A quantitative relationship between rotational head kinematics and brain tissue strain from a 2-D parametric finite element analysis

American Football On-Field Head Impact Kinematics: Influence of Acceleration Signal Characteristics on Peak Maximal Principal Strain

Recorded head kinematics from head-impact measurement devices (HIMd) are pivotal for evaluating brain stress and strain through head finite element models (hFEM). The variability in kinematic recording windows across HIMd presents challenges as they yield inconsistent hFEM responses. Despite establishing an ideal recording window for maximum principal strain (MPS) in brain tissue, uncertainties persist about the impact characteristics influencing vulnerability when this window is shortened. This study aimed to scrutinize factors within impact kinematics affecting the reliability of different recording windows on whole-brain peak MPS using a validated hFEM. Utilizing 53 on-field head impacts recorded via an instrumented mouthguard during a Canadian varsity football game, 10 recording windows were investigated with varying pre- and post-impact-trigger durations. Tukey pair-wise comparisons revealed no statistically significant differences in MPS responses for the different recording windows. However, specific impacts showed marked variability up to 40%. It was found, through correlation analyses, that impacts with lower peak linear acceleration exhibited greater response variability across different pre-trigger durations. Signal shape, analyzed through spectral analysis, influenced the time required for MPS development, resulting in specific impacts requiring a prolonged post-trigger duration. This study adds to the existing consensus on standardizing HIMd acquisition time windows and sheds light on impact characteristics leading to peak MPS variation across different head impact kinematic recording windows. Considering impact characteristics in research assessments is crucial, as certain impacts, affected by recording duration, may lead to significant errors in peak MPS responses during cumulative longitudinal exposure assessments.

A mechanics theory for the exploration of a high-throughput, sterile 3D in vitro traumatic brain injury model

Brain injuries resulting from mechanical trauma represent an ongoing global public health issue. Several in vitro and in vivo models for traumatic brain injury (TBI) continue to be developed for delineating the various complex pathophysiological processes involved in its onset and progression. Developing an in vitro TBI model that is based on cortical spheroids is especially of great interest currently because they can replicate key aspects of in vivo brain tissue, including its electrophysiology, physicochemical microenvironment, and extracellular matrix composition. Being able to mechanically deform the spheroids are a key requirement in any effective in vitro TBI model. The spheroids' shape and size, however, make mechanically loading them, especially in a high-throughput, sterile, and reproducible manner, quite challenging. To address this challenge, we present an idea for a spheroid-based, in vitro TBI model in which the spheroids are mechanically loaded by being spun by a centrifuge. (An experimental demonstration of this new idea will be published shortly elsewhere.) An issue that can limit its utility and scope is that imaging techniques used in 2D and 3D in vitro TBI models cannot be readily applied in it to determine spheroid strains. In order to address this issue, we developed a continuum mechanics-based theory to estimate the spheroids' strains when they are being spun at a constant angular velocity. The mechanics theory, while applicable here to a special case of the centrifuge-based TBI model, is also of general value since it can help with the further exploration and development of TBI models.

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.

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.

Assessment of brain response in operators subject to recoil force from firing long-range rifles

Mild traumatic brain injury (mTBI) may be caused by occupational hazards military personnel encounter, such as falls, shocks, exposure to blast overpressure events, and recoil from weapon firing. While it is important to protect against injurious head impacts, the repeated exposure of Canadian Armed Forces (CAF) service members to sub-concussive events during the course of their service may lead to a significant reduction in quality of life. Symptoms may include headaches, difficulty concentrating, and noise sensitivity, impacting how personnel complete their duties and causing chronic health issues. This study investigates how the exposure to the recoil force of long-range rifles results in head motion and brain deformation. Direct measurements of head kinematics of a controlled population of military personnel during firing events were obtained using instrumented mouthguards. The experimentally measured head kinematics were then used as inputs to a finite element (FE) head model to quantify the brain strains observed during each firing event. The efficacy of a concept recoil mitigation system (RMS), designed to mitigate loads applied to the operators was quantified, and the RMS resulted in lower loading to the operators. The outcomes of this study provide valuable insights into the magnitudes of head kinematics observed when firing long-range rifles, and a methodology to quantify effects, which in turn will help craft exposure guidelines, guide training to mitigate the risk of injury, and improve the quality of lives of current and future CAF service members and veterans.

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.

