A Pre-computed Brain Response Atlas for Instantaneous Strain Estimation in Contact Sports

Finite element models of the human head play an important role in investigating the mechanisms of traumatic brain injury, including sports concussion. A critical limitation, however, is that they incur a substantial computational cost to simulate even a single impact. Therefore, current simulation schemes significantly hamper brain injury studies based on model-estimated tissue-level responses. In this study, we present a pre-computed brain response atlas (pcBRA) to substantially increase the simulation efficiency in estimating brain strains using isolated rotational acceleration impulses parameterized with four independent variables (peak magnitude and duration, and rotational axis azimuth and elevation angles) with values determined from on-field measurements. Using randomly generated testing datasets, the partially established pcBRA achieved a 100% success rate in interpolation based on element-wise differences in accumulated peak strain ($$\varepsilon^{p}$$εp) according to a “double-10%” criterion or average regional $$\varepsilon^{p}$$εp in generic regions and the corpus callosum. A similar performance was maintained in extrapolation. The pcBRA performance was further successfully validated against directly simulated responses from two independently measured typical real-world rotational profiles. The computational cost to estimate element-wise whole-brain or regional $$\varepsilon^{p}$$εp was 6 s and <0.01 s, respectively, vs. ~50 min directly simulating a 40 ms impulse. These findings suggest the pcBRA could substantially increase the throughput in impact simulation without significant loss of accuracy from the estimation itself and, thus, its potential to accelerate the exploration of the mechanisms of sports concussion in general. If successful, the pcBRA may also become a diagnostic adjunct in conjunction with sensors that measure head impact kinematics on the field to objectively monitor and identify tissue-level brain trauma in real-time for “return-to-play” decision-making on the sideline.

Related papers:

title: Subject-specific changes in brain white matter on diffusion tensor imaging after sports-related concussion.
abstract: Current approaches to diffusion tensor imaging (DTI) analysis do not permit identification of individual-level changes in DTI indices. We investigated the ability of wild bootstrapping analysis to detect subject-specific changes in brain white matter (WM) before and after sports-related concussion.



A prospective cohort study was performed in nine high school athletes engaged in hockey or football and six controls. Subjects underwent DTI pre- and postseason within a 3-month interval. One athlete was diagnosed with concussion (scanned within 72 h), and eight suffered between 26 and 399 subconcussive head blows. Fractional anisotropy (FA) and mean diffusivity (MD) were measured in each WM voxel. Bootstrap samples were generated, and a permuted t test was used to compare voxel-wise FA/MD changes in each subject pre- vs. postseason.



The percentage of WM voxels with significant (p<.05) pre-post FA changes was highest for the concussion subject (3.2%), intermediary for those with subconcussive head blows (mean 1.05%±.15%) and lowest for controls (mean 0.28%±.01%). Similarly, the percentage of WM voxels with significant MD changes was highest for the concussion subject (3.44%), intermediary for those with subconcussive head blows (mean 1.48%±.17%) and lowest for controls (mean 0.48%±.05%). Significantly changed FA and MD voxels colocalized in the concussion subject to the right corona radiata and right inferior longitudinal fasciculus.



Wild bootstrap analysis detected significantly changed WM in a single concussed athlete. Athletes with multiple subconcussive head blows had significant changes in a percentage of their WM that was over three times higher than controls. Efforts to understand the significance of these WM changes and their relationship to head impact forces appear warranted.

title: Effect of head impacts on diffusivity measures in a cohort of collegiate contact sport athletes
abstract: To determine whether exposure to repetitive head impacts over a single season affects white matter diffusion measures in collegiate contact sport athletes.  A prospective cohort study at a Division I NCAA athletic program of 80 nonconcussed varsity football and ice hockey players who wore instrumented helmets that recorded the acceleration-time history of the head following impact, and 79 non–contact sport athletes. Assessment occurred preseason and shortly after the season with diffusion tensor imaging and neurocognitive measures.  There was a significant (p = 0.011) athlete-group difference for mean diffusivity (MD) in the corpus callosum. Postseason fractional anisotropy (FA) differed (p = 0.001) in the amygdala (0.238 vs 0.233). Measures of head impact exposure correlated with white matter diffusivity measures in several brain regions, including the corpus callosum, amygdala, cerebellar white matter, hippocampus, and thalamus. The magnitude of change in corpus callosum MD postseason was associated with poorer performance on a measure of verbal learning and memory.  This study suggests a relationship between head impact exposure, white matter diffusion measures, and cognition over the course of a single season, even in the absence of diagnosed concussion, in a cohort of college athletes. Further work is needed to assess whether such effects are short term or persistent.

title: Biomechanical correlates of symptomatic and asymptomatic neurophysiological impairment in high school football.
abstract: Concussion is a growing public health issue in the United States, and chronic traumatic encephalopathy (CTE) is the chief long-term concern linked to repeated concussions. Recently, attention has shifted toward subconcussive blows and the role they may play in the development of CTE. We recruited a cohort of high school football players for two seasons of observation. Acceleration sensors were placed in the helmets, and all contact activity was monitored. Pre-season computer-based neuropsychological tests and functional magnetic resonance imaging (fMRI) tests were also obtained in order to assess cognitive and neurophysiological health. In-season follow-up scans were then obtained both from individuals who had sustained a clinically-diagnosed concussion and those who had not. These changes were then related through stepwise regression to history of blows recorded throughout the football season up to the date of the scan. In addition to those subjects who had sustained a concussion, a substantial portion of our cohort who did not sustain concussions showed significant neurophysiological changes. Stepwise regression indicated significant relationships between the number of blows sustained by a subject and the ensuing neurophysiological change. Our findings reinforce the hypothesis that the effects of repetitive blows to the head are cumulative and that repeated exposure to subconcussive blows is connected to pathologically altered neurophysiology.

title: Timing of concussion diagnosis is related to head impact exposure prior to injury.
abstract: Concussions are commonly undiagnosed in an athletic environment because the postinjury signs and symptoms may be mild, masked by the subject, or unrecognized. This study compares measures of head impact frequency, location, and kinematic response before cases of immediate and delayed concussion diagnosis.



Football players from eight collegiate and six high school teams wore instrumented helmets during play (n = 1208), of which 95 were diagnosed with concussion (105 total cases). Acceleration data recorded by the instrumented helmets were reduced to five kinematic metrics: peak linear and rotational acceleration, Gadd severity index, head injury criterion, and change in head velocity (Δv). In addition, each impact was assigned to one of four general location regions (front, back, side, and top), and the number of impacts sustained before injury was calculated over two periods (1 and 7 days).



All head kinematic measures associated with injury, except peak rotational acceleration (P = 0.284), were significantly higher for cases of immediate diagnosis than delayed diagnosis (P < 0.05). Players with delayed diagnosis sustained a significantly higher number of head impacts on the day of injury (32.9 ± 24.9, P < 0.001) and within 7 d of injury (69.7 ± 43.3, P = 0.006) than players with immediate diagnosis (16.5 ± 15.1 and 50.2 ± 43.6). Impacts associated with concussion occurred most frequently to the front of the head (46%) followed by the top (25%), side (16%), and back (13%) with the number of impacts by location independent of temporal diagnosis (χ(3) = 4.72, P = 0.19).



