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

Dynamic strain fields of the mouse brain during rotation

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

A computational pipeline towards large-scale and multiscale modeling of traumatic axonal injury

Contemporary biomechanical modeling of traumatic brain injury (TBI) focuses on either the global brain as an organ or a representative tiny section of a single axon. In addition, while it is common for a global brain model to employ real-world impacts as input, axonal injury models have largely been limited to inputs of either tension or compression with assumed peak strain and strain rate. These major gaps between global and microscale modeling preclude a systematic and mechanistic investigation of how tissue strain from impact leads to downstream axonal damage throughout the white matter. In this study, a unique subject-specific multimodality dataset from a male ice-hockey player sustaining a diagnosed concussion is used to establish an efficient and scalable computational pipeline. It is then employed to derive voxelized brain deformation, maximum principal strains and white matter fiber strains, and finally, to produce diverse fiber strain profiles of various shapes in temporal history necessary for the development and application of a deep learning axonal injury model in the future. The pipeline employs a structured, voxelized representation of brain deformation with adjustable spatial resolution independent of model mesh resolution. The method can be easily extended to other head impacts or individuals. The framework established in this work is critical for enabling large-scale (i.e., across the entire white matter region, head impacts, and individuals) and multiscale (i.e., from organ to cell length scales) modeling for the investigation of traumatic axonal injury (TAI) triggering mechanisms. Ultimately, these efforts could enhance the assessment of concussion risks and design of protective headgear. Therefore, this work contributes to improved strategies for concussion detection, mitigation, and prevention.

Biomechanical Response of Head Surrogate With and Without the Helmet

Measurements of brain deformations under injurious loading scenarios are actively sought. In this work, we report experimentally measured head kinematics and corresponding dynamic, two-dimensional brain simulant deformations in head surrogates under a blunt impact, with and without a helmet. Head surrogates used in this work consisted of skin, skull, dura, falx, tentorium, and brain stimulants. The head surrogate geometry was based on the global human body models consortium's head model. A base head surrogate consisting of skin-skull-brain was considered. In addition, the response of two other head surrogates, skin-skull-dura-brain, and skin-skull-dura-brain-falx-tentorium, was investigated. Head surrogate response was studied for sagittal and coronal plane rotations for impactor velocities of 1 and 3 m/s. Response of head surrogates was compared against strain measurements in PMHS. The strain pattern in the brain simulant was heterogenous, and peak strains were established within ∼30 ms. The choice of head surrogate affect the spatiotemporal evolution of strain. For no helmet case, peak MPS of ∼50-60% and peak MSS of ∼35-50% were seen in brain simulant corresponding to peak rotational accelerations of ∼5000-7000 rad/s2. Peak head kinematics and peak MPS have been reduced by up to 75% and 45%, respectively, with the conventional helmet and by up to 90% and 85%, respectively, with the helmet with antirotational pads. Overall, these results provide important, new data on brain simulant strains under a variety of loading scenarios-with and without the helmets.

Diffusion Tensor Imaging Reveals Elevated Diffusivity of White Matter Microstructure that Is Independently Associated with Long-Term Outcome after Mild Traumatic Brain Injury: A TRACK-TBI Study

Diffusion tensor imaging (DTI) literature on single-center studies contains conflicting results regarding acute effects of mild traumatic brain injury (mTBI) on white matter (WM) microstructure and the prognostic significance. This larger-scale multi-center DTI study aimed to determine how acute mTBI affects WM microstructure over time and how early WM changes affect long-term outcome. From Transforming Research and Clinical Knowledge in Traumatic Brain Injury (TRACK-TBI), a cohort study at 11 United States level 1 trauma centers, a total of 391 patients with acute mTBI ages 17 to 60 years were included and studied at two weeks and six months post-injury. Demographically matched friends or family of the participants were the control group (n = 148). Axial diffusivity (AD), fractional anisotropy (FA), mean diffusivity (MD), and radial diffusivity (RD) were the measures of WM microstructure. The primary outcome was the Glasgow Outcome Scale Extended (GOSE) score of injury-related functional limitations across broad life domains at six months post-injury. The AD, MD, and RD were higher and FA was lower in mTBI versus friend control (FC) at both two weeks and six months post-injury throughout most major WM tracts of the cerebral hemispheres. In the mTBI group, AD and, to a lesser extent, MD decreased in WM from two weeks to six months post-injury. At two weeks post-injury, global WM AD and MD were both independently associated with six-month incomplete recovery (GOSE <8 vs = 8) even after accounting for demographic, clinical, and other imaging factors. DTI provides reliable imaging biomarkers of dynamic WM microstructural changes after mTBI that have utility for patient selection and treatment response in clinical trials. Continued technological advances in the sensitivity, specificity, and precision of diffusion magnetic resonance imaging hold promise for routine clinical application in mTBI.

