mechanical response of the intra-cranial contents due to an impact.