Computation of axonal elongation in head trauma finite element simulation

Embedded finite element modeling of the mechanics of brain axonal fiber tracts under head impact conditions

Investigating and understanding the biomechanical kinematics and kinetics of human brain axonal fibers during head impact process is crucial to study the mechanisms of Traumatic Axonal Injury (TAI). Such a study may require the explicit incorporation of brain fiber tracts into the host brain in order to distinguish the mechanical states of axonal fibers and brain tissue. Herein we extend our previously developed human head model by using an embedded element method to include fiber tracts reconstructed from diffusion tensor images in a host brain with the purpose of numerically tracking the deformation state of axonal fiber tracts during a head impact simulation. The updated model is validated by comparing its prediction of intracranial pressures with experimental data, followed by a thorough study of the effects of element types used for fiber tracts and the stiffness ratios of fiber to host brain. The validated model is also used to predict and visualize the damaged region of fiber tracts during the head impact process based on different injury criteria. The model is promising in tracking the state of fiber tracts and can add more objective functions such as axonal fiber deformation if used in the future design optimization of head protective equipment such as a football helmet.

Altered lateralization of the cingulum in deployment-related traumatic brain injury: An ENIGMA military-relevant brain injury study

Traumatic brain injury (TBI) in military populations can cause disruptions in brain structure and function, along with cognitive and psychological dysfunction. Diffusion magnetic resonance imaging (dMRI) can detect alterations in white matter (WM) microstructure, but few studies have examined brain asymmetry. Examining asymmetry in large samples may increase sensitivity to detect heterogeneous areas of WM alteration in mild TBI. Through the Enhancing Neuroimaging Genetics Through Meta-Analysis Military-Relevant Brain Injury working group, we conducted a mega-analysis of neuroimaging and clinical data from 16 cohorts of Active Duty Service Members and Veterans (n = 2598). dMRI data were processed together along with harmonized demographic, injury, psychiatric, and cognitive measures. Fractional anisotropy in the cingulum showed greater asymmetry in individuals with deployment-related TBI, driven by greater left lateralization in TBI. Results remained significant after accounting for potentially confounding variables including posttraumatic stress disorder, depression, and handedness, and were driven primarily by individuals whose worst TBI occurred before age 40. Alterations in the cingulum were also associated with slower processing speed and poorer set shifting. The results indicate an enhancement of the natural left laterality of the cingulum, possibly due to vulnerability of the nondominant hemisphere or compensatory mechanisms in the dominant hemisphere. The cingulum is one of the last WM tracts to mature, reaching peak FA around 42 years old. This effect was primarily detected in individuals whose worst injury occurred before age 40, suggesting that the protracted development of the cingulum may lead to increased vulnerability to insults, such as TBI.

Bidirectional hyperelastic characterization of brain white matter tissue

Biomechanical study of brain injuries originated from mechanical damages to white matter tissue requires detailed information on mechanical characteristics of its main components, the axonal fibers and extracellular matrix, which is very limited due to practical difficulties of direct measurement. In this paper, a new theoretical framework was established based on microstructural modeling of brain white matter tissue as a soft composite for bidirectional hyperelastic characterization of its main components. First the tissue was modeled as an Ogden hyperelastic material, and its principal Cauchy stresses were formulated in the axonal and transverse directions under uniaxial and equibiaxial tension using the theory of homogenization. Upon fitting these formulae to the corresponding experimental test data, direction-dependent hyperelastic constants of the tissue were obtained. These directional properties then were used to estimate the strain energy stored in the homogenized model under each loading scenario. A new microstructural composite model of the tissue was also established using principles of composites micromechanics, in which the axonal fibers and surrounding matrix are modeled as different Ogden hyperelastic materials with unknown constants. Upon balancing the strain energies stored in the homogenized and composite models under different loading scenarios, fully coupled nonlinear equations as functions of unknown hyperelastic constants were derived, and their optimum solutions were found in a multi-parametric multi-objective optimization procedure using the response surface methodology. Finally, these solutions were implemented, in a bottom-up approach, into a micromechanical finite element model to reproduce the tissue responses under the same loadings and predict the tissue responses under unseen non-equibiaxial loadings. Results demonstrated a very good agreement between the model predictions and experimental results in both directions under different loadings. Moreover, the axonal fibers with hyperelastic characteristics stiffer than the extracellular matrix were shown to play the dominant role in directional reinforcement of the tissue.

Use of Brain Biomechanical Models for Monitoring Impact Exposure in Contact Sports

Head acceleration measurement sensors are now widely deployed in the field to monitor head kinematic exposure in contact sports. The wealth of impact kinematics data provides valuable, yet challenging, opportunities to study the biomechanical basis of mild traumatic brain injury (mTBI) and subconcussive kinematic exposure. Head impact kinematics are translated into brain mechanical responses through physics-based computational simulations using validated brain models to study the mechanisms of injury. First, this article reviews representative legacy and contemporary brain biomechanical models primarily used for blunt impact simulation. Then, it summarizes perspectives regarding the development and validation of these models, and discusses how simulation results can be interpreted to facilitate injury risk assessment and head acceleration exposure monitoring in the context of contact sports. Recommendations and consensus statements are presented on the use of validated brain models in conjunction with kinematic sensor data to understand the biomechanics of mTBI and subconcussion. Mainly, there is general consensus that validated brain models have strong potential to improve injury prediction and interpretation of subconcussive kinematic exposure over global head kinematics alone. Nevertheless, a major roadblock to this capability is the lack of sufficient data encompassing different sports, sex, age and other factors. The authors recommend further integration of sensor data and simulations with modern data science techniques to generate large datasets of exposures and predicted brain responses along with associated clinical findings. These efforts are anticipated to help better understand the biomechanical basis of mTBI and improve the effectiveness in monitoring kinematic exposure in contact sports for risk and injury mitigation purposes.

Correlating the microstructural architecture and macrostructural behaviour of the brain

The computational simulation of pathological conditions and surgical procedures, for example the removal of cancerous tissue, can contribute crucially to the future of medicine. Especially for brain surgery, these methods can be important, as the ultra-soft tissue controls vital functions of the body. However, the microstructural interactions and their effects on macroscopic material properties remain incompletely understood. Therefore, we investigated the mechanical behaviour of brain tissue under three different deformation modes, axial tension, compression, and semi-confined compression, in different anatomical regions, and for varying axon orientation. In addition, we characterised the underlying microstructure in terms of myelin, cells, glial cells and neuron area fraction, and density. The correlation of these quantities with the material parameters of the anisotropic Ogden model reveals a decrease in shear modulus with increasing myelin area fraction. Strikingly, the tensile shear modulus correlates positively with cell and neuronal area fraction (Spearman's correlation coefficient of r_s=0.40 and r_s=0.33), whereas the compressive shear modulus decreases with increasing glial cell area (r_s=-0.33). Our study finds that tissue non-linearity significantly depends on the myelin area fraction (r_s=0.47), cell density (r_s=0.41) and glial cell area (r_s=0.49). Our results provide an important step towards understanding the micromechanical load transfer that leads to the non-linear macromechanical behaviour of the brain. STATEMENT OF SIGNIFICANCE: Within this article, we investigate the mechanical behaviour of brain tissue under three different deformation modes, in different anatomical regions, and for varying axon orientation. Further, we characterise the underlying microstructure in terms of various constituents. The correlation of these quantities with the material parameters of the anisotropic Ogden model reveals a decrease in shear modulus with increasing myelin area fraction. Strikingly, the tensile shear modulus correlates positively with cell and neuronal area fraction, whereas the compressive shear modulus decreases with increasing glial cell area. Our study finds that tissue non-linearity significantly depends on the myelin area fraction, cell density, and glial cell area. Our results provide an important step towards understanding the micromechanical load transfer that leads to the non-linear macromechanical behaviour of the brain.