Concussions diagnosed immediately after an impact event are associated with the highest kinematic measures, whereas those characterized by delayed diagnosis are preceded by a higher number of impacts.

title: Head impact exposure sustained by football players on days of diagnosed concussion.
abstract: This study compares the frequency and severity of head impacts sustained by football players on days with and without diagnosed concussion and to identify the sensitivity and specificity of single-impact severity measures to diagnosed injury.



One thousand two hundred eight players from eight collegiate football teams and six high school football teams wore instrumented helmets to measure head impacts during all team sessions, of which 95 players were diagnosed with concussion. Eight players sustained two injuries and one sustained three, providing 105 injury cases. Measures of head kinematics (peak linear and rotational acceleration, Gadd severity index, head injury criteria (HIC15), and change in head velocity (Δv)) and the number of head impacts sustained by individual players were compared between days with and without diagnosed concussion. Receiver operating characteristic curves were generated to evaluate the sensitivity and specificity of each kinematic measure to diagnosed concussion using only those impacts that directly preceded diagnosis.



Players sustained a higher frequency of impacts and impacts with more severe kinematic properties on days of diagnosed concussion than on days without diagnosed concussion. Forty-five injury cases were immediately diagnosed after head impact. For these cases, peak linear acceleration and HIC15 were most sensitive to immediately diagnosed concussion (area under the curve = 0.983). Peak rotational acceleration was less sensitive to diagnosed injury than all other kinematic measures (P = 0.01), which are derived from linear acceleration (peak linear, HIC15, Gadd severity index, and Δv).



Players sustained more impacts and impacts of higher severity on days of diagnosed concussion than on days without diagnosed concussion. In addition, of historical measures of impact severity, those associated with peak linear acceleration are the best predictors of immediately diagnosed concussion.

title: A generalized acceleration model for brain injury threshold (GAMBIT)
abstract: A c r i t e ri o n f o r brain inj ury threshold i s proposed w h i c h , for the f i r s t time, endeavours to take into consideration the combined effects of both t rans l a t ional and rotat ional kinema t i cs. The val i d i t y of the mode l is as s e s s ed by w ay of a review of a l l known head inj u ry data bases in which translational and rotational accelerations have been monitored. Available data appears to support no more than a simple linear proportioning of the two types of motion though a squared weighting, as originally proposed (and which intuitively is more plaus ible) also seems valid.

title: A proposed new biomechanical head injury assessment function - the maximum power index.
abstract: Recently, several cases of mild traumatic brain injury to American professional football players have been reconstructed using instrumented Hybrid III anthropomorphic test dummies ATDs. The translational and rotational acceleration responses of injured and uninjured players' heads have been documented. The acceleration data have been processed according to all current head injury assessment functions including the GSI, HIC and GAMBIT among others. A new hypothesis is propounded that the threshold for head injury will be exceeded if the rate of change of kinetic energy of the head exceeds some limiting value. A functional relation is proposed, which includes all six degrees of motion and directional sensitivity characteristics, relating the rate of change of kinetic energy to the probability of head injury. The maximum value that the function achieves during impact is the maximum power input to the head and serves as an index by which the probability of head injury can be assessed.

title: Is head injury caused by linear or angular acceleration
abstract: Currently, angular acceleration is believed to be more damaging to the brain than linear acceleration, even though both are present in any head impact. In a recent experiment, it was found that a helmeted head sustained the same degree of angular acceleration as the unhelmeted head for the same impact, but its linear acceleration was decreased significantly. So, if angular acceleration is the cause of brain injury, then how is the brain protected by the helmet? This paper proposes a new hypothesis of brain injury and suggests that input acceleration limits should be replaced by response variables.

title: Mild Traumatic Brain Injury Predictors Based on Angular Accelerations During Impacts
abstract: Although Head Injury Criterion (HIC) is an effective criterion for head injuries caused by linear acceleration such as skull fractures, no criteria for head injuries caused by rotational kinematics has been accepted as effective so far. This study proposed two criteria based on angular accelerations for Traumatic Brain Injury (TBI), which we call Rotational Injury Criterion (RIC) and Power Rotational Head Injury Criterion (PRHIC). Concussive and non-concussive head acceleration data obtained from football head impacts were utilized to develop new injury criteria. A well-validated human brain Finite Element (FE) model was employed to find out effective injury criteria for TBI. Correlation analyses were performed between the proposed criteria and FE-based brain injury predictors such as Cumulative Strain Damage Measure (CSDM), which is defined as the percent volume of the brain that exceeds a specified first principal strain threshold, proposed to predict Diffuse Axonal Injury (DAI) which is one of TBI. The RIC was significantly correlated with the CSDMs with the strain thresholds of less than 15% (R > 0.89), which might predict mild TBI. In addition, PRHIC was also strongly correlated with the CSDMs with the strain thresholds equal to or greater than 20% (R > 0.90), which might predict more severe TBI.

title: Rotational Head Kinematics in Football Impacts: An Injury Risk Function for Concussion
abstract: Recent research has suggested a possible link between sports-related concussions and neurodegenerative processes, highlighting the importance of developing methods to accurately quantify head impact tolerance. The use of kinematic parameters of the head to predict brain injury has been suggested because they are indicative of the inertial response of the brain. The objective of this study is to characterize the rotational kinematics of the head associated with concussive impacts using a large head acceleration dataset collected from human subjects. The helmets of 335 football players were instrumented with accelerometer arrays that measured head acceleration following head impacts sustained during play, resulting in data for 300,977 sub-concussive and 57 concussive head impacts. The average sub-concussive impact had a rotational acceleration of 1230 rad/s2 and a rotational velocity of 5.5 rad/s, while the average concussive impact had a rotational acceleration of 5022 rad/s2 and a rotational velocity of 22.3 rad/s. An injury risk curve was developed and a nominal injury value of 6383 rad/s2 associated with 28.3 rad/s represents 50% risk of concussion. These data provide an increased understanding of the biomechanics associated with concussion and they provide critical insight into injury mechanisms, human tolerance to mechanical stimuli, and injury prevention techniques.

