An axonal strain injury criterion for traumatic brain injury

Computational models are often used as tools to study traumatic brain injury. The fidelity of such models depends on the incorporation of an appropriate level of structural detail, the accurate representation of the material behavior, and the use of an appropriate measure of injury. In this study, an axonal strain injury criterion is used to estimate the probability of diffuse axonal injury (DAI), which accounts for a large percentage of deaths due to brain trauma and is characterized by damage to neural axons in the deep white matter regions of the brain. We present an analytical and computational model that treats the white matter as an anisotropic, hyperelastic material. Diffusion tensor imaging is used to incorporate the structural orientation of the neural axons into the model. It is shown that the degree of injury that is predicted in a computational model of DAI is highly dependent on the incorporation of the axonal orientation information and the inclusion of anisotropy into the constitutive model for white matter.     

Modeling of microstructural kinematics during simple elongation of central nervous system tissue

Damage to axons and glial cells in the central nervous system (CNS) white matter is a nearly universal feature of traumatic brain injury, yet it is not clear how the tissue mechanical deformations are transferred to the cellular components of the CNS. Defining how cellular deformations relate to the applied tissue deformation field can both highlight cellular populations at risk for mechanical injury, and define the fraction of cells in a specific population that will exhibit damage. In this investigation, microstructurally based models of CNS white matter were developed and tested against measured transformations of the CNS tissue microstructure under simple elongation. Results show that axons in the unstretched optic nerves were significantly wavy or undulated, where the measured axonal path length was greater than the end-to-end distance of the axon. The average undulation parameter--defined as the true axonal length divided by the end-to-end length--was 1.13. In stretched nerves, mean axonal undulations decreased with increasing applied stretch ratio (lambda)--the mean undulation values decreased to 1.06 at lambda = 1.06, 1.04 at lambda = 1.12, and 1.02 at lambda = 1.25. A model describing the gradual coupling, or tethering, of the axons to the surrounding glial cells best fit the experimental data. These modeling efforts indicate the fraction of the axonal and glial populations experiencing deformation increases with applied elongation, consistent with the observation that both axonal and glial cell injury increases at higher levels of white matter injury. Ultimately, these results can be used in conjunction with computational simulations of traumatic brain injury to aid in establishing the relative risk of cellular structures in the CNS white matter to mechanical injury.     

Combining the Finite Element Method with Structural Connectome-based Analysis for Modeling Neurotrauma: Connectome Neurotrauma Mechanics

This article presents the integration of brain injury biomechanics and graph theoretical analysis of neuronal connections, or connectomics, to form a neurocomputational model that captures spatiotemporal characteristics of trauma. We relate localized mechanical brain damage predicted from biofidelic finite element simulations of the human head subjected to impact with degradation in the structural connectome for a single individual. The finite element model incorporates various length scales into the full head simulations by including anisotropic constitutive laws informed by diffusion tensor imaging. Coupling between the finite element analysis and network-based tools is established through experimentally-based cellular injury thresholds for white matter regions. Once edges are degraded, graph theoretical measures are computed on the "damaged" network. For a frontal impact, the simulations predict that the temporal and occipital regions undergo the most axonal strain and strain rate at short times (less than 24 hrs), which leads to cellular death initiation, which results in damage that shows dependence on angle of impact and underlying microstructure of brain tissue. The monotonic cellular death relationships predict a spatiotemporal change of structural damage. Interestingly, at 96 hrs post-impact, computations predict no network nodes were completely disconnected from the network, despite significant damage to network edges. At early times ([Formula: see text]) network measures of global and local efficiency were degraded little; however, as time increased to 96 hrs the network properties were significantly reduced. In the future, this computational framework could help inform functional networks from physics-based structural brain biomechanics to obtain not only a biomechanics-based understanding of injury, but also neurophysiological insight.     

Dynamic mechanical response of bovine gray matter and white matter brain tissues under compression

Dynamic responses of brain tissues are needed for predicting traumatic brain injury (TBI). We modified a dynamic experimental technique for characterizing high strain-rate mechanical behavior of brain tissues. Using the setup, the gray and white matters from bovine brains were characterized under compression to large strains at five different strain rates ranging from 0.01 to 3000/s. The white matter was examined both along and perpendicular to the coronal section for anisotropy characterization. The results show that both brain tissue matters are highly strain-rate sensitive. Differences between the white matter and gray matter in their mechanical responses are recorded. The white matter shows insignificant anisotropy over all strain rates. These results will lead to rate-dependent material modeling for dynamic event simulations.     

