An analytical model of traumatic diffuse brain injury

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

A centric/non-centric impact protocol and finite element model methodology for the evaluation of American football helmets to evaluate risk of concussion

American football reports high incidences of head injuries, in particular, concussion. Research has described concussion as primarily a rotation dominant injury affecting the diffuse areas of brain tissue. Current standards do not measure how helmets manage rotational acceleration or how acceleration loading curves influence brain deformation from an impact and thus are missing important information in terms of how concussions occur. The purpose of this study was to investigate a proposed three-dimensional impact protocol for use in evaluating football helmets. The dynamic responses resulting from centric and non-centric impact conditions were examined to ascertain the influence they have on brain deformations in different functional regions of the brain that are linked to concussive symptoms. A centric and non-centric protocol was used to impact an American football helmet; the resulting dynamic response data was used in conjunction with a three-dimensional finite element analysis of the human brain to calculate brain tissue deformation. The direction of impact created unique loading conditions, resulting in peaks in different regions of the brain associated with concussive symptoms. The linear and rotational accelerations were not predictive of the brain deformation metrics used in this study. In conclusion, the test protocol used in this study revealed that impact conditions influences the region of loading in functional regions of brain tissue that are associated with the symptoms of concussion. The protocol also demonstrated that using brain deformation metrics may be more appropriate when evaluating risk of concussion than using dynamic response data alone.     

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.     

A proposed tolerance criterion for diffuse axonal injury in man.

The head injury criterion (HIC) is currently the government-accepted head injury indicator. The HIC is not injury-specific, does not relate to injury severity, nor does it take into account variations in the brain mass or load direction. This report focuses on one type of inertial brain injury, diffuse axonal injury (DAI), and utilizes animal studies, physical model experiments, and analytical model simulations to determine the kinematics of DAI in the subhuman primate and to scale these results to man. A human injury tolerance for moderate to severe DAI, which includes the influences of rotational loads and brain mass, is proposed.     

High-Field Proton Magnetic Resonance Spectroscopy of a Swine Model for Axonal Injury

Abstract: A miniature swine model for diffuse brain injury has recently been developed that replicates the inertial loading conditions associated with rotational acceleration during automotive accidents. The swine model induces diffuse axonal pathology without macroscopic injury such as contusions and hematomas, thus affording a unique opportunity to study axonal injury with noninvasive techniques such as magnetic resonance imaging (MRI) and spectroscopy (MRS). In the present study, we evaluated this diffuse injury model with proton MRS, in vivo, using a high-field (4.0-T) MR scanner, since MRS has been demonstrated as a sensitive probe for detecting neurochemical abnormalities. Our study examined a region of the swine brain at timepoints before and after brain injury. Spectroscopic results indicate that N -acetylaspartate/creatine is diminished by at least 20% in regions of confirmed axonal pathology, whereas conventional MRI did not detect any abnormalities. These findings suggest that MRS has high sensitivity in diagnosing microscopic pathology following diffuse brain injury.     

Peak linear and rotational acceleration magnitude and duration effects on maximum principal strain in the corpus callosum for sport impacts

Concussion has been linked to the presence of injurious strains in the brain tissues. Research investigating severe brain injury has reported that strains in the brain may be affected by two parameters: magnitude of the acceleration, and duration of that acceleration. However, little is known how this relationship changes in terms of creating risk for brain injury for magnitudes and durations of acceleration common in sporting environments. This has particular implications for the understanding and prevention of concussive risk of injury in sporting environments. The purpose of this research was to examine the interaction between linear and rotational acceleration and duration on maximum principal strain in the brain tissues for loading conditions incurred in sporting environments. Linear and rotational acceleration loading curves of magnitudes and durations similar to those from impact in sport were used as input to the University College Brain Trauma Model and maximum principal strain (MPS) was measured for the different curves. The results demonstrated that magnitude and duration do have an effect on the strain incurred by the brain tissue. As the duration of the acceleration increases, the magnitude required to achieve strains reflecting a high risk of concussion decreases, with rotational acceleration becoming the dominant contributor. The magnitude required to attain a magnitude of MPS representing risk of brain injury was found to be as low as 2500 rad/s² for impacts of 10–15 ms; indicating that interventions to reduce the risk of concussion in sport must consider the duration of the event while reducing the magnitude of acceleration the head incurs.     

