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

Effect of Human Head Shape on the Risk of Traumatic Brain Injury: A Gaussian Process Regression-based Machine Learning Approach

INTRODUCTION

Computational head injury models are promising tools for understanding and predicting traumatic brain injuries. However, most available head injury models are "average" models that employ a single set of head geometry (e.g., 50th-percentile U.S. male) without considering variability in these parameters across the human population. A significant variability of head shapes exists in U.S. Army soldiers, evident from the Anthropometric Survey of U.S. Army Personnel (ANSUR II). The objective of this study is to elucidate the effects of head shape on the predicted risk of traumatic brain injury from computational head injury models.

MATERIALS AND METHODS

Magnetic resonance imaging scans of 25 human subjects are collected. These images are registered to the standard MNI152 brain atlas, and the resulting transformation matrix components (called head shape parameters) are used to quantify head shapes of the subjects. A generative machine learning model is used to generate 25 additional head shape parameter datasets to augment our database. Head injury models are developed for these head shapes, and a rapid injurious head rotation event is simulated to obtain several brain injury predictor variables (BIPVs): Peak cumulative maximum principal strain (CMPS), average CMPS, and the volume fraction of brain exceeding an injurious CMPS threshold. A Gaussian process regression model is trained between head shape parameters and BIPVs, which is then used to study the relative sensitivity of the various BIPVs on individual head shape parameters. We distinguish head shape parameters into 2 types: Scaling components ${T_{xx}}$, ${T_{yy}}$, and ${T_{zz}}$ that capture the breadth, length, and height of the head, respectively, and shearing components (${T_{xy}},{T_{xz}},{T_{yx}},{T_{yz}},{T_{zx}}$, and ${T_{zy}}$) that capture the relative skewness of the head shape.

RESULTS

An overall positive correlation is evident between scaling components and BIPVs. Notably, a very high, positive correlation is seen between the BIPVs and the head volume. As an example, a 57% increase in peak CMPS was noted between the smallest and the largest investigated head volume parameters. The variation in shearing components ${T_{xy}},{T_{xz}},{T_{yx}},{T_{yz}},{T_{zx}}$, and ${T_{zy}}$ on average does not cause notable changes in the BIPVs. From the Gaussian process regression model, all 3 BIPVs showed an increasing trend with each of the 3 scaling components, but the BIPVs are found to be most sensitive to the height dimension of the head. From the Sobol sensitivity analysis, the ${T_{zz}}$ scaling parameter contributes nearly 60% to the total variance in peak and average CMPS; ${T_{yy}}$ contributes approximately 20%, whereas ${T_{xx}}$ contributes less than 5%. The remaining contribution is from the 6 shearing components. Unlike peak and average CMPS, the VF-CMPS BIPV is associated with relatively evenly distributed Sobol indices across the 3 scaling parameters. Furthermore, the contribution of shearing components on the total variance in this case is negligible.

CONCLUSIONS

Head shape has a considerable influence on the injury predictions of computational head injury models. Available "average" head injury models based on a 50th-percentile U.S. male are likely associated with considerable uncertainty. In general, larger head sizes correspond to greater BIPV magnitudes, which point to potentially a greater injury risk under rapid neck rotation for people with larger heads.

Head Impact Kinematics and Brain Tissue Strains in High School Lacrosse

Male lacrosse and female lacrosse have differences in history, rules, and equipment. There is current debate regarding the need for enhanced protective headwear in female lacrosse like that worn by male lacrosse players. To inform this discussion, 17 high school lacrosse players (6 female and 11 male) wore the Stanford Instrumented Mouthguard during 26 competitive games over the 2021 season. Time-windowing and video review were used to remove false-positive recordings and verify head acceleration events (HAEs). The HAE rate in high school female lacrosse (0.21 per athlete exposure and 0.24 per player hour) was approximately 35% lower than the HAE rate in high school male lacrosse (0.33 per athlete exposure and 0.36 per player hour). Previously collected kinematics data from the 2019 high school male and female lacrosse season were combined with the newly collected 2021 kinematics data, which were used to drive a finite element head model and simulate 42 HAEs. Peak linear acceleration (PLA), peak angular velocity (PAV), and 95th percentile maximum principal strain (MPS95) of brain tissue were compared between HAEs in high school female and male lacrosse. Median values for peak kinematics and MPS95 of HAEs in high school female lacrosse (PLA, 22.3 g; PAV, 10.4 rad/s; MPS95, 0.05) were lower than for high school male lacrosse (PLA, 24.2 g; PAV, 15.4 rad/s; MPS95, 0.07), but the differences were not statistically significant. Quantifying a lower HAE rate in high school female lacrosse compared to high school male lacrosse, but similar HAE magnitudes, provides insight into the debate regarding helmets in female lacrosse. However, due to the small sample size, additional video-verified data from instrumented mouthguards are required.