Real-time dynamic simulation for highly accurate spatiotemporal brain deformation from impact

Real-time dynamic simulation remains a significant challenge for spatiotemporal data of high dimension and resolution. In this study, we establish a transformer neural network (TNN) originally developed for natural language processing and a separate convolutional neural network (CNN) to estimate five-dimensional (5D) spatiotemporal brain-skull relative displacement resulting from impact (isotropic spatial resolution of 4 mm with temporal resolution of 1 ms). Sequential training is applied to train (N = 5184 samples) the two neural networks for estimating the complete 5D displacement across a temporal duration of 60 ms. We find that TNN slightly but consistently outperforms CNN in accuracy for both displacement and the resulting voxel-wise four-dimensional (4D) maximum principal strain (e.g., root mean squared error (RMSE) of ~1.0% vs. ~1.6%, with coefficient of determination, R ² >0.99 vs. >0.98, respectively, and normalized RMSE (NRMSE) at peak displacement of 2%-3%, based on an independent testing dataset; N = 314). Their accuracies are similar for a range of real-world impacts drawn from various published sources (dummy, helmet, football, soccer, and car crash; average RMSE/NRMSE of ~0.3 mm/~4%-5% and average R ² of ~0.98 at peak displacement). Sequential training is effective for allowing instantaneous estimation of 5D displacement with high accuracy, although TNN poses a heavier computational burden in training. This work enables efficient characterization of the intrinsically dynamic brain strain in impact critical for downstream multiscale axonal injury model simulation. This is also the first application of TNN in biomechanics, which offers important insight into how real-time dynamic simulations can be achieved across diverse engineering fields.

Displacement voxelization to resolve mesh-image mismatch: Application in deriving dense white matter fiber strains

BACKGROUND AND OBJECTIVE

It is common to combine biomechanical modeling and medical images for multimodal analyses. However, mesh-image mismatch may occur that prevents direct information exchange. To eliminate mesh-image mismatch, we develop a simple but elegant displacement voxelization technique based on image voxel corner nodes to achieve voxel-wise strain. We then apply the technique to derive dense white matter fiber strains along whole-brain tractography (∼35 k fiber tracts consisting of ∼3.3 million sampling points) resulting from head impact.

METHODS

Displacements at image voxel corner nodes are first obtained from model simulation via scattered interpolation. Each voxel is then scaled linearly to form a unit hexahedral element. This allows convenient and efficient voxel-wise strain tensor calculation and displacement interpolation at arbitrary fiber sampling points via shape functions. Fiber strains from displacement interpolation are then compared with those from the commonly used strain tensor projection using either voxel- or element-wise strain tensors.

RESULTS

Based on a synthetic displacement field, fiber strains interpolated from voxelized displacement are considerably more accurate than those from strain tensor projection relative to the prescribed ground-truth (determinant of coefficient (R²) of 1.00 and root mean squared error (RMSE) of 0.01 vs. 0.87 and 0.10, respectively). For a set of real-world reconstructed head impacts (N = 53), the strain tensor projection method performs similarly poorly (R² of 0.80-0.90 and RMSE of 0.03-0.07), with overestimation strongly correlated with strain magnitude (Pearson correlation coefficient >0.9). Up to ∼15% of the fiber strains are overestimated by more than the lower bound of a conservative injury threshold of 0.09. The percentage increases to ∼37% when halving the threshold. Voxel interpolation is also significantly more efficient (15 s vs. 40 s for element strain tensor projection, without parallelization).

CONCLUSIONS

Voxelized displacement interpolation is considerably more accurate and efficient in deriving dense white matter fiber strains than strain tensor projection. The latter generally overestimates with overestimation magnitude strongly correlating with fiber strain magnitude. Displacement voxelization is an effective technique to eliminate mesh-image mismatch and generates a convenient image representation of tissue deformation. This technique can be generalized to broadly facilitate a diverse range of image-related biomechanical problems for multimodal analyses. The convenient image format may also promote and facilitate biomechanical data sharing in the future.

Relating strain fields with microtubule changes in porcine cortical sulci following drop impact

The biomechanical response of brain tissue to strain and the immediate neural outcomes are of fundamental importance in understanding mild traumatic brain injury (mTBI). The sensitivity of neural tissue to dynamic strain events and the resulting strain-induced changes are considered to be a primary factor in injury. Rodent models have been used extensively to investigate impact-induced injury. However, the lissencephalic structure is inconsistent with the human brain, which is gyrencephalic (convoluted structure), and differs considerably in strain field localization effects. Porcine brains have a similar structure to the human brain, containing a similar ratio of white-grey matter and gyrification in the cortex. In this study, coronal brain slabs were extracted from female pig brains within 2hrs of sacrifice. Slabs were implanted with neutral density radiopaque markers, sealed inside an elastomeric encasement, and dropped from 0.9 m onto a steel anvil. Particle tracking revealed elevated tensile strains in the sulcus. One hour after impact, decreased microtubule associated protein 2 (MAP2) was found exclusively within the sulcus with no increase in cell death. These results suggest that elevated tensile strain in the sulcus may result in compromised cytoskeleton, possibly indicating a vulnerability to pathological outcomes under the right circumstances. The results demonstrated that the observed changes were unrelated to shear strain loading of the tissues but were more sensitive to tensile load.

