3-D Measurements of Acceleration-Induced Brain Deformation via Harmonic Phase Analysis and Finite-Element Models

Average Biomechanical Responses of the Human Brain Grouped by Age and Sex

Traumatic brain injuries (TBIs) occur from rapid head motion that results in brain deformation. Computational models are typically used to estimate brain deformation to predict risk of injury and evaluate the effectiveness of safety countermeasures. The accuracy of these models relies on validation to experimental brain deformation data. In this study, we create the first group-average biomechanical responses of the brain, including structure, material properties, and deformation response, by age and sex from 157 subjects. Subjects were sorted intro three age groups-young, mid-age, and older-and by sex to create group-average neuroanatomy, material properties, and brain deformation response to non-injurious loading using structural and specialized magnetic resonance imaging data. Computational models were also built using the group-average geometry and material properties for each of the six groups. The material properties did not depend on sex, but showed a decrease in shear stiffness in the older adult group. The brain deformation response also showed differences in the distribution of strain and a decrease in the magnitude of maximum strain in the older adult group. The computational models were simulated using the same non-injurious loading conditions as the subject data. While the models' strain response showed differences among the models, there were no clear relationships with age. Further studies, both modeling and experimental, with more data from subjects in each age group, are needed to clarify the mechanisms underlying the observed changes in strain response with age, and for computational models to better match the trends observed across the group-average responses.

Bridging biomechanics with neuropathological and neuroimaging insights for mTBI understanding through multiscale and multiphysics computational modeling

Mild traumatic brain injury (mTBI) represents a significant public health challenge in modern society. An in-depth analysis of the injury mechanisms, pathological forms, and assessment criteria of mTBI has underscored the pivotal role of craniocerebral models in comprehending and addressing mTBI. Research indicates that although existing finite element craniocerebral models have made strides in simulating the macroscopic biomechanical responses of the brain, they still fall short in accurately depicting the complexity of mTBI. Consequently, this paper emphasizes the necessity of integrating biomechanics, neuropathology, and neuroimaging to develop multiscale and multiphysics craniocerebral models, which are crucial for precisely capturing microscopic injuries, establishing pathological mechanical indicators, and simulating secondary and long-term brain functional impairments. The comprehensive analysis and in-depth discussion presented in this paper offer new perspectives and approaches for understanding, diagnosing, and preventing mTBI, potentially contributing to alleviating the global burden of mTBI.

The White Matter Fiber Tract Deforms Most in the Perpendicular Direction During In Vivo Volunteer Impacts

White matter (WM) tract-related strains are increasingly used to quantify brain mechanical responses, but their dynamics in live human brains during in vivo impact conditions remain largely unknown. Existing research primarily looked into the normal strain along the WM fiber tracts (i.e., tract-oriented normal strain), but it is rarely the case that the fiber tract only endures tract-oriented normal strain during impacts. In this study, we aim to extend the in vivo measurement of WM fiber deformation by quantifying the normal strain perpendicular to the fiber tract (i.e., tract-perpendicular normal strain) and the shear strain along and perpendicular to the fiber tract (i.e., tract-oriented shear strain and tract-perpendicular shear strain, respectively). To achieve this, we combine the three-dimensional strain tensor from the tagged magnetic resonance imaging with the diffusion tensor imaging (DTI) from an open-access dataset, including 44 volunteer impacts under two head loading modes, i.e., neck rotations (N = 30) and neck extensions (N = 14). The strain tensor is rotated to the coordinate system with one axis aligned with DTI-revealed fiber orientation, and then four tract-related strain measures are calculated. The results show that tract-perpendicular normal strain peaks are the largest among the four strain types (p < 0.05, Friedman's test). The distribution of tract-related strains is affected by the head loading mode, of which laterally symmetric patterns with respect to the midsagittal plane are noted under neck extensions, but not under neck rotations. Our study presents a comprehensive in vivo strain quantification toward a multifaceted understanding of WM dynamics. We find that the WM fiber tract deforms most in the perpendicular direction, illuminating new fundamentals of brain mechanics. The reported strain images can be used to evaluate the fidelity of computational head models, especially those intended to predict fiber deformation under noninjurious conditions.