Toward a Comprehensive Delineation of White Matter Tract-Related Deformation

Finite element (FE) models of the human head are valuable instruments to explore the mechanobiological pathway from external loading, localized brain response, and resultant injury risks. The injury predictability of these models depends on the use of effective criteria as injury predictors. The FE-derived normal deformation along white matter (WM) fiber tracts (i.e., tract-oriented strain) recently has been suggested as an appropriate predictor for axonal injury. However, the tract-oriented strain only represents a partial depiction of the WM fiber tract deformation. A comprehensive delineation of tract-related deformation may improve the injury predictability of the FE head model by delivering new tract-related criteria as injury predictors. Thus, the present study performed a theoretical strain analysis to comprehensively characterize the WM fiber tract deformation by relating the strain tensor of the WM element to its embedded fiber tract. Three new tract-related strains with exact analytical solutions were proposed, measuring the normal deformation perpendicular to the fiber tracts (i.e., tract-perpendicular strain), and shear deformation along and perpendicular to the fiber tracts (i.e., axial-shear strain and lateral-shear strain, respectively). The injury predictability of these three newly proposed strain peaks along with the previously used tract-oriented strain peak and maximum principal strain (MPS) were evaluated by simulating 151 impacts with known outcome (concussion or non-concussion). The results preliminarily showed that four tract-related strain peaks exhibited superior performance than MPS in discriminating concussion and non-concussion cases. This study presents a comprehensive quantification of WM tract-related deformation and advocates the use of orientation-dependent strains as criteria for injury prediction, which may ultimately contribute to an advanced mechanobiological understanding and enhanced computational predictability of brain injury.

Orientation of neurites influences severity of mechanically induced tau pathology

Chronic traumatic encephalopathy is a neurodegenerative disease associated with repeated traumatic brain injury (TBI). Chronic traumatic encephalopathy is a tauopathy, in which cognitive decline is accompanied by the accumulation of neurofibrillary tangles of the protein tau in patients' brains. We recently found that mechanical force alone can induce tau mislocalization to dendritic spines and loss of synaptic function in in vitro neuronal cultures with random cell organization. However, in the brain, neurons are highly aligned, so here we aimed to determine how neuronal organization influences early-stage tauopathy caused by mechanical injury. Using microfabricated cell culture constructs to control the growth of neurites and an in vitro simulated TBI device to apply controlled mechanical deformation, we found that neuronal orientation with respect to the direction of a uniaxial high-strain-rate stretch injury influences the degree of tau pathology in injured neurons. We found that a mechanical stretch applied parallel to the neurite alignment induces greater mislocalization of tau proteins to dendritic spines than does a stretch with the same strain applied perpendicular to the neurites. Synaptic function, characterized by the amplitude of miniature excitatory postsynaptic currents, was similarly decreased in neurons with neurites aligned parallel to stretch, whereas in neurons aligned perpendicular to stretch, it had little to no functional loss. Experimental injury parameters (strain, strain rate, direction of stretch) were combined with a standard viscoelastic solid model to show that in our in vitro model, neurite work density during stretch correlates with tau mislocalization. These findings suggest that in a TBI, the magnitude of brain deformation is not wholly predictive of neurodegenerative consequences of TBI but that deformation relative to local neuronal architecture and the neurite mechanical energy during injury are better metrics for predicting trauma-induced tauopathy.

Brain Strain: Computational Model-Based Metrics for Head Impact Exposure and Injury Correlation

Athletes participating in contact sports are exposed to repetitive subconcussive head impacts that may have long-term neurological consequences. To better understand these impacts and their effects, head impacts are often measured during football to characterize head impact exposure and estimate injury risk. Despite widespread use of kinematic-based metrics, it remains unclear whether any single metric derived from head kinematics is well-correlated with measurable changes in the brain. This shortcoming has motivated the increasing use of finite element (FE)-based metrics, which quantify local brain deformations. Additionally, quantifying cumulative exposure is of increased interest to examine the relationship to brain changes over time. The current study uses the atlas-based brain model (ABM) to predict the strain response to impacts sustained by 116 youth football athletes and proposes 36 new, or derivative, cumulative strain-based metrics that quantify the combined burden of head impacts over the course of a season. The strain-based metrics developed and evaluated for FE modeling and presented in the current study present potential for improved analytics over existing kinematically-based and cumulative metrics. Additionally, the findings highlight the importance of accounting for directional dependence and expand the techniques to explore spatial distribution of the strain response throughout the brain.

A mesoscale finite element modeling approach for understanding brain morphology and material heterogeneity effects in chronic traumatic encephalopathy

Chronic Traumatic Encephalopathy (CTE) affects a significant portion of athletes in contact sports but is difficult to quantify using clinical examinations and modeling approaches. We use an in silico approach to quantify CTE biomechanics using mesoscale Finite Element (FE) analysis that bridges with macroscale whole head FE analysis. The sulci geometry produces complex stress waves that interact with one another to create increased shear stresses at the sulci depth that are significantly larger than in analyses without sulci (from 0.5 to 18.0 kPa). Sulci peak stress concentration regions coincide with experimentally observed CTE sites documented in the literature. HighlightsSulci introduce stress localizations at their depth in the gray matterSulci stress fields interact to produce stress concentration sites in white matterDifferentiating brain tissue properties did not significantly affect peak stresses.