Instantaneous Brain Strain Estimation for Automotive Head Impacts via Deep Learning

Efficient brain strain estimation is critical for routine application of a head injury model. Lately, a convolutional neural network (CNN) has been successfully developed to estimate spatially detailed brain strains instantly and accurately in contact sports. Here, we extend its application to automotive head impacts, where impact profiles are typically more complex with longer durations. Head impact kinematics (N=458) from two public databases were used to generate augmented impacts (N=2694). They were simulated using the anisotropic Worcester Head Injury Model (WHIM) V1.0, which provided baseline elementwise peak maximum principal strain (MPS). For each augmented impact, rotational velocity (v_rot) and the corresponding rotational acceleration (a_rot) profiles were concatenated as static images to serve as CNN input. Three training strategies were evaluated: 1) "baseline", using random initial weights; 2) "transfer learning", using weight transfer from a previous CNN model trained on head impacts drawn from contact sports; and 3) "combined training", combining previous training data from contact sports (N=5661) for training. The combined training achieved the best performances. For peak MPS, the CNN achieved a coefficient of determination (R²) of 0.932 and root mean squared error (RMSE) of 0.031 for the real-world testing dataset. It also achieved a success rate of 60.5% and 94.8% for elementwise MPS, where the linear regression slope, k, and correlation coefficient, r, between estimated and simulated MPS did not deviate from 1.0 (when identical) by more than 0.1 and 0.2, respectively. Cumulative strain damage measure (CSDM) from the CNN estimation was also highly accurate compared to those from direct simulation across a range of thresholds (R² of 0.899-0.943 with RMSE of 0.054-0.069). Finally, the CNN achieved an average k and r of 0.98±0.12 and 0.90±0.07, respectively, for six reconstructed car crash impacts drawn from two other sources independent of the training dataset. Importantly, the CNN is able to efficiently estimate elementwise MPS with sufficient accuracy while conventional kinematic injury metrics cannot. Therefore, the CNN has the potential to supersede current kinematic injury metrics that can only approximate a global peak MPS or CSDM. The CNN technique developed here may offer enhanced utility in the design and development of head protective countermeasures, including in the automotive industry. This is the first study aimed at instantly estimating spatially detailed brain strains for automotive head impacts, which employs >8.8 thousand impact simulations generated from ~1.5 years of nonstop computations on a high-performance computing platform.

Toward a Comprehensive Delineation of White Matter Tract-Related Deformation

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

Measurement of brain simulant strains in head surrogate under impact loading

Impact-induced traumatic brain injury (TBI) is a major source of disability and mortality. Knowledge of brain strains during impact (accelerative) loading is critical for the overall management of TBI, including the development of injury thresholds, personal protective equipment, and validation of computational models. Despite these needs, the current understanding of brain strains in humans or humanlike surrogates is limited, especially for injury causing loading magnitudes. Toward this end, we measured full-field, in-plane (2D) strains in a brain simulant using the hemispherical head surrogate. The hemispherical head was mounted on the Hybrid-III neck and subjected to impact loading using a linear impactor system. The resulting head kinematics was measured using a triaxial accelerometer and angular rate sensors. Dynamic, 2D strains in a brain simulant were obtained using high-speed imaging and digital image correlation. Concurrent finite element (FE) simulations of the experiment were also performed to gain additional insights. The role of stiff membranes of the head was also studied using experiments. Our results suggest that rotational modes dominate the response of the brain simulant. The wave propagation in the brain simulant as a result of impact has a timescale of ~100 ms. We obtain peak strains of ~20%, ~40%, ~60% for peak rotational accelerations of ~838, ~5170, ~11,860 rad/s², respectively. Further, peak strains in cortical regions are higher than subcortical regions by up to ~70%. The agreement between the experiments and FE simulations is reasonable in terms of spatiotemporal evolution of strain pattern and peak strain magnitudes. Experiments with the addition of falx and tentorium indicate significant strain concentration (up to 115%) in the brain simulant near the interface of falx or tentorium and brain simulant. Overall, this work provides important insights into the biomechanics of strain in the brain simulant during impact loading.

An anatomically detailed and personalizable head injury model: Significance of brain and white matter tract morphological variability on strain

Finite element head (FE) models are important numerical tools to study head injuries and develop protection systems. The generation of anatomically accurate and subject-specific head models with conforming hexahedral meshes remains a significant challenge. The focus of this study is to present two developmental works: first, an anatomically detailed FE head model with conforming hexahedral meshes that has smooth interfaces between the brain and the cerebrospinal fluid, embedded with white matter (WM) fiber tracts; second, a morphing approach for subject-specific head model generation via a new hierarchical image registration pipeline integrating Demons and Dramms deformable registration algorithms. The performance of the head model is evaluated by comparing model predictions with experimental data of brain-skull relative motion, brain strain, and intracranial pressure. To demonstrate the applicability of the head model and the pipeline, six subject-specific head models of largely varying intracranial volume and shape are generated, incorporated with subject-specific WM fiber tracts. DICE similarity coefficients for cranial, brain mask, local brain regions, and lateral ventricles are calculated to evaluate personalization accuracy, demonstrating the efficiency of the pipeline in generating detailed subject-specific head models achieving satisfactory element quality without further mesh repairing. The six head models are then subjected to the same concussive loading to study the sensitivity of brain strain to inter-subject variability of the brain and WM fiber morphology. The simulation results show significant differences in maximum principal strain and axonal strain in local brain regions (one-way ANOVA test, p < 0.001), as well as their locations also vary among the subjects, demonstrating the need to further investigate the significance of subject-specific models. The techniques developed in this study may contribute to better evaluation of individual brain injury and the development of individualized head protection systems in the future. This study also contains general aspects the research community may find useful: on the use of experimental brain strain close to or at injury level for head model validation; the hierarchical image registration pipeline can be used to morph other head models, such as smoothed-voxel models.