Dynamic strain fields of the mouse brain during rotation

Mouse models are used to better understand brain injury mechanisms in humans, yet there is a limited understanding of biomechanical relevance, beginning with how the murine brain deforms when the head undergoes rapid rotation from blunt impact. This problem makes it difficult to translate some aspects of diffuse axonal injury from mouse to human. To address this gap, we present the two-dimensional strain field of the mouse brain undergoing dynamic rotation in the sagittal plane. Using a high-speed camera with digital image correlation measurements of the exposed mid-sagittal brain surface, we found that pure rotations (no direct impact to the skull) of 100-200 rad/s are capable of producing complex strain fields that evolve over time with respect to rotational acceleration and deceleration. At the highest rotational velocity tested, the largest tensile strains (≥ 21% elongation) in selected regions of the mouse brain approach strain thresholds previously associated with axonal injury in prior work. These findings provide a benchmark to validate the mechanical response in biomechanical computational models predicting diffuse axonal injury, but much work remains in correlating tissue deformation patterns from computational models with underlying neuropathology.

Comparison of Deformation Patterns Excited in the Human Brain In Vivo by Harmonic and Impulsive Skull Motion

Noninvasive measurements of brain deformation in human participants in vivo are needed to develop models of brain biomechanics and understand traumatic brain injury (TBI). Tagged magnetic resonance imaging (tagged MRI) and magnetic resonance elastography (MRE) are two techniques to study human brain deformation; these techniques differ in the type of motion and difficulty of implementation. In this study, oscillatory strain fields in the human brain caused by impulsive head acceleration and measured by tagged MRI were compared quantitatively to strain fields measured by MRE during harmonic head motion at 10 and 50 Hz. Strain fields were compared by registering to a common anatomical template, then computing correlations between the registered strain fields. Correlations were computed between tagged MRI strain fields in six participants and MRE strain fields at 10 Hz and 50 Hz in six different participants. Correlations among strain fields within the same experiment type were compared statistically to correlations from different experiment types. Strain fields from harmonic head motion at 10 Hz imaged by MRE were qualitatively and quantitatively similar to modes excited by impulsive head motion, imaged by tagged MRI. Notably, correlations between strain fields from 10 Hz MRE and tagged MRI did not differ significantly from correlations between strain fields from tagged MRI. These results suggest that low-frequency modes of oscillation dominate the response of the brain during impact. Thus, low-frequency MRE, which is simpler and more widely available than tagged MRI, can be used to illuminate the brain's response to head impact.

A Weighted Head Accelerator Mechanism (WHAM) for visualizing brain rheology using magnetic resonance imaging

BACKGROUND

A device for moving the head during MR imaging, called a Weighted Head Accelerator Mechanism (WHAM), rotates the head of a supine subject within programmable rotation limits and acceleration profiles. The WHAM can be used with custom MRI sequences to visualize the deformation and recoil of in vivo brain parenchyma with high temporal resolution, allowing element-wise calculation of strain and shear forces in the brain. Unlike previous devices, the WHAM can be configured to provide a wide range of motion and acceleration profiles.

NEW METHOD

The WHAM was calibrated using a high-speed camera on a laboratory bench and in 1.5 Tesla and 3.0 Tesla MRI scanners using gel phantoms and human subjects. The MR imaging studies employed a spatial spin-saturation tagging sub-sequence, followed by serial image acquisition. In these studies, 256 images were acquired with a temporal resolution of 2.56 ms. Deformation of the brain was quantified by following the spatial tags in the images.

RESULTS

MR imaging showed that the WHAM drove quantifiable brain motions using g forces less than those typically observed in day-to-day activities, with peak accelerations of ∼250 rad/sec².

COMPARISON WITH EXISTING METHODS

The peak pre-contact accelerations and velocities achieved by the WHAM device in this study are both higher than devices used in previous studies, while also allowing for modification of these factors.

CONCLUSIONS

MR imaging performed with the WHAM provides a direct method to visualize and quantify "brain slosh" in response to rotational acceleration. Consequently, this approach might find utility in evaluating strategies to protect the brain from mild traumatic brain injury (mTBI).