White Matter Tract-Oriented Deformation Is Dependent on Real-Time Axonal Fiber Orientation

Traumatic axonal injury (TAI) is a critical public health issue with its pathogenesis remaining largely elusive. Finite element (FE) head models are promising tools to bridge the gap between mechanical insult, localized brain response, and resultant injury. In particular, the FE-derived deformation along the direction of white matter (WM) tracts (i.e., tract-oriented strain) has been shown to be an appropriate predictor for TAI. The evolution of fiber orientation in time during the impact and its potential influence on the tract-oriented strain remains unknown, however. To address this question, the present study leveraged an embedded element approach to track real-time fiber orientation during impacts. A new scheme to calculate the tract-oriented strain was proposed by projecting the strain tensors from pre-computed simulations along the temporal fiber direction instead of its static counterpart directly obtained from diffuse tensor imaging. The results revealed that incorporating the real-time fiber orientation not only altered the direction but also amplified the magnitude of the tract-oriented strain, resulting in a generally more extended distribution and a larger volume ratio of WM exposed to high deformation along fiber tracts. These effects were exacerbated with the impact severities characterized by the acceleration magnitudes. Results of this study provide insights into how best to incorporate fiber orientation in head injury models and derive the WM tract-oriented deformation from computational simulations, which is important for furthering our understanding of the underlying mechanisms of TAI.

Multi-Scale White Matter Tract Embedded Brain Finite Element Model Predicts the Location of Traumatic Diffuse Axonal Injury

Finite element models (FEMs) are used increasingly in the traumatic brain injury (TBI) field to provide an estimation of tissue responses and predict the probability of sustaining TBI after a biomechanical event. However, FEM studies have mainly focused on predicting the absence/presence of TBI rather than estimating the location of injury. In this study, we created a multi-scale FEM of the pig brain with embedded axonal tracts to estimate the sites of acute (≤6 h) traumatic axonal injury (TAI) after rapid head rotation. We examined three finite element (FE)-derived metrics related to the axonal bundle deformation and three FE-derived metrics based on brain tissue deformation for prediction of acute TAI location. Rapid head rotations were performed in pigs, and TAI neuropathological maps were generated and colocalized to the FEM. The distributions of the FEM-derived brain/axonal deformations spatially correlate with the locations of acute TAI. For each of the six metric candidates, we examined a matrix of different injury thresholds (th_x) and distance to actual TAI sites (d_s) to maximize the average of two optimization criteria. Three axonal deformation-related TAI candidates predicted the sites of acute TAI within 2.5 mm, but no brain tissue metric succeeded. The optimal range of thresholds for maximum axonal strain, maximum axonal strain rate, and maximum product of axonal strain and strain rate were 0.08-0.14, 40-90, and 2.0-7.5 s^-1, respectively. The upper bounds of these thresholds resulted in higher true-positive prediction rate. In summary, this study confirmed the hypothesis that the large axonal-bundle deformations occur on/close to the areas that sustained TAI.

Embedded axonal fiber tracts improve finite element model predictions of traumatic brain injury

With the growing rate of traumatic brain injury (TBI), there is an increasing interest in validated tools to predict and prevent brain injuries. Finite element models (FEM) are valuable tools to estimate tissue responses, predict probability of TBI, and guide the development of safety equipment. In this study, we developed and validated an anisotropic pig brain multi-scale FEM by explicitly embedding the axonal tract structures and utilized the model to simulate experimental TBI in piglets undergoing dynamic head rotations. Binary logistic regression, survival analysis with Weibull distribution, and receiver operating characteristic curve analysis, coupled with repeated k-fold cross-validation technique, were used to examine 12 FEM-derived metrics related to axonal/brain tissue strain and strain rate for predicting the presence or absence of traumatic axonal injury (TAI). All 12 metrics performed well in predicting of TAI with prediction accuracy rate of 73-90%. The axonal-based metrics outperformed their rival brain tissue-based metrics in predicting TAI. The best predictors of TAI were maximum axonal strain times strain rate (MASxSR) and its corresponding optimal fraction-based metric (AF-MASxSR7.5) that represents the fraction of axonal fibers exceeding MASxSR of 7.5 s-1. The thresholds compare favorably with tissue tolerances found in in-vitro/in-vivo measurements in the literature. In addition, the damaged volume fractions (DVF) predicted using the axonal-based metrics, especially MASxSR (DVF = 0.05-4.5%), were closer to the actual DVF obtained from histopathology (AIV = 0.02-1.65%) in comparison with the DVF predicted using the brain-related metrics (DVF = 0.11-41.2%). The methods and the results from this study can be used to improve model prediction of TBI in humans.

Estimation of Anisotropic Material Properties of Soft Tissue by MRI of Ultrasound-Induced Shear Waves

This paper describes a new method for estimating anisotropic mechanical properties of fibrous soft tissue by imaging shear waves induced by focused ultrasound (FUS) and analyzing their direction-dependent speeds. Fibrous materials with a single, dominant fiber direction may exhibit anisotropy in both shear and tensile moduli, reflecting differences in the response of the material when loads are applied in different directions. The speeds of shear waves in such materials depend on the propagation and polarization directions of the waves relative to the dominant fiber direction. In this study, shear waves were induced in muscle tissue (chicken breast) ex vivo by harmonically oscillating the amplitude of an ultrasound beam focused in a cylindrical tissue sample. The orientation of the fiber direction relative to the excitation direction was varied by rotating the sample. Magnetic resonance elastography (MRE) was used to visualize and measure the full 3D displacement field due to the ultrasound-induced shear waves. The phase gradient (PG) of radially propagating "slow" and "fast" shear waves provided local estimates of their respective wave speeds and directions. The equations for the speeds of these waves in an incompressible, transversely isotropic (TI), linear elastic material were fitted to measurements to estimate the shear and tensile moduli of the material. The combination of focused ultrasound and MR imaging allows noninvasive, but comprehensive, characterization of anisotropic soft tissue.

Dynamics of spinal cord compression with different patterns of thoracolumbar burst fractures: Numerical simulations using finite element modelling

BACKGROUND

In thoracolumbar burst fractures, spinal cord primary injury involves a direct impact and energy transfer from bone fragments to the spinal cord. Unfortunately, imaging studies performed after the injury only depict the residual bone fragments position and pattern of spinal cord compression, with little insight on the dynamics involved during traumas. Knowledge of underlying mechanisms could be helpful in determining the severity of the primary injury, hence the extent of spinal cord damage and associated potential for recovery. Finite element models are often used to study dynamic processes, but have never been used specifically to simulate different severities of thoracolumbar burst fractures.

METHODS

Previously developed thoracolumbar spine and spinal cord finite element models were used and further validated, and representative vertebral fragments were modelled. A full factorial design was used to investigate the effects of comminution of the superior fragment, presence of an inferior fragment, fragments rotation and velocity, on maximum Von Mises stress and strain, maximum major strain, and pressure in the spinal cord.

FINDINGS

Fragment velocity clearly was the most influential factor. Fragments rotation and presence of an inferior fragment increased pressure, but rotation decreased both strains outputs. Although significant for both strains outputs, comminution of the superior fragment isn't estimated to influence outputs.

INTERPRETATION

This study is the first, to the authors' knowledge, to examine a detailed spinal cord model impacted in situ by fragments from burst fractures. This numeric model could be used in the future to comprehensively link traumatic events or imaging study characteristics to known spinal cord injuries severity and potential for recovery.