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

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

Changes to the viscoelastic properties of brain tissue after traumatic axonal injury

While it has been shown that repetitive mild brain injuries can cause cumulative damage to the brain, changes to the mechanical properties of brain tissue at large deformations were also noted in the literature. The goal of this study was to show that the viscoelastic properties of brain tissue significantly change after traumatic axonal injury (TAI). An impact acceleration model was used to create TAI in the rat brainstem which was quantified with an immunohistochemistry technique at the ponto-medullary junction (PmJ) and pyramidal decussation (PDx). The viscoelastic properties at these two points with and without preconditioning were characterized using an indentation technique combined with finite element analysis and a comparison was made between injured and uninjured specimens, which revealed statistically significant reduction in the instantaneous elastic force at PDx where the brain tissue sustained a significantly higher level of injury. The result of this study can be used to characterize a damage function for the brain tissue undergoing large deformation.     

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.     

Compression-induced damage and internal tissue strains are related

Prolonged mechanical loading of soft tissues adjacent to bony prominences can lead to degeneration of muscle tissue, resulting in a condition termed pressure-related deep tissue injury. This type of deep pressure ulcers can develop into a severe wound, associated with problematic healing and a variable prognosis. Limited knowledge of the underlying damage pathways impedes effective preventive strategies and early detection. Traditionally, pressure-induced ischaemia has been thought to be the main aetiological factor for initiating damage. Recent research, however, proposes tissue deformation per se as another candidate for initiating pressure-induced deep tissue injury. In this study, different strain parameters were evaluated on their suitability as a generic predictive indicator for deep tissue injury. With a combined animal-experimental numerical approach, we show that there is a reproducible monotonic increase in damage with increasing maximum shear strain once a strain threshold has been exceeded. This relationship between maximum shear strain and damage seems to reflect an intrinsic muscle property, as it applied across a considerable number of the experiments. This finding confirms that tissue deformation per se is important in the aetiology of deep tissue injury. Using dedicated finite element modeling, a considerable reduction in the inherent biological variation was obtained, leading to the proposal that muscle deformation can prove a generic predictive indicator of damage.     

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.     

In vivo imaging of rapid deformation and strain in an animal model of traumatic brain injury

In traumatic brain injury (TBI) rapid deformation of brain tissue leads to axonal injury and cell death. In vivo quantification of such fast deformations is extremely difficult, but important for understanding the mechanisms of degeneration post-trauma and for development of numerical models of injury biomechanics. In this paper, strain fields in the brain of the perinatal rat were estimated from data obtained in vivo during rapid indentation. Tagged magnetic resonance (MR) images were obtained with high spatial (0.2 mm) and temporal (3.9 ms) resolution by gated image acquisition during and after impact. Impacts were repeated either 64 or 128 times to obtain images of horizontal and vertical tag lines in coronal and sagittal planes. Strain fields were estimated by harmonic phase (HARP) analysis of the tagged images. The original MR data was filtered and Fourier-transformed to obtain HARP images, following a method originally developed by Osman et al. (IEEE Trans. Med. Imaging 19(3) (2000) 186). The displacements of material points were estimated from intersections of HARP contours and used to generate estimates of the deformation gradient and Lagrangian strain tensors. Maximum principal Lagrangian strains of >0.20 at strain rates >40/s were observed during indentations of 2 mm depth and 21 ms duration.     

The influence of impact force redistribution and redirection on maximum principal strain for helmeted head impacts

Abstract

Sporting helmets with linear attenuating strategies are proficient at reducing the risk of traumatic brain injury. However, the continued high incidence of concussion in American football, has led researchers to investigate novel helmet liner strategies. These strategies typically supplement existing technologies by adding or integrating head-helmet decoupling mechanisms. Decoupling strategies aim to redirect or redistribute impact force around the head, reducing impact energy transferred to the brain. This results in decreased brain tissue strain, which is beneficial in injury risk reduction due to the link between tissue strain and concussive injury.