Development and validation of subject-specific 3D human head models based on a nonlinear visco-hyperelastic constitutive framework

Computational head models are promising tools for understanding and predicting traumatic brain injuries. Most available head models are developed using inputs (i.e. head geometry, material properties and boundary conditions) from experiments on cadavers or animals and employ hereditary integral-based constitutive models that assume linear viscoelasticity in part of the rate-sensitive material response. This leads to high uncertainty and poor accuracy in capturing the nonlinear brain tissue response. To resolve these issues, a framework for the development of subject-specific three-dimensional head models is proposed, in which all inputs are derived in vivo from the same living human subject: head geometry via magnetic resonance imaging (MRI), brain tissue properties via magnetic resonance elastography (MRE), and full-field strain-response of the brain under rapid head rotation via tagged MRI. A nonlinear, viscous dissipation-based visco-hyperelastic constitutive model is employed to capture brain tissue response. Head models are validated using quantitative metrics that compare spatial strain distribution, temporal strain evolution, and the magnitude of strain maxima, with the corresponding experimental observations from tagged MRI. Results show that our head models accurately capture the strain-response of the brain. Further, employment of the nonlinear visco-hyperelastic constitutive framework provides improvements in the prediction of peak strains and temporal strain evolution over hereditary integral-based models.

MR Imaging of Human Brain Mechanics In Vivo: New Measurements to Facilitate the Development of Computational Models of Brain Injury

Computational models of the brain and its biomechanical response to skull accelerations are important tools for understanding and predicting traumatic brain injuries (TBIs). However, most models have been developed using experimental data collected on animal models and cadaveric specimens, both of which differ from the living human brain. Here we describe efforts to noninvasively measure the biomechanical response of the human brain with MRI-at non-injurious strain levels-and generate data that can be used to develop, calibrate, and evaluate computational brain biomechanics models. Specifically, this paper reports on a project supported by the National Institute of Neurological Disorders and Stroke to comprehensively image brain anatomy and geometry, mechanical properties, and brain deformations that arise from impulsive and harmonic skull loadings. The outcome of this work will be a publicly available dataset ( http://www.nitrc.org/projects/bbir ) that includes measurements on both males and females across an age range from adolescence to older adulthood. This article describes the rationale and approach for this study, the data available, and how these data may be used to develop new computational models and augment existing approaches; it will serve as a reference to researchers interested in using these data.

Toward subject-specific evaluation: methods of evaluating finite element brain models using experimental high-rate rotational brain motion

Computational models of the brain have become the gold standard in biomechanics to understand, predict, and mitigate traumatic brain injuries. Many models have been created and evaluated with limited experimental data and without accounting for subject-specific morphometry of the specimens in the dataset. Recent advancements in the measurement of brain motion using sonomicrometry allow for a comprehensive evaluation of brain model biofidelity using a high-rate, rotational brain motion dataset. In this study, four methods were used to determine the best technique to compare nodal displacement to experimental brain motion, including a new morphing method to match subject-specific inner skull geometry. Three finite element brain models were evaluated in this study: the isotropic GHBMC and SIMon models, as well as an anisotropic model with explicitly embedded axons (UVA-EAM). Using a weighted cross-correlation score (between 0 and 1), the anisotropic model yielded the highest average scores across specimens and loading conditions ranging from 0.53 to 0.63, followed by the isotropic GHBMC with average scores ranging from 0.46 to 0.58, and then the SIMon model with average scores ranging from 0.36 to 0.51. The choice of comparison method did not significantly affect the cross-correlation score, and differences of global strain up to 0.1 were found for the morphed geometry relative to baseline models. The morphed or scaled geometry is recommended when evaluating computational brain models to capture the subject-specific skull geometry of the experimental specimens.

Group characterization of impact-induced, in vivo human brain kinematics

Brain movement during an impact can elicit a traumatic brain injury, but tissue kinematics vary from person to person and knowledge regarding this variability is limited. This study examines spatio-temporal brain-skull displacement and brain tissue deformation across groups of subjects during a mild impact in vivo. The heads of two groups of participants were imaged while subjected to a mild (less than 350 rad s^-2) impact during neck extension (NE, n = 10) and neck rotation (NR, n = 9). A kinematic atlas of displacement and strain fields averaged across all participants was constructed and compared against individual participant data. The atlas-derived mean displacement magnitude was 0.26 ± 0.13 mm for NE and 0.40 ± 0.26 mm for NR, which is comparable to the displacement magnitudes from individual participants. The strain tensor from the atlas displacement field exhibited maximum shear strain (MSS) of 0.011 ± 0.006 for NE and 0.017 ± 0.009 for NR and was lower than the individual MSS averaged across participants. The atlas illustrates common patterns, containing some blurring but visible relationships between anatomy and kinematics. Conversely, the direction of the impact, brain size, and fluid motion appear to underlie kinematic variability. These findings demonstrate the biomechanical roles of key anatomical features and illustrate common features of brain response for model evaluation.