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

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

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

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

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

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

Low-Rank Representation of Head Impact Kinematics: A Data-Driven Emulator

Head motion induced by impacts has been deemed as one of the most important measures in brain injury prediction, given that the vast majority of brain injury metrics use head kinematics as input. Recently, researchers have focused on using fast approaches, such as machine learning, to approximate brain deformation in real time for early brain injury diagnosis. However, training such models requires large number of kinematic measurements, and therefore data augmentation is required given the limited on-field measured data available. In this study we present a principal component analysis-based method that emulates an empirical low-rank substitution for head impact kinematics, while requiring low computational cost. In characterizing our existing data set of 537 head impacts, each consisting of 6 degrees of freedom measurements, we found that only a few modes, e.g., 15 in the case of angular velocity, is sufficient for accurate reconstruction of the entire data set. Furthermore, these modes are predominantly low frequency since over 70% of the angular velocity response can be captured by modes that have frequencies under 40 Hz. We compared our proposed method against existing impact parametrization methods and showed significantly better performance in injury prediction using a range of kinematic-based metrics—such as head injury criterion (HIC), rotational injury criterion (RIC), and brain injury metric (BrIC)—and brain tissue deformation-based metrics—such as brain angle metric (BAM), maximum principal strain (MPS), and axonal fiber strains (FS). In all cases, our approach reproduced injury metrics similar to the ground truth measurements with no significant difference, whereas the existing methods obtained significantly different (p < 0.01) values as well as substantial differences in injury classification sensitivity and specificity. This emulator will enable us to provide the necessary data augmentation to build a head impact kinematic data set of any size. The emulator and corresponding examples are available on our website¹.

An anatomically detailed and personalizable head injury model: Significance of brain and white matter tract morphological variability on strain

Finite element head (FE) models are important numerical tools to study head injuries and develop protection systems. The generation of anatomically accurate and subject-specific head models with conforming hexahedral meshes remains a significant challenge. The focus of this study is to present two developmental works: first, an anatomically detailed FE head model with conforming hexahedral meshes that has smooth interfaces between the brain and the cerebrospinal fluid, embedded with white matter (WM) fiber tracts; second, a morphing approach for subject-specific head model generation via a new hierarchical image registration pipeline integrating Demons and Dramms deformable registration algorithms. The performance of the head model is evaluated by comparing model predictions with experimental data of brain-skull relative motion, brain strain, and intracranial pressure. To demonstrate the applicability of the head model and the pipeline, six subject-specific head models of largely varying intracranial volume and shape are generated, incorporated with subject-specific WM fiber tracts. DICE similarity coefficients for cranial, brain mask, local brain regions, and lateral ventricles are calculated to evaluate personalization accuracy, demonstrating the efficiency of the pipeline in generating detailed subject-specific head models achieving satisfactory element quality without further mesh repairing. The six head models are then subjected to the same concussive loading to study the sensitivity of brain strain to inter-subject variability of the brain and WM fiber morphology. The simulation results show significant differences in maximum principal strain and axonal strain in local brain regions (one-way ANOVA test, p < 0.001), as well as their locations also vary among the subjects, demonstrating the need to further investigate the significance of subject-specific models. The techniques developed in this study may contribute to better evaluation of individual brain injury and the development of individualized head protection systems in the future. This study also contains general aspects the research community may find useful: on the use of experimental brain strain close to or at injury level for head model validation; the hierarchical image registration pipeline can be used to morph other head models, such as smoothed-voxel models.

Displacement- and Strain-Based Discrimination of Head Injury Models across a Wide Range of Blunt Conditions

Successful validation of a head injury model is critical to ensure its biofidelity. However, there is an ongoing debate on what experimental data are suitable for model validation. Here, we report that CORrelation and Analysis (CORA) scores based on the commonly adopted relative brain-skull displacements or recent marker-based strains from cadaveric head impacts may not be effective in discriminating model-simulated whole-brain strains across a wide range of blunt conditions. We used three versions of the Worcester Head Injury Model (WHIM; isotropic and anisotropic WHIM V1.0, and anisotropic WHIM V1.5) to simulate 19 experiments, including eight high-rate cadaveric impacts, seven mid-rate cadaveric pure rotations simulating impacts in contact sports, and four in vivo head rotation/extension tests. All WHIMs achieved similar average CORA scores based on cadaveric displacement (~ 0.70; 0.47-0.88) and strain (V1.0: 0.86; 0.73-0.97 vs. V1.5: 0.78; 0.62-0.96), using the recommended settings. However, WHIM V1.5 produced ~ 1.17-2.69 times strain of the two V1.0 variants with substantial differences in strain distribution as well (Pearson correlation of ~ 0.57-0.92) when comparing their whole-brain strains across the range of blunt conditions. Importantly, their strain magnitude differences were similar to that in cadaveric marker-based strain (~ 1.32-3.79 times). This suggests that cadaveric strains are capable of discriminating head injury models for their simulated whole-brain strains (e.g., by using CORA magnitude sub-rating alone or peak strain magnitude ratio), although the aggregated CORA may not. This study may provide fresh insight into head injury model validation and the harmonization of simulation results from diverse head injury models. It may also facilitate future experimental designs to improve model validation.

