Modelling the Brain for Rotational Loading: Shear Effects and Other Complications

Abstract

This study considers modelling the brain due to rotation of the skull where, at lower frequencies, the shear property of the material is important. Investigations reported here cover the effect of elastic and viscoelastic (lossy) cerebral material, the effect of the Falx protruding into the brain, the gap around the Falx and the brain filled with non viscous fluid in addition to different models of the Falx with bending or membrane stiffness. Analytical benchmark formulations are also described for the simple 2D plane strain in a cylinder produced by a half-sine rotation on the outer periphery which allows numerical (Finite Element) models to be validated. The results show the importance of the material properties, duration of loading and amplitude of loading as well as the influence of the partition. The results are shown for predicted maximum Principal strains in the models, as this may well be indicative of whether damage of the brain tissue occurs.     

Influence of angular acceleration-deceleration pulse shapes on regional brain strains

Recognizing the association of angular loading with brain injuries and inconsistency in previous studies in the application of the biphasic loads to animal, physical, and experimental models, the present study examined the role of the acceleration-deceleration pulse shapes on region-specific strains. An experimentally validated two-dimensional finite element model representing the adult male human head was used. The model simulated the skull and falx as a linear elastic material, cerebrospinal fluid as a hydrodynamic material, and cerebrum as a linear viscoelastic material. The angular loading matrix consisted coronal plane rotation about a center of rotation that was acceleration-only (4.5 ms duration, 7.8 krad/s/s peak), deceleration-only (20 ms, 1.4 krad/s/s peak), acceleration-deceleration, and deceleration-acceleration pulses. Both biphasic pulses had peaks separated by intervals ranging from 0 to 25 ms. Principal strains were determined at the corpus callosum, base of the postcentral sulcus, and cerebral cortex of the parietal lobe. The cerebrum was divided into 17 regions and peak values of average maximum principal strains were determined. In all simulations, the corpus callosum responded with the highest strains. Strains were the least under all simulations in the lower parietal lobes. In all regions peak strains were the same for both monophase pulses suggesting that the angular velocity may be a better metric than peak acceleration or deceleration. In contrast, for the biphasic pulse, peak strains were region- and pulse-shape specific. Peak values were lower in both biphasic pulses when there was no time separation between the pulses than the corresponding monophase pulse. Increasing separation time intervals increased strains, albeit non-uniformly. Acceleration followed by deceleration pulse produced greater strains in all regions than the other form of biphasic pulse. Thus, pulse shape appears to have an effect on regional strains in the brain.     

Mechanical properties of brain tissue in tension

This paper contains experimental results of in vitro, uniaxial tension of swine brain tissue in finite deformation as well as proposes a new hyper-viscoelastic constitutive model for the brain tissue. The experimental results obtained for two loading velocities, corresponding to strain rates of 0.64 and 0.64 x 10(-2)s(-1), are presented. We believe that these are the first ever experiments of this kind. The applied strain rates were similar to those applied in our previous study, focused on explaining brain tissue properties in compression. The stress-strain curves are convex downward for all extension rates. The tissue response stiffened as the loading speed increased, indicating a strong stress-strain rate dependence. Swine brain tissue was found to be considerably softer in extension than in compression. Previously proposed in the literature brain tissue constitutive models, developed based on experimental data collected in compression are shown to be inadequate to explain tissue behaviour in tension. A new, non-linear, viscoelastic model based on the generalisation of the Ogden strain energy hyper-elastic constitutive equation is proposed. The new model accounts well for brain tissue deformation behaviour in both tension and compression (natural strain in <-0.3,0.2>) for strain rates ranging over five orders of magnitude.     

Constitutive modelling of brain tissue: Experiment and theory

Recent developments in computer-integrated and robot-aided surgery—in particular, the emergence of automatic surgical tools and robots—as well as advances in virtual reality techniques, call for closer examination of the mechanical properties of very soft tissues (such as brain, liver, kidney, etc.). The ultimate goal of our research into the biomechanics of these tissues is the development of corresponding, realistic mathematical models. This paper contains experimental results of in vitro, uniaxial, unconfined compression of swine brain tissue and discusses a single-phase, non-linear, viscoelastic tissue model. The experimental results obtained for three loading velocities, ranging over five orders of magnitude, are presented. The applied strain rates have been much lower than those applied in previous studies, focused on injury modelling. The stress-strain curves are concave upward for all compression rates containing no linear portion from which a meaningful elastic modulus might be determined. The tissue response stiffened as the loading speed increased, indicating a strong stress-strain rate dependence. The use of the single-phase model is recommended for applications in registration, surgical operation planning and training systems as well as a control system of an image-guided surgical robot. The material constants for the brain tissue are evaluated. Agreement between the proposed theoretical model and experiment is good for compression levels reaching 30% and for loading velocities varying over five orders of magnitude.     