Calibration of a Heterogeneous Brain Model Using a Subject-Specific Inverse Finite Element Approach

Central to the investigation of the biomechanics of traumatic brain injury (TBI) and the assessment of injury risk from head impact are finite element (FE) models of the human brain. However, many existing FE human brain models have been developed with simplified representations of the parenchyma, which may limit their applicability as an injury prediction tool. Recent advances in neuroimaging techniques and brain biomechanics provide new and necessary experimental data that can improve the biofidelity of FE brain models. In this study, the CAB-20MSym template model was developed, calibrated, and extensively verified. To implement material heterogeneity, a magnetic resonance elastography (MRE) template image was leveraged to define the relative stiffness gradient of the brain model. A multi-stage inverse FE (iFE) approach was used to calibrate the material parameters that defined the underlying non-linear deviatoric response by minimizing the error between model-predicted brain displacements and experimental displacement data. This process involved calibrating the infinitesimal shear modulus of the material using low-severity, low-deformation impact cases and the material non-linearity using high-severity, high-deformation cases from a dataset of in situ brain displacements obtained from cadaveric specimens. To minimize the geometric discrepancy between the FE models used in the iFE calibration and the cadaveric specimens from which the experimental data were obtained, subject-specific models of these cadaveric brain specimens were developed and used in the calibration process. Finally, the calibrated material parameters were extensively verified using independent brain displacement data from 33 rotational head impacts, spanning multiple loading directions (sagittal, coronal, axial), magnitudes (20–40 rad/s), durations (30–60 ms), and severity. Overall, the heterogeneous CAB-20MSym template model demonstrated good biofidelity with a mean overall CORA score of 0.63 ± 0.06 when compared to in situ brain displacement data. Strains predicted by the calibrated model under non-injurious rotational impacts in human volunteers (N = 6) also demonstrated similar biofidelity compared to in vivo measurements obtained from tagged magnetic resonance imaging studies. In addition to serving as an anatomically accurate model for further investigations of TBI biomechanics, the MRE-based framework for implementing material heterogeneity could serve as a foundation for incorporating subject-specific material properties in future models.

Natural oscillatory modes of 3D deformation of the human brain in vivo

Natural modes and frequencies of three-dimensional (3D) deformation of the human brain were identified from in vivo tagged magnetic resonance images (MRI) acquired dynamically during transient mild acceleration of the head. Twenty 3D strain fields, estimated from tagged MRI image volumes in 19 adult subjects, were analyzed using dynamic mode decomposition (DMD). These strain fields represented dynamic, 3D brain deformations during constrained head accelerations, either involving rotation about the vertical axis of the neck or neck extension. DMD results reveal fundamental oscillatory modes of deformation at damped frequencies near 7 Hz (in neck rotation) and 11 Hz (in neck extension). Modes at these frequencies were found consistently among all subjects. These characteristic features of 3D human brain deformation are important for understanding the response of the brain in head impacts and provide valuable quantitative criteria for the evaluation and use of computer models of brain mechanics.

Rapid Estimation of Entire Brain Strain Using Deep Learning Models

OBJECTIVE

Many recent studies have suggested that brain deformation resulting from a head impact is linked to the corresponding clinical outcome, such as mild traumatic brain injury (mTBI). Even though several finite element (FE) head models have been developed and validated to calculate brain deformation based on impact kinematics, the clinical application of these FE head models is limited due to the time-consuming nature of FE simulations. This work aims to accelerate the process of brain deformation calculation and thus improve the potential for clinical applications.

METHODS

We propose a deep learning head model with a five-layer deep neural network and feature engineering, and trained and tested the model on 2511 total head impacts from a combination of head model simulations and on-field college football and mixed martial arts impacts.

RESULTS

The proposed deep learning head model can calculate the maximum principal strain (Green Lagrange) for every element in the entire brain in less than 0.001s with an average root mean squared error of 0.022, and with a standard deviation of 0.001 over twenty repeats with random data partition and model initialization.

CONCLUSION

Trained and tested using the dataset of 2511 head impacts, this model can be applied to various sports in the calculation of brain strain with accuracy, and its applicability can even further be extended by incorporating data from other types of head impacts.