Micromechanical analysis of brain’s diffuse axonal injury

Computational models are important tools which help researchers understand traumatic brain injury (TBI). A mechanistic multi-scale numerical approach is introduced to quantify diffuse axonal injury (DAI), the most important mechanism of TBI, induced by a mechanical insult at micro-scale regions of the white matter or voxels where fiber orientations are the same. Using the mechanical properties of a single axon with a viscoelastic constitutive relation and its functional failure in terms of electrophysiological impairment, a numerical 2D micro-level lattice method is implemented to directly analyze the percentage of injured axons in a voxel containing a bundle of axons all with the same orientation under biaxial stretches. Reference micro-injury maps are then developed with the input parameters based on the principal strain or stretch values and their direction with respect to axons, which provide the percentage of injured axons in the voxel of interest as the output. The methodology is independent of any statistical analyses of the accident data and medical reports to derive probabilistic injury risk curves for DAI. Avoiding a structurally detailed full finite element head model, this study proposes a micro-mechanical approach which considers the anatomical structure of neural axons in the white matter together with their mechanical properties using a numerical lattice method to analyze the brain’s diffuse axonal injury. This work has the potential to help develop safer prevention tools and more effective diagnosis methods for DAI.     

Tissue-level thresholds for axonal damage in an experimental model of central nervous system white matter injury

In vivo, tissue-level, mechanical thresholds for axonal injury were determined by comparing morphological injury and electrophysiological impairment to estimated tissue strain in an in vivo model of axonal injury. Axonal injury was produced by dynamically stretching the right optic nerve of an adult male guinea pig to one of seven levels of ocular displacement (Nlevel = 10; Ntotal = 70). Morphological injury was detected with neurofilament immunohistochemical staining (NF68, SM132). Simultaneously, functional injury was determined by the magnitude of the latency shift of the N35 peak of the visual evoked potentials (VEPs) recorded before and after stretch. A companion set of in situ experiments (Nlevel = 5) was used to determine the empirical relationship between the applied ocular displacement and the magnitude of optic nerve stretch. Logistic regression analysis, combined with sensitivity and specificity measures and receiver operating characteristic (ROC) curves were used to predict strain thresholds for axonal injury. From this analysis, we determined three Lagrangian strain-based thresholds for morphological damage to white matter. The liberal threshold, intended to minimize the detection of false positives, was a strain of 0.34, and the conservative threshold strain that minimized the false negative rate was 0.14. The optimal threshold strain criterion that balanced the specificity and sensitivity measures was 0.21. Similar comparisons for electrophysiological impairment produced liberal, conservative, and optimal strain thresholds of 0.28, 0.13, and 0.18, respectively. With these threshold data, it is now possible to predict more accurately the conditions that cause axonal injury in human white matter.     

Multi-scale mechanics of traumatic brain injury: predicting axonal strains from head loads

The length scales involved in the development of diffuse axonal injury typically range from the head level (i.e., mechanical loading) to the cellular level. The parts of the brain that are vulnerable to this type of injury are mainly the brainstem and the corpus callosum, which are regions with highly anisotropically oriented axons. Within these parts, discrete axonal injuries occur mainly where the axons have to deviate from their main course due to the presence of an inclusion. The aim of this study is to predict axonal strains as a result of a mechanical load at the macroscopic head level. For this, a multi-scale finite element approach is adopted, in which a macro-level head model and a micro-level critical volume element are coupled. The results show that the axonal strains cannot be trivially correlated to the tissue strain without taking into account the axonal orientations, which indicates that the heterogeneities at the cellular level play an important role in brain injury and reliable predictions thereof. In addition to the multi-scale approach, it is shown that a novel anisotropic equivalent strain measure can be used to assess these micro-scale effects from head-level simulations only.     