Study of cerebrospinal injuries by force transmission secondary to mandibular impacts using a finite element model

Brain and cervical injuries are often described after major facial impacts but rarely after low-intensity mandibular impacts. Force transmission to the brain and spinal cord from a mandibular impact such as a punch was evaluated by the creation and validation of a complete finite element model of the head and neck. Anteroposterior uppercut impacts on the jaw were associated with considerable extension and strong stresses at the junction of the brainstem and spinal cord. Hook punch impacts transmitted forces directly to the brainstem and the spinal cord without extension of the spinal cord. Deaths after this type of blow with no observed histological lesions may be related to excessive stressing of the brainstem, through which pass the sensory-motor pathways and the vagus nerve and which is the regulatory center of the major vegetative functions. Biological parameters are different in each individual, and by using digital modeling they can be modulated at will (jaw shape, dentition…) for a realistic approach to forensic applications.

The Influence of Shear Anisotropy in mTBI: A White Matter Constitutive Model

We examine the influence of shear anisotropy of brain tissue on the potential for mild traumatic brain injury. First we develop a new constitutive description for the white matter in the brain that can capture the anisotropic behavior of the white matter in both tension and shear. The material parameters for the models are determined using a set of three experiments already published in the literature. The calibrated and parameterized model is then implemented in a computational (finite element) model of the head. This computational model is two-dimensional and is used to simulate a previously published injury-causing event in the National Hockey League, using axonal strain as criterion to assess the level of diffuse axonal injury. It is demonstrated that the inclusion of shear anisotropy affects both the nature and the extent of predicted injury. Further, the locations of the predicted injury are more consistent with observations in the literature.

Determining constitutive behavior of the brain tissue using digital image correlation and finite element modeling

Detailed knowledge about the mechanical properties of brain can improve numerical modeling of the brain under various loading conditions. The success of this modeling depends on constitutive model and reliable extraction of its material constants. The isotropy of the brain tissue is a key factor which affects the form of constitutive models. In this study, compression tests were performed on different parts of the sheep brain tissue. Also, the digital image correlation (DIC) method was utilized to investigate the direction dependency of brain parts considering their microstructures. To this aim, the DIC method was employed to measure the transverse strain of two lateral sides of the tissue samples. The results of DIC method revealed that the brain stem and corona radiata were isotropic, while the mixed white and gray matter showed an unrepeatable behavior depending on the extracted sample. To examine and validate DIC method, stress-strain diagrams were also used to investigate the isotropy. It could be concluded that axonal fibers had no reinforcing role in the brain tissue. Furthermore, the DIC method indicated incompressibility of the brain tissue. Then, the significance of using a correct method to extract the material constants of brain was discussed. In other words, the effect of the real boundary conditions in experiments, which was neglected in most previous studies, was taken into account here. Finally, the particle swarm optimization algorithm along with the finite element modeling was used to estimate the hyper-viscoelastic constants of different parts of the brain tissue.

Identification of the visco-hyperelastic properties of brain white matter based on the combination of inverse method and experiment

To fully understand the brain injury mechanism and develop effective protective approaches, an accurate constitutive model of brain tissue is firstly required. Generally, the brain tissue is regarded as a kind of viscoelastic material and is simply used in the simulation of brain injury. In fact, the brain tissue has the behavior of the visco-hyperelastic property. Therefore, this paper presents an effective computational inverse method to determine the material parameters of visco-hyperelastic constitutive model of brain white matter through compression experiments. First, with the help of 3D hand scanner, 3D geometries of brain white matter specimens are obtained to make it possible to establish the accurate simulation models of the specific specimens. Then, the global sensitivity analysis is adopted to evaluate the importance of the material parameters and further determine the parameters which may be identified. Subsequently, based on the genetic algorithm, the optimal material parameters of brain white matter can be identified by minimizing the match error between the experimental and simulated responses. Finally, by comparing the experiment and simulation results on the other specific specimen, and the simulation results with the material parameters from the references, respectively, the accuracy and reliability of the constitutive model parameters of brain white matter are demonstrated. Graphical abstract The main flowchart of the computational inverse technique for determining the material parameters of specimen-specific on brain white matter. Generalization: Combining the computational inverse method and unconfined uniaxial compression experiment of the specific specimen, an effective identification method is presented to accurately determine the hyperelastic and viscoelastic parameters of brain white matter in this paper.

Mesh Convergence Behavior and the Effect of Element Integration of a Human Head Injury Model

Numerous head injury models exist that vary in mesh density by orders of magnitude. A careful study of the mesh convergence behavior is necessary, especially in terms of strain most relevant to brain injury. To this end, as well as to investigate the effect of element integration scheme on simulated strains, we re-meshed the Worcester Head Injury Model at five mesh densities (~ 7.2-1000 k high-quality hexahedral elements of the brain). Results from explicit dynamic simulations of three cadaveric impacts and an in vivo head rotation were compared. First, scalar metrics of the whole brain only considering magnitude were used, including peak maximum principal strain and population-based median strain. They were further extended to deep white matter regions and the entire brain elements, respectively, to form two "response vectors" to account for both magnitude and distribution. Using benchmark enhanced full-integration elements (C3D8I), a minimum of 202.8 k brain elements were necessary to converge for response vectors of the deep white matter regions. This model was further used to simulate with reduced integration (C3D8R). We found that hourglass energy higher than the common rule of thumb (e.g., up to 44.38% vs. < 10% of internal energy) was necessary to maintain comparable strain relative to C3D8I. Based on these results, it is recommended that a human head injury model should have a minimum number of 202.8 k elements, or an average element size of no larger than 1.8 mm, for the brain. C3D8R formulation with relax stiffness hourglass control using a high scaling factor is also recommended to achieve sufficient accuracy without substantial computational cost.

A three-dimensional micromechanical model of brain white matter with histology-informed probabilistic distribution of axonal fibers

This paper presents a three-dimensional micromechanical model of brain white matter tissue as a transversely isotropic soft composite described by the generalized Ogden hyperelastic model. The embedded element technique, with corrected stiffness redundancy in large deformations, was used for the embedment of a histology-informed probabilistic distribution of the axonal fibers in the extracellular matrix. The model was linked to a multi-objective, multi-parametric optimization algorithm, using the response surface methodology, for characterization of material properties of the axonal fibers and extracellular matrix in an inverse finite element analysis. The optimum hyperelastic characteristics of the tissue constituents, obtained based on the axonal and transverse direction test results of the corona radiata tissue samples, indicated that the axonal fibers were almost thirteen times stiffer than the extracellular matrix under large deformations. Simulation of the same tissue under a different loading condition, as well as that of another white matter tissue, i.e., the corpus callosum, in the axonal and transverse directions, using the optimized hyperelastic characteristics revealed tissue responses very close to those of the experiments. The results of the model at the sub-tissue level indicated that the stress concentrations were considerably large around the small axons, which might contribute into the brain injury.