Neuroimaging, wearable sensors, and blood-based biomarkers reveal hyperacute changes in the brain after sub-concussive impacts

Impacts in mixed martial arts (MMA) have been studied mainly in regard to the long-term effects of concussions. However, repetitive sub-concussive head impacts at the hyperacute phase (minutes after impact), are not understood. The head experiences rapid acceleration similar to a concussion, but without clinical symptoms. We utilize portable neuroimaging technology - transcranial Doppler (TCD) ultrasound and functional near infrared spectroscopy (fNIRS) - to estimate the extent of pre- and post-differences following contact and non-contact sparring sessions in nine MMA athletes. In addition, the extent of changes in neurofilament light (NfL) protein biomarker concentrations, and neurocognitive/balance parameters were determined following impacts. Athletes were instrumented with sensor-based mouth guards to record head kinematics. TCD and fNIRS results demonstrated significantly increased blood flow velocity (p = 0.01) as well as prefrontal (p = 0.01) and motor cortex (p = 0.04) oxygenation, only following the contact sparring sessions. This increase after contact was correlated with the cumulative angular acceleration experienced during impacts (p = 0.01). In addition, the NfL biomarker demonstrated positive correlations with angular acceleration (p = 0.03), and maximum principal and fiber strain (p = 0.01). On average athletes experienced 23.9 ± 2.9 g peak linear acceleration, 10.29 ± 1.1 rad/s peak angular velocity, and 1,502.3 ± 532.3 rad/s2 angular acceleration. Balance parameters were significantly increased following contact sparring for medial-lateral (ML) center of mass (COM) sway, and ML ankle angle (p = 0.01), illustrating worsened balance. These combined results reveal significant changes in brain hemodynamics and neurophysiological parameters that occur immediately after sub-concussive impacts and suggest that the physical impact to the head plays an important role in these changes.

A technique for in situ intracranial strain measurement within a helmeted deformable headform

Despite the broad use of helmets, incidence of concussion remains high. Current methods for helmet evaluation focus on the measurement of head kinematics as the primary tool for quantifying risk of brain injury. Though the primary cause of mild Traumatic Brain Injury (mTBI) is thought to be intracranial strain, helmet testing methodologies are not able to directly resolve these parameters. Computational injury models and impact severity measures are currently used to approximate intracranial strains from head kinematics and predict injury outcomes. Advancing new methodologies that enable experimental intracranial strain measurements in a physical model would be useful in the evaluation of helmet performance. This study presents a proof-of-concept head surrogate and novel helmet evaluation platform that allows for the measurement of intracranial strain using high-speed X-ray digital image correlation (XDIC). In the present work, the head surrogate was subjected to a series of bare and helmeted impacts using a pneumatically-driven linear impactor. Impacts were captured at 5,000 fps using a high-speed X-ray cineradiography system, and strain fields were computed using digital image correlation. This test platform, once validated, will open the door to using brain tissue-level measurements to evaluate helmet performance, providing a tool that can be translated to represent mTBI injury mechanisms, benefiting the helmet design processes.

A Morphologically Individualized Deep Learning Brain Injury Model

The brain injury modeling community has recommended improving model subject specificity and simulation efficiency. Here, we extend an instantaneous (< 1 sec) convolutional neural network (CNN) brain model based on the anisotropic Worcester Head Injury Model (WHIM) V1.0 to account for strain differences due to individual morphological variations. Linear scaling factors relative to the generic WHIM along the three anatomical axes are used as additional CNN inputs. To generate training samples, the WHIM is randomly scaled to pair with augmented head impacts randomly generated from real-world data for simulation. An estimation of voxelized peak maximum principal strain of the whole-brain is said to be successful when the linear regression slope and Pearson's correlation coefficient relative to directly simulated do not deviate from 1.0 (when identical) by more than 0.1. Despite a modest training dataset (N = 1363 vs. ∼5.7 k previously), the individualized CNN achieves a success rate of 86.2% in cross-validation for scaled model responses, and 92.1% for independent generic model testing for impacts considered as complete capture of kinematic events. Using 11 scaled subject-specific models (with scaling factors determined from pre-established regression models based on head dimensions and sex and age information, and notably, without neuroimages), the morphologically individualized CNN remains accurate for impacts that also yield successful estimations for the generic WHIM. The individualized CNN instantly estimates subject-specific and spatially detailed peak strains of the entire brain and thus, supersedes others that report a scalar peak strain value incapable of informing the location of occurrence. This tool could be especially useful for youths and females due to their anticipated greater morphological differences relative to the generic model, even without the need for individual neuroimages. It has potential for a wide range of applications for injury mitigation purposes and the design of head protective gears. The voxelized strains also allow for convenient data sharing and promote collaboration among research groups.

Efficient Generation of Pretraining Samples for Developing a Deep Learning Brain Injury Model via Transfer Learning

The large amount of training samples required to develop a deep learning brain injury model demands enormous computational resources. Here, we study how a transformer neural network (TNN) of high accuracy can be used to efficiently generate pretraining samples for a convolutional neural network (CNN) brain injury model to reduce computational cost. The samples use synthetic impacts emulating real-world events or augmented impacts generated from limited measured impacts. First, we verify that the TNN remains highly accurate for the two impact types (N = 100 each; [Formula: see text] of 0.948-0.967 with root mean squared error, RMSE, ~ 0.01, for voxelized peak strains). The TNN-estimated samples (1000-5000 for each data type) are then used to pretrain a CNN, which is further finetuned using directly simulated training samples (250-5000). An independent measured impact dataset considered of complete capture of impact event is used to assess estimation accuracy (N = 191). We find that pretraining can significantly improve CNN accuracy via transfer learning compared to a baseline CNN without pretraining. It is most effective when the finetuning dataset is relatively small (e.g., 2000-4000 pretraining synthetic or augmented samples improves success rate from 0.72 to 0.81 with 500 finetuning samples). When finetuning samples reach 3000 or more, no obvious improvement occurs from pretraining. These results support using the TNN to rapidly generate pretraining samples to facilitate a more efficient training strategy for future deep learning brain models, by limiting the number of costly direct simulations from an alternative baseline model. This study could contribute to a wider adoption of deep learning brain injury models for large-scale predictive modeling and ultimately, enhancing safety protocols and protective equipment.