title: Brain Injury Prediction: Assessing the Combined Probability of Concussion Using Linear and Rotational Head Acceleration
abstract: Recent research has suggested possible long term effects due to repetitive concussions, highlighting the importance of developing methods to accurately quantify concussion risk. This study introduces a new injury metric, the combined probability of concussion, which computes the overall risk of concussion based on the peak linear and rotational accelerations experienced by the head during impact. The combined probability of concussion is unique in that it determines the likelihood of sustaining a concussion for a given impact, regardless of whether the injury would be reported or not. The risk curve was derived from data collected from instrumented football players (63,011 impacts including 37 concussions), which was adjusted to account for the underreporting of concussion. The predictive capability of this new metric is compared to that of single biomechanical parameters. The capabilities of these parameters to accurately predict concussion incidence were evaluated using two separate datasets: the Head Impact Telemetry System (HITS) data and National Football League (NFL) data collected from impact reconstructions using dummies (58 impacts including 25 concussions). Receiver operating characteristic curves were generated, and all parameters were significantly better at predicting injury than random guessing. The combined probability of concussion had the greatest area under the curve for all datasets. In the HITS dataset, the combined probability of concussion and linear acceleration were significantly better predictors of concussion than rotational acceleration alone, but not different from each other. In the NFL dataset, there were no significant differences between parameters. The combined probability of concussion is a valuable method to assess concussion risk in a laboratory setting for evaluating product safety.

title: Modeling of the Brain for Injury Prevention
abstract: From an ethical point of view, it is extremely difficult to propose a well-controlled human subject study aimed at understanding brain injury mechanisms and establishing the associated tolerance values. For this reason, many numerical models of the human and animal head or brain have been developed over the past several decades in an attempt to obtain in-depth insights into brain injury biomechanics, minimizing the need for human subject research. This chapter highlights and contrasts the essence of human and animal head numerical models developed for studying blunt impact and blast-induced brain injuries. Even with the vast amount of literature produced by these investigations and studies, the precise mechanisms of brain injury have not yet been fully established to date. Through this review, it is clear that a lot of information can be garnered by numerical brain modeling but few efforts have been devoted so far in using these numerical models to provide guidelines in the discovery of brain injury mechanisms. Based on the brain models reported in the current literature, there are some inherent deficiencies. However, with further revisions and improvements to the currently available models, as opposed to developing new models from scratch, these issues can be overcome, and the state of the art can be advanced. More research effort into brain injury mechanisms, especially under in vivo conditions, is needed for computational model improvements so that the injury mechanisms can be thoroughly understood and effective countermeasures for protecting human from traumatic brain injury can be developed.

title: Predictors for traumatic brain injuries evaluated through accident reconstructions.
abstract: The aim of this study is to evaluate all the 58 available NFL cases and compare various predictors for mild traumatic brain injuries using a detailed and extensively validated finite element model of the human head. Global injury measures such as magnitude in angular and translational acceleration, change in angular velocity, head impact power (HIP) and HIC were also investigated with regard to their ability to predict the intracranial pressure and strains associated with injury. The brain material properties were modeled using a hyperelastic and viscoelastic constitutive law. Also, three different stiffness parameters, encompassing a range of published brain tissue properties, were tested. 8 tissue injury predictors were evaluated for 6 different regions, covering the entire cerebrum, as well as for the whole brain. In addition, 10 head kinematics based predictors were evaluated both for correlation with injury as well as with strain and pressure. When evaluating the results, a statistical correlation between strain, strain rate, product of strain and strain rate, Cumulative Strain Damage Measure (CSDM), strain energy density, maximum pressure, magnitude of minimum pressure, as well as von Mises effective stress, with injury was found when looking into specific regions of the brain. However, the maximal pressure in the gray matter showed a higher correlation with injury than other evaluated measures. On the other hand, it was possible, through the reconstruction of a motocross accident, to re-create the injury pattern in the brain of the injured rider using maximal principal strain. It was also found that a simple linear combination of peak change in rotational velocity and HIC showed a high correlation (R=0.98) with the maximum principal strain in the brain, in addition to being a significant predictor of injury. When applying the rotational and translational kinematics separately for one of the cases, it was found that the translational kinematics contribute very little to the intracranial distortional strains while the rotational kinematics contributes insignificantly to the pressure response. This study underlines that the strain based brain tissue injury predictors are very sensitive to the choice of stiffness for the brain tissue.

title: Head injury prediction capability of the HIC, HIP, SIMon and ULP criteria.
abstract: The objective of the present study is to synthesize and investigate using the same set of sixty-one real-world accidents the human head injury prediction capability of the head injury criterion (HIC) and the head impact power (HIP) based criterion as well as the injury mechanisms related criteria provided by the simulated injury monitor (SIMon) and the Louis Pasteur University (ULP) finite element head models. Each accident has been classified according to whether neurological injuries, subdural haematoma and skull fractures were reported. Furthermore, the accidents were reconstructed experimentally or numerically in order to provide loading conditions such as acceleration fields of the head or initial head impact conditions. Finally, thanks to this large statistical population of head trauma cases, injury risk curves were computed and the corresponding regression quality estimators permitted to check the correlation of the injury criteria with the injury occurrences. As different kinds of accidents were used, i.e. footballer, motorcyclist and pedestrian cases, the case-independency could also be checked. As a result, FE head modeling provides essential information on the intracranial mechanical behavior and, therefore, better injury criteria can be computed. It is clearly shown that moderate and severe neurological injuries can only be distinguished with a criterion that is computed using intracranial variables and not with the sole global head acceleration.

title: A proposed injury threshold for mild traumatic brain injury.
abstract: Traumatic brain injuries constitute a significant portion of injury resulting from automotive collisions, motorcycle crashes, and sports collisions. Brain injuries not only represent a serious trauma for those involved but also place an enormous burden on society, often exacting a heavy economical, social, and emotional price. Development of intervention strategies to prevent or minimize these injuries requires a complete understanding of injury mechanisms, response and tolerance level. In this study, an attempt is made to delineate actual injury causation and establish a meaningful injury criterion through the use of the actual field accident data. Twenty-four head-to-head field collisions that occurred in professional football games were duplicated using a validated finite element human head model. The injury predictors and injury levels were analyzed based on resulting brain tissue responses and were correlated with the site and occurrence of mild traumatic brain injury (MTBI). Predictions indicated that the shear stress around the brainstem region could be an injury predictor for concussion. Statistical analyses were performed to establish the new brain injury tolerance level.

title: Numerical and physical modelling of the human head under impact - towards new injury criteria
abstract: This paper presents original physical and numerical human head models followed by their modal and temporal validation against human head vibration analysis in vivo and cadaver impact tests. The human head FE model developed by ULP presents two particularities: one at the brain-skull interface level where fluid-structure interaction is taken into account, the other at the skull modelling level by integrating the bone fracture simulation. Validation shows that the model correlated well with a number of experimental cadaver tests and predicted intracranial pressure accurately. However, for long duration impacts the model reaches its limits. The skull stiffness and fracture force were very accurately predicted when compared with values from the literature. In a second step, a new dummy head prototype, named Bimass, is presented. It has been constructed using a Hybrid III headform and comprises two masses: a skull and a mass to represent the brain attached to the skull with a damped spring system. The novel feature of this device is that it can simulate the brain-skull relative displacement at a frequency close to 150 Hz as recorded under vibration analysis in vivo. Helmet damage from thirteen motorcycle accidents was replicated in drop tests conducted in collaboration with Transport Research Laboratory (UK). Simulation of these accidents using both FE model and Bimass dummy head led to the first tentative proposals for tolerance limits and injury criteria relative to specific injury mechanisms.