White Matter Anisotropy for Impact Simulation and Response Sampling in Traumatic Brain Injury

Advanced neuroimaging provides new opportunities to enhance head injury models, including the incorporation of white matter (WM) structural anisotropy. Information from high-resolution neuroimaging, however, usually has to be "down-sampled" to match a typically coarse brain mesh. To understand how this mesh-image resolution mismatch affects impact simulation and subsequent response sampling, we compared three competing anisotropy implementations (using either voxels, tractography, or a multiscale submodeling) and two response sampling strategies (element-wise or tractography-based, using brain mesh or neuroimaging for region segmentation, respectively). Using the combination of high resolution options as a baseline, we studied how the choice in each individual category affected the resulting injury metrics. By simulating a recorded loss of consciousness head impact, we found that injury metrics including peak strain and injury susceptibility in the deep WM regions based on fiber strain, but not on maximum principal strain, were sensitive to the anisotropy implementation, response sampling, and region segmentation. Overall, it was recommended to use tractography for anisotropy implementation and response sampling, and to employ neuroimaging for region segmentation, because they led to more accurate injury metrics. Further refining mesh locally via submodeling was unnecessary. Brain strain responses were also parametrically found to be closer to that from minimum fiber reinforcement, consistent with the fact that the majority of WM had a rather high degree of fiber dispersion. Finally, the upgraded Worcester Head Injury Model incorporating WM anisotropy was successfully re-validated against cadaveric impacts and an in vivo head rotation ("good" to "excellent" validation with an average Correlation Analysis score of 0.437 and 0.509, respectively). These investigations may facilitate further continual development of head injury models to better study traumatic brain injury.

Cognitive fatigue is associated with reduced anterior internal capsule integrity in veterans with history of mild to moderate traumatic brain injury

No known studies have directly examined white matter microstructural correlates of cognitive fatigue post-TBI in a Veteran sample. We therefore investigated the relationship between cognitive fatigue and white matter integrity in Veterans with history of mild to moderate TBI (mmTBI). 59 Veterans (TBI = 34, Veteran Controls [VCs] = 25]) with and without history of mmTBI underwent structural 3T DTI scans and completed questionnaires related to cognitive fatigue and psychiatric symptoms. Tractography was employed on six regions of interest, including the anterior and posterior limbs of the internal capsule; genu; body and splenium of the corpus callosum; and cingulum bundle. Group analyses revealed that those with history of mmTBI displayed significantly greater levels of cognitive fatigue relative to those with no history of head injury (p = .02). Within the mmTBI group, independent of psychiatric symptoms, decreased white matter microstructural integrity of the left anterior internal capsule was associated with greater levels of cognitive fatigue (p = .01). Results show that the subjective experience of cognitive fatigue following neurotrauma may be linked to the disruption of striato-thalamo-cortical tracts that are important in mediating arousal and higher-order cognitive processes. These findings build upon those from existing functional neuroimaging studies in those with history of TBI, providing further evidence for the neural basis of cognitive fatigue in head injured adults.

Combat Helmet Suspension System Stiffness Influences Linear Head Acceleration and White Matter Tissue Strains: Implications for Future Helmet Design

Combat helmets are expected to protect the warfighter from a variety of blunt, blast, and ballistic threats. Their blunt impact performance is evaluated by measuring linear headform acceleration in drop tower tests, which may be indicative of skull fracture, but not necessarily brain injury. The current study leverages a blunt impact biomechanics model consisting of a head, neck, and helmet with a suspension system to predict how pad stiffness affects both (1) linear acceleration alone and (2) brain tissue response induced by both linear and rotational acceleration. The approach leverages diffusion tensor imaging information to estimate how pad stiffness influences white matter tissue strains, which may be representative of diffuse axonal injury. Simulation results demonstrate that a softer pad material reduces linear head accelerations for mild and moderate impact velocities, but a stiffer pad design minimizes linear head accelerations at high velocities. Conversely, white matter tract-oriented strains were found to be smallest with the softer pads at the severe impact velocity. The results demonstrate that the current helmet blunt impact testing standards' standalone measurement of linear acceleration does not always convey how the brain tissue responds to changes in helmet design. Consequently, future helmet testing should consider the brain's mechanical response when evaluating new designs.

Micromechanics of brain white matter tissue: A fiber-reinforced hyperelastic model using embedded element technique

A transverse-plane hyperelastic micromechanical model of brain white matter tissue was developed using the embedded element technique (EET). The model consisted of a histology-informed probabilistic distribution of axonal fibers embedded within an extracellular matrix, both described using the generalized Ogden hyperelastic material model. A correcting method, based on the strain energy density function, was formulated to resolve the stiffness redundancy problem of the EET in large deformation regime. The model was then used to predict the homogenized tissue behavior and the associated localized responses of the axonal fibers under quasi-static, transverse, large deformations. Results indicated that with a sufficiently large representative volume element (RVE) and fine mesh, the statistically randomized microstructure implemented in the RVE exhibits directional independency in transverse plane, and the model predictions for the overall and local tissue responses, characterized by the normalized strain energy density and Cauchy and von Mises stresses, are independent from the modeling parameters. Comparison of the responses of the probabilistic model with that of a simple uniform RVE revealed that only the first one is capable of representing the localized behavior of the tissue constituents. The validity test of the model predictions for the corona radiata against experimental data from the literature indicated a very close agreement. In comparison with the conventional direct meshing method, the model provided almost the same results after correcting the stiffness redundancy, however, with much less computational cost and facilitated geometrical modeling, meshing, and boundary conditions imposing. It was concluded that the EET can be used effectively for detailed probabilistic micromechanical modeling of the white matter in order to provide more accurate predictions for the axonal responses, which are of great importance when simulating the brain trauma or tumor growth.

Effect of cerebrospinal fluid modeling on spherically convergent shear waves during blunt head trauma

The MRI-based computational model, previously validated by tagged MRI and harmonic phase imaging analysis technique on in vivo human brain deformation, is used to study transient wave dynamics during blunt head trauma. Three different constitutive models are used for the cerebrospinal fluid: incompressible solid elastic, viscoelastic, and fluid-like elastic using an equation of state model. Three impact cases are simulated, which indicate that the blunt impacts give rise not only to a fast pressure wave but also to a slow, and potentially much more damaging, shear (distortional) wave that converges spherically towards the brain center. The wave amplification due to spherical geometry is balanced by damping due to tissues' viscoelasticity and the heterogeneous brain structure, suggesting a stochastic competition of these 2 opposite effects. It is observed that this convergent shear wave is dependent on the constitutive property of the cerebrospinal fluid, whereas the peak pressure is not as significantly affected.