Approximating subject-specific brain injury models via scaling based on head-brain morphological relationships

Most human head/brain models represent a generic adult male head/brain. They may suffer in accuracy when investigating traumatic brain injury (TBI) on a subject-specific basis. Subject-specific models can be developed from neuroimages; however, neuroimages are not typically available in practice. In this study, we establish simple and elegant regression models between brain outer surface morphology and head dimensions measured from neuroimages along with age and sex information (N = 191; 141 males and 50 females with age ranging 14-25 years). The regression models are then used to approximate subject-specific brain models by scaling a generic counterpart, without using neuroimages. Model geometrical accuracy is assessed using adjusted [Formula: see text] and absolute percentage error (e.g., 0.720 and 3.09 ± 2.38%, respectively, for brain volume when incorporating tragion-to-top). For a subset of 11 subjects (from smallest to largest in brain volume), impact-induced brain strains are compared with those from "morphed models" derived from neuroimage-based mesh warping. We find that regional peak strains from the scaled subject-specific models are comparable to those of the morphed counterparts but could be considerably different from those of the generic model (e.g., linear regression slope of 1.01-1.03 for gray and white matter regions versus 1.16-1.19, or up to ~ 20% overestimation for the smallest brain studied). These results highlight the importance of incorporating brain morphological variations in impact simulation and demonstrate the feasibility of approximating subject-specific brain models without neuroimages using age, sex, and easily measurable head dimensions. The scaled models may improve subject specificity for future TBI investigations.

Development and validation of subject-specific 3D human head models based on a nonlinear visco-hyperelastic constitutive framework

Computational head models are promising tools for understanding and predicting traumatic brain injuries. Most available head models are developed using inputs (i.e. head geometry, material properties and boundary conditions) from experiments on cadavers or animals and employ hereditary integral-based constitutive models that assume linear viscoelasticity in part of the rate-sensitive material response. This leads to high uncertainty and poor accuracy in capturing the nonlinear brain tissue response. To resolve these issues, a framework for the development of subject-specific three-dimensional head models is proposed, in which all inputs are derived in vivo from the same living human subject: head geometry via magnetic resonance imaging (MRI), brain tissue properties via magnetic resonance elastography (MRE), and full-field strain-response of the brain under rapid head rotation via tagged MRI. A nonlinear, viscous dissipation-based visco-hyperelastic constitutive model is employed to capture brain tissue response. Head models are validated using quantitative metrics that compare spatial strain distribution, temporal strain evolution, and the magnitude of strain maxima, with the corresponding experimental observations from tagged MRI. Results show that our head models accurately capture the strain-response of the brain. Further, employment of the nonlinear visco-hyperelastic constitutive framework provides improvements in the prediction of peak strains and temporal strain evolution over hereditary integral-based models.

Data-driven Uncertainty Quantification in Computational Human Head Models

Computational models of the human head are promising tools for estimating the impact-induced response of the brain, and thus play an important role in the prediction of traumatic brain injury. The basic constituents of these models (i.e., model geometry, material properties, and boundary conditions) are often associated with significant uncertainty and variability. As a result, uncertainty quantification (UQ), which involves quantification of the effect of this uncertainty and variability on the simulated response, becomes critical to ensure reliability of model predictions. Modern biofidelic head model simulations are associated with very high computational cost and high-dimensional inputs and outputs, which limits the applicability of traditional UQ methods on these systems. In this study, a two-stage, data-driven manifold learning-based framework is proposed for UQ of computational head models. This framework is demonstrated on a 2D subject-specific head model, where the goal is to quantify uncertainty in the simulated strain fields (i.e., output), given variability in the material properties of different brain substructures (i.e., input). In the first stage, a data-driven method based on multi-dimensional Gaussian kernel-density estimation and diffusion maps is used to generate realizations of the input random vector directly from the available data. Computational simulations of a small number of realizations provide input-output pairs for training data-driven surrogate models in the second stage. The surrogate models employ nonlinear dimensionality reduction using Grassmannian diffusion maps, Gaussian process regression to create a low-cost mapping between the input random vector and the reduced solution space, and geometric harmonics models for mapping between the reduced space and the Grassmann manifold. It is demonstrated that the surrogate models provide highly accurate approximations of the computational model while significantly reducing the computational cost. Monte Carlo simulations of the surrogate models are used for uncertainty propagation. UQ of the strain fields highlights significant spatial variation in model uncertainty, and reveals key differences in uncertainty among commonly used strain-based brain injury predictor variables.