title: Investigation of traumatic brain injuries using the next generation of simulated injury monitor (SIMon) finite element head model.
abstract: The objective of this study was to investigate potential for traumatic brain injuries (TBI) using a newly developed, geometrically detailed, finite element head model (FEHM) within the concept of a simulated injury monitor (SIMon). The new FEHM is comprised of several parts: cerebrum, cerebellum, falx, tentorium, combined pia-arachnoid complex (PAC) with cerebro-spinal fluid (CSF), ventricles, brainstem, and parasagittal blood vessels. The model's topology was derived from human computer tomography (CT) scans and then uniformly scaled such that the mass of the brain represents the mass of a 50th percentile male's brain (1.5 kg) with the total head mass of 4.5 kg. The topology of the model was then compared to the preliminary data on the average topology derived from Procrustes shape analysis of 59 individuals. Material properties of the various parts were assigned based on the latest experimental data. After rigorous validation of the model using neutral density targets (NDT) and pressure data, the stability of FEHM was tested by loading it simultaneously with translational (up to 400 g) combined with rotational (up to 24,000 rad/s2) acceleration pulses in both sagittal and coronal planes. Injury criteria were established in the manner shown in Takhounts et al. (2003a). After thorough validation and injury criteria establishment (cumulative strain damage measure--CSDM for diffuse axonal injuries (DAI), relative motion damage measure--RMDM for acute subdural hematoma (ASDH), and dilatational damage measure--DDM for contusions and focal lesions), the model was used in investigation of mild TBI cases in living humans based on a set of head impact data taken from American football players at the collegiate level. It was found that CSDM and especially RMDM correlated well with angular acceleration and angular velocity. DDM was close to zero for most impacts due to their mild severity implying that cavitational pressure anywhere in the brain was not reached. Maximum principal strain was found to correlate well with RMDM and angular head kinematic measures. Maximum principal stress didn't correlate with any kinematic measure or injury metric. The model was then used in the investigation of brain injury potential in NHTSA conducted side impact tests. It was also used in parametric investigations of various "what if" scenarios, such as side versus frontal impact, to establish a potential link between head kinematics and injury outcomes. The new SIMon FEHM offers an advantage over the previous version because it is geometrically more representative of the human head. This advantage, however, is made possible at the expense of additional computational time.

title: Maximum Principal Strain and Strain Rate Associated with Concussion Diagnosis Correlates with Changes in Corpus Callosum White Matter Indices
abstract: On-field monitoring of head impacts, combined with finite element (FE) biomechanical simulation, allow for predictions of regional strain associated with a diagnosed concussion. However, attempts to correlate these predictions with in vivo measures of brain injury have not been published. This article reports an approach to and preliminary results from the correlation of subject-specific FE model-predicted regions of high strain associated with diagnosed concussion and diffusion tensor imaging to assess changes in white matter integrity in the corpus callosum (CC). Ten football and ice hockey players who wore instrumented helmets to record head impacts sustained during play completed high field magnetic resonance imaging preseason and within 10 days of a diagnosed concussion. The Dartmouth Subject-Specific FE Head model was used to generate regional predictions of strain and strain rate following each impact associated with concussion. Maps of change in fractional anisotropy (FA) and median diffusivity (MD) were generated for the CC of each athlete to correlate strain with change in FA and MD. Mean and maximum strain rate correlated with change in FA (Spearman ρ = 0.77, p = 0.01; 0.70, p = 0.031), and there was a similar trend for mean and maximum strain (0.56, p = 0.10; 0.6, p = 0.07), as well as for maximum strain with change in MD (−0.63, p = 0.07). Change in MD correlated with injury-to-imaging interval (ρ = −0.80, p = 0.006) but change in FA did not (ρ = 0.18, p = 0.62). These results provide preliminary confirmation that model-predicted strain and strain rate in the CC correlate with changes in indices of white matter integrity.

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

title: Head impact accelerations for brain strain-related responses in contact sports: a model-based investigation
abstract: Both linear $$(\mathbf{a}_{\mathrm{lin}})$$(alin) and rotational $$(\mathbf{a}_{\mathrm{rot}} )$$(arot) accelerations contribute to head impacts on the field in contact sports; however, they are often isolated in injury studies. It is critical to evaluate the feasibility of estimating brain responses using isolated instead of full degrees-of-freedom (DOFs) accelerations. In this study, we investigated the sensitivities of regional brain strain-related responses to resultant $$\mathbf{a}_{\mathrm{lin}}$$alin and $$\mathbf{a}_{\mathrm{rot}}$$arot as well as the relative contributions of these acceleration components to the responses via random sampling and linear regression using parameterized, triangulated head impacts with kinematic variable values based on on-field measurements. Two independently established and validated finite element models of the human head were employed to evaluate model-consistency and dependency in results: the Dartmouth Head Injury Model and Simulated Injury Monitor. For the majority of the brain, volume-weighted regional peak strain, strain rate, and von Mises stress accumulated from the simulation significantly correlated with the product of the magnitude and duration of $$\mathbf{a}_{\mathrm{rot}}$$arot, or effectively, the rotational velocity, but not to $$\mathbf{a}_{\mathrm{lin}}$$alin. Responses from $$\mathbf{a}_{\mathrm{rot}}$$arot-only were comparable to the full-DOF counterparts especially when normalized by injury-causing thresholds (e.g., volume fractions of large differences virtually diminished (i.e., $$<$$<1 %) at typical difference percentage levels of 1–4 % on average). These model-consistent results support the inclusion of both rotational acceleration magnitude and duration into kinematics-based injury metrics and demonstrate the feasibility of estimating strain-related responses from isolated $$\mathbf{a}_{\mathrm{rot}}$$arot for analyses of strain-induced injury relevant to contact sports without significant loss of accuracy, especially for the cerebrum.

title: Evaluation of head injury criteria using a finite element model validated against experiments on localized brain motion, intracerebral acceleration, and intracranial pressure
abstract: The objective of the present study was to analyze the effect of different load directions and durations following impact using a finite element (FE) model of the human head. A detailed FE model of the human head was developed and validated against available cadaver experiment data for three impact directions (frontal, occipital, and lateral). Loads corresponding to the same impact power were imposed in different directions. Furthermore, the head injury criterion (HIC), the recently proposed head impact power (HIP) criterion, as well as peak angular acceleration, and change in angular and translational velocity were evaluated with respect to the strain in the central nervous system (CNS) tissue. A significant correlation was found between experiments and simulations with regard to intracranial pressure data for a short-duration impulse and intracerebral acceleration characteristics for a long-duration impulse with a high-angular component. However, a poor correlation with the simulations was found for the intracranial pressures for the long-duration impulse. This is thought to be a result of air introduced to the intracranial cavity during experimental testing. Smaller relative motion between the brain and skull results from lateral impact than from a frontal or occipital blow for both the experiments and FE simulations. It was found that the influence of impact direction had a substantial effect on the intracranial response. When evaluating the global kinematic injury measures for the rotational pulses, the change in angular velocity corresponded best with the intracranial strains found in the FE model. For the translational impulse, on the other hand, the HIC and the HIP showed the best correlation with the strain levels found in the model.