The purpose of this study was to mathematically demonstrate the effect of ten cases, representing theoretical redirection and redistribution helmet liner strategies, on brain tissue strain resulting from impacts to the head. The kinematic response data from twenty head impacts collected in the laboratory was mathematically modified to represent the altered response of the ten different cases and used as input parameters to determine the effect on maximum principal strain (MPS) values, calculated using finite element modeling. The results showed that a reduced dominant coordinate component (contributes the greatest to resultant) of rotational acceleration decreased maximum principal strain in American football helmets. The study theoretically demonstrates that liner strategies, if applied correctly, can influence brain motion, reduce brain tissue strain, and could decrease injury risk in an American football helmet.     

How does muscle stiffness affect the internal deformations within the soft tissue layers of the buttocks under constant loading?

Mechanical loading of soft tissues covering bony prominences can cause skeletal muscle damage, ultimately resulting in a severe pressure ulcer termed deep tissue injury (DTI). Deformation plays an important role in the aetiology of DTI. Therefore, it is essential to minimise internal muscle deformations in subjects at risk of DTI. As an example, spinal cord-injured (SCI) individuals exhibit structural changes leading to a decrease in muscle thickness and stiffness, which subsequently increase the tissue deformations. In the present study, an animal-specific finite element model, where the geometry and boundary conditions were derived from magnetic resonance images, was developed. It was used to investigate the internal deformations in the muscle, fat and skin layers of the porcine buttocks during loading. The model indicated the presence of large deformations in both the muscle and the fat layers, with maximum shear strains up to 0.65 in muscle tissue and 0.63 in fat. Furthermore, a sensitivity analysis showed that the tissue deformations depend considerably on the relative stiffness values of the different tissues. For example, a change in muscle stiffness had a large effect on the muscle deformations. A 50% decrease in stiffness caused an increase in maximum shear strain from 0.65 to 0.99, whereas a 50% increase in stiffness resulted in a decrease in maximum shear strain from 0.65 to 0.49. These results indicate the importance of restoring tissue properties after SCI, with the use of, for example, electrical stimulation, to prevent the development of DTI.     

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.     

Helmet liner evaluation to mitigate head response from primary blast exposure

Head injury resulting from blast loading, including mild traumatic brain injury, has been identified as an important blast-related injury in modern conflict zones. A study was undertaken to investigate potential protective ballistic helmet liner materials to mitigate primary blast injury using a detailed sagittal plane head finite element model, developed and validated against previous studies of head kinematics resulting from blast exposure. Five measures reflecting the potential for brain injury that were investigated included intracranial pressure, brain tissue strain, head acceleration (linear and rotational) and the head injury criterion. In simulations, these measures provided consistent predictions for typical blast loading scenarios. Considering mitigation, various characteristics of foam material response were investigated and a factor analysis was performed which showed that the four most significant were the interaction effects between modulus and hysteretic response, stress–strain response, damping factor and density. Candidate materials were then identified using the predicted optimal material values. Polymeric foam was found to meet the density and modulus requirements; however, for all significant parameters, higher strength foams, such as aluminum foam, were found to provide the highest reduction in the potential for injury when compared against the unprotected head.     

The influence of impact source on variables associated with strain for impacts in ice hockey

Concussion can occur from a variety of events (falls to ice, collisions etc) in ice hockey, and as a result it is important to identify how these different impact sources affect the relationship between impact kinematics and strain that has been found to be associated to this injury. The purpose of this research was to examine the relationship between kinematic variables and strain in the brain for impact sources that led to concussion in ice hockey. Video of professional ice hockey games was analyzed for impacts that resulted in reported clinically diagnosed concussions. The impacts were reconstructed using physical models/ATDs to determine the impact kinematics and then simulated using finite element modelling to determine maximum principal strain and cumulative strain damage measure. A stepwise linear regression was conducted between linear acceleration, change in linear velocity, rotational acceleration, rotational velocity, and strain response in the brain. The results for the entire dataset was that rotational acceleration had the highest r² value for MPS (r² = 0.581) and change in rotational velocity for cumulative strain damage measure (r² = 450). When the impact source (shoulder, elbow, boards, or ice impacts) was isolated the rotational velocity and acceleration r² value increased, indicating that when evaluating the relationships between kinematics and strain based metrics the characteristics of the impact is an important factor. These results suggest that rotational measures should be included in future standard methods and helmet innovation and design in ice hockey as they have the highest association with strain in the brain tissues.     