Constitutive model for brain tissue under finite compression

While advances in computational models of mechanical phenomena have made it possible to simulate dynamically complex problems in biomechanics, accurate material models for soft tissues, particularly brain tissue, have proven to be very challenging. Most studies in the literature on material properties of brain tissue are performed in shear loading and very few tackle the behavior of brain in compression. In this study, a viscoelastic constitutive model of bovine brain tissue under finite step-and-hold uniaxial compression with 10 s(-1) ramp rate and 20 s hold time has been developed. The assumption of quasi-linear viscoelasticity (QLV) was validated for strain levels of up to 35%. A generalized Rivlin model was used for the isochoric part of the deformation and it was shown that at least three terms (C(10), C(01) and C(11)) are needed to accurately capture the material behavior. Furthermore, for the volumetric deformation, a two parameter Ogden model was used and the extent of material incompressibility was studied. The hyperelastic material parameters were determined through extracting and fitting to two isochronous curves (0.06 s and 14 s) approximating the instantaneous and steady-state elastic responses. Viscoelastic relaxation was characterized at five decay rates (100, 10, 1, 0.1, 0 s(-1)) and the results in compression and their extrapolation to tension were compared against previous models.     

Inverse identification of region-specific hyperelastic material parameters for human brain tissue

The identification of material parameters accurately describing the region-dependent mechanical behavior of human brain tissue is crucial for computational models used to assist, e.g., the development of safety equipment like helmets or the planning and execution of brain surgery. While the division of the human brain into different anatomical regions is well established, knowledge about regions with distinct mechanical properties remains limited. Here, we establish an inverse parameter identification scheme using a hyperelastic Ogden model and experimental data from multi-modal testing of tissue from 19 anatomical human brain regions to identify mechanically distinct regions and provide the corresponding material parameters. We assign the 19 anatomical regions to nine governing regions based on similar parameters and microstructures. Statistical analyses confirm differences between the regions and indicate that at least the corpus callosum and the corona radiata should be assigned different material parameters in computational models of the human brain. We provide a total of four parameter sets based on the two initial Poisson’s ratios of 0.45 and 0.49 as well as the pre- and unconditioned experimental responses, respectively. Our results highlight the close interrelation between the Poisson’s ratio and the remaining model parameters. The identified parameters will contribute to more precise computational models enabling spatially resolved predictions of the stress and strain states in human brains under complex mechanical loading conditions.

     

Validation and application of an intervertebral disc finite element model utilizing independently constructed tissue-level constitutive formulations that are nonlinear,anisotropic, and time-dependent

Finite element (FE) models are advantageous in the study of intervertebral disc mechanics as the stress–strain distributions can be determined throughout the tissue and the applied loading and material properties can be controlled and modified. However, the complicated nature of the disc presents a challenge in developing an accurate and predictive disc model, which has led to limitations in FE geometry, material constitutive models and properties, and model validation. The objective of this study was to develop a new FE model of the intervertebral disc, to validate the model?s nonlinear and time-dependent responses without tuning or calibration, and to evaluate the effect of changes in nucleus pulposus (NP), cartilaginous endplate (CEP), and annulus fibrosus (AF) material properties on the disc mechanical response. The new FE disc model utilized an analytically-based geometry. The model was created from the mean shape of human L4/L5 discs, measured from high-resolution 3D MR images and averaged using signed distance functions. Structural hyperelastic constitutive models were used in conjunction with biphasic-swelling theory to obtain material properties from recent tissue tests in confined compression and uniaxial tension. The FE disc model predictions fit within the experimental range (mean±95% confidence interval) of the disc?s nonlinear response for compressive slow loading ramp, creep, and stress-relaxation simulations. Changes in NP and CEP properties affected the neutral-zone displacement but had little effect on the final stiffness during slow-ramp compression loading. These results highlight the need to validate FE models using the disc?s full nonlinear response in multiple loading scenarios.     