The influence of anisotropy on brain injury prediction

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

White matter tract-oriented deformation predicts traumatic axonal brain injury and reveals rotational direction-specific vulnerabilities

A systematic correlation between finite element models (FEMs) and histopathology is needed to define deformation thresholds associated with traumatic brain injury (TBI). In this study, a FEM of a transected piglet brain was used to reverse engineer the range of optimal shear moduli for infant (5 days old, 553–658 Pa) and 4-week-old toddler piglet brain (692–811 Pa) from comparisons with measured in situ tissue strains. The more mature brain modulus was found to have significant strain and strain rate dependencies not observed with the infant brain. Age-appropriate FEMs were then used to simulate experimental TBI in infant (\(n=36\)) and preadolescent (\(n=17\)) piglets undergoing a range of rotational head loads. The experimental animals were evaluated for the presence of clinically significant traumatic axonal injury (TAI), which was then correlated with FEM-calculated measures of overall and white matter tract-oriented tissue deformations, and used to identify the metric with the highest sensitivity and specificity for detecting TAI. The best predictors of TAI were the tract-oriented strain (6–7 %), strain rate (38–40 s\(^{-1})\), and strain times strain rate (1.3–1.8 s\(^{-1})\) values exceeded by 90 % of the brain. These tract-oriented strain and strain rate thresholds for TAI were comparable to those found in isolated axonal stretch studies. Furthermore, we proposed that the higher degree of agreement between tissue distortion aligned with white matter tracts and TAI may be the underlying mechanism responsible for more severe TAI after horizontal and sagittal head rotations in our porcine model of nonimpact TAI than coronal plane rotations.     

Primary paranode demyelination modulates slowly developing axonal depolarization in a model of axonal injury

Neurological sequelae of mild traumatic brain injury are associated with the damage to white matter myelinated axons. In vitro models of axonal injury suggest that the progression to pathological ruin is initiated by the mechanical damage to tetrodotoxin-sensitive voltage-gated sodium channels that breaches the ion balance through alteration in kinetic properties of these channels. In myelinated axons, sodium channels are concentrated at nodes of Ranvier, making these sites vulnerable to mechanical injury. Nodal damage can also be inflicted by injury-induced partial demyelination of paranode/juxtaparanode compartments that flank the nodes and contain high density of voltage-gated potassium channels. Demyelination-induced potassium deregulation can further aggravate axonal damage; however, the role of paranode/juxtaparanode demyelination in immediate impairment of axonal function, and its contribution to the development of axonal depolarization remain elusive. A biophysically realistic computational model of myelinated axon that incorporates ion exchange mechanisms and nodal/paranodal/juxtaparanodal organization was developed and used to study the impact of injury-induced demyelination on axonal signal transmission. Injured axons showed alterations in signal propagation that were consistent with the experimental findings and with the notion of reduced axonal excitability immediately post trauma. Injury-induced demyelination strongly modulated the rate of axonal depolarization, suggesting that trauma-induced damage to paranode myelin can affect axonal transition to degradation. Results of these studies clarify the contribution of paranode demyelination to immediate post trauma alterations in axonal function and suggest that partial paranode demyelination should be considered as another “injury parameter” that is likely to determine the stability of axonal function.     

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

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

Characterizing Brain Structures and Remodeling after TBI Based on Information Content,Diffusion Entropy

Background

To overcome the limitations of conventional diffusion tensor magnetic resonance imaging resulting from the assumption of a Gaussian diffusion model for characterizing voxels containing multiple axonal orientations, Shannon''s entropy was employed to evaluate white matter structure in human brain and in brain remodeling after traumatic brain injury (TBI) in a rat.

Methods

Thirteen healthy subjects were investigated using a Q-ball based DTI data sampling scheme. FA and entropy values were measured in white matter bundles, white matter fiber crossing areas, different gray matter (GM) regions and cerebrospinal fluid (CSF). Axonal densities'' from the same regions of interest (ROIs) were evaluated in Bielschowsky and Luxol fast blue stained autopsy (n = 30) brain sections by light microscopy. As a case demonstration, a Wistar rat subjected to TBI and treated with bone marrow stromal cells (MSC) 1 week after TBI was employed to illustrate the superior ability of entropy over FA in detecting reorganized crossing axonal bundles as confirmed by histological analysis with Bielschowsky and Luxol fast blue staining.

Results

Unlike FA, entropy was less affected by axonal orientation and more affected by axonal density. A significant agreement (r = 0.91) was detected between entropy values from in vivo human brain and histologically measured axonal density from post mortum from the same brain structures. The MSC treated TBI rat demonstrated that the entropy approach is superior to FA in detecting axonal remodeling after injury. Compared with FA, entropy detected new axonal remodeling regions with crossing axons, confirmed with immunohistological staining.