Modeling of active skeletal muscles: a 3D continuum approach incorporating multiple muscle interactions

Skeletal muscles have a highly organized hierarchical structure, whose main function is to generate forces for movement and stability. To understand the complex heterogeneous behaviors of muscles, computational modeling has advanced as a non-invasive approach to evaluate relevant mechanical quantities. Aiming to improve musculoskeletal predictions, this paper presents a framework for modeling 3D deformable muscles that includes continuum constitutive representation, parametric determination, model validation, fiber distribution estimation, and integration of multiple muscles into a system level for joint motion simulation. The passive and active muscle properties were modeled based on the strain energy approach with Hill-type hyperelastic constitutive laws. A parametric study was conducted to validate the model using experimental datasets of passive and active rabbit leg muscles. The active muscle model with calibrated material parameters was then implemented to simulate knee bending during a squat with multiple quadriceps muscles. A computational fluid dynamics (CFD) fiber simulation approach was utilized to estimate the fiber arrangements for each muscle, and a cohesive contact approach was applied to simulate the interactions among muscles. The single muscle simulation results showed that both passive and active muscle elongation responses matched the range of the testing data. The dynamic simulation of knee flexion and extension showed the predictive capability of the model for estimating the active quadriceps responses, which indicates that the presented modeling pipeline is effective and stable for simulating multiple muscle configurations. This work provided an effective framework of a 3D continuum muscle model for complex muscle behavior simulation, which will facilitate additional computational and experimental studies of skeletal muscle mechanics. This study will offer valuable insight into the future development of multiscale neuromuscular models and applications of these models to a wide variety of relevant areas such as biomechanics and clinical research.

Head Impact Modeling to Support a Rotational Combat Helmet Drop Test

INTRODUCTION

The Advanced Combat Helmet (ACH) military specification (mil-spec) provides blunt impact acceleration criteria that must be met before use by the U.S. warfighter. The specification, which requires a helmeted magnesium Department of Transportation (DOT) headform to be dropped onto a steel hemispherical target, results in a translational headform impact response. Relative to translations, rotations of the head generate higher brain tissue strains. Excessive strain has been implicated as a mechanical stimulus leading to traumatic brain injury (TBI). We hypothesized that the linear constrained drop test method of the ACH specification underreports the potential for TBI.

MATERIALS AND METHODS

To establish a baseline of translational acceleration time histories, we conducted linear constrained drop tests based on the ACH specification and then performed simulations of the same to verify agreement between experiment and simulation. We then produced a high-fidelity human head digital twin and verified that biological tissue responses matched experimental results. Next, we altered the ACH experimental configuration to use a helmeted Hybrid III headform, a freefall cradle, and an inclined anvil target. This new, modified configuration allowed both a translational and a rotational headform response. We applied this experimental rotation response to the skull of our human digital twin and compared brain deformation relative to the translational baseline.

RESULTS

The modified configuration produced brain strains that were 4.3 times the brain strains from the linear constrained configuration.

CONCLUSIONS

We provide a scientific basis to motivate revision of the ACH mil-spec to include a rotational component, which would enhance the test's relevance to TBI arising from severe head impacts.

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.

Oblique impact responses of Hybrid III and a new headform with more biofidelic coefficient of friction and moments of inertia

New oblique impact methods for evaluating head injury mitigation effects of helmets are emerging, which mandate measuring both translational and rotational kinematics of the headform. These methods need headforms with biofidelic mass, moments of inertia (MoIs), and coefficient of friction (CoF). To fulfill this need, working group 11 of the European standardization head protection committee (CEN/TC158) has been working on the development of a new headform with realistic MoIs and CoF, based on recent biomechanics research on the human head. In this study, we used a version of this headform (Cellbond) to test a motorcycle helmet under the oblique impact at 8 m/s at five different locations. We also used the Hybrid III headform, which is commonly used in the helmet oblique impact. We tested whether there is a difference between the predictions of the headforms in terms of injury metrics based on head kinematics, including peak translational and rotational acceleration, peak rotational velocity, and BrIC (brain injury criterion). We also used the Imperial College finite element model of the human head to predict the strain and strain rate across the brain and tested whether there is a difference between the headforms in terms of the predicted strain and strain rate. We found that the Cellbond headform produced similar or higher peak translational accelerations depending on the impact location (−3.2% in the front-side impact to 24.3% in the rear impact). The Cellbond headform, however, produced significantly lower peak rotational acceleration (−41.8% in a rear impact to −62.7% in a side impact), peak rotational velocity (−29.5% in a side impact to −47.6% in a rear impact), and BrIC (−29% in a rear-side impact to −45.3% in a rear impact). The 90th percentile values of the maximum brain strain and strain rate were also significantly lower using this headform. Our results suggest that MoIs and CoF have significant effects on headform rotational kinematics, and consequently brain deformation, during the helmeted oblique impact. Future helmet standards and rating methods should use headforms with realistic MoIs and CoF (e.g., the Cellbond headform) to ensure more accurate representation of the head in laboratory impact tests.

Piecewise Multivariate Linearity Between Kinematic Features and Cumulative Strain Damage Measure (CSDM) Across Different Types of Head Impacts

In a previous study, we found that the relationship between brain strain and kinematic features cannot be described by a generalized linear model across different types of head impacts. In this study, we investigate if such a linear relationship exists when partitioning head impacts using a data-driven approach. We applied the K-means clustering method to partition 3161 impacts from various sources including simulation, college football, mixed martial arts, and car crashes. We found piecewise multivariate linearity between the cumulative strain damage (CSDM; assessed at the threshold of 0.15) and head kinematic features. Compared with the linear regression models without partition and the partition according to the types of head impacts, K-means-based data-driven partition showed significantly higher CSDM regression accuracy, which suggested the presence of piecewise multivariate linearity across types of head impacts. Additionally, we compared the piecewise linearity with the partitions based on individual features used in clustering. We found that the partition with maximum angular acceleration magnitude at 4706 rad/s² led to the highest piecewise linearity. This study may contribute to an improved method for the rapid prediction of CSDM in the future.