Lateral Fluid Percussion: Model of Traumatic Brain Injury in Mice

Traumatic brain injury (TBI) research has attained renewed momentum due to the increasing awareness of head injuries, which result in morbidity and mortality. Based on the nature of primary injury following TBI, complex and heterogeneous secondary consequences result, which are followed by regenerative processes ^1,2. Primary injury can be induced by a direct contusion to the brain from skull fracture or from shearing and stretching of tissue causing displacement of brain due to movement ^3,4. The resulting hematomas and lacerations cause a vascular response ^3,5, and the morphological and functional damage of the white matter leads to diffuse axonal injury ^6-8. Additional secondary changes commonly seen in the brain are edema and increased intracranial pressure ⁹. Following TBI there are microscopic alterations in biochemical and physiological pathways involving the release of excitotoxic neurotransmitters, immune mediators and oxygen radicals ^10-12, which ultimately result in long-term neurological disabilities ^13,14. Thus choosing appropriate animal models of TBI that present similar cellular and molecular events in human and rodent TBI is critical for studying the mechanisms underlying injury and repair.Various experimental models of TBI have been developed to reproduce aspects of TBI observed in humans, among them three specific models are widely adapted for rodents: fluid percussion, cortical impact and weight drop/impact acceleration ¹. The fluid percussion device produces an injury through a craniectomy by applying a brief fluid pressure pulse on to the intact dura. The pulse is created by a pendulum striking the piston of a reservoir of fluid. The percussion produces brief displacement and deformation of neural tissue ^1,15. Conversely, cortical impact injury delivers mechanical energy to the intact dura via a rigid impactor under pneumatic pressure ^16,17. The weight drop/impact model is characterized by the fall of a rod with a specific mass on the closed skull ¹⁸. Among the TBI models, LFP is the most established and commonly used model to evaluate mixed focal and diffuse brain injury ¹⁹. It is reproducible and is standardized to allow for the manipulation of injury parameters. LFP recapitulates injuries observed in humans, thus rendering it clinically relevant, and allows for exploration of novel therapeutics for clinical translation ²⁰.We describe the detailed protocol to perform LFP procedure in mice. The injury inflicted is mild to moderate, with brain regions such as cortex, hippocampus and corpus callosum being most vulnerable. Hippocampal and motor learning tasks are explored following LFP.     

Strain relief from the cerebral ventricles during head impact: experimental studies on natural protection of the brain

Physical models of the parasagittal human skull/brain have been tested to investigate whether the cerebral ventricles provide natural protection of the brain by relieving strain during head rotation. A sophisticated model included anatomical structures, and a semicircular model consisted of a cylinder divided into two semicircles. Silicone gel simulated the brain and was detached from the vessel by a layer of liquid paraffin simulating the cerebrospinal fluid. Both models were run with and without an elliptical inclusion filled with liquid paraffin simulating a cerebral ventricle. The 2D models were exposed to angular acceleration by a pendulum impact causing 7600 rad/s2 peak rotational acceleration with 6 ms pulse duration. After rotating 100 degrees, the models were decelerated during 30 ms. The trajectory of grid markers was analyzed from high-speed video (1000 frames/s). Rigid-body displacement, shear strain and principal strain were determined from the displacement of three-point sets inferior and superior to the ventricle. For the subventricular (inferior) region in the sophisticated model, approximately 40% lower peak strain values were obtained in the model with ventricle than in the one without. Subcortical displacement was reduced by 12%. Corresponding strain reduction in the subcortical (superior) region was approximately 40% following the acceleration and 25% following the deceleration. Similar but less pronounced effects were found for the semicircular model. The lateral ventricles play an important role as strain relievers and provide natural protection against brain injury.     

A triaxial-measurement shear-test device for soft biological tissues

A novel shear-test device for soft biological tissue, capable of applying simple shear deformations simultaneously in two orthogonal directions while measuring the resulting forces generated in three axes, is described. We validated the device using a synthetic gel, the properties of which were ascertained from independent tensile and rotational shear tests. Material parameters for the gel were fitted using neo-Hookean analytical solutions to the independent test data, and these matched the results from the device. Preliminary results obtained with rat septal myocardium are also presented to demonstrate the feasibility of the apparatus in determining the shear characteristics of living tissue.