Brain Strain

Local and Global Effects of Inertial Force Components Producing Brain Strain During Head Impacts

Inertial force components and corresponding brain strain distributions.

Abstract

Traumatic brain injury (TBI) is a brain dysfunction caused by an external mechanical force and is a leading cause of disability worldwide. In traumatic brain injury, the brain strain is driven by inertial force associated with head acceleration. We identified three distinct mechanisms by which inertial forces induce brain strain: the global rotation effect, the global translation effect, and the local force effect. The global rotation and translation effects arise from whole-brain movement relative to the skull, producing brain strain through shearing, pushing, and pulling, respectively. In contrast, the local force effect refers to the strain produced inside the brain by the local force without whole-brain movement. These effects correspond to different inertial force components: Euler force (angular acceleration), linear force (linear acceleration), and centrifugal force (angular velocity). In this study, we applied impact loading by each inertial force component independently to quantify their contributions and clarify the conditions under which Holbourn’s hypothesis applies. We found that 97% of the total MPS in American football impacts was produced by the Euler force. When head kinematics were extended to extreme scenarios such as aviation or high-impact accidents, both linear and centrifugal forces were also capable of producing significant brain strain. Independent kinematic thresholds were estimated, showing that most injurious head impacts consistently exceed angular acceleration thresholds, while corresponding linear accelerations and angular velocities remain below them.

DOI Source Document
Local and Global Effects of Inertial Force Components Producing Brain Strain During Head Impacts
Differences between two maximal principal strain rate calculation schemes in traumatic brain analysis with in-vivo and in-silico datasets

Comparison of two maximal principal strain rate calculation schemes.

Abstract

Brain deformation caused by a head impact leads to traumatic brain injury (TBI). The maximum principal strain (MPS) was used to measure the extent of brain deformation and predict injury, and recent evidence has indicated that incorporating the maximum principal strain rate (MPSR) and the product of MPS and MPSR, denoted as MPS × SR, enhances the accuracy of TBI prediction. However, ambiguities have arisen about the calculation of MPSR. Two schemes have been utilized: one is to use the time derivative of MPS (MPSR1), and another is to use the first eigenvalue of the strain rate tensor (MPSR2). To quantify the discrepancies between these two methodologies, we compared them across eight in-vivo and one in-silico head impact datasets and found that 95MPSR1 was slightly larger than 95MPSR2 and 95MPS × SR1 was 4.85% larger than 95MPS × SR2 on average. Across every element in all head impacts, the average MPSR1 was 12.73% smaller than MPSR2, and MPS × SR1 was 11.95% smaller than MPSR2. Logistic regression models trained to predict TBI showed no significant difference in predictability between the two schemes. The consequence of misuse of MPSR and MPS × SR thresholds was also examined, showing false decision rates around 1%, suggesting that the two methodologies are not significantly different in detecting TBI.

DOI Source Document
Differences between two maximal principal strain rate calculation schemes in traumatic brain analysis with in-vivo and in-silico datasets
Adaptive Machine Learning Head Model Across Different Head Impact Types Using Unsupervised Domain Adaptation and Generative Adversarial Networks

Brain deformation prediction using adaptive machine learning head models.

Abstract

Machine-learning head models (MLHMs) have shown promise in estimating traumatic brain injury (TBI)-related brain deformation from head kinematics, but overfitting to simulated impacts and performance degradation under distribution shift hinder clinical deployment. This study introduces an adaptive MLHM combining unsupervised domain adaptation and generative adversarial networks to address dataset distributional differences across simulated impacts, college football, mixed martial arts, and boxing datasets. Using domain regularized component analysis (DRCA) and cycle-GAN-based adaptation, the proposed models markedly improved maximum principal strain (MPS) and strain-rate (MPSR) prediction accuracy. The DRCA-based approach achieved the best performance with MPS mean absolute errors of 0.017 (college football) and 0.020 (MMA), and MPSR MAE of 4.09 s⁻¹ and 6.61 s⁻¹, outperforming baseline MLHMs across multiple hold-out test sets. These results demonstrate that unsupervised domain adaptation effectively reduces cross-domain error and moves MLHMs toward clinically reliable TBI detection.

DOI Source Document
Adaptive Machine Learning Head Model Across Different Head Impact Types Using Unsupervised Domain Adaptation and Generative Adversarial Networks
Finite element evaluation of an American football helmet featuring liquid shock absorbers for protecting against concussive and subconcussive head impacts

Helmet finite element model configurations used for impact simulations.

Abstract

This study develops and evaluates a finite element (FE) model of an American football helmet incorporating 21 liquid shock absorbers distributed throughout the shell. Using an anthropomorphic test headform and impactor FE setup, the helmet was tested under a protocol representative of National Football League concussive impacts at multiple locations and velocities, as well as lower-velocity subconcussive impacts. Head kinematics were used to compute the Head Acceleration Response Metric (HARM) and brain strain from an FE head model. The liquid helmet achieved the lowest HARM values in most conditions and yielded substantial reductions in both HARM and brain strain compared to four existing helmet designs, demonstrating the promise of liquid shock absorbers for improved helmet safety performance.

DOI Source Document
Finite element evaluation of an American football helmet featuring liquid shock absorbers for protecting against concussive and subconcussive head impacts
Finding the Spatial Co-Variation of Brain Deformation With Principal Component Analysis

Spatial co-variation patterns of brain deformation across impact types.