The Presence of the Temporal Horn Exacerbates the Vulnerability of Hippocampus During Head Impacts

Hippocampal injury is common in traumatic brain injury (TBI) patients, but the underlying pathogenesis remains elusive. In this study, we hypothesize that the presence of the adjacent fluid-containing temporal horn exacerbates the biomechanical vulnerability of the hippocampus. Two finite element models of the human head were used to investigate this hypothesis, one with and one without the temporal horn, and both including a detailed hippocampal subfield delineation. A fluid-structure interaction coupling approach was used to simulate the brain-ventricle interface, in which the intraventricular cerebrospinal fluid was represented by an arbitrary Lagrangian-Eulerian multi-material formation to account for its fluid behavior. By comparing the response of these two models under identical loadings, the model that included the temporal horn predicted increased magnitudes of strain and strain rate in the hippocampus with respect to its counterpart without the temporal horn. This specifically affected cornu ammonis (CA) 1 (CA1), CA2/3, hippocampal tail, subiculum, and the adjacent amygdala and ventral diencephalon. These computational results suggest that the presence of the temporal horn exacerbate the vulnerability of the hippocampus, highlighting the mechanobiological dependency of the hippocampus on the temporal horn.

Cerebral vascular strains in dynamic head impact using an upgraded model with brain material property heterogeneity

Cerebral vascular injury (CVI) is a frequent consequence of traumatic brain injury but has often been neglected. Substantial experimental work exists on vascular material properties and failure/subfailure thresholds. However, little is known about vascular in vivo loading conditions in dynamic head impact, which is necessary to investigate the risk, severity, and extent of CVI. In this study, we resort to the Worcester Head Injury Model (WHIM) V2.1 for investigation. The model embeds the cerebral vasculature network and is further upgraded to incorporate brain material property heterogeneity based on magnetic resonance elastography. The brain material property is calibrated to match with the previously validated anisotropic V1.0 version in terms of whole-brain strains against six experimental datasets of a wide range of blunt impact conditions. The upgraded WHIM is finally used to simulate five representative real-world head impacts drawn from contact sports and automotive crashes. We find that peak strains in veins are considerably higher than those in arteries and that peak circumferential strains are also higher than peak axial strains. For a typical concussive head impact, cerebral vascular axial strains reach the lowest reported yield strain of ∼7-8%. For severe automotive impacts, axial strains could reach ∼20%, which is on the order of the lowest reported ultimate failure strain of ∼24%. These results suggest in vivo mechanical loading conditions of the cerebral vasculature (excluding bridging veins not assessed here) due to rapid head rotation are at the lower end of failure/subfailure thresholds established from ex vivo experiments. This study provides some first insight into the risk, severity, and extent of CVI in real-world head impacts.

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.

Tractography methods and findings in brain tumors and traumatic brain injury

White matter fiber tracking using diffusion magnetic resonance imaging (dMRI) provides a noninvasive approach to map brain connections, but improving anatomical accuracy has been a significant challenge since the birth of tractography methods. Utilizing tractography in brain studies therefore requires understanding of its technical limitations to avoid shortcomings and pitfalls. This review explores tractography limitations and how different white matter pathways pose different challenges to fiber tracking methodologies. We summarize the pros and cons of commonly-used methods, aiming to inform how tractography and its related analysis may lead to questionable results. Extending these experiences, we review the clinical utilization of tractography in patients with brain tumors and traumatic brain injury, starting from tensor-based tractography to more advanced methods. We discuss current limitations and highlight novel approaches in the context of these two conditions to inform future tractography developments.

Integrating Human and Non-Human Primate Data to Estimate Human Tolerances for Traumatic Brain Injury

Traumatic brain injury (TBI) contributes to a significant portion of the injuries resulting from motor vehicle crashes, falls, and sports collisions. The development of advanced countermeasures to mitigate these injuries requires a complete understanding of the tolerance of the human brain to injury. In this study, we developed a new method to establish human injury tolerance levels using an integrated database of reconstructed football impacts, sub-injurious human volunteer data, and non-human primate data. The human tolerance levels were analyzed using tissue-level metrics determined using harmonized species-specific finite element brain models. Kinematics-based metrics involving complete characterization of angular motion (e.g., DAMAGE) showed better power of predicting tissue-level deformation in a variety of impact conditions and were subsequently used to characterize injury tolerance. The proposed human brain tolerances for mild and severe TBI were estimated and presented in the form of injury risk curves based on selected tissue-level and kinematics-based injury metrics. The application of the estimated injury tolerances was finally demonstrated using real-world automotive crash data.

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.

A Machine Learning Approach to Investigate the Uncertainty of Tissue-Level Injury Metrics for Cerebral Contusion