Stepwise reduction of functional spinal structures increase vertebral translation and intradiscal pressure

To date, there are only a few studies that provide data to efficiently calibrate finite element models for the spine due to its complexity. In a recent study, we quantified the range of motion rotation and the lordosis angle. This paper provides complementary results regarding two more parameters, intradiscal pressure and vertebral translation. All parameters were obtained as a function of stepwise anatomical reduction, loading direction and magnitude. Eight lumbar spinal segments (L4-5) with a median age of 52 years (38-59 years) and no signs of disc degeneration were used for the in vitro testing. A miniaturized pressure probe was implanted into the nucleus. An ultrasound-based motion-tracking system was employed to record spatial movements of several landmarks on the specimens. The center of L4, the anterior, posterior, left and right point of the lower endplate of L4 were digitized as landmarks and its translation was determined. Specimens were loaded with pure moments (1-10Nm) in the three principal anatomical planes at a loading rate of 1.0 degrees /s. Anatomy was stepwise reduced by cutting different ligaments, facet capsules and joints and removing nucleus. Translation analysis showed that the L4 center point had its largest displacement in sagittal direction and almost none vertically. Removal of the supra- and interspinous, flaval ligaments showed a slight increase and further removal of structures, a higher increase of translation. Axial rotation also was accompanied with L4 to elevate when torsion was applied. This effect was found to be larger with progressing defects. Nucleotomy exhibited the most unstable situation for specimens. Results of the intradiscal pressure indicated a large increase after removing the facet capsules and joints. Furthermore, it was found that intradiscal pressure correlated well with data of range of motion for rotation. Predicting and simulating clinical defects, surgical intervention or treatment methods requires a well performed calibration based on in vitro data, whereas it is important to adapt all including structures with as many known parameters as possible. Results provided by these studies may be used as a database for researchers aiming to calibrate or validate finite element models of L4-5 segments.     

Patient-specific model of brain deformation: application to medical image registration

This contribution presents finite element computation of the deformation field within the brain during craniotomy-induced brain shift. The results were used to illustrate the capabilities of non-linear (i.e. accounting for both geometric and material non-linearities) finite element analysis in non-rigid registration of pre- and intra-operative magnetic resonance images of the brain. We used patient-specific hexahedron-dominant finite element mesh, together with realistic material properties for the brain tissue and appropriate contact conditions at boundaries. The model was loaded by the enforced motion of nodes (i.e. through prescribed motion of a boundary) at the brain surface in the craniotomy area. We suggest using explicit time-integration scheme for discretised equations of motion, as the computational times are much shorter and accuracy, for practical purposes, the same as in the case of implicit integration schemes. Application of the computed deformation field to register (i.e. align) the pre-operative images with the intra-operative ones indicated that the model very accurately predicts the displacements of the tumour and the lateral ventricles even for limited information about the brain surface deformation. The prediction accuracy improves when information about deformation of not only exposed (during craniotomy) but also unexposed parts of the brain surface is used when prescribing loading. However, it appears that the accuracy achieved using information only about the deformation of the exposed surface, that can be determined without intra-operative imaging, is acceptable. The presented results show that non-linear biomechanical models can complement medical image processing techniques when conducting non-rigid registration. Important advantage of such models over the previously used linear ones is that they do not require unrealistic assumptions that brain deformations are infinitesimally small and brain stress-strain relationship is linear.     

The peculiar properties of the falx and tentorium in brain injury biomechanics

The influence of the falx and tentorium on brain injury biomechanics during impact was studied with finite element (FE) analysis. Three detailed 3D FE head models were created based on the images of a healthy, normal size head. Two of the models contained the addition of falx and tentorium with material properties from previously published experiments. Impact loadings from a reconstructed concussive case in a sport accident were applied to the two players involved. The results suggested that the falx and tentorium could induce large strains to the surrounding brain tissues, especially to the corpus callosum and brainstem. The tentorium seemed to constrain the motion of the cerebellum while inducing large strain in the brainstem in both players involved in the accident (one player had mainly coronal head rotation and the other had both coronal and transversal rotations). Since changed strain levels were observed in the brainstem and corpus callosum, which are classical sites for diffuse axonal injuries (DAI), we confirmed the importance of using accurate material properties for falx and tentorium in a FE head model when studying traumatic brain injuries.     