A network-based response feature matrix as a brain injury metric

Conventional brain injury metrics are scalars that treat the whole head/brain as a single unit but do not characterize the distribution of brain responses. Here, we establish a network-based "response feature matrix" to characterize the magnitude and distribution of impact-induced brain strains. The network nodes and edges encode injury risks to the gray matter regions and their white matter interconnections, respectively. The utility of the metric is illustrated in injury prediction using three independent, real-world datasets: two reconstructed impact datasets from the National Football League (NFL) and Virginia Tech, respectively, and measured concussive and non-injury impacts from Stanford University. Injury predictions with leave-one-out cross-validation are conducted using the two reconstructed datasets separately, and then by combining all datasets into one. Using support vector machine, the network-based injury predictor consistently outperforms four baseline scalar metrics including peak maximum principal strain of the whole brain (MPS), peak linear/rotational acceleration, and peak rotational velocity across all five selected performance measures (e.g., maximized accuracy of 0.887 vs. 0.774 and 0.849 for MPS and rotational acceleration with corresponding positive predictive values of 0.938, 0.772, and 0.800, respectively, using the reconstructed NFL dataset). With sufficient training data, real-world injury prediction is similar to leave-one-out in-sample evaluation, suggesting the potential advantage of the network-based injury metric over conventional scalar metrics. The network-based response feature matrix significantly extends scalar metrics by sampling the brain strains more completely, which may serve as a useful framework potentially allowing for other applications such as characterizing injury patterns or facilitating targeted multi-scale modeling in the future.

Novel strain analysis informs about injury susceptibility of the corpus callosum to repeated impacts

Increasing evidence for the cumulative effects of head trauma on structural integrity of the brain has emphasized the need to understand the relationship between tissue mechanic properties and injury susceptibility. Here, diffusion tensor imaging, helmet accelerometers and amplified magnetic resonance imaging were combined to gather insight about the region-specific vulnerability of the corpus callosum to microstructural changes in white-matter integrity upon exposure to sub-concussive impacts. A total of 33 male Canadian football players (mean_age = 20.3 ± 1.4 years) were assessed at three time points during a football season (baseline pre-season, mid-season and post-season). The athletes were split into a LOW (N = 16) and HIGH (N = 17) exposure group based on the frequency of sub-concussive impacts sustained on a per-session basis, measured using the helmet-mounted accelerometers. Longitudinal decreases in fractional anisotropy were observed in anterior and posterior regions of the corpus callosum (average cluster size = 40.0 ± 4.4 voxels; P < 0.05, corrected) for athletes from the HIGH exposure group. These results suggest that the white-matter tract may be vulnerable to repetitive sub-concussive collisions sustained over the course of a football season. Using these findings as a basis for further investigation, a novel exploratory analysis of strain derived from sub-voxel motion of brain tissues in response to cardiac impulses was developed using amplified magnetic resonance imaging. This approach revealed specific differences in strain (and thus possibly stiffness) along the white-matter tract (P < 0.0001) suggesting a possible signature relationship between changes in white-matter integrity and tissue mechanical properties. In light of these findings, additional information about the viscoelastic behaviour of white-matter tissues may be imperative in elucidating the mechanisms responsible for region-specific differences in injury susceptibility observed, for instance, through changes in microstructural integrity following exposure to sub-concussive head impacts.

Statistical Characterization of Human Brain Deformation During Mild Angular Acceleration Measured In Vivo by Tagged Magnetic Resonance Imaging

Understanding of in vivo brain biomechanical behavior is critical in the study of traumatic brain injury (TBI) mechanisms and prevention. Using tagged magnetic resonance imaging, we measured spatiotemporal brain deformations in 34 healthy human volunteers under mild angular accelerations of the head. Two-dimensional (2D) Lagrangian strains were examined throughout the brain in each subject. Strain metrics peaked shortly after contact with a padded stop, corresponding to the inertial response of the brain after head deceleration. Maximum shear strain of at least 3% was experienced at peak deformation by an area fraction (median±standard error) of 23.5±1.8% of cortical gray matter, 15.9±1.4% of white matter, and 4.0±1.5% of deep gray matter. Cortical gray matter strains were greater in the temporal cortex on the side of the initial contact with the padded stop and also in the contralateral temporal, frontal, and parietal cortex. These tissue-level deformations from a population of healthy volunteers provide the first in vivo measurements of full-volume brain deformation in response to known kinematics. Although strains differed in different tissue type and cortical lobes, no significant differences between male and female head accelerations or strain metrics were found. These cumulative results highlight important kinematic features of the brain's mechanical response and can be used to facilitate the evaluation of computational simulations of TBI.