Controlled cortical impact (CCI) on porcine brain is often utilized to investigate the pathophysiology and functional outcome of focal traumatic brain injury (TBI), such as cerebral contusion (CC). Using a finite element (FE) model of the porcine brain, the localized brain strain and strain rate resulting from CCI can be computed and compared to the experimentally assessed cortical lesion. This way, tissue-level injury metrics and corresponding thresholds specific for CC can be established. However, the variability and uncertainty associated with the CCI experimental parameters contribute to the uncertainty of the provoked cortical lesion and, in turn, of the predicted injury metrics. Uncertainty quantification via probabilistic methods (Monte Carlo simulation, MCS) requires a large number of FE simulations, which results in a time-consuming process. Following the recent success of machine learning (ML) in TBI biomechanical modeling, we developed an artificial neural network as surrogate of the FE porcine brain model to predict the brain strain and the strain rate in a computationally efficient way. We assessed the effect of several experimental and modeling parameters on four FE-derived CC injury metrics (maximum principal strain, maximum principal strain rate, product of maximum principal strain and strain rate, and maximum shear strain). Next, we compared the in silico brain mechanical response with cortical damage data from in vivo CCI experiments on pig brains to evaluate the predictive performance of the CC injury metrics. Our ML surrogate was capable of rapidly predicting the outcome of the FE porcine brain undergoing CCI. The now computationally efficient MCS showed that depth and velocity of indentation were the most influential parameters for the strain and the strain rate-based injury metrics, respectively. The sensitivity analysis and comparison with the cortical damage experimental data indicate a better performance of maximum principal strain and maximum shear strain as tissue-level injury metrics for CC. These results provide guidelines to optimize the design of CCI tests and bring new insights to the understanding of the mechanical response of brain tissue to focal traumatic brain injury. Our findings also highlight the potential of using ML for computationally efficient TBI biomechanics investigations.

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.

Regional White Matter Diffusion Changes Associated with the Cumulative Tensile Strain and Strain Rate in Nonconcussed Youth Football Players

The purpose of this study is to assess the relationship between regional white matter diffusion imaging changes and finite element strain measures in nonconcussed youth football players. Pre- and post-season diffusion-weighted imaging was performed in 102 youth football subject-seasons, in which no concussions were diagnosed. The diffusion data were normalized to the IXI template. Percent change in fractional anisotropy (%ΔFA) images were generated. Using data from the head impact telemetry system, the cumulative maximum principal strain one times strain rate (CMPS1 × SR), a measure of the cumulative tensile brain strain and strain rate for one season, was calculated for each subject. Two linear regression analyses were performed to identify significant positive or inverse relationships between CMPS1 × SR and %ΔFA within the international consortium for brain mapping white matter mask. Age, body mass index, days between pre- and post-season imaging, previous brain injury, attention disorder diagnosis, and imaging protocol were included as covariates. False discovery rate correction was used with corrected alphas of 0.025 and voxel thresholds of zero. Controlling for all covariates, a significant, positive linear relationship between %ΔFA and CMPS1 × SR was identified in the bilateral cingulum, fornix, internal capsule, external capsule, corpus callosum, corona radiata, corticospinal tract, cerebral and middle cerebellar peduncle, superior longitudinal fasciculus, and right superior fronto-occipital fasciculus. Post hoc analyses further demonstrated significant %ΔFA differences between high-strain football subjects and noncollision control athletes, no significant %ΔFA differences between low-strain subjects and noncollision control athletes, and that CMPS1 × SR significantly explained more %ΔFA variance than number of head impacts alone.

Instantaneous Whole-Brain Strain Estimation in Dynamic Head Impact

Head injury models are notoriously time consuming and resource demanding in simulations, which prevents routine application. Here, we extend a convolutional neural network (CNN) to instantly estimate element-wise distribution of peak maximum principal strain (MPS) of the entire brain (>36 k speedup accomplished on a low-end computing platform). To achieve this, head impact rotational velocity and acceleration temporal profiles are combined into two-dimensional images to serve as CNN input for training and prediction of MPS. Compared with the directly simulated counterparts, the CNN-estimated responses (magnitude and distribution) are sufficiently accurate for 92.1% of the cases via 10-fold cross-validation using impacts drawn from the real world (n = 5661; range of peak rotational velocity in augmented data extended to 2-40 rad/sec). The success rate further improves to 97.1% for "in-range" impacts (n = 4298). When using the same CNN architecture to train (n = 3064) and test on an independent, reconstructed National Football League (NFL) impact dataset (n = 53; 20 concussions and 33 non-injuries), 51 out of 53, or 96.2% of the cases, are sufficiently accurate. The estimated responses also achieve virtually identical concussion prediction performances relative to the directly simulated counterparts, and they often outperform peak MPS of the whole brain (e.g., accuracy of 0.83 vs. 0.77 via leave-one-out cross-validation). These findings support the use of CNN for accurate and efficient estimation of spatially detailed brain strains across the vast majority of head impacts in contact sports. Our technique may hold the potential to transform traumatic brain injury (TBI) research and the design and testing standards of head protective gears by facilitating the transition from acceleration-based approximation to strain-based design and analysis. This would have broad implications in the TBI biomechanics field to accelerate new scientific discoveries. The pre-trained CNN is freely available online at https://github.com/Jilab-biomechanics/CNN-brain-strains.

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.

Brain response of a computational head model for prescribed skull kinematics and simulated football helmet impact boundary conditions

Computational human body models (HBM) present a novel approach to predict brain response in football impact scenarios, with prescribed kinematic boundary conditions for the HBM skull typically used at present. However, computational optimization of helmets requires simulation of the coupled helmet and HBM model; which is much more complex and has not been assessed in the context of brain deformation and existing simplified approaches. In the current study, two boundary conditions and the resulting brain deformations were compared using a HBM head model: (1) a prescribed skull kinematics (PK) boundary condition using measured head kinematics from experimental impacts; and (2) a novel detailed simulation of a HBM head and neck, helmet and linear impactor (HBM-S). While lateral and rear impacts exhibited similar levels of maximum principal strain (MPS) in the brain tissue using both boundary conditions, differences were noted in the frontal orientation (at 9.3 m/s, MPS was 0.39 for PK, 0.54 for HBM-S). Importantly, both PK and HBM-S boundary conditions produced a similar distribution of MPS throughout the brain for each impact orientation considered. Within the corpus callosum and thalamus, high MPS was associated with lateral impacts and lower values with frontal and rear impacts. The good correspondence of both boundary conditions is encouraging for future optimization of helmet designs. A limitation of the PK approach is the need for experimental head kinematics data, while the HBM-S can predict brain response for varying impact conditions and helmet configurations, with potential as a tool to improve helmet protection performance.

