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Wearable devices have been shown to effectively measure the head movement during impacts in sports like American football. When a head impact occurs, the device is triggered to collect and save the kinematic measurements during a predefined time window. Then, based on the collected kinematics, finite element (FE) head models can calculate brain strain, which is used to evaluate the risk of mild traumatic brain injury. To find a time window that can provide a sufficient duration of kinematics for FE analysis, we investigated 118 on-field video-confirmed head impacts collected by the Stanford Instrumented Mouthguard. Because the individual differences in brain geometry influence these calculations, we included six representative brain geometries and found that larger brains need a longer time window of kinematics for accurate calculation. Among the different sizes of brains, a pre-trigger time of 20 ms and a post-trigger time of 70 ms were found to yield calculations of brain strain and strain rate that were not significantly different from calculations using the original 200 ms time window recorded by the mouthguard., Comment: 23 pages; 8 figures; 2 tables

Brain tissue deformation resulting from head impacts is primarily caused by rotation and can lead to traumatic brain injury. To quantify brain injury risk based on measurements of kinematics on the head, finite element (FE) models and various brain injury criteria based on different factors of these kinematics have been developed, but the contribution of different kinematic factors has not been comprehensively analyzed across different types of head impacts in a data-driven manner. To better design brain injury criteria, the predictive power of rotational kinematics factors, which are different in 1) the derivative order (angular velocity, angular acceleration, angular jerk), 2) the direction and 3) the power (e.g., square-rooted, squared, cubic) of the angular velocity, were analyzed based on different datasets including laboratory impacts, American football, mixed martial arts (MMA), NHTSA automobile crashworthiness tests and NASCAR crash events. Ordinary least squares regressions were built from kinematics factors to the 95\% maximum principal strain (MPS95), and we compared zero-order correlation coefficients, structure coefficients, commonality analysis, and dominance analysis. The angular acceleration, the magnitude, and the first power factors showed the highest predictive power for the majority of impacts including laboratory impacts, American football impacts, with few exceptions (angular velocity for MMA and NASCAR impacts). The predictive power of rotational kinematics in three directions (x: posterior-to-anterior, y: left-to-right, z: superior-to-inferior) of kinematics varied with different sports and types of head impacts.

Mild traumatic brain injury (mTBI, also known as concussion) caused by the head impact is a crucial global public health problem, but the physics of mTBI is still unclear. During the impact, the rapid movement of the head injures the brain, so researchers have been endeavoring to investigate the relationship between head kinematic parameters (e.g., linear acceleration, angular velocity, angular acceleration) and brain strain, which is associated with the injury of the brain tissue. Although previous studies have shown that linear acceleration had a limited contribution to brain strain, whether angular velocity or angular acceleration causes brain strain is still unclear because of their interdependency (acceleration being the velocity time-derivative). By reframing the problem through the lens of inertial forces, we propose to use the skull frame of reference instead of the ground frame of reference to describe brain deformation during head impact. Based on the rigid-body rotation of the brain, we present a theoretical framework of mechanical analysis about how the inertial forces cause brain strain. In this way, we theoretically show that angular acceleration determines brain strain, and we validate this by numerical simulations using a finite element head model. We also provide an explanation of why previous studies based on peak values found the opposite: that angular velocity determined brain strain in certain situations. Furthermore, we use the same framework to show that linear acceleration causes brain strain in a different mechanism from angular acceleration. However, because of the brain's different resistances to compressing and shearing, the brain strain caused by linear acceleration is small compared with angular acceleration., Comment: 10 pages, 7 figures

Multiple brain injury criteria (BIC) are developed to quickly quantify brain injury risks after head impacts. These BIC originated from different types of head impacts (e.g., sports and car crashes) are widely used in risk evaluation. However, the accuracy of using the BIC on brain injury risk estimation across different types of head impacts has not been evaluated. Physiologically, brain strain is often considered the key parameter of brain injury. To evaluate the BIC's risk estimation accuracy across five datasets comprising different head impact types, linear regression was used to model 95% maximum principal strain, 95% maximum principal strain at the corpus callosum, and cumulative strain damage (15%) on each of 18 BIC respectively. The results show a significant difference in the relationship between BIC and brain strain across datasets, indicating the same BIC value may suggest different brain strain in different head impact types. The accuracy of brain strain regression is generally decreasing if the BIC regression models are fit on a dataset with a different type of head impact rather than on the dataset with the same type. Given this finding, this study raises concerns for applying BIC to estimate the brain injury risks for head impacts different from the head impacts on which the BIC was developed., Comment: 28 pages, 11 figures

Objective: Many recent studies have suggested that brain deformation resulting from a head impact is linked to the corresponding clinical outcome, such as mild traumatic brain injury (mTBI). Even though several finite element (FE) head models have been developed and validated to calculate brain deformation based on impact kinematics, the clinical application of these FE head models is limited due to the time-consuming nature of FE simulations. This work aims to accelerate the process of brain deformation calculation and thus improve the potential for clinical applications. Methods: We propose a deep learning head model with a five-layer deep neural network and feature engineering, and trained and tested the model on 1803 total head impacts from a combination of head model simulations and on-field college football and mixed martial arts impacts. Results: The proposed deep learning head model can calculate the maximum principal strain for every element in the entire brain in less than 0.001s (with an average root mean squared error of 0.025, and with a standard deviation of 0.002 over twenty repeats with random data partition and model initialization). The contributions of various features to the predictive power of the model were investigated, and it was noted that the features based on angular acceleration were found to be more predictive than the features based on angular velocity. Conclusion: Trained using the dataset of 1803 head impacts, this model can be applied to various sports in the calculation of brain strain with accuracy, and its applicability can even further be extended by incorporating data from other types of head impacts. Significance: In addition to the potential clinical application in real-time brain deformation monitoring, this model will help researchers estimate the brain strain from a large number of head impacts more efficiently than using FE models., Comment: 12 pages, 6 figures, IEEE journal