title: Finite element analysis of the effect of loading curve shape on brain injury predictors.
abstract: Prediction of traumatic and mild traumatic brain injury is an important factor in managing their prevention. Currently, the prediction of these injuries is limited to peak linear and angular acceleration loading curves derived from laboratory reconstructions. However it remains unclear as to what aspect of these loading curves contributes to brain tissue damage. This research uses the University College Dublin Brain Trauma Model (UCDBTM) to analyse three distinct loading curve shapes meant to represent different helmet loading scenarios. The loading curves were applied independently in each axis of linear and angular acceleration and their effect on currently used predictors of TBI and mTBI was examined. Loading curve shape A had a late time to peak, B an early time to peak and C had a consistent plateau. The areas under the curve for all three loading curve shapes were identical. The results indicate that loading curve A produced consistently higher maximum principal strains and Von Mises stress than the other two loading curve types. Loading curve C consistently produced the lowest values of maximum principal strain and Von Mises stress, with loading curve B being lowest in only 2 cases. The areas of peak Von Mises stress and Principal strain also varied depending on loading curve shape and acceleration input.

title: Modeling Brain Injury Response for Rotational Velocities of Varying Directions and Magnitudes
abstract: An estimated 1.7 million people in the United States sustain a traumatic brain injury (TBI) annually. To investigate the effects of rotational motions on TBI risk and location, this study modeled rotational velocities of five magnitudes and 26 directions of rotation using the Simulated Injury Monitor finite element brain model. The volume fraction of the total brain exceeding a predetermined strain threshold, the Cumulative Strain Damage Measure (CSDM), was investigated to evaluate global model response. To evaluate regional response, this metric was computed relative to individual brain structures and termed the Structure Cumulative Strain Damage Measure (SCSDM). CSDM increased as input magnitude increased and varied with the direction of rotation. CSDM was 0.55–1.7 times larger in simulations with transverse plane rotation compared to those without transverse plane rotation. The largest SCSDM in the cerebrum and brainstem occurred with rotations in the transverse and sagittal planes, respectively. Velocities causing medial rotation of the cerebellum resulted in the largest SCSDM in this structure. For velocities of the same magnitude, injury risk calculated from CSDM varied from 0 to 97% with variations in the direction of rotation. These findings demonstrate injury risk, as estimated by CSDM and SCSDM, is affected by the direction of rotation and input magnitude, and these may be important considerations for injury prediction.

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

title: MRI-based finite element modeling of head trauma: spherically focusing shear waves
abstract: A powerful tool for investigating the physical process producing head trauma is finite element (FE) modeling. In this paper, we present a 3D FE model of the human head that accounts for important geometric characteristics of the various components within the human head through an efficient magnetic resonance imaging voxel-based mesh generation method. To validate the FE model, a previous cadaver experiment of frontal impact is simulated, and this is where heretofore unknown wave patterns are discovered. The model is run under either of two extreme assumptions concerning the head-neck junction—free or fixed—and the experimental measurements are well bounded by the computed pressures from the two boundary conditions. In both cases the impact gives rise to not only a fast pressure wave but also a slow and spherically convergent shear stress wave which is potentially more damaging to the brain tissue.

title: Parametric Comparisons of Intracranial Mechanical Responses from Three Validated Finite Element Models of the Human Head
abstract: A number of human head finite element (FE) models have been developed from different research groups over the years to study the mechanisms of traumatic brain injury. These models can vary substantially in model features and parameters, making it important to evaluate whether simulation results from one model are readily comparable with another, and whether response-based injury thresholds established from a specific model can be generalized when a different model is employed. The purpose of this study is to parametrically compare regional brain mechanical responses from three validated head FE models to test the hypothesis that regional brain responses are dependent on the specific head model employed as well as the region of interest (ROI). The Dartmouth Scaled and Normalized Model (DSNM), the Simulated Injury Monitor (SIMon), and the Wayne State University Head Injury Model (WSUHIM) were selected for comparisons. For model input, 144 unique kinematic conditions were created to represent the range of head impacts sustained by male collegiate hockey players during play. These impacts encompass the 50th, 95th, and 99th percentile peak linear and rotational accelerations at 16 impact locations around the head. Five mechanical variables (strain, strain rate, strain × strain rate, stress, and pressure) in seven ROIs reported from the FE models were compared using Generalized Estimating Equation statistical models. Highly significant differences existed among FE models for nearly all output variables and ROIs. The WSUHIM produced substantially higher peak values for almost all output variables regardless of the ROI compared to the DSNM and SIMon models (p < 0.05). DSNM also produced significantly different stress and pressure compared with SIMon for all ROIs (p < 0.05), but such differences were not consistent across ROIs for other variables. Regardless of FE model, most output variables were highly correlated with linear and rotational peak accelerations. The significant disparities in regional brain responses across head models regardless of the output variables strongly suggest that model-predicted brain responses from one study should not be extended to other studies in which a different model is utilized. Consequently, response-based injury tolerance thresholds from a specific model should not be generalized to other studies either in which a different model is used. However, the similar relationships between regional responses and the linear/rotational peak accelerations suggest that each FE model can be used independently to assess regional brain responses to impact simulations in order to perform statistical correlations with medical images and/or well-selected experiments with documented injury findings.

title: Concussion in professional football: reconstruction of game impacts and injuries.
abstract: Concussion in professional football was studied with respect to impact types and injury biomechanics. A combination of video surveillance and laboratory reconstruction of game impacts was used to evaluate concussion biomechanics.



Between 1996 and 2001, videotapes of concussions and significant head impacts were collected from National Football League games. There were clear views of the direction and location of the helmet impact for 182 cases. In 31 cases, the speed of impact could be determined with analysis of multiple videos. Those cases were reconstructed in laboratory tests using helmeted Hybrid III dummies and the same impact velocity, direction, and head kinematics as in the game. Translational and rotational accelerations were measured, to define concussion biomechanics. Several studies were performed to ensure the accuracy and reproducibility of the video analysis and laboratory methods used.



Concussed players experienced head impacts of 9.3 +/- 1.9 m/s (20.8 +/- 4.2 miles/h). There was a rapid change in head velocity of 7.2 +/- 1.8 m/s (16.1 +/- 4.0 miles/h), which was significantly greater than that for uninjured struck players (5.0 +/- 1.1 m/s, 11.2 +/- 2.5 miles/h; t = 2.9, P < 0.005) or striking players (4.0 +/- 1.2 m/s, 8.9 +/- 2.7 miles/h; t = 7.6, P < 0.001). The peak head acceleration in concussion was 98 +/- 28 g with a 15-millisecond half-sine duration, which was statistically greater than the 60 +/- 24 g for uninjured struck players (t = 3.1, P < 0.005). Concussion was primarily related to translational acceleration resulting from impacts on the facemask or side, or falls on the back of the helmet. Concussion could be assessed with the severity index or head injury criterion (the conventional measures of head injury risk). Nominal tolerance levels for concussion were a severity index of 300 and a head injury criterion of 250.