The Hammer and the Nail: Biomechanics of Striking and Struck Canadian University Football Players

This study sought to evaluate head accelerations in both players involved in a football collision. Players on two opposing Canadian university teams were equipped with helmet mounted sensors during one game per season, for two consecutive seasons. A total of 276 collisions between 58 instrumented players were identified via video and cross-referenced with sensor timestamps. Player involvement (striking and struck), impact type (block or tackle), head impact location (front, back, left and right), and play type were recorded from video footage. While struck players did not experience significantly different linear or rotational accelerations between any play types, striking players had the highest linear and rotational head accelerations during kickoff plays (p ≤ .03). Striking players also experienced greater linear and rotational head accelerations than struck players during kickoff plays (p = .001). However, struck players experienced greater linear and rotational accelerations than striking players during kick return plays (p ≤ .008). Other studies have established that the more severe the head impact, the greater risk for injury to the brain. This paper's results highlight that kickoff play rule changes, as implemented in American college football, would decrease head impact exposure of Canadian university football athletes and make the game safer.

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.

A machine learning approach for magnetic resonance image-based mouse brain modeling and fast computation in controlled cortical impact

Computational modeling of the brain is crucial for the study of traumatic brain injury. An anatomically accurate model with refined details could provide the most accurate computational results. However, computational models with fine mesh details could take prolonged computation time that impedes the clinical translation of the models. Therefore, a way to construct a model with low computational cost while maintaining a computational accuracy comparable with that of the high-fidelity model is desired. In this study, we constructed magnetic resonance (MR) image-based finite element (FE) models of a mouse brain for simulations of controlled cortical impact. The anatomical details were kept by mapping each image voxel to a corresponding FE mesh element. We constructed a super-resolution neural network that could produce computational results of a refined FE model with a mesh size of 70 μm from a coarse FE model with a mesh size of 280 μm. The peak signal-to-noise ratio of the reconstructed results was 33.26 dB, while the computational speed was increased by 50-fold. This proof-of-concept study showed that using machine learning techniques, MR image-based computational modeling could be applied and evaluated in a timely fashion. This paved ways for fast FE modeling and computation based on MR images. Results also support the potential clinical applications of MR image-based computational modeling of the human brain in a variety of scenarios such as brain impact and intervention.Graphical abstract MR image-based FE models with different mesh sizes were generated for CCI. The training and testing data sets were computed with 5 different impact locations and 3 different impact velocities. High-resolution strain maps were estimated using a SR neural network with greatly reduced computational cost.

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

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

Mitigating the Consequences of Subconcussive Head Injuries

Subconcussive head injury represents a pathophysiology that spans the expertise of both clinical neurology and biomechanical engineering. From both viewpoints, the terms injury and damage, presented without qualifiers, are synonymously taken to mean a tissue alteration that may be recoverable. For clinicians, concussion is evolving from a purely clinical diagnosis to one that requires objective measurement, to be achieved by biomedical engineers. Subconcussive injury is defined as subclinical pathophysiology in which underlying cellular- or tissue-level damage (here, to the brain) is not severe enough to present readily observable symptoms. Our concern is not whether an individual has a (clinically diagnosed) concussion, but rather, how much accumulative damage an individual can tolerate before they will experience long-term deficit(s) in neurological health. This concern leads us to look for the history of damage-inducing events, while evaluating multiple approaches for avoiding injury through reduction or prevention of the associated mechanically induced damage.

Predicting Concussion Outcome by Integrating Finite Element Modeling and Network Analysis

Concussion is a significant public health problem affecting 1.6-2.4 million Americans annually. An alternative to reducing the burden of concussion is to reduce its incidence with improved protective equipment and injury mitigation systems. Finite element (FE) models of the brain response to blunt trauma are often used to estimate injury potential and can lead to improved helmet designs. However, these models have yet to incorporate how the patterns of brain connectivity disruption after impact affects the relay of information in the injured brain. Furthermore, FE brain models typically do not consider the differences in individual brain structural connectivities and their purported role in concussion risk. Here, we use graph theory techniques to integrate brain deformations predicted from FE modeling with measurements of network efficiency to identify brain regions whose connectivity characteristics may influence concussion risk. We computed maximum principal strain in 129 brain regions using head kinematics measured from 53 professional football impact reconstructions that included concussive and non-concussive cases. In parallel, using diffusion spectrum imaging data from 30 healthy subjects, we simulated structural lesioning of each of the same 129 brain regions. We simulated lesioning by removing each region one at a time along with all its connections. In turn, we computed the resultant change in global efficiency to identify regions important for network communication. We found that brain regions that deformed the most during an impact did not overlap with regions most important for network communication (Pearson's correlation, ρ = 0.07; p = 0.45). Despite this dissimilarity, we found that predicting concussion incidence was equally accurate when considering either areas of high strain or of high importance to global efficiency. Interestingly, accuracy for concussion prediction varied considerably across the 30 healthy connectomes. These results suggest that individual network structure is an important confounding variable in concussion prediction and that further investigation of its role may improve concussion prediction and lead to the development of more effective protective equipment.