Fitted hyperelastic parameters for Human brain tissue from reported tension,compression, and shear tests

The mechanical properties of human brain tissue are the subject of interest because of their use in understanding brain trauma and in developing therapeutic treatments and procedures. To represent the behavior of the tissue, we have developed hyperelastic mechanical models whose parameters are fitted in accordance with experimental test results. However, most studies available in the literature have fitted parameters with data of a single type of loading, such as tension, compression, or shear. Recently, Jin et al. (Journal of Biomechanics 46:2795−2801, 2013) reported data from ex vivo tests of human brain tissue under tension, compression, and shear loading using four strain rates and four different brain regions. However, they do not report parameters of energy functions that can be readily used in finite element simulations. To represent the tissue behavior for the quasi-static loading conditions, we aimed to determine the best fit of the hyperelastic parameters of the hyperfoam, Ogden, and polynomial strain energy functions available in ABAQUS for the low strain rate data, while simultaneously considering all three loading modes. We used an optimization process conducted in MATLAB, calling iteratively three finite element models developed in ABAQUS that represent the three loadings. Results showed a relatively good fit to experimental data in all loading modes using two terms in the energy functions. Values for the shear modulus obtained in this analysis (897−1653 Pa) are in the range of those presented in other studies. These energy-function parameters can be used in brain tissue simulations using finite element models.     

Effect of intercostal muscle and costovertebral joint material properties on human ribcage stiffness and kinematics

Current finite element (FE) models of the human thorax are limited by the lack of local-level validation, especially in the ribcage. This study exercised an existing FE ribcage model for a 50th percentile male under quasi-static point loading and dynamic sternal loading. Both force-displacement and kinematic responses of the ribcage were compared against experimental data. The sensitivity of the model response to changes in the material properties of the costovertebral (CV) joints and intercostal muscles was assessed. The simulations found that adjustments to the CV joints tended to change the amount of rib rotation in the sagittal plane, while changes to the elastic modulus and thickness of the intercostal muscles tended to alter both the stiffness and the direction and magnitude of rib motions. This study can lend insight into the role that the material properties of these two thoracic structures play in the dynamics of the ribcage during a frontal loading condition.     

An analytical model of traumatic diffuse brain injury

Diffuse axonal injury (DAI) with prolonged coma has been produced in the primate using an impulsive, rotational acceleration of the head without impact. This pathophysiological entity has been studied subsequently from a biomechanics perspective using physical models of the skull-brain structure. Subjected to identical loading conditions as the primate, these physical models permit one to measure the deformation within the surrogate brain tissue as a function of the forces applied to the head. An analytical model designed to approximate these experiments has been developed in order to facilitate an analysis of the parameters influencing brain deformation. These three models together are directed toward the development of injury tolerance criteria based upon the shear strain magnitude experienced by the deep white matter of the brain. The analytical model geometry consists of a rigid, right-circular cylindrical shell filled with a Kelvin-Voigt viscoelastic material. Allowing no slip on the boundary, the shell is subjected to a sudden, distributed, axisymmetric, rotational load. A Fourier series representation of the load allows unrestricted load-time histories. The exact solution for the relative angular displacement (V) and the infinitesimal shear strain (epsilon) at any radial location in the viscoelastic material with respect to the shell was determined.(ABSTRACT TRUNCATED AT 250 WORDS)     

The hydromechanics of hydrocephalus: Steady-state solutions for cylindrical geometry

Hydrocephalus is a state in which the circulation of cerebrospinal fluid is disturbed. This fluid, produced within the brain at a constant rate, moves through internal cavities in it (ventricles), then exits through passages so that it may be absorbed by the surrounding membranes (meninges). Failure of fluid to move properly through these passages results in the distention of the passages and the ventricles. Ultimately, this distention causes large displacements and distortion of brain tissue as well as an increase of fluid in the extracellular space of the brain (edema). We use a two-phase model of fluid-saturated material to simulate the steady state of the hydrocephalic brain. Analytic solutions for the displacement of brain tissue and the distribution of edema for the annular regions of an idealized cylindrical geometry and small-strain theory are found. The solutions are used for a large-deformation analysis by superposition of the responses obtained for incrementally increasing loading. The effects of structural and hydraulic differences of white and gray brain matter, and the ependymal lining surrounding the venticles, are examined. The results reproduce the characteristic steady-state distribution of edema seen in hydrocephalus, and are compared with experiment.     