Conclusions

Entropy measurement is more effective in distinguishing axonal remodeling after injury, when compared with FA. Entropy is also more sensitive to axonal density than axonal orientation, and thus may provide a more accurate reflection of axonal changes that occur in neurological injury and disease.     

Mapping traumatic axonal injury using diffusion tensor imaging: correlations with functional outcome

Background

Traumatic brain injury is a major cause of morbidity and mortality worldwide. Ameliorating the neurocognitive and physical deficits that accompany traumatic brain injury would be of substantial benefit, but the mechanisms that underlie them are poorly characterized. This study aimed to use diffusion tensor imaging to relate clinical outcome to the burden of white matter injury.

Methodology/Principal Findings

Sixty-eight patients, categorized by the Glasgow Outcome Score, underwent magnetic resonance imaging at a median of 11.8 months (range 6.6 months to 3.7 years) years post injury. Control data were obtained from 36 age-matched healthy volunteers. Mean fractional anisotropy, apparent diffusion coefficient (ADC), and eigenvalues were obtained for regions of interest commonly affected in traumatic brain injury. In a subset of patients where conventional magnetic resonance imaging was completely normal, diffusion tensor imaging was able to detect clear abnormalities. Significant trends of increasing ADC with worse outcome were noted in all regions of interest. In the white matter regions of interest worse clinical outcome corresponded with significant trends of decreasing fractional anisotropy.

Conclusions/Significance

This study found that clinical outcome was related to the burden of white matter injury, quantified by diffusivity parameters late after traumatic brain injury. These differences were seen even in patients with the best outcomes and patients in whom conventional magnetic resonance imaging was normal, suggesting that diffusion tensor imaging can detect subtle injury missed by other techniques. An improved in vivo understanding of the pathology of traumatic brain injury, including its distribution and extent, may enhance outcome evaluation and help to provide a mechanistic basis for deficits that remain unexplained by other approaches.     

Viscoelasticity of Tau Proteins Leads to Strain Rate-Dependent Breaking of?Microtubules during Axonal Stretch Injury: Predictions from a Mathematical Model

The unique viscoelastic nature of axons is thought to underlie selective vulnerability to damage during traumatic brain injury. In particular, dynamic loading of axons has been shown to mechanically break microtubules at the time of injury. However, the mechanism of this rate-dependent response has remained elusive. Here, we present a microstructural model of the axonal cytoskeleton to quantitatively elucidate the interaction between microtubules and tau proteins under mechanical loading. Mirroring the axon ultrastructure, the microtubules were arranged in staggered arrays, cross-linked by tau proteins. We found that the viscoelastic behavior specifically of tau proteins leads to mechanical breaking of microtubules at high strain rates, whereas extension of tau allows for reversible sliding of microtubules without any damage at small strain rates. Based on the stiffness and viscosity of tau proteins inferred from single-molecule force spectroscopy studies, we predict the critical strain rate for microtubule breaking to be in the range 22–44 s⁻¹, in excellent agreement with recent experiments on dynamic loading of micropatterned neuronal cultures. We also identified a characteristic length scale for load transfer that depends on microstructural properties and have derived a phase diagram in the parameter space spanned by loading rate and microtubule length that demarcates those regions where axons can be loaded and unloaded reversibly and those where axons are injured due to breaking of the microtubules.     

Viscoelasticity of Tau Proteins Leads to Strain Rate-Dependent Breaking of Microtubules during Axonal Stretch Injury: Predictions from a Mathematical Model

The unique viscoelastic nature of axons is thought to underlie selective vulnerability to damage during traumatic brain injury. In particular, dynamic loading of axons has been shown to mechanically break microtubules at the time of injury. However, the mechanism of this rate-dependent response has remained elusive. Here, we present a microstructural model of the axonal cytoskeleton to quantitatively elucidate the interaction between microtubules and tau proteins under mechanical loading. Mirroring the axon ultrastructure, the microtubules were arranged in staggered arrays, cross-linked by tau proteins. We found that the viscoelastic behavior specifically of tau proteins leads to mechanical breaking of microtubules at high strain rates, whereas extension of tau allows for reversible sliding of microtubules without any damage at small strain rates. Based on the stiffness and viscosity of tau proteins inferred from single-molecule force spectroscopy studies, we predict the critical strain rate for microtubule breaking to be in the range 22–44 s⁻¹, in excellent agreement with recent experiments on dynamic loading of micropatterned neuronal cultures. We also identified a characteristic length scale for load transfer that depends on microstructural properties and have derived a phase diagram in the parameter space spanned by loading rate and microtubule length that demarcates those regions where axons can be loaded and unloaded reversibly and those where axons are injured due to breaking of the microtubules.     