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.

Incorporation of vasculature in a head injury model lowers local mechanical strains in dynamic impact

Cerebral vasculature is several orders of magnitude stiffer than the brain tissue. However, only a handful of studies have investigated its potential stiffening effect on dynamic brain strains; yet, they report contradictory findings. Here, we reanalyze the cerebrovascular stiffening effect by incorporating vasculature derived from the latest neuroimaging atlases into a re-meshed Worcester Head Injury Model using an embedded element method. Regional brain strains with and without vasculature were simulated using a reconstructed, predominantly sagittal head impact. Using the two previously adopted linear or non-linear vessel material models, we reproduced the earlier conflicting results (~40% vs. ~1-6% in regional strain reductions). Nevertheless, with refitted non-linear material models chosen to represent the average dynamic tension behaviors of arteries and veins, respectively, inclusion of vasculature reduced regional brain strains by ~13-36% relative to the baselines without vasculature. Compared to the whole brain baseline response, inclusion of vasculature led to an element-wise linear regression slope of 0.8 and a Pearson correlation coefficient of 0.8. The vascular stiffening effect appears mild for the whole brain but more significant locally, which should not be ignored in head injury models. Nevertheless, more work is necessary to investigate the cerebrovascular mechanical behaviors and loading environment to allow for more biofidelic modeling of the brain in the future.

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.

Convolutional neural network for efficient estimation of regional brain strains

Head injury models are important tools to study concussion biomechanics but are impractical for real-world use because they are too slow. Here, we develop a convolutional neural network (CNN) to estimate regional brain strains instantly and accurately by conceptualizing head rotational velocity profiles as two-dimensional images for input. We use two impact datasets with augmentation to investigate the CNN prediction performances with a variety of training-testing configurations. Three strain measures are considered, including maximum principal strain (MPS) of the whole brain, MPS of the corpus callosum, and fiber strain of the corpus callosum. The CNN is further tested using an independent impact dataset (N = 314) measured in American football. Based on 2592 training samples, it achieves a testing R² of 0.916 and root mean squared error (RMSE) of 0.014 for MPS of the whole brain. Combining all impact-strain response data available (N = 3069), the CNN achieves an R² of 0.966 and RMSE of 0.013 in a 10-fold cross-validation. This technique may enable a clinical diagnostic capability to a sophisticated head injury model, such as facilitating head impact sensors in concussion detection via a mobile device. In addition, it may transform current acceleration-based injury studies into focusing on regional brain strains. The trained CNN is publicly available along with associated code and examples at https://github.com/Jilab-biomechanics/CNN-brain-strains. They will be updated as needed in the future.

Development of a Single-Degree-of-Freedom Mechanical Model for Predicting Strain-Based Brain Injury Responses

Linking head kinematics to injury risk has been the focus of numerous brain injury criteria. Although many early forms were developed using mechanics principles, recent criteria have been developed using empirical methods based on subsets of head impact data. In this study, a single-degree-of-freedom (sDOF) mechanical analog was developed to parametrically investigate the link between rotational head kinematics and brain deformation. Model efficacy was assessed by comparing the maximum magnitude of displacement to strain-based brain injury predictors from finite element (FE) human head models. A series of idealized rotational pulses covering a broad range of acceleration and velocity magnitudes (0.1-15 krad/s2 and 1-100 rad/s) with durations between 1 and 3000 ms were applied to the mechanical models about each axis of the head. Results show that brain deformation magnitude is governed by three categories of rotational head motion each distinguished by the duration of the pulse relative to the brain's natural period: for short-duration pulses, maximum brain deformation depended primarily on angular velocity magnitude; for long-duration pulses, brain deformation depended primarily on angular acceleration magnitude; and for pulses relatively close to the natural period, brain deformation depended on both velocity and acceleration magnitudes. These results suggest that brain deformation mechanics can be adequately explained by simple mechanical systems, since FE model responses and experimental brain injury tolerances exhibited similar patterns to the sDOF model. Finally, the sDOF model was the best correlate to strain-based responses and highlighted fundamental limitations with existing rotational-based brain injury metrics.

A reanalysis of football impact reconstructions for head kinematics and finite element modeling

BACKGROUND

Head kinematics generated by laboratory reconstructions of professional football helmet impacts have been applied to computational models to study the biomechanics of concussion. Since the original publication of this data, techniques for evaluating accelerometer consistency and error correction have been developed. This study applies these techniques to the original reconstruction data and reanalyzes the results given the current state of concussion biomechanics.

METHODS

Consistency checks were applied to the sensor data collected in the head of each test dummy. Inconsistent data were corrected using analytical techniques, and head kinematics were recalculated from the corrected data. Reconstruction videos were reviewed to identify artefactual impacts during the reconstruction to establish the region of applicability for simulations. Corrected head kinematics were input into finite element brain models to investigate strain response to the corrected dataset.