SIGNIFICANCE

In addition to the potential clinical application in real-time brain deformation monitoring, this model will help researchers estimate the brain strain from a large number of head impacts more efficiently than using FE models.

Integrating material properties from magnetic resonance elastography into subject-specific computational models for the human brain

Advances in brain imaging and computational methods have facilitated the creation of subject-specific computational brain models that aid researchers in investigating brain trauma using simulated impacts. The emergence of magnetic resonance elastography (MRE) as a non-invasive mechanical neuroimaging tool has enabled in vivo estimation of material properties at low-strain, harmonic loading. An open question in the field has been how this data can be integrated into computational models. The goals of this study were to use a novel MRI dataset acquired in human volunteers to generate models with subject-specific anatomy and material properties, and then to compare simulated brain deformations to subject-specific brain deformation data under non-injurious loading. Models of five subjects were simulated with linear viscoelastic (LVE) material properties estimated directly from MRE data. Model predictions were compared to experimental brain deformation acquired in the same subjects using tagged MRI. Outcomes from the models matched the spatial distribution and magnitude of the measured peak strain components as well as the 95^th percentile in-plane peak strains within 0.005 mm/mm and maximum principal strain within 0.012 mm/mm. Sensitivity to material heterogeneity was also investigated. Simulated brain deformations from a model with homogenous brain properties and a model with brain properties discretized with up to ten regions were very similar (a mean absolute difference less than 0.0015 mm/mm in peak strains). Incorporating material properties directly from MRE into a biofidelic subject-specific model is an important step toward future investigations of higher-order model features and simulations under more severe loading conditions.

A Review of Validation Methods for the Intracranial Response of FEHM to Blunt Impacts

The following is a review of the processes currently employed when validating the intracranial response of Finite Element Head Models (FEHM) against blunt impacts. The authors aim to collate existing validation tools, their applications and findings on their effectiveness to aid researchers in the validation of future FEHM and potential efforts in improving procedures. In this vain, publications providing experimental data on the intracranial pressure, relative brain displacement and brain strain responses to impacts in human subjects are surveyed and key data are summarised. This includes cases that have previously been used in FEHM validation and alternatives with similar potential uses. The processes employed to replicate impact conditions and the resulting head motion are reviewed, as are the analytical techniques used to judge the validity of the models. Finally, publications exploring the validation process and factors affecting it are critically discussed. Reviewing FEHM validation in this way highlights the lack of a single best practice, or an obvious solution to create one using the tools currently available. There is clear scope to improve the validation process of FEHM, and the data available to achieve this. By collecting information from existing publications, it is hoped this review can help guide such developments and provide a point of reference for researchers looking to validate or investigate FEHM in the future, enabling them to make informed choices about the simulation of impacts, how they are generated numerically and the factors considered during output assessment, whilst being aware of potential limitations in the process.

In vivo estimates of axonal stretch and 3D brain deformation during mild head impact

The rapid deformation of brain tissue in response to head impact can lead to traumatic brain injury. In vivo measurements of brain deformation during non-injurious head impacts are necessary to understand the underlying mechanisms of traumatic brain injury and compare to computational models of brain biomechanics. Using tagged magnetic resonance imaging (MRI), we obtained measurements of three-dimensional strain tensors that resulted from a mild head impact after neck rotation or neck extension. Measurements of maximum principal strain (MPS) peaked shortly after impact, with maximal values of 0.019-0.053 that correlated strongly with peak angular velocity. Subject-specific patterns of MPS were spatially heterogeneous and consistent across subjects for the same motion, though regions of high deformation differed between motions. The largest MPS values were seen in the cortical gray matter and cerebral white matter for neck rotation and the brainstem and cerebellum for neck extension. Axonal fiber strain (Ef) was estimated by combining the strain tensor with diffusion tensor imaging data. As with MPS, patterns of Ef varied spatially within subjects, were similar across subjects within each motion, and showed group differences between motions. Values were highest and most strongly correlated with peak angular velocity in the corpus callosum for neck rotation and in the brainstem for neck extension. The different patterns of brain deformation between head motions highlight potential areas of greater risk of injury between motions at higher loading conditions. Additionally, these experimental measurements can be directly compared to predictions of generic or subject-specific computational models of traumatic brain injury.