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.

Revealing the Effect of Skull Deformation on Intracranial Pressure Variation During the Direct Interaction Between Blast Wave and Surrogate Head

Intracranial pressure (ICP) during the interaction between blast wave and the head is a crucial evaluation criterion for blast-induced traumatic brain injury (bTBI). ICP variation is mainly induced by the blast wave transmission and skull deformation. However, how the skull deformation influences the ICP remains unclear, which is meaningful for mitigating bTBI. In this study, both experimental and numerical models are developed to elucidate the effect of skull deformation on ICP variation. Firstly, we performed the shock tube experiment of the high-fidelity surrogate head to measure the ICP, the blast overpressure, and the skull surface strain of specific positions. The results show that the ICP profiles of all measured points show oscillations with positive and negative change, and the variation is consistent with the skull surface strain. Further numerical analysis reveals that when the blast wave reaches the measured point, the peak overpressure transmits directly through the skull to the brain, forming the local positive ICP peak, and the impulse induces the local inward deformation of the skull. As the peak overpressure passes through, the blast impulse impacts the nearby skull supported by the soft and incompressible brain tissue and extrudes the skull outward in the initial position. The inward and outward skull deformation leads to the oscillation of ICP. These numerical analyses agree with experimental results, which explain the appearance of negative and positive ICP peaks and the synchronization of negative ICP with surface strain. The study has implications for medical injury diagnosis and protective equipment design.

Head Impact Kinematics and Brain Deformation in Paired Opposing Youth Football Players

Head impact exposure is often quantified using peak resultant kinematics. While kinematics describes the inertial response of the brain to impact, they do not fully capture the dynamic brain response. Strain, a measure of the tissue-level response of the brain, may be a better predictor of injury. In this study, kinematic and strain metrics were compared to contact characteristics in youth football. Players on 2 opposing teams were instrumented with head impact sensors to record impact kinematics. Video was collected to identify contact scenarios involving opposing instrumented players (ie, paired contact scenarios) and code contact characteristics (eg, player role, impact location). A previously validated, high-resolution brain finite element model, the atlas-based brain model, was used to simulate head impacts and calculate strain metrics. Fifty-two paired contact scenarios (n = 105 impacts) were evaluated. Lighter players tended to have greater biomechanical metrics compared to heavier players. Impacts to the top of the helmet were associated with lower strain metrics. Overall, strain was better correlated with rotational kinematics, suggesting these metrics may be better predictors of the tissue-level brain response than linear kinematics. Understanding the effect of contact characteristics on brain strain will inform future efforts to improve sport safety.

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.

Effect of Strain Rate on Single Tau, Dimerized Tau and Tau-Microtubule Interface: A Molecular Dynamics Simulation Study

Microtubule-associated protein (MAP) tau is a cross-linking molecule that provides structural stability to axonal microtubules (MT). It is considered a potential biomarker for Alzheimer's disease (AD), dementia, and other neurological disorders. It is also a signature protein for Traumatic Brain Injury (TBI) assessment. In the case of TBI, extreme dynamic mechanical energies can be felt by the axonal cytoskeletal members. As such, fundamental understandings of the responses of single tau protein, polymerized tau protein, and tau-microtubule interfaces under high-rate mechanical forces are important. This study attempts to determine the high-strain rate mechanical behavior of single tau, dimerized tau, and tau-MT interface using molecular dynamics (MD) simulation. The results show that a single tau protein is a highly stretchable soft polymer. During deformation, first, it significantly unfolds against van der Waals and electrostatic bonds. Then it stretches against strong covalent bonds. We found that tau acts as a viscoelastic material, and its stiffness increases with the strain rate. The unfolding stiffness can be ~50-500 MPa, while pure stretching stiffness can be >2 GPa. The dimerized tau model exhibits similar behavior under similar strain rates, and tau sliding from another tau is not observed until it is stretched to >7 times of original length, depending on the strain rate. The tau-MT interface simulations show that very high strain and strain rates are required to separate tau from MT suggesting Tau-MT bonding is stronger than MT subunit bonding between themselves. The dimerized tau-MT interface simulations suggest that tau-tau bonding is stronger than tau-MT bonding. In summary, this study focuses on the structural response of individual cytoskeletal components, namely microtubule (MT) and tau protein. Furthermore, we consider not only the individual response of a component, but also their interaction with each other (such as tau with tau or tau with MT). This study will eventually pave the way to build a bottom-up multiscale brain model and analyze TBI more comprehensively.