Multiscale modeling in the clinic: diseases of the brain and nervous system

Computational neuroscience is a field that traces its origins to the efforts of Hodgkin and Huxley, who pioneered quantitative analysis of electrical activity in the nervous system. While also continuing as an independent field, computational neuroscience has combined with computational systems biology, and neural multiscale modeling arose as one offshoot. This consolidation has added electrical, graphical, dynamical system, learning theory, artificial intelligence and neural network viewpoints with the microscale of cellular biology (neuronal and glial), mesoscales of vascular, immunological and neuronal networks, on up to macroscales of cognition and behavior. The complexity of linkages that produces pathophysiology in neurological, neurosurgical and psychiatric disease will require multiscale modeling to provide understanding that exceeds what is possible with statistical analysis or highly simplified models: how to bring together pharmacotherapeutics with neurostimulation, how to personalize therapies, how to combine novel therapies with neurorehabilitation, how to interlace periodic diagnostic updates with frequent reevaluation of therapy, how to understand a physical disease that manifests as a disease of the mind. Multiscale modeling will also help to extend the usefulness of animal models of human diseases in neuroscience, where the disconnects between clinical and animal phenomenology are particularly pronounced. Here we cover areas of particular interest for clinical application of these new modeling neurotechnologies, including epilepsy, traumatic brain injury, ischemic disease, neurorehabilitation, drug addiction, schizophrenia and neurostimulation.

Injury prediction and vulnerability assessment using strain and susceptibility measures of the deep white matter

Reliable prediction and diagnosis of concussion is important for its effective clinical management. Previous model-based studies largely employ peak responses from a single element in a pre-selected anatomical region of interest (ROI) and utilize a single training dataset for injury prediction. A more systematic and rigorous approach is necessary to scrutinize the entire white matter (WM) ROIs as well as ROI-constrained neural tracts. To this end, we evaluated injury prediction performances of the 50 deep WM regions using predictor variables based on strains obtained from simulating the 58 reconstructed American National Football League head impacts. To objectively evaluate performance, repeated random subsampling was employed to split the impacts into independent training and testing datasets (39 and 19 cases, respectively, with 100 trials). Univariate logistic regressions were conducted based on training datasets to compute the area under the receiver operating characteristic curve (AUC), while accuracy, sensitivity, and specificity were reported based on testing datasets. Two tract-wise injury susceptibilities were identified as the best overall via pair-wise permutation test. They had comparable AUC, accuracy, and sensitivity, with the highest values occurring in superior longitudinal fasciculus (SLF; 0.867-0.879, 84.4-85.2, and 84.1-84.6%, respectively). Using metrics based on WM fiber strain, the most vulnerable ROIs included genu of corpus callosum, cerebral peduncle, and uncinate fasciculus, while genu and main body of corpus callosum, and SLF were among the most vulnerable tracts. Even for one un-concussed athlete, injury susceptibility of the cingulum (hippocampus) right was elevated. These findings highlight the unique injury discriminatory potentials of computational models and may provide important insight into how best to incorporate WM structural anisotropy for investigation of brain injury.

A Mechanistic End-to-End Concussion Model That Translates Head Kinematics to Neurologic Injury

Past concussion studies have focused on understanding the injury processes occurring on discrete length scales (e.g., tissue-level stresses and strains, cell-level stresses and strains, or injury-induced cellular pathology). A comprehensive approach that connects all length scales and relates measurable macroscopic parameters to neurological outcomes is the first step toward rationally unraveling the complexity of this multi-scale system, for better guidance of future research. This paper describes the development of the first quantitative end-to-end (E2E) multi-scale model that links gross head motion to neurological injury by integrating fundamental elements of tissue and cellular mechanical response with axonal dysfunction. The model quantifies axonal stretch (i.e., tension) injury in the corpus callosum, with axonal functionality parameterized in terms of axonal signaling. An internal injury correlate is obtained by calculating a neurological injury measure (the average reduction in the axonal signal amplitude) over the corpus callosum. By using a neurologically based quantity rather than externally measured head kinematics, the E2E model is able to unify concussion data across a range of exposure conditions and species with greater sensitivity and specificity than correlates based on external measures. In addition, this model quantitatively links injury of the corpus callosum to observed specific neurobehavioral outcomes that reflect clinical measures of mild traumatic brain injury. This comprehensive modeling framework provides a basis for the systematic improvement and expansion of this mechanistic-based understanding, including widening the range of neurological injury estimation, improving concussion risk correlates, guiding the design of protective equipment, and setting safety standards.

Modeling the mechanics of axonal fiber tracts using the embedded finite element method

A subject-specific human head finite element model with embedded axonal fiber tractography obtained from diffusion tensor imaging was developed. The axonal fiber tractography finite element model was coupled with the volumetric elements in the head model using the embedded element method. This technique enables the calculation of axonal strains and real-time tracking of the mechanical response of the axonal fiber tracts. The coupled model was then verified using pressure and relative displacement-based (between skull and brain) experimental studies and was employed to analyze a head impact, demonstrating the applicability of this method in studying axonal injury. Following this, a comparison study of different injury criteria was performed. This model was used to determine the influence of impact direction on the extent of the axonal injury. The results suggested that the lateral impact loading is more dangerous compared to loading in the sagittal plane, a finding in agreement with previous studies. Through this analysis, we demonstrated the viability of the embedded element method as an alternative numerical approach for studying axonal injury in patient-specific human head models.

Anisotropic finite element models for brain injury prediction: the sensitivity of axonal strain to white matter tract inter-subject variability

Computational models incorporating anisotropic features of brain tissue have become a valuable tool for studying the occurrence of traumatic brain injury. The tissue deformation in the direction of white matter tracts (axonal strain) was repeatedly shown to be an appropriate mechanical parameter to predict injury. However, when assessing the reliability of axonal strain to predict injury in a population, it is important to consider the predictor sensitivity to the biological inter-subject variability of the human brain. The present study investigated the axonal strain response of 485 white matter subject-specific anisotropic finite element models of the head subjected to the same loading conditions. It was observed that the biological variability affected the orientation of the preferential directions (coefficient of variation of 39.41% for the elevation angle—coefficient of variation of 29.31% for the azimuth angle) and the determination of the mechanical fiber alignment parameter in the model (gray matter volume 55.55–70.75%). The magnitude of the maximum axonal strain showed coefficients of variation of 11.91%. On the contrary, the localization of the maximum axonal strain was consistent: the peak of strain was typically located in a 2 cm³ volume of the brain. For a sport concussive event, the predictor was capable of discerning between non-injurious and concussed populations in several areas of the brain. It was concluded that, despite its sensitivity to biological variability, axonal strain is an appropriate mechanical parameter to predict traumatic brain injury.