Concussion occurs with considerable head impact velocity and velocity changes in professional football. Current National Operating Committee on Standards for Athletic Equipment standards primarily address impacts to the periphery and crown of the helmet, whereas players are experiencing injuries in impacts to the facemask, side, and back of the helmet. New tests are needed to assess the performance of helmets in reducing concussion risks involving high-velocity and long-duration injury biomechanics.

title: Head Impact Exposure in Youth Football: High School Ages 14 to 18 Years and Cumulative Impact Analysis
abstract: Sports-related concussion is the most common athletic head injury with football having the highest rate among high school athletes. Traditionally, research on the biomechanics of football-related head impact has been focused at the collegiate level. Less research has been performed at the high school level, despite the incidence of concussion among high school football players. The objective of this study is to twofold: to quantify the head impact exposure in high school football, and to develop a cumulative impact analysis method. Head impact exposure was measured by instrumenting the helmets of 40 high school football players with helmet mounted accelerometer arrays to measure linear and rotational acceleration. A total of 16,502 head impacts were collected over the course of the season. Biomechanical data were analyzed by team and by player. The median impact for each player ranged from 15.2 to 27.0 g with an average value of 21.7 (±2.4) g. The 95th percentile impact for each player ranged from 38.8 to 72.9 g with an average value of 56.4 (±10.5) g. Next, an impact exposure metric utilizing concussion injury risk curves was created to quantify cumulative exposure for each participating player over the course of the season. Impacts were weighted according to the associated risk due to linear acceleration and rotational acceleration alone, as well as the combined probability (CP) of injury associated with both. These risks were summed over the course of a season to generate risk weighted cumulative exposure. The impact frequency was found to be greater during games compared to practices with an average number of impacts per session of 15.5 and 9.4, respectively. However, the median cumulative risk weighted exposure based on combined probability was found to be greater for practices vs. games. These data will provide a metric that may be used to better understand the cumulative effects of repetitive head impacts, injury mechanisms, and head impact exposure of athletes in football.

title: Investigation of Head Injury Mechanisms Using Neutral Density Technology and High-Speed Biplanar X-ray.
abstract: The principal focus of this study was the measurement of relative brain motion with respect to the skull using a high-speed, biplanar x-ray system and neutral density targets (NDTs). A suspension fixture was used for testing of inverted, perfused, human cadaver heads. Each specimen was subjected to multiple tests, either struck at rest using a 152-mm-diameter padded impactor face, or stopped against an angled surface from steady-state motion. The impacts were to the frontal and occipital regions. An array of multiple NDTs was implanted in a double-column scheme of 5 and 6 targets, with 10 mm between targets in each column and 80 mm between columns. These columns were implanted in the temporoparietal and occipitoparietal regions. The impacts produced peak resultant accelerations of 10 to 150 g, and peak angular accelerations between 1000 and 8000 rad/s(2). For all but one test, the peak angular speeds ranged from 17 to 22 rad/s. The relative 3D displacements between the skull and the NDTs were analyzed. The localized motions of the brain generally followed loop or figure eight patterns, with peak displacements on the order of +/- 5 mm. These results can be used to further finite-element modeling efforts.

title: A study of the response of the human cadaver head to impact.
abstract: High-speed biplane x-ray and neutral density targets were used to examine brain displacement and deformation during impact. Relative motion, maximum principal strain, maximum shear strain, and intracranial pressure were measured in thirty-five impacts using eight human cadaver head and neck specimens. The effect of a helmet was evaluated. During impact, local brain tissue tends to keep its position and shape with respect to the inertial frame, resulting in relative motion between the brain and skull and deformation of the brain. The local brain motions tend to follow looping patterns. Similar patterns are observed for impact in different planes, with some degree of posterior-anterior and right-left symmetry. Peak coup pressure and pressure rate increase with increasing linear acceleration, but coup pressure pulse duration decreases. Peak average maximum principal strain and maximum shear are on the order of 0.09 for CFC 60 Hz data for these tests. Peak average maximum principal strain and maximum shear decrease with increasing linear acceleration, coup pressure, and coup pressure rate. Linear and angular acceleration of the head are reduced with use of a helmet, but strain increases. These results can be used for the validation of finite element models of the human head.

title: Deformation of the human brain induced by mild angular head acceleration.
abstract: Deformation of the human brain was measured in tagged magnetic resonance images (MRI) obtained dynamically during angular acceleration of the head. This study was undertaken to provide quantitative experimental data to illuminate the mechanics of traumatic brain injury (TBI). Mild angular acceleration was imparted to the skull of a human volunteer inside an MR scanner, using a custom MR-compatible device to constrain motion. A grid of MR "tag" lines was applied to the MR images via spatial modulation of magnetization (SPAMM) in a fast gradient echo imaging sequence. Images of the moving brain were obtained dynamically by synchronizing the imaging process with the motion of the head. Deformation of the brain was characterized quantitatively via Lagrangian strain. Consistent patterns of radial-circumferential shear strain occur in the brain, similar to those observed in models of a viscoelastic gel cylinder subjected to angular acceleration. Strain fields in the brain, however, are clearly mediated by the effects of heterogeneity, divisions between regions of the brain (such as the central fissure and central sulcus) and the brain's tethering and suspension system, including the dura mater, falx cerebri, and tentorium membranes.

title: Brain pressure responses in translational head impact: a dimensional analysis and a further computational study
abstract: Brain pressure responses resulting from translational head impact are typically related to focal injuries at the coup and contrecoup sites. Despite significant efforts characterizing brain pressure responses using experimental and modeling approaches, a thorough investigation of the key controlling parameters appears lacking. In this study, we identified three parameters specific and important for brain pressure responses induced by isolated linear acceleration $$( )$$(alin) via a dimensional analysis: $$a_{\text {lin}} $$alin itself (magnitude and directionality), brain size and shape. These findings were verified using our recently developed Dartmouth Head Injury Model (DHIM).  $$alin to the rigid skull, we found that the temporal profile of the given $$a_{\text {lin}} $$alin directly determined that of pressure. Brain pressure was also found to be linearly proportional to brain size and dependent on impact direction. In addition, we investigated perturbations to brain pressure responses as a result of non-rigid skull deformation. Finally, DHIM pressure responses were quantitatively validated against two representative cadaveric head impacts (categorized as “good” to “excellent” in performance). These results suggest that both the magnitude and directionality of $$a_{\text {lin}} $$alin as well as brain size and shape should be considered when interpreting brain pressure responses. Further, a model validated against pressure responses alone is not sufficient to ensure its fidelity in strain-related responses. These findings provide important insights into brain pressure responses in translational head impact and the resulting risk of pressure-induced injury. In addition, they establish the feasibility of creating a pre-computed atlas for real-time tissue-level pressure responses without a direct simulation in the future.