Biomechanical Analysis of Woodpecker Response During Pecking Using a Two-Dimensional Computational Model

Traumatic brain injury (TBI) and chronic traumatic encephalopathy (CTE) due to the impact is a critical health concern. Impact mitigation strategy is a vital design paradigm to reduce the burden of TBI and CTE. In this regard, woodpecker biomimicry continues to attract attention. However, a direct comparison between a woodpecker and human biomechanical responses is lacking. Toward this end, we investigate the biomechanical response of a woodpecker during pecking using a two-dimensional head model. We also analyze the response of concurrent human head model to facilitate direct comparison with woodpecker response. The head models of woodpecker and human were built from medical images, the material properties were adopted from the literature. Both woodpecker and human head models were subjected to head kinematics obtained during pecking and resulting biomechanical response is studied. For the pecking cycle simulated in this work, peak rotational velocity and acceleration were ∼15 rad/s and 7,057 rad/s². These peak values are commensurate with the kinematics threshold values reported in human TBI. Our results show that, for the same input acceleration, the strains and stresses in the woodpecker brain are approximately six times lower than that of the human brain. The stress reduction is mainly attributed to the smaller size of the woodpecker head. The effect of pecking frequency and multiple pecking cycles have also been studied. It is observed that the strains and stresses in the brain are increased by ∼100% as pecking frequency is doubled. During multiple pecking cycle, dwell period of ∼90 ms tend to relax the stresses in the woodpecker brain; however, the amount of relaxation depends on the value of the decay constant. The comparison of biomechanical response against the axonal injury threshold suggests that for peak rotational acceleration of 7,057 rad/s² the maximum principal strain in the brains of woodpecker and human exceed the threshold limit. Acceleration scaling relationship between a woodpecker and equivalent human response is also developed as a function of head size. We obtain a scaling factor, ahaw, of 0.11 for baseline head sizes and a scaling factor of 1.03 as the human head size approaches woodpecker head size.

Brain Strain from Motion of Sparse Markers

Brain strain secondary to head impact or inertial loading is closely associated with pathologic observations in the brain. The only experimental brain strain dataset under loadings close to traumatic levels was calculated by imposing the experimentally measured motion of markers embedded in the brain to an auxiliary model formed by triad elements (Hardy et al., 2007). However, fidelity of the calculated strain as well as the suitability of using triad elements for three-dimensional (3D) strain estimation remains to be verified. Therefore, this study proposes to use tetrahedron elements as a new approach to estimate the brain strain. Fidelity of this newly-proposed approach along with the previous triad-based approach is evaluated with the aid of three independently-developed finite element (FE) head models by numerically replicating the experimental impacts and strain estimation procedures. Strain in the preselected brain elements obtained from the whole head simulation exhibits good correlation with its tetra estimation and exceeds its triad estimation, indicating that the tetra approach more accurately estimates the strain in the preselected region. The newly calculated brain strain curves using tetra elements provide better approximations for the 3D experimental brain deformation and can be used for strain validation of FE models of human head.

Insights Into Traumatic Brain Injury From MRI of Harmonic Brain Motion

Measurements of dynamic deformation of the human brain, induced by external harmonic vibration of the skull, were analyzed to illuminate the mechanics of mild traumatic brain injury (TBI). Shear wave propagation velocity vector fields were obtained to illustrate the role of the skull and stiff internal membranes in transmitting motion to the brain. Relative motion between the cerebrum and cerebellum was quantified to assess the vulnerability of connecting structures. Mechanical deformation was quantified throughout the brain to investigate spatial patterns of strain and axonal stretch. Strain magnitude was generally attenuated as shear waves propagated into interior structures of the brain; this attenuation was greater at higher frequencies. Analysis of shear wave propagation direction indicates that the stiff membranes (falx and tentorium) greatly affect brain deformation during imposed skull motion as they serve as sites for both initiation and reflection of shear waves. Relative motion between the cerebellum and cerebrum was small in comparison with the overall motion of both structures, which suggests that such relative motion might play only a minor role in TBI mechanics. Strain magnitudes and the amount of axonal stretch near the bases of sulci were similar to those in other areas of the cortex, and local strain concentrations at the gray-white matter boundary were not observed. We tentatively conclude that observed differences in neuropathological response in these areas might be due to heterogeneity in the response to mechanical deformation rather than heterogeneity of the deformation itself.