Abstract

This study applies principal component analysis (PCA) to investigate spatial co-variation patterns of traumatic brain injury metrics, including maximum principal strain (MPS), MPS rate (MPSR), and their product, across four types of head impacts: simulations, football, mixed martial arts, and car crashes. PCA was used to decompose element-wise injury metrics into principal components, with the first principal component (PC1) explaining over 80% of the variance in all datasets. High PC1 coefficients were consistently observed in regions such as the corpus callosum and midbrain. A PCA-based machine learning head model (PCA-MLHM) was then developed to predict PC1 and inverse-transform to reconstruct whole-brain injury metrics. Compared with the previous MLHM, PCA-MLHM achieved similar MPS estimation accuracy while reducing model parameters by 74%, improving interpretability and computational efficiency.

DOI Source Document
Finding the Spatial Co-Variation of Brain Deformation With Principal Component Analysis
Identifying Factors Associated with Head Impact Kinematics and Brain Strain in High School American Football via Instrumented Mouthguards

Brain strain patterns in high school American football impacts.

Abstract

This study investigates head impact kinematics and brain strain in high school American football athletes using an improved instrumented mouthguard (MiG2.0). Across 888 athlete exposures and 602 verified impacts, peak linear acceleration, angular velocity, angular acceleration, and 95th percentile maximum principal strain were quantified. Forward-direction impacts produced significantly higher kinematic magnitudes and brain strain than lateral or rearward impacts, and skill-position athletes experienced greater impact severity than line-position players. No significant differences were found for concussion history, helmet model, or team level. These results offer novel insight into real-world head impact exposure and resulting brain strain in high school athletes.

DOI Source Document
Identifying Factors Associated with Head Impact Kinematics and Brain Strain in High School American Football via Instrumented Mouthguards
Time Window of Head Impact Kinematics Measurement for Calculation of Brain Strain and Strain Rate in American Football

Instrumented mouthguard and finite element head model components.

Abstract

Wearable devices have been shown to effectively measure head movement during impacts in sports such as American football. The device collects kinematic signals within a predefined time window when triggered by an impact, which are then used by finite element (FE) head models to compute brain strain and strain rate. To identify the minimum sufficient time window for FE analysis, 118 video-confirmed on-field football impacts recorded by the Stanford Instrumented Mouthguard were analyzed. Simulations using truncated kinematics were compared with the original full window. Considering individual differences in brain geometry, six representative brain models were included. Larger brains required longer time windows, but a pre-trigger of 40 ms and post-trigger of 70 ms yielded strain and strain-rate calculations not significantly different from the original 200 ms window. A total duration of approximately 110 ms is recommended for accurate modeling of football impacts.

DOI Source Document
Time Window of Head Impact Kinematics Measurement for Calculation of Brain Strain and Strain Rate in American Football
The Relationship Between Brain Injury Criteria and Brain Strain Across Different Types of Head Impacts Can Be Different

Brain injury criteria and head impact kinematics across datasets.

Abstract

This study evaluates how brain injury criteria (BIC) relate to brain strain across diverse types of head impacts including sports collisions and automotive crash tests. Using linear regression models, the study analyzes 95% maximum principal strain, regional strain metrics, and cumulative strain damage across 18 BIC. Results demonstrate significantly different relationships between BIC and brain strain across datasets, showing that a given BIC value can correspond to different strain levels depending on impact type. These findings highlight the limitations of applying a BIC developed from one impact type to another and emphasize the need for context-specific injury risk estimation.

DOI Source Document
The Relationship Between Brain Injury Criteria and Brain Strain Across Different Types of Head Impacts Can Be Different
Rapid Estimation of Entire Brain Strain Using Deep Learning Models

Predicted whole-brain strain fields from the deep learning head model.

Abstract

This study proposes a deep learning head model for rapid estimation of whole-brain strain during head impacts. A five-layer deep neural network with feature engineering was trained on 2511 head impacts obtained from finite element simulations and on-field measurements in college football and mixed martial arts. The model predicts the maximum principal strain (Green–Lagrange) for all brain elements in less than 0.001 seconds, achieving an average RMSE of 0.022 with a standard deviation of 0.001 across repeated training runs. This approach enables fast, accurate estimation of brain deformation and supports potential clinical use in real-time traumatic brain injury detection.

DOI Source Document
Rapid Estimation of Entire Brain Strain Using Deep Learning Models
Validation and Comparison of Instrumented Mouthguards for Measuring Head Kinematics and Assessing Brain Deformation in Football Impacts

Instrumented mouthguard validation setup and devices.

Abstract

Instrumented mouthguards are widely used to measure head kinematics due to the rigid coupling of upper dentition and skull. This study validates and compares five commonly used instrumented mouthguards using pneumatic impacts delivered to a Hybrid III headform. Results show all devices accurately measure peak angular acceleration, angular velocity, and brain injury criteria values. Mouthguards with sufficiently long sampling windows also provide accurate inputs for a convolutional neural network–based brain model to compute brain strain. Measurement accuracy varies with impact location but is largely insensitive to impact velocity.

DOI Source Document
Validation and Comparison of Instrumented Mouthguards for Measuring Head Kinematics and Assessing Brain Deformation in Football Impacts