An anatomically detailed and personalizable head injury model: Significance of brain and white matter tract morphological variability on strain

Finite element head (FE) models are important numerical tools to study head injuries and develop protection systems. The generation of anatomically accurate and subject-specific head models with conforming hexahedral meshes remains a significant challenge. The focus of this study is to present two developmental works: first, an anatomically detailed FE head model with conforming hexahedral meshes that has smooth interfaces between the brain and the cerebrospinal fluid, embedded with white matter (WM) fiber tracts; second, a morphing approach for subject-specific head model generation via a new hierarchical image registration pipeline integrating Demons and Dramms deformable registration algorithms. The performance of the head model is evaluated by comparing model predictions with experimental data of brain–skull relative motion, brain strain, and intracranial pressure. To demonstrate the applicability of the head model and the pipeline, six subject-specific head models of largely varying intracranial volume and shape are generated, incorporated with subject-specific WM fiber tracts. DICE similarity coefficients for cranial, brain mask, local brain regions, and lateral ventricles are calculated to evaluate personalization accuracy, demonstrating the efficiency of the pipeline in generating detailed subject-specific head models achieving satisfactory element quality without further mesh repairing. The six head models are then subjected to the same concussive loading to study the sensitivity of brain strain to inter-subject variability of the brain and WM fiber morphology. The simulation results show significant differences in maximum principal strain and axonal strain in local brain regions (one-way ANOVA test, p < 0.001), as well as their locations also vary among the subjects, demonstrating the need to further investigate the significance of subject-specific models. The techniques developed in this study may contribute to better evaluation of individual brain injury and the development of individualized head protection systems in the future. This study also contains general aspects the research community may find useful: on the use of experimental brain strain close to or at injury level for head model validation; the hierarchical image registration pipeline can be used to morph other head models, such as smoothed-voxel models.

     

Validation of lumbar spine loading from a musculoskeletal model including the lower limbs and lumbar spine

Low back mechanics are important to quantify to study injury, pain and disability. As in vivo forces are difficult to measure directly, modeling approaches are commonly used to estimate these forces. Validation of model estimates is critical to gain confidence in modeling results across populations of interest, such as people with lower-limb amputation. Motion capture, ground reaction force and electromyographic data were collected from ten participants without an amputation (five male/five female) and five participants with a unilateral transtibial amputation (four male/one female) during trunk-pelvis range of motion trials in flexion/extension, lateral bending and axial rotation. A musculoskeletal model with a detailed lumbar spine and the legs including 294 muscles was used to predict L4-L5 loading and muscle activations using static optimization. Model estimates of L4-L5 intervertebral joint loading were compared to measured intradiscal pressures from the literature and muscle activations were compared to electromyographic signals. Model loading estimates were only significantly different from experimental measurements during trunk extension for males without an amputation and for people with an amputation, which may suggest a greater portion of L4-L5 axial load transfer through the facet joints, as facet loads are not captured by intradiscal pressure transducers. Pressure estimates between the model and previous work were not significantly different for flexion, lateral bending or axial rotation. Timing of model-estimated muscle activations compared well with electromyographic activity of the lumbar paraspinals and upper erector spinae. Validated estimates of low back loading can increase the applicability of musculoskeletal models to clinical diagnosis and treatment.     

The effect of cross-sectional stem shape on the torsional stability of cemented implant components

Stability of a cemented implant, once the stem-cement interface has debonded, is reliant upon stem geometry and surface finish. There are relatively few studies addressing the effect of cross-sectional stem shape on cemented implant fixation. The purpose of this investigation was to compare the torsional stability of five different stem cross-sectional shapes-circular, oval, triangular, rectangular with rounded edges, and rectangular with sharp edges-under monotonically increasing and cyclic loading conditions. Seven samples of each stem geometry were tested. Stems were potted in bone cement and loaded to 5 deg of rotation. For monotonic loading, torque was applied at a constant rate of 2.5 deg/min. For cyclic loading, a sine wave torque pattern was applied, with a maximum magnitude that began at 4.5 Nm for 1500 cycles and then increased by 2.25 Nm every 1500 cycles until 5 deg of rotation. The rectangular stem with the sharp edges always provided the greatest resistance to torque, followed by the rectangular with rounded edges, triangular, oval, and circular. These results, including the effects of sharp corners, may differ for modes of loading other than torsion. These experimental results support the findings of earlier finite element models, indicating stem shape has a significant effect on resistance to torsional loading.     