title: An atlas-based method to compensate for brain shift: Preliminary results
abstract: Compensating for intraoperative brain shift using computational models has shown promising results. Since computational time is an important factor during neurosurgery, a priori knowledge of the possible sources of deformation can increase the accuracy of model-updated image-guided systems. In this paper, a strategy to compensate for distributed loading conditions in the brain such as brain sag, volume changes due to drug reactions, and brain swelling due to edema is presented. An atlas of model deformations based on these complex loading conditions is computed preoperatively and used with a constrained linear inverse model to predict the intraoperative distributed brain shift. This relatively simple inverse finite-element approach is investigated within the context of a series of phantom experiments, two in vivo cases, and a simulation study. Preliminary results indicate that the approach recaptured on average 93% of surface shift for the simulation, phantom, and in vivo experiments. With respect to subsurface shift, comparisons were only made with simulation and phantom experiments and demonstrated an ability to recapture 85% of the shift. This translates to a remaining surface and subsurface shift error of 0.7+/-0.3 mm, and 1.0+/-0.4 mm, respectively, for deformations on the order of 1cm.

title: Head impacts during high school football: a biomechanical assessment.
abstract: Little is known about the impact biomechanics sustained by players during interscholastic football.



To characterize the location and magnitude of impacts sustained by players during an interscholastic football season.



Observational design.



On the field.



High school varsity football team (n = 35; age = 16.85 +/- 0.75 years, height = 183.49 +/- 5.31 cm, mass = 89.42 +/- 12.88 kg).



Biomechanical variables (linear acceleration, rotational acceleration, jerk, force, impulse, and impact duration) related to head impacts were categorized by session type, player position, and helmet impact location.



Differences in grouping variables were found for each impact descriptor. Impacts occurred more frequently and with greater intensity during games. Linear acceleration was greatest in defensive linemen and offensive skill players and when the impact occurred at the top of the helmet. The largest rotational acceleration occurred in defensive linemen and with impacts to the front of the helmet. Impacts with the highest-magnitude jerk, force, and impulse and shortest duration occurred in the offensive skill, defensive line, offensive line, and defensive skill players, respectively. Top-of-the-helmet impacts yielded the greatest magnitude for the same variables.



We are the first to provide a biomechanical characterization of head impacts in an interscholastic football team across a season of play. The intensity of game play manifested with more frequent and intense impacts. The highest-magnitude variables were distributed across all player groups, but impacts to the top of the helmet yielded the highest values. These high school football athletes appeared to sustain greater accelerations after impact than their older counterparts did. How this finding relates to concussion occurrence has yet to be elucidated.

title: An Instrumented Mouthguard for Measuring Linear and Angular Head Impact Kinematics in American Football
abstract: The purpose of this study was to evaluate a novel instrumented mouthguard as a research device for measuring head impact kinematics. To evaluate kinematic accuracy, laboratory impact testing was performed at sites on the helmet and facemask for determining how closely instrumented mouthguard data matched data from an anthropomorphic test device. Laboratory testing results showed that peak linear acceleration (r2 = 0.96), peak angular acceleration (r2 = 0.89), and peak angular velocity (r2 = 0.98) measurements were highly correlated between the instrumented mouthguard and anthropomorphic test device. Normalized root-mean-square errors for impact time traces were 9.9 ± 4.4% for linear acceleration, 9.7 ± 7.0% for angular acceleration, and 10.4 ± 9.9% for angular velocity. This study demonstrates the potential of an instrumented mouthguard as a research tool for measuring in vivo impacts, which could help uncover the link between head impact kinematics and brain injury in American football.

title: High School and Collegiate Football Athlete Concussions: A Biomechanical Review
abstract: Researchers are striving to understand the biomechanics of concussive injury that occur in the context of sport by using a number of methodologies. Animal models, video reconstruction, and helmet-based accelerometers have all been used, but have their limitations.  This review provides a theoretical discussion of concussion mechanics and examines the current literature on the effects of the number of impacts, impact magnitude, impact distribution, and concussion threshold in high school and collegiate football athletes recorded by the HIT System.

title: Linear and angular head acceleration measurements in collegiate football.
abstract: Each year, between 1.6x10(6) and 3.8x10(6) concussions are sustained by athletes playing sports, with football having the highest incidence. The high number of concussions in football provides a unique opportunity to collect biomechanical data to characterize mild traumatic brain injury. Human head acceleration data for a range of impact severities were collected by instrumenting the helmets of collegiate football players with accelerometers. The helmets of ten Virginia Tech football players were instrumented with measurement devices for every game and practice for the 2007 football season. The measurement devices recorded linear and angular accelerations about each of the three axes of the head. Data for each impact were downloaded wirelessly to a sideline data collection system shortly after each impact occurred. Data were collected for 1712 impacts, creating a large and unbiased data set. While a majority of the impacts were of relatively low severity (<30 g and <2000 rad/s2), 172 impacts were greater than 40 g and 143 impacts were greater than 3000 rad/s2. No instrumented player sustained a clinically diagnosed concussion during the 2007 season. A large and unbiased data set was compiled by instrumenting the helmets of collegiate football players. Football provides a unique opportunity to collect head acceleration data of varying severity from human volunteers. The addition of concurrent concussive data may advance the understanding of the mechanics of mild traumatic brain injury. With an increased understanding of the biomechanics of head impacts in collegiate football and human tolerance to head acceleration, better equipment can be designed to prevent head injuries.

title: Biomechanical properties of concussions in high school football.
abstract: Sport concussion represents the majority of brain injuries occurring in the United States with 1.6–3.8 million cases annually. Understanding the biomechanical properties of this injury will support the development of better diagnostics and preventative techniques.



We monitored all football related head impacts in 78 high school athletes (mean age = 16.7 yr) from 2005 to 2008 to better understand the biomechanical characteristics of concussive impacts.



Using the Head Impact Telemetry System, a total of 54,247 impacts were recorded, and 13 concussive episodes were captured for analysis. A classification and regression tree analysis of impacts indicated that rotational acceleration (95582.3 rad·s−²), linear acceleration (996.1g), and impact location (front, top, and back) yielded the highest predictive value of concussion.



These threshold values are nearly identical with those reported at the collegiate and professional level. If the Head Impact Telemetry System were implemented for medical use, sideline personnel can expect to diagnose one of every five athletes with a concussion when the impact exceeds these tolerance levels. Why all athletes did not sustain a concussion when the impacts generated variables in excess of our threshold criteria is not entirely clear, although individual differences between participants may play a role. A similar threshold to concussion in adolescent athletes compared with their collegiate and professional counterparts suggests an equal concussion risk at all levels of play.

title: Multivariate Spline Functions, B-Spline Basis and Polynomial Interpolations
abstract: The main result of this paper is a formula relating a multivariate B-spline and a certain directional derivative to a lower order B-spline.The structure of discontinuous B-splines is given. A formula relates the discontinuous k-variate B-spline to a $(k - 1)$-variate B-spline.With the help of these formulas, we have succeeded in determining the exact class of local and global smoothness of a multivariate B-spline depending on the configuration of the knots.