FINDINGS

Multiple reconstruction cases had inconsistent sensor arrays caused by a problematic sensor; corrections to the arrays caused changes in calculated rotational head motion. These corrections increased median peak angular velocity for the concussion cases from 35.6 to 41.5 rad/s. Using the original kinematics resulted in an average error of 20% in maximum principal strain results for each case. Simulations of the reconstructions also demonstrated that simulation lengths less than 40 ms did not capture the entire brain strain response and under-predicted strain.

INTERPRETATION

This study corrects data that were used to determine concussion risk, and indicates altered head angular motion and brain strain response for many reconstructions. Conclusions based on the original data should be re-examined based on this new study.

Embedded Finite Elements for Modeling Axonal Injury

The purpose of this paper is to propose and develop a large strain embedded finite element formulation that can be used to explicitly model axonal fiber bundle tractography from diffusion tensor imaging of the brain. Once incorporated, the fibers offer the capability to monitor tract-level strains that give insight into the biomechanics of brain injury. We show that one commercial software has a volume and mass redundancy issue when including embedded axonal fiber and that a newly developed algorithm is able to correct this discrepancy. We provide a validation analysis for stress and energy to demonstrate the method.

Development of a Second-Order System for Rapid Estimation of Maximum Brain Strain

Diffuse brain injuries are assessed with deformation-based criteria that utilize metrics based on rotational head kinematics to estimate brain injury severity. Although numerous metrics have been proposed, many are based on empirically-derived models that use peak kinematics, which often limit their applicability to a narrow range of head impact conditions. However, over a broad range of impact conditions, brain deformation response to rotational head motion behaves similarly to a second-order mechanical system, which utilizes the full kinematic time history of a head impact. This study describes a new brain injury metric called Diffuse Axonal Multi-Axis General Evaluation (DAMAGE). DAMAGE is based on the equations of motion of a three-degree-of-freedom, coupled 2nd-order system, and predicts maximum brain strain using the directionally dependent angular acceleration time-histories from a head impact. Parameters for the effective mass, stiffness, and damping were determined using simplified rotational pulses which were applied multiaxially to a 50th percentile adult human male finite element model. DAMAGE was then validated with a separate database of 1747 head impacts including helmet, crash, and sled tests and human volunteer responses. Relative to existing rotational brain injury metrics that were evaluated in this study, DAMAGE was found to be the best predictor of maximum brain strain.

A Reanalysis of Experimental Brain Strain Data: Implication for Finite Element Head Model Validation

Relative motion between the brain and skull and brain deformation are biomechanics aspects associated with many types of traumatic brain injury (TBI). Thus far, there is only one experimental endeavor (Hardy et al., 2007) reported brain strain under loading conditions commensurate with levels that were capable of producing injury. Most of the existing finite element (FE) head models are validated against brain-skull relative motion and then used for TBI prediction based on strain metrics. However, the suitability of using a model validated against brain-skull relative motion for strain prediction remains to be determined. To partially address the deficiency of experimental brain deformation data, this study revisits the only existing dynamic experimental brain strain data and updates the original calculations, which reflect incremental strain changes. The brain strain is recomputed by imposing the measured motion of neutral density target (NDT) to the NDT triad model. The revised brain strain and the brain-skull relative motion data are then used to test the hypothesis that an FE head model validated against brainskull relative motion does not guarantee its accuracy in terms of brain strain prediction. To this end, responses of brain strain and brain-skull relative motion of a previously developed FE head model (Kleiven, 2007) are compared with available experimental data. CORrelation and Analysis (CORA) and Normalized Integral Square Error (NISE) are employed to evaluate model validation performance for both brain strain and brain-skull relative motion. Correlation analyses (Pearson coefficient) are conducted between average cluster peak strain and average cluster peak brain-skull relative motion, and also between brain strain validation scores and brain-skull relative motion validation scores. The results show no significant correlations, neither between experimentally acquired peaks nor between computationally determined validation scores. These findings indicate that a head model validated against brain-skull relative motion may not be sufficient to assure its strain prediction accuracy. It is suggested that a FE head model with intended use for strain prediction should be validated against the experimental brain deformation data and not just the brain-skull relative motion.

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.

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.

Estimated Brain Tissue Response Following Impacts Associated With and Without Diagnosed Concussion

Kinematic measurements of head impacts are sensitive to sports concussion, but not highly specific. One potential reason is these measures reflect input conditions only and may have varying degrees of correlation to regional brain tissue deformation. In this study, previously reported head impact data recorded in the field from high school and collegiate football players were analyzed using two finite element head models (FEHM). Forty-five impacts associated with immediately diagnosed concussion were simulated along with 532 control impacts without identified concussion obtained from the same players. For each simulation, intracranial response measures (max principal strain, strain rate, von Mises stress, and pressure) were obtained for the whole brain and within four regions of interest (ROI; cerebrum, cerebellum, brain stem, corpus callosum). All response measures were sensitive to diagnosed concussion; however, large inter-athlete variability was observed and sensitivity strength depended on measure, ROI, and FEHM. Interestingly, peak linear acceleration was more sensitive to diagnosed concussion than all intracranial response measures except pressure. These findings suggest FEHM may provide unique and potentially important information on brain injury mechanisms, but estimations of concussion risk based on individual intracranial response measures evaluated in this study did not improve upon those derived from input kinematics alone.