Compromised Neurocircuitry in Chronic Blast-Related Mild Traumatic Brain Injury

The aim of this study was to apply recently developed automated fiber segmentation and quantification methods using diffusion tensor imaging (DTI) and DTI-based deterministic and probabilistic tractography to access local and global diffusion changes in blast-induced mild traumatic brain injury (bmTBI). Two hundred and two (202) male active US service members who reported persistent post-concussion symptoms for more than 6 months after injury were recruited. An additional forty (40) male military controls were included for comparison. DTI results were examined in relation to post-concussion and post-traumatic stress disorder (PTSD) symptoms. No significant group difference in DTI metrics was found using voxel-wise analysis. However, group comparison using tract profile analysis and tract specific analysis, as well as single subject analysis using tract profile analysis revealed the most prominent white matter microstructural injury in chronic bmTBI patients over the frontal fiber tracts, that is, the front-limbic projection fibers (cingulum bundle, uncinate fasciculus), the fronto-parieto-temporal association fibers (superior longitudinal fasciculus), and the fronto-striatal pathways (anterior thalamic radiation). Effects were noted to be sensitive to the number of previous blast exposures, with a negative association between fractional anisotropy (FA) and time since most severe blast exposure in a subset of the multiple blast-exposed group. However, these patterns were not observed in the subgroups classified using macrostructural changes (T2 white matter hyperintensities). Moreover, post-concussion symptoms and PTSD symptoms, as well as neuropsychological function were associated with low FA in the major nodes of compromised neurocircuitry. Hum Brain Mapp 38:352-369, 2017. © 2016 Wiley Periodicals, Inc.

Dynamic association between perfusion and white matter integrity across time since injury in Veterans with history of TBI

OBJECTIVE

Cerebral blood flow (CBF) plays a critical role in the maintenance of neuronal integrity, and CBF alterations have been linked to deleterious white matter changes. Although both CBF and white matter microstructural alterations have been observed within the context of traumatic brain injury (TBI), the degree to which these pathological changes relate to one another and whether this association is altered by time since injury have not been examined. The current study therefore sought to clarify associations between resting CBF and white matter microstructure post-TBI.

METHODS

37 veterans with history of mild or moderate TBI (mmTBI) underwent neuroimaging and completed health and psychiatric symptom questionnaires. Resting CBF was measured with multiphase pseudocontinuous arterial spin labeling (MPPCASL), and white matter microstructural integrity was measured with diffusion tensor imaging (DTI). The cingulate cortex and cingulum bundle were selected as a priori regions of interest for the ASL and DTI data, respectively, given the known vulnerability of these regions to TBI.

RESULTS

Regression analyses controlling for age, sex, and posttraumatic stress disorder (PTSD) symptoms revealed a significant time since injury × resting CBF interaction for the left cingulum (p < 0.005). Decreased CBF was significantly associated with reduced cingulum fractional anisotropy (FA) in the chronic phase; however, no such association was observed for participants with less remote TBI.

CONCLUSIONS

Our results showed that reduced CBF was associated with poorer white matter integrity in those who were further removed from their brain injury. Findings provide preliminary evidence of a possible dynamic association between CBF and white matter microstructure that warrants additional consideration within the context of the negative long-term clinical outcomes frequently observed in those with history of TBI. Additional cross-disciplinary studies integrating multiple imaging modalities (e.g., DTI, ASL) and refined neuropsychiatric assessment are needed to better understand the nature, temporal course, and dynamic association between brain changes and clinical outcomes post-injury.

Numerical Simulation of Focused Shock Shear Waves in Soft Solids and a Two-Dimensional Nonlinear Homogeneous Model of the Brain

Shear waves that propagate in soft solids, such as the brain, are strongly nonlinear and can develop into shock waves in less than one wavelength. We hypothesize that these shear shock waves could be responsible for certain types of traumatic brain injuries (TBI) and that the spherical geometry of the skull bone could focus shear waves deep in the brain, generating diffuse axonal injuries. Theoretical models and numerical methods that describe nonlinear polarized shear waves in soft solids such as the brain are presented. They include the cubic nonlinearities that are characteristic of soft solids and the specific types of nonclassical attenuation and dispersion observed in soft tissues and the brain. The numerical methods are validated with analytical solutions, where possible, and with self-similar scaling laws where no known solutions exist. Initial conditions based on a human head X-ray microtomography (CT) were used to simulate focused shear shock waves in the brain. Three regimes are investigated with shock wave formation distances of 2.54 m, 0.018 m, and 0.0064 m. We demonstrate that under realistic loading scenarios, with nonlinear properties consistent with measurements in the brain, and when the shock wave propagation distance and focal distance coincide, nonlinear propagation can easily overcome attenuation to generate shear shocks deep inside the brain. Due to these effects, the accelerations in the focal are larger by a factor of 15 compared to acceleration at the skull surface. These results suggest that shock wave focusing could be responsible for diffuse axonal injuries.

Brain injury tolerance limit based on computation of axonal strain

Traumatic brain injury (TBI) is the leading cause of death and permanent impairment over the last decades. In both the severe and mild TBIs, diffuse axonal injury (DAI) is the most common pathology and leads to axonal degeneration. Computation of axonal strain by using finite element head model in numerical simulation can enlighten the DAI mechanism and help to establish advanced head injury criteria. The main objective of this study is to develop a brain injury criterion based on computation of axonal strain. To achieve the objective a state-of-the-art finite element head model with enhanced brain and skull material laws, was used for numerical computation of real world head trauma. The implementation of new medical imaging data such as, fractional anisotropy and axonal fiber orientation from Diffusion Tensor Imaging (DTI) of 12 healthy patients into the finite element brain model was performed to improve the brain constitutive material law with more efficient heterogeneous anisotropic visco hyper-elastic material law. The brain behavior has been validated in terms of brain deformation against Hardy et al. (2001), Hardy et al. (2007), and in terms of brain pressure against Nahum et al. (1977) and Trosseille et al. (1992) experiments. Verification of model stability has been conducted as well. Further, 109 well-documented TBI cases were simulated and axonal strain computed to derive brain injury tolerance curve. Based on an in-depth statistical analysis of different intra-cerebral parameters (brain axonal strain rate, axonal strain, first principal strain, Von Mises strain, first principal stress, Von Mises stress, CSDM (0.10), CSDM (0.15) and CSDM (0.25)), it was shown that axonal strain was the most appropriate candidate parameter to predict DAI. The proposed brain injury tolerance limit for a 50% risk of DAI has been established at 14.65% of axonal strain. This study provides a key step for a realistic novel injury metric for DAI.