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

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

Head Impact Kinematics Estimation With Network of Inertial Measurement Units

Wearable sensors embedded with inertial measurement units have become commonplace for the measurement of head impact biomechanics, but individual systems often suffer from a lack of measurement fidelity. While some researchers have focused on developing highly accurate, single sensor systems, we have taken a parallel approach in investigating optimal estimation techniques with multiple noisy sensors. In this work, we present a sensor network methodology that utilizes multiple skin patch sensors arranged on the head and combines their data to obtain a more accurate estimate than any individual sensor in the network. Our methodology visually localizes subject-specific sensor transformations, and based on rigid body assumptions, applies estimation algorithms to obtain a minimum mean squared error estimate. During mild soccer headers, individual skin patch sensors had over 100% error in peak angular velocity magnitude, angular acceleration magnitude, and linear acceleration magnitude. However, when properly networked using our visual localization and estimation methodology, we obtained kinematic estimates with median errors below 20%. While we demonstrate this methodology with skin patch sensors in mild soccer head impacts, the formulation can be generally applied to any dynamic scenario, such as measurement of cadaver head impact dynamics using arbitrarily placed sensors.

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

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

Concussion classification via deep learning using whole-brain white matter fiber strains

Developing an accurate and reliable injury predictor is central to the biomechanical studies of traumatic brain injury. State-of-the-art efforts continue to rely on empirical, scalar metrics based on kinematics or model-estimated tissue responses explicitly pre-defined in a specific brain region of interest. They could suffer from loss of information. A single training dataset has also been used to evaluate performance but without cross-validation. In this study, we developed a deep learning approach for concussion classification using implicit features of the entire voxel-wise white matter fiber strains. Using reconstructed American National Football League (NFL) injury cases, leave-one-out cross-validation was employed to objectively compare injury prediction performances against two baseline machine learning classifiers (support vector machine (SVM) and random forest (RF)) and four scalar metrics via univariate logistic regression (Brain Injury Criterion (BrIC), cumulative strain damage measure of the whole brain (CSDM-WB) and the corpus callosum (CSDM-CC), and peak fiber strain in the CC). Feature-based machine learning classifiers including deep learning, SVM, and RF consistently outperformed all scalar injury metrics across all performance categories (e.g., leave-one-out accuracy of 0.828-0.862 vs. 0.690-0.776, and .632+ error of 0.148-0.176 vs. 0.207-0.292). Further, deep learning achieved the best cross-validation accuracy, sensitivity, AUC, and .632+ error. These findings demonstrate the superior performances of deep learning in concussion prediction and suggest its promise for future applications in biomechanical investigations of traumatic brain injury.

Profiling biomarkers of traumatic axonal injury: From mouse to man

Traumatic brain injury (TBI) poses a major public health problem on a global scale. Its burden results from high mortality and significant morbidity in survivors. This stems, in part, from an ongoing inadequacy in diagnostic and prognostic indicators despite significant technological advances. Traumatic axonal injury (TAI) is a key driver of the ongoing pathological process following TBI, causing chronic neurological deficits and disability. The science underpinning biomarkers of TAI has been a subject of many reviews in recent literature. However, in this review we provide a comprehensive account of biomarkers from animal models to clinical studies, bridging the gap between experimental science and clinical medicine. We have discussed pathogenesis, temporal kinetics, relationships to neuro-imaging, and, most importantly, clinical applicability in order to provide a holistic perspective of how this could improve TBI diagnosis and predict clinical outcome in a real-life setting. We conclude that early and reliable identification of axonal injury post-TBI with the help of body fluid biomarkers could enhance current care of TBI patients by (i) increasing speed and accuracy of diagnosis, (ii) providing invaluable prognostic information, (iii) allow efficient allocation of rehabilitation services, and (iv) provide potential therapeutic targets. The optimal model for assessing TAI is likely to involve multiple components, including several blood biomarkers and neuro-imaging modalities, at different time points.

Do blast induced skull flexures result in axonal deformation?

Subject-specific computer models (male and female) of the human head were used to investigate the possible axonal deformation resulting from the primary phase blast-induced skull flexures. The corresponding axonal tractography was explicitly incorporated into these finite element models using a recently developed technique based on the embedded finite element method. These models were subjected to extensive verification against experimental studies which examined their pressure and displacement response under a wide range of loading conditions. Once verified, a parametric study was developed to investigate the axonal deformation for a wide range of loading overpressures and directions as well as varying cerebrospinal fluid (CSF) material models. This study focuses on early times during a blast event, just as the shock transverses the skull (< 5 milliseconds). Corresponding boundary conditions were applied to eliminate the rotation effects and the resulting axonal deformation. A total of 138 simulations were developed– 128 simulations for studying the different loading scenarios and 10 simulations for studying the effects of CSF material model variance–leading to a total of 10,702 simulation core hours. Extreme strains and strain rates along each of the fiber tracts in each of these scenarios were documented and presented here. The results suggest that the blast-induced skull flexures result in strain rates as high as 150–378 s^-1. These high-strain rates of the axonal fiber tracts, caused by flexural displacement of the skull, could lead to a rate dependent micro-structural axonal damage, as pointed by other researchers.