Despite numerous research efforts, the precise mechanisms of concussion have yet to be fully uncovered. Clinical studies on high-risk populations, such as contact sports athletes, have become more common and give insight on the link between impact severity and brain injury risk through the use of wearable sensors and neurological testing. However, as the number of institutions operating these studies grows, there is a growing need for a platform to share these data to facilitate our understanding of concussion mechanisms and aid in the development of suitable diagnostic tools. To that end, this paper puts forth two contributions: 1) a centralized, open-source platform for storing and sharing head impact data, in collaboration with the Federal Interagency Traumatic Brain Injury Research informatics system (FITBIR), and 2) a deep learning impact detection algorithm (MiGNet) to differentiate between true head impacts and false positives for the previously biomechanically validated instrumented mouthguard sensor (MiG2.0), all of which easily interfaces with FITBIR. We report 96% accuracy using MiGNet, based on a neural network model, improving on previous work based on Support Vector Machines achieving 91% accuracy, on an out of sample dataset of high school and collegiate football head impacts. The integrated MiG2.0 and FITBIR system serve as a collaborative research tool to be disseminated across multiple institutions towards creating a standardized dataset for furthering the knowledge of concussion biomechanics., Comment: 21 pages, 3 figures, 1 table

Because of the relatively rigid coupling between the upper dentition and the skull, instrumented mouthguards have been shown to be a viable way of measuring head impact kinematics for assisting in understanding the underlying biomechanics of concussions. This has led various companies and institutions to further develop instrumented mouthguards. However, their use as a research tool for understanding concussive impacts makes quantification of their accuracy critical, especially given the conflicting results from various recent studies. Here we present a study that uses a pneumatic impactor to deliver impacts characteristic to football to a Hybrid III headform, in order to validate and compare five of the most commonly used instrumented mouthguards. We found that all tested mouthguards gave accurate measurements for the peak angular acceleration (mean relative error, MRE < 13%), the peak angular velocity (MRE < 8%), brain injury criteria values (MRE < 13%) and brain deformation (described as maximum principal strain and fiber strain, calculated by a convolutional neural network based brain model, MRE < 9%). Finally, we found that the accuracy of the measurement varies with the impact locations yet is not sensitive to the impact velocity for the most part., Comment: Annals of Biomedical Engineering: Concussion Biomechanics in Football

The discovery that repetitive mild traumatic brain injury (mTBI) can result in chronic traumatic encephalopathy (CTE) in high risk contact sports has led to increased scrutiny of head protective gear. In this work, we asked if it was physically possible to prevent mTBI in American football with helmets alone. Here, we show that modern helmets of several types are unlikely to prevent mTBI from high speed collisions as might be seen in the NFL, but that introducing liquid as an energy absorbing medium can dramatically reduce the forces of impact across a spectrum of impact severities. We hypothesized that a helmet which transmits a nearly constant force during football impacts is sufficient to reduce biomechanical loading in the brain below the threshold of mTBI. To test this hypothesis, we first show that the optimal impact force transmitted to the head, in terms of brain strain, is in fact a constant force profile. Then, to generate a constant force with a helmet, we implement a computational model of a fluid-based shock absorber that adapts passively to any given impact speed. Computer simulation of head impacts with liquid shock absorption indicate that, at the highest impact speed, the average brain tissue strain is reduced by 27.6% $\pm$ 9.3 compared to existing helmet padding that is available on the market. These simulations are based on the NFL's helmet test protocol and predict that adding liquid shock absorbers could reduce the number of concussions by at least 75%. Taken together, these results suggest that the majority of mTBI in football could be prevented with more efficient helmet technology.

Phase retrieval in real or complex Hilbert spaces is the task of recovering a vector, up to an overall unimodular multiplicative constant, from magnitudes of linear measurements. In this paper, we assume that the vector is normalized, but retain only qualitative, binary information about the measured magnitudes by comparing them with a threshold. In more specific, geometric terms, we choose a sequence of subspaces in a real or complex Hilbert space and only record whether a given vector is closer to the subspace than to the complementary subspace. The subspaces have half the dimension of the Hilbert space and are independent, uniformly distributed with respect to the action of the orthogonal or unitary groups. The main goal of this paper is to find a feasible algorithm for approximate recovery based on the information gained about the vector from these binary questions and to establish error bounds for its approximate recovery. We provide a pointwise bound for fixed input vectors and a uniform bound that controls the worst-case scenario among all inputs. Both bounds hold with high probability with respect to the choice of the subspaces. For real or complex vectors of dimension $n$, the pointwise bound requires $m \ge C \delta^{-2} n \log(n)$ and the uniform bound $m \ge C \delta^{-2} n^2 \log(\delta^{-1} n)$ binary questions in order to achieve an accuracy of $\delta$. The accuracy $\delta$ is measured by the operator norm of the difference between the rank-one orthogonal projections corresponding to the normalized input vector and its approximate recovery., Comment: 29 pages AMS LaTeX, 3 figures; v2 has figures and an added result on adversarial noise