White Matter Injury Susceptibility via Fiber Strain Evaluation Using Whole-Brain Tractography

Microscale brain injury studies suggest axonal elongation as a potential mechanism for diffuse axonal injury (DAI). Recent studies have begun to incorporate white matter (WM) structural anisotropy in injury analysis, with initial evidence suggesting improved injury prediction performance. In this study, we further develop a tractography-based approach to analyze fiber strains along the entire lengths of fibers from voxel- or anatomically constrained whole-brain tractography. This technique potentially extends previous element- or voxel-based methods that instead utilize WM fiber orientations averaged from typically coarse elements or voxels. Perhaps more importantly, incorporating tractography-based axonal structural information enables assessment of the overall injury risks to functionally important neural pathways and the anatomical regions they connect, which is not possible with previous methods. A DAI susceptibility index was also established to quantify voxel-wise WM local structural integrity and tract-wise damage of individual neural pathways. This "graded" injury susceptibility potentially extends the commonly employed treatment of injury as a simple binary condition. As an illustration, we evaluate the DAI susceptibilities of WM voxels and transcallosal fiber tracts in three idealized head impacts. Findings suggest the potential importance of the tractography-based approach for injury prediction. These efforts may enable future studies to correlate WM mechanical responses with neuroimaging, cognitive alteration, and concussion, and to reveal the relative vulnerabilities of neural pathways and identify the most vulnerable ones in real-world head impacts.

Connectomic and Surface-Based Morphometric Correlates of Acute Mild Traumatic Brain Injury

Reduced integrity of white matter (WM) pathways and subtle anomalies in gray matter (GM) morphology have been hypothesized as mechanisms in mild traumatic brain injury (mTBI). However, findings on structural brain changes in early stages after mTBI are inconsistent and findings related to early symptoms severity are rare. Fifty-one patients were assessed with multimodal neuroimaging and clinical methods exclusively within 7 days following mTBI and compared to 53 controls. Whole-brain connectivity based on diffusion tensor imaging was subjected to network-based statistics, whereas cortical surface area, thickness, and volume based on T1-weighted MRI scans were investigated using surface-based morphometric analysis. Reduced connectivity strength within a subnetwork of 59 edges located predominantly in bilateral frontal lobes was significantly associated with higher levels of self-reported symptoms. In addition, cortical surface area decreases were associated with stronger complaints in five clusters located in bilateral frontal and postcentral cortices, and in the right inferior temporal region. Alterations in WM and GM were localized in similar brain regions and moderately-to-strongly related to each other. Furthermore, the reduction of cortical surface area in the frontal regions was correlated with poorer attentive-executive performance in the mTBI group. Finally, group differences were detected in both the WM and GM, especially when focusing on a subgroup of patients with greater complaints, indicating the importance of classifying mTBI patients according to severity of symptoms. This study provides evidence that mTBI affects not only the integrity of WM networks by means of axonal damage but also the morphology of the cortex during the initial post-injury period. These anomalies might be greater in the acute period than previously believed and the involvement of frontal brain regions was consistently pronounced in both findings. The dysconnected subnetwork suggests that mTBI can be conceptualized as a dysconnection syndrome. It remains unclear whether reduced WM integrity is the trigger for changes in cortical surface area or whether tissue deformations are the direct result of mechanical forces acting on the brain. The findings suggest that rapid identification of high-risk patients with the use of clinical scales should be assessed acutely as part of the mTBI protocol.

Nodal versus Total Axonal Strain and the Role of Cholesterol in Traumatic Brain Injury

Traumatic brain injury (TBI) is a health threat that affects every year millions of people involved in motor vehicle and sporting accidents, and thousands of soldiers in battlefields. Diffuse axonal injury (DAI) is one of the most frequent types of TBI leading to death. In DAI, the initial traumatic event is followed by a cascade of biochemical changes that take time to develop in full, so that symptoms may not become apparent until days or weeks after the original injury. Hence, DAI is a dynamic process, and the opportunity exists to prevent its progression provided the initial trauma can be predicted at the molecular level. Here, we present preliminary evidence from micro-finite element (FE) simulations that the mechanical response of central nervous system myelinated fibers is dependent on the axonal diameter, the ratio between axon diameter and fiber diameter (g-ratio), the microtubules density, and the cholesterol concentration in the axolemma and myelin. A key outcome of the simulations is that there is a significant difference between the overall level of strain in a given axonal segment and the level of local strain in the Ranvier nodes contained in that segment, with the nodal strain being much larger than the total strain. We suggest that the acquisition of this geometric and biochemical information by means of already available high resolution magnetic resonance imaging techniques, and its incorporation in current FE models of the brain will enhance the models capacity to predict the site and magnitude of primary axonal damage upon TBI.

The importance of structural anisotropy in computational models of traumatic brain injury

Understanding the mechanisms of injury might prove useful in assisting the development of methods for the management and mitigation of traumatic brain injury (TBI). Computational head models can provide valuable insight into the multi-length-scale complexity associated with the primary nature of diffuse axonal injury. It involves understanding how the trauma to the head (at the centimeter length scale) translates to the white-matter tissue (at the millimeter length scale), and even further down to the axonal-length scale, where physical injury to axons (e.g., axon separation) may occur. However, to accurately represent the development of TBI, the biofidelity of these computational models is of utmost importance. There has been a focused effort to improve the biofidelity of computational models by including more sophisticated material definitions and implementing physiologically relevant measures of injury. This paper summarizes recent computational studies that have incorporated structural anisotropy in both the material definition of the white matter and the injury criterion as a means to improve the predictive capabilities of computational models for TBI. We discuss the role of structural anisotropy on both the mechanical response of the brain tissue and on the development of injury. We also outline future directions in the computational modeling of TBI.

Group-wise evaluation and comparison of white matter fiber strain and maximum principal strain in sports-related concussion

Sports-related concussion is a major public health problem in the United States and yet its biomechanical mechanisms remain unclear. In vitro studies demonstrate axonal elongation as a potential injury mechanism; however, current response-based injury predictors (e.g., maximum principal strain, ε(ep)) typically do not incorporate axonal orientations. We investigated the significance of white matter (WM) fiber orientation in strain estimation and compared fiber strain (ε(n)) with ε(ep) for 11 athletes with a clinical diagnosis of concussion. Geometrically accurate subject-specific head models with high mesh quality were created based on the Dartmouth Head Injury Model (DHIM), which was successfully validated (performance categorized as "good" to "excellent"). For WM regions estimated to be exposed to high strains using a range of injury thresholds (0.09-0.28), substantial differences existed between ε(n) and ε(ep) in both distribution (Dice coefficient of 0.13-0.33) and extent (∼ 5-10-fold differences), especially at higher threshold levels and higher rotational acceleration magnitudes. For example, an average of 3.2% vs. 29.8% of WM was predicted above an optimal threshold of 0.18 established from an in vivo animal study using ε(n) and ε(ep), respectively, with an average Dice coefficient of 0.14. The distribution of WM regions with high ε(n) was consistent with typical heterogeneous patterns of WM disruptions in diffuse axonal injury, and the group-wise extent at the optimal threshold matched well with the percentage of WM voxels experiencing significant longitudinal changes of fractional anisotropy and mean diffusivity (3.2% and 3.44%, respectively) found from a separate independent study. These results suggest the significance of incorporating WM microstructural anisotropy in future brain injury studies.