A Fast-Running, End-to-End Concussion Risk Model for Assessment of Complex Human Head Kinematics

An end-to-end, mechanism-based concussion risk model, linking head motion to axonal injury, has been demonstrated to predict concussion outcomes with greater sensitivity and specificity than external correlates such as peak head acceleration. The development of this model was driven by the need to more accurately translate head-worn sensor measurements into injury assessment in near-real time. The full end-to-end model is a detailed multi-scale model, composed of complex components (e.g., a human head finite element model), is computationally expensive, and requires specialized software. For practicality, this research-level model must be simplified into a standalone, fast-running algorithm that can be embedded on the microprocessor of a head-worn sensor. This article describes the development of a simplified, fast-running algorithm that delivers comparable results to those of the full end-to-end model. The dynamic axonal response of the human head finite element model to head motion is mathematically modeled using a lumped parameter system fitted to the finite element model response for a range of head motions. The other component models of the full end-to-end model were similarly reduced. For the same head kinematic scenarios, the probabilities of concussion obtained from the end-to-end model and from the simplified algorithm are compared well.

Material properties of the brain in injury-relevant conditions - Experiments and computational modeling

Material properties of the brain have been extensively studied but remain poorly characterized. The vast variations in constitutive models and material constants are well documented. However, no study exists to translate the variations into disparities in impact-induced brain strains most relevant to brain injury. Here, we reviewed a subset of injury-relevant brain material properties either characterized in experiments or adopted in recent head injury models. To highlight how variations in measured brain material properties manifested in simulated brain strains, we selected six experiments that have provided a complete set of brain material model and constants to implement a common head injury model. Responses resulting from two extreme events representing a high-rate cadaveric head impact and a low-rate in vivo head rotation, respectively, varied substantially. We hypothesized, and further confirmed, that the time-varying shear moduli at the appropriate time scales (e.g., ~5 ms and ~40 ms corresponding to the impulse durations of the major acceleration peaks for the two impacts, respectively), rather than the initial or long-term shear moduli, were the most indicative of impact-induced brain strains. These results underscored the need to implement measured brain material properties into an actual head injury model for evaluation. They may also provide guidelines to better characterize brain material properties in future experiments and head injury models. Finally, our finding provided a practical solution to satisfy head injury model validation requirements at both ends of the impact severity spectrum. This would improve the confidence in model simulation performance across a range of time scales relevant to concussion and sub-concussion in the real-world.

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

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

Pilot Findings of Brain Displacements and Deformations during Roller Coaster Rides

With 300,000,000 riders annually, roller coasters are a popular recreational activity. Although the number of roller coaster injuries is relatively low, the precise effect of roller coaster rides on our brains remains unknown. Here we present the quantitative characterization of brain displacements and deformations during roller coaster rides. For two healthy adult male subjects, we recorded head accelerations during three representative rides, and, for comparison, during running and soccer headers. From the recordings, we simulated brain displacements and deformations using rigid body dynamics and finite element analyses. Our findings show that despite having lower linear accelerations than sports head impacts, roller coasters may lead to brain displacements and strains comparable to mild soccer headers. The peak change in angular velocity on the rides was 9.9 rad/sec, which was higher than the 5.6 rad/sec in soccer headers with ball velocities reaching 7 m/sec. Maximum brain surface displacements of 4.0 mm and maximum principal strains of 7.6% were higher than in running and similar to soccer headers, but below the reported average concussion strain. Brain strain rates during roller coaster rides were similar to those in running, and lower than those in soccer headers. Strikingly, on the same ride and at a similar position, the two subjects experienced significantly different head kinematics and brain deformation. These results indicate that head motion and brain deformation during roller coaster rides are highly sensitive to individual subjects. Although our study suggests that roller coaster rides do not present an immediate risk of acute brain injury, their long-term effects require further longitudinal study.

Performance Evaluation of a Pre-computed Brain Response Atlas in Dummy Head Impacts

A pre-computed brain response atlas (pcBRA) may have the potential to accelerate the investigation of the biomechanical mechanisms of traumatic brain injury on a large-scale. In this study, we further enhance the technique and evaluate its performance using six degree-of-freedom angular velocity profiles from dummy head impacts. Using the pcBRA to simplify profiles into acceleration-only shapes, sufficiently accurate strain estimates were obtained for impacts with a major dominating velocity peak. However, they were largely under-estimated when substantial deceleration occurred that reversed the direction of the angular velocity. For these impacts, estimation accuracy was substantially improved with a biphasic profile simplification (average correlation coefficient and linear regression slope of 0.92 ± 0.03 and 0.95 ± 0.07 for biphasic shapes, respectively, vs. 0.80 ± 0.06 and 0.80 ± 0.08 for acceleration-only shapes). Peak maximum principal strain (ɛ p) and cumulative strain damage measure (CSDM) from the estimated strains consistently correlated stronger than kinematic metrics with respect to the baseline ɛ p and CSDM from the directly simulated responses, regardless of the brain region, and by a large margin (e.g., correlation of 0.93 vs. 0.75 compared to Brain Injury Criterion (BrIC) for ɛ p in the whole-brain, and 0.91 vs. 0.47 compared to BrIC for CSDM in the corpus callosum). These findings further support the pre-computation technique for accurate, real-time strain estimation, which could be important to accelerate model-based brain injury studies in the future.