血清硫氧还蛋白1与脑外伤患者的白质恢复的相关性分析

为探讨血清硫氧还蛋白1 (thioredoxin 1, Trx1)含量与脑外伤后白质恢复的相关性关系,本研究选取60例脑外伤患者,根据格拉斯哥昏迷指数(Glasgow coma scale, GCS)将患者分为3组(轻度,中度和重度脑外伤患者),每组20例,采用核磁共振成像(magnetic resonance imaging, MRI)检测各组患者头颅白质情况,并通过ELISA方法检测各组患者血清Trx1水平,最后利用SPSS软件Pearson方法检测血清硫氧还蛋白1含量与脑外伤后白质恢复的相关性。结果显示,轻度脑损伤患者的GCS分值明显高于中度和重度脑外伤患者;轻度脑外伤患者的Trx1含量明显高于中度和重度患者;轻度和中度脑外伤患者的白质恢复情况明显优于重度患者;脑损伤患者的血清Trx1含量和白质恢复程度呈正相关。本研究初步结论表明脑外伤患者的白质恢复情况与血清Trx1存在正相关性关系,这将为脑外伤的治疗提供新思路。     

Physical model simulations of brain injury in the primate

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

Altered Cerebellar White Matter Integrity in Patients with Mild Traumatic Brain Injury in the Acute Stage

Background and Purpose

Imaging studies of traumatic brain injury demonstrate that the cerebellum is often affected. We aim to examine fractional anisotropy alteration in acute-phase mild traumatic brain injury patients in cerebellum-related white matter tracts.

Materials and Methods

This prospective study included 47 mild traumatic brain injury patients in the acute stage and 37 controls. MR imaging and neurocognitive tests were performed in patients within 7 days of injury. White matter integrity was examined by using diffusion tensor imaging. We used three approaches, tract-based spatial statistics, graphical-model-based multivariate analysis, and region-of-interest analysis, to detect altered cerebellar white matter integrity in mild traumatic brain injury patients.

Results

Results from three analysis methods were in accordance with each other, and suggested fractional anisotropy in the middle cerebellar peduncle and the pontine crossing tract was changed in the acute-phase mild traumatic brain injury patients, relative to controls (adjusted p-value < 0.05). Higher fractional anisotropy in the middle cerebellar peduncle was associated with worse performance in the fluid cognition composite (r = -0.289, p-value = 0.037).

Conclusion

Altered cerebellar fractional anisotropy in acute-phase mild traumatic brain injury patients is localized in specific regions and statistically associated with cognitive deficits detectable on neurocognitive testing.     

Citicoline Protects Brain Against Closed Head Injury in Rats Through Suppressing Oxidative Stress and Calpain Over-Activation

Citicoline, a natural compound that functions as an intermediate in the biosynthesis of cell membrane phospholipids, is essential for membrane integrity and repair. It has been reported to protect brain against trauma. This study was designed to investigate the protective effects of citicoline on closed head injury (CHI) in rats. Citicoline (250 mg/kg i.v. 30 min and 4 h after CHI) lessened body weight loss, and improved neurological functions significantly at 7 days after CHI. It markedly lowered brain edema and blood–brain barrier permeability, enhanced the activities of superoxide dismutase and the levels of glutathione, reduced the levels of malondialdehyde and lactic acid. Moreover, citicoline suppressed the activities of calpain, and enhanced the levels of calpastatin, myelin basic protein and αII-spectrin in traumatic tissue 24 h after CHI. Also, it attenuated the axonal and myelin sheath damage in corpus callosum and the neuronal cell death in hippocampal CA1 and CA3 subfields 7 days after CHI. These data demonstrate the protection of citicoline against white matter and grey matter damage due to CHI through suppressing oxidative stress and calpain over-activation, providing additional support to the application of citicoline for the treatment of traumatic brain injury.