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

title: A six degree of freedom head acceleration measurement device for use in football.
abstract: The high incidence rate of concussions in football provides a unique opportunity to collect biomechanical data to characterize mild traumatic brain injury. The goal of this study was to validate a six degree of freedom (6DOF) measurement device with 12 single-axis accelerometers that uses a novel algorithm to compute linear and angular head accelerations for each axis of the head. The 6DOF device can be integrated into existing football helmets and is capable of wireless data transmission. A football helmet equipped with the 6DOF device was fitted to a Hybrid III head instrumented with a 9 accelerometer array. The helmet was impacted using a pneumatic linear impactor. Hybrid III head accelerations were compared with that of the 6DOF device. For all impacts, peak Hybrid III head accelerations ranged from 24 g to 176 g and 1,506 rad/s(2) to 14,431 rad/s(2). Average errors for peak linear and angular head acceleration were 1% ± 18% and 3% ± 24%, respectively. The average RMS error of the temporal response for each impact was 12.5 g and 907 rad/s(2).

title: Automated subject-specific, hexahedral mesh generation via image registration.
abstract: Generating subject-specific, all-hexahedral meshes for finite element analysis continues to be of significant interest in biomechanical research communities. To date, most automated methods "morph" an existing atlas mesh to match with a subject anatomy, which usually result in degradation in mesh quality because of mesh distortion. We present an automated meshing technique that produces satisfactory mesh quality and accuracy without mesh repair. An atlas mesh is first developed using a script. A subject-specific mesh is generated with the same script after transforming the geometry into the atlas space following rigid image registration, and is transformed back into the subject space. By meshing the brain in 11 subjects, we demonstrate that the technique's performance is satisfactory in terms of both mesh quality (99.5% of elements had a scaled Jacobian >0.6 while <0.01% were between 0 and 0.2) and accuracy (average distance between mesh boundary and geometrical surface was 0.07 mm while <1% greater than 0.5mm). The combined computational cost for image registration and meshing was <4 min. Our results suggest that the technique is effective for generating subject-specific, all-hexahedral meshes and that it may be useful for meshing a variety of anatomical structures across different biomechanical research fields.

title: Computation of axonal elongation in head trauma finite element simulation.
abstract: In the case of head trauma, elongation of axons is thought to result in brain damage and to lead to Diffuse Axonal Injuries (DAI). Mechanical parameters have been previously proposed as DAI metric. Typically, brain injury parameters are expressed in terms of pressure, shearing stresses or invariants of the strain tensor. Addressing axonal deformation within the brain during head impact can improve our understanding of DAI mechanisms. A new technique based on directional measurements of water diffusion in soft tissue using Magnetic Resonance Imaging (MRI), called Diffusion Tensor Imaging (DTI), provides information on axonal orientation within the brain. The present study aims at coupling axonal orientation from a 12-patient-based DTI 3D picture, called "DTI atlas", with the Strasbourg University Finite Element Head Model (SUFEHM). This information is then integrated in head trauma simulation by computing axonal elongation for each finite element of the brain model in a post-processing of classical simulation results. Axonal elongation was selected as computation endpoint for its strong potential as a parameter for DAI prediction and location. After detailing the coupling technique between DTI atlas and the head FE model, two head trauma cases presenting different DAI injury levels are reconstructed and analyzed with the developed methodology as an illustration of axonal elongation computation. Results show that anisotropic brain structures can be realistically implemented into an existing finite element model of the brain. The feasibility of integrating axon fiber direction information within a dedicated post-processor is also established in the context of the computation of axonal elongation. The accuracy obtained when estimating level and location of the computed axonal elongation indicates that coupling classical isotropic finite element simulation with axonal structural anisotropy is an efficient strategy. Using this method, tensile elongation of the axons can be directly invoked as a mechanism for Diffuse Axonal Injury.

title: Micromechanics of diffuse axonal injury: influence of axonal orientation and anisotropy
abstract: Multiple length scales are involved in the development of traumatic brain injury, where the global mechanics of the head level are responsible for local physiological impairment of brain cells. In this study, a relation between the mechanical state at the tissue level and the cellular level is established. A model has been developed that is based on pathological observations of local axonal injury. The model contains axons surrounding an obstacle (e.g., a blood vessel or a brain soma). The axons, which are described by an anisotropic fiber-reinforced material model, have several physically different orientations. The results of the simulations reveal axonal strains being higher than the applied maximum principal tissue strain. For anisotropic brain tissue with a relatively stiff inclusion, the relative logarithmic strain increase is above 60%. Furthermore, it is concluded that individual axons oriented away from the main axonal direction at a specific site can be subjected to even higher axonal strains in a stress-driven process, e.g., invoked by inertial forces in the brain. These axons can have a logarithmic strain of about 2.5 times the maximum logarithmic strain of the axons in the main axonal direction over the complete range of loading directions. The results indicate that cellular level heterogeneities have an important influence on the axonal strain, leading to an orientation and location-dependent sensitivity of the tissue to mechanical loads. Therefore, these effects should be accounted for in injury assessments relying on finite element head models.

title: Combining the Finite Element Method with Structural Connectome-based Analysis for Modeling Neurotrauma: Connectome Neurotrauma Mechanics
abstract: 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 () 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.

title: A multiscale computational approach to estimating axonal damage under inertial loading of the head.
abstract: A computational modeling framework is developed to estimate the location and degree of diffuse axonal injury (DAI) under inertial loading of the head. DAI is one of the most common pathological features of traumatic brain injury and is characterized by damage to the neural axons in the white matter regions of the brain. We incorporate the microstructure of the white matter (i.e., the fiber orientations and fiber dispersion) through the use of diffusion tensor imaging (DTI), and model the white matter with an anisotropic, hyper-viscoelastic constitutive model. The extent of DAI is estimated using an axonal strain injury criterion. A novel injury analysis method is developed to quantify the degree of axonal damage in the fiber tracts of the brain and identify the tracts that are at the greatest risk for functional failure. Our modeling framework is applied to analyze DAI in a real-life ice hockey incident that resulted in concussive injury. To simulate the impact, two-dimensional finite element (FE) models of the head were constructed from detailed MRI and DTI data and validated using available human head experimental data. Acceleration loading curves from accident reconstruction data were then applied to the FE models. The rotational (rather than translational) accelerations were shown to dominate the injury response, which is consistent with previous studies. Through this accident reconstruction, we demonstrate a conceptual framework to estimate the degree of axonal injury in the fiber tracts of the human brain, enabling the future development of relationships between computational simulation and neurocognitive impairment.