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

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

Propagation of errors from skull kinematic measurements to finite element tissue responses

Real-time quantification of head impacts using wearable sensors is an appealing approach to assess concussion risk. Traditionally, sensors were evaluated for accurately measuring peak resultant skull accelerations and velocities. With growing interest in utilizing model-estimated tissue responses for injury prediction, it is important to evaluate sensor accuracy in estimating tissue response as well. Here, we quantify how sensor kinematic measurement errors can propagate into tissue response errors. Using previous instrumented mouthguard validation datasets, we found that skull kinematic measurement errors in both magnitude and direction lead to errors in tissue response magnitude and distribution. For molar design instrumented mouthguards susceptible to mandible disturbances, 150-400% error in skull kinematic measurements resulted in 100% error in regional peak tissue response. With an improved incisor design mitigating mandible disturbances, errors in skull kinematics were reduced to <50%, and several tissue response errors were reduced to <10%. Applying 30[Formula: see text] rotations to reference kinematic signals to emulate sensor transformation errors yielded below 10% error in regional peak tissue response; however, up to 20% error was observed in peak tissue response for individual finite elements. These findings demonstrate that kinematic resultant errors result in regional peak tissue response errors, while kinematic directionality errors result in tissue response distribution errors. This highlights the need to account for both kinematic magnitude and direction errors and accurately determine transformations between sensors and the skull.

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

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

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

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

A computational study of invariant I5 in a nearly incompressible transversely isotropic model for white matter

The aligned axonal fiber bundles in white matter make it suitable to be modeled as a transversely isotropic material. Recent experimental studies have shown that a minimal form, nearly incompressible transversely isotropic (MITI) material model, is capable of describing mechanical anisotropy of white matter. Here, we used a finite element (FE) computational approach to demonstrate the significance of the fifth invariant (I₅) when modeling the anisotropic behavior of white matter in the large-strain regime. We first implemented and validated the MITI model in an FE simulation framework for large deformations. Next, we applied the model to a plate-hole structural problem to highlight the significance of the invariant I₅ by comparing with the standard fiber reinforcement (SFR) model. We also compared the two models by fitting the experiment data of asymmetric indentation, shear test, and uniaxial stretch of white matter. Our results demonstrated the significance of I₅ in describing shear deformation/anisotropy, and illustrated the potential of the MITI model to characterize transversely isotropic white matter tissues in the large-strain regime.

Brain strain uncertainty due to shape variation in and simplification of head angular velocity profiles

Head angular velocity, instead of acceleration, is more predictive of brain strains. Surprisingly, no study exists that investigates how shape variation in angular velocity profiles affects brain strains, beyond characteristics such as peak magnitude and impulse duration. In this study, we evaluated brain strain uncertainty due to variation in angular velocity profiles and further compared with that resulting from simplifying the profiles into idealized shapes. To do so, we used reconstructed head impacts from American National Football League for shape extraction and simulated head uniaxial coronal rotations from onset to full stop. The velocity profiles were scaled to maintain an identical peak velocity magnitude and duration in order to isolate the shape for investigation. Element-wise peak maximum principal strains from 44 selected impacts were obtained. We found that the shape of angular velocity profile could significantly affect brain strain magnitude (e.g., percentage difference of 4.29-17.89 % in the whole brain relative to the group average, with cumulative strain damage measure (CSDM) uncertainty range of 23.9 %) but not pattern (correlation coefficient of 0.94-0.99). Strain differences resulting from simplifying angular velocity profiles into idealized shapes were largely within the range due to shape variation, in both percentage difference and CSDM (signed difference of 3.91 % on average, with a typical range of 0-6 %). These findings provide important insight into the uncertainty or confidence in the performance of kinematics-based injury metrics. More importantly, they suggest the feasibility to simplify head angular velocity profiles into idealized shapes, at least within the confinements of the profiles evaluated, to enable real-time strain estimation via pre-computation in the future.

Systems Biology, Neuroimaging, Neuropsychology, Neuroconnectivity and Traumatic Brain Injury

The patient who sustains a traumatic brain injury (TBI) typically undergoes neuroimaging studies, usually in the form of computed tomography (CT) and magnetic resonance imaging (MRI). In most cases the neuroimaging findings are clinically assessed with descriptive statements that provide qualitative information about the presence/absence of visually identifiable abnormalities; though little if any of the potential information in a scan is analyzed in any quantitative manner, except in research settings. Fortunately, major advances have been made, especially during the last decade, in regards to image quantification techniques, especially those that involve automated image analysis methods. This review argues that a systems biology approach to understanding quantitative neuroimaging findings in TBI provides an appropriate framework for better utilizing the information derived from quantitative neuroimaging and its relation with neuropsychological outcome. Different image analysis methods are reviewed in an attempt to integrate quantitative neuroimaging methods with neuropsychological outcome measures and to illustrate how different neuroimaging techniques tap different aspects of TBI-related neuropathology. Likewise, how different neuropathologies may relate to neuropsychological outcome is explored by examining how damage influences brain connectivity and neural networks. Emphasis is placed on the dynamic changes that occur following TBI and how best to capture those pathologies via different neuroimaging methods. However, traditional clinical neuropsychological techniques are not well suited for interpretation based on contemporary and advanced neuroimaging methods and network analyses. Significant improvements need to be made in the cognitive and behavioral assessment of the brain injured individual to better interface with advances in neuroimaging-based network analyses. By viewing both neuroimaging and neuropsychological processes within a systems biology perspective could represent a significant advancement for the field.