The influence of anisotropy on brain injury prediction

Traumatic Brain Injury (TBI) occurs when a mechanical insult produces damage to the brain and disrupts its normal function. Numerical head models are often used as tools to analyze TBIs and to measure injury based on mechanical parameters. However, the reliability of such models depends on the incorporation of an appropriate level of structural detail and accurate representation of the material behavior. Since recent studies have shown that several brain regions are characterized by a marked anisotropy, constitutive equations should account for the orientation-dependence within the brain. Nevertheless, in most of the current models brain tissue is considered as completely isotropic. To study the influence of the anisotropy on the mechanical response of the brain, a head model that incorporates the orientation of neural fibers is used and compared with a fully isotropic model. A simulation of a concussive impact based on a sport accident illustrates that significantly lowered strains in the axonal direction as well as increased maximum principal strains are detected for anisotropic regions of the brain. Thus, the orientation-dependence strongly affects the response of the brain tissue. When anisotropy of the whole brain is taken into account, deformation spreads out and white matter is particularly affected. The introduction of local axonal orientations and fiber distribution into the material model is crucial to reliably address the strains occurring during an impact and should be considered in numerical head models for potentially more accurate predictions of brain injury.     

The rib cage reduces intervertebral disc pressures in cadaveric thoracic spines by sharing loading under applied dynamic moments

The effects of the rib cage on thoracic spine loading are not well studied, but the rib cage may provide stability or share loads with the spine. Intervertebral disc pressure provides insight into spinal loading, but such measurements are lacking in the thoracic spine. Thus, our objective was to examine thoracic intradiscal pressures under applied pure moments, and to determine the effect of the rib cage on these pressures. Human cadaveric thoracic spine specimens were positioned upright in a testing machine, and Dynamic pure moments (0 to ±5 N·m) with a compressive follower load of 400 N were applied in axial rotation, flexion - extension, and lateral bending. Disc pressures were measured at T4-T5 and T8-T9 using needle-mounted pressure transducers, first with the rib cage intact, and again after the rib cage was removed. Changes in pressure vs. moment slopes with rib cage removal were examined. Pressure generally increased with applied moments, and pressure-moment slope increased with rib cage removal at T4-T5 for axial rotation, extension, and lateral bending, and at T8-T9 for axial rotation. The results suggest the intact rib cage carried about 62% and 56% of axial rotation moments about T4-T5 and T8-T9, respectively, as well as 42% of extension moment and 36–43% of lateral bending moment about T4-T5 only. The rib cage likely plays a larger role in supporting moments than compressive loads, and may also play a larger role in the upper thorax than the lower thorax.     

Effects of tissue preservation temperature on high strain-rate material properties of brain

Postmortem preservation conditions may be one of factors contributing to wide material property variations in brain tissues in literature. The objective of present study was to determine the effects of preservation temperatures on high strain-rate material properties of brain tissues using the split Hopkinson pressure bar (SHPB). Porcine brains were harvested immediately after sacrifice, sliced into 2 mm thickness, preserved in ice cold (group A, 10 samples) and 37°C (group B, 9 samples) saline solution and warmed to 37°C just prior to the test. A SHPB with tube aluminum transmission bar and semi-conductor strain gauges were used to enhance transmitted wave signals. Data were gathered using a digital acquisition system and processed to obtain stress-strain curves. All tests were conducted within 4 h postmortem. The mean strain-rate was 2487±72 s(-1). A repeated measures model with specimen-level random effects was used to analyze log transformed stress-strain responses through the entire loading range. The mean stress-strain curves with ±95% confidence bands demonstrated typical power relationships with the power value of 2.4519 (standard error, 0.0436) for group A and 2.2657 (standard error, 0.0443) for group B, indicating that responses for the two groups are significantly different. Stresses and tangent moduli rose with increasing strain levels in both groups. These findings indicate that storage temperatures affected brain tissue material properties and preserving tissues at 37°C produced a stiffer response at high strain-rates. Therefore, it is necessary to incorporate material properties obtained from appropriately preserved tissues to accurately predict the responses of brain using stress analyses models, such as finite element simulations.