Introduction

According to the World Health Organization, more than 40 million people worldwide suffer a mild traumatic brain injury (mTBI) each year.15 These injuries are classified as focal or diffuse to describe a wide spectrum of pathological outcomes and distinguish between distinct injury mechanisms. Focal injuries are common in unprotected falls and comprise lacerations, skull fracture, cerebral contusions and hemorrhage caused by concentrated contact forces.25,68 In contrast, diffuse injuries may occur in the absence of concentrated contact forces, as in whiplash, blast exposure, or impact with a padded surface, and commonly describe cerebral concussion associated with inertial acceleration of the brain.18,48,62 As many as 3.8 million concussions occur in the United States each year during sports and recreation alone, and an estimated 50% of incidents may go unreported.34 Neurodegenerative disease has been reported in soldiers, professional athletes, and more recently, amateur athletes who have experienced repeated concussions.17,28,31,36,73

mTBI is thought to be caused by sudden translation and rotation of the head, but this motion has yet to be directly and independently measured in humans until now. In 1943, Holbourn first hypothesized that rapid rotation, and not translation, produces diffuse brain injury during blunt head trauma.37 Assuming brain tissue and cerebrospinal fluid are incompressible inside the skull (like water or gel that fill a rigid vessel), Holbourn speculated that the brain does not deform due to pure head translation. He proposed the brain deforms considerably due to rotational acceleration because of its low shear modulus, a response that was recently demonstrated for normal head motion in a live human 6 and for concussive-severity head motion in a human cadaver.33 While later studies confirmed that cerebral concussion and loss of consciousness (LOC) could be induced in primates with rotational acceleration, injuries were more severe when rotation was combined with translational contact trauma, possibly due to coupled pressure gradients and diffuse strain.60 Moreover, animal and computational studies found tolerance to acceleration varies substantially by anatomical direction: coronal rotation produced more severe injuries in primates26 and larger brainstem and corpus callosum tissue strains in a finite element (FE) model46 while sagittal rotation produced more severe injuries in neonatal piglets (with different head and neck geometry).11,20,74 These studies suggest direct measurement of head rotation should capture directional components, and not just the magnitude, of rotational acceleration.

Although previous research has shed light on the potential mechanism of mTBI, there is a lack of consensus and supporting data for criteria to predict injury risk. Several (head) kinematic criteria and brain FE criteria have been previously proposed to predict the risk of mTBI (Table 1), but none have amassed widespread acceptance. Regulatory safety standards have traditionally used 3 degree-of-freedom (3DOF) translation-only kinematic criteria.21,45,51 Criteria that use rotation measurements may better capture the mechanism of mTBI, but direct 6DOF measurements of human mTBI necessary to investigate this hypothesis have been previously unavailable (Table 2). Earlier efforts to measure or deduce human head kinematics in the field have employed headband-mounted sensors,50,64,67 helmet-mounted sensors,19,53,70 and laboratory reconstructions of impacts recorded in broadcast video.63 However, these datasets are limited due to their indirect (dependent) estimates of head rotation,8,19,50,53,67 measurement errors from non-rigid skull fixation,2,39,56 and restriction to test populations that typically wear helmets.7,69 A few laboratory studies proposed the use of mouthpiece-mounted sensors as an alternative means of measuring head kinematics,5,35,52 but to the best of our knowledge, field data with these devices have not yet been published.

Table 1 Existing injury criteria
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Table 2 Measurements of human head impacts
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Our objective was to investigate whether direct measurement of head rotation improves prediction of mTBI. To that end, we measured 6DOF translational and rotational head kinematics using instrumented mouthguards that conformed and affixed to the upper dentition for a close approximation of skull motion. We used this preliminary data to evaluate the deviance of existing injury criteria from a perfectly predictive model and investigate new approaches to injury prediction.

Materials and Methods

Athletes were fitted with instrumented mouthguards and monitored for symptoms of mild traumatic brain injury (mTBI) by trained clinicians. These devices monitored acceleration to determine if an impact occurred. When an impact triggered the device, six sensors recorded measurements to compare the data signatures of clinically diagnosed injuries with other head impacts. Video-confirmed impact measurements were used to calculate kinematic criteria and estimate brain finite element (FE) criteria using finite element analysis. Injury prediction for each criteria was compared using univariate logistic regression. Finally, a novel multivariate machine learning approach to injury prediction was investigated.

Mouthguard Design and Impact Detection

To detect impacts and investigate how impact forces combine to cause mTBI, we built instrumented mouthguards that measure six degree-of-freedom (6DOF) head kinematics (Fig. 1a). Each device contained a tri-axis accelerometer measuring translational acceleration in the anterior to posterior, left to right, and superior to inferior directions, and a tri-axis gyroscope measuring rotational velocity in the coronal, sagittal, and horizontal planes. Activity that exceeded a programmed accelerometer threshold was recorded and downloaded following each athletic event (game, practice, sparring session, or match). The threshold was chosen at 7g (7 times gravity) or 10g depending on the length of the athletic event, to maximize data collection with limited on-board memory (16 Mbit) and battery life. A microprocessor recorded time-stamped kinematic sensor measurements at 1 kHz for 10 ms prior to the triggering acceleration, and 90 ms post-trigger. The electronics were embedded in material that was fitted to each subject through a standard boil-and-bite process, or by pressure forming around the subject’s dental mold. The custom fit provided a conforming, rigid coupling to the athlete’s skull through the maxillary (upper) dentition, and estimates of head center of gravity kinematics. We used a laboratory head impact model and previously published validation protocol to quantify the measurement accuracy of each mouthguard design used in the study.13

Figure 1
figure 1

Mouthguard design and data acquisition. When an athlete experiences high head acceleration, we collect (a) six degree-of-freedom (6DOF) kinematic measurements using custom-fit mouthguards, and (b) time-stamped, high-definition video of all events to qualitatively study each impact and (c) confirm that device measurements correspond to true head impacts

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Four mouthguard designs were used in the present study and validated against an anthropomorphic dummy head instrumented with a 6aω sensor package (Table 3).13,41 Design differences among the four models included form factor (sensors embedded in the mouth, or sensors embedded in a cantilever tab between the lips), accelerometer (ADXL377, Analog Devices, Inc., Norwood, MA, USA, or H3LIS331DL, ST Microelectronics, Geneva, Switzerland), and gyroscope (L3G4200D, ST Microelectronics, Geneva, Switzerland, or ITG-3500A, InvenSense Inc., San Jose, CA, USA).

Table 3 Mouthguard accuracy and deployment
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Video of all athletic events was used to purify the mouthguard dataset for investigation of injury biomechanics (Fig. 1b). Time-stamped high definition video (30 frames s−1) captured the timing and sequence of head impacts. Using this video, activity recorded on the mouthguard was manually classified in two categories: head impacts and spurious triggers (Fig. 1c). Head impacts were defined as contact between a player’s head and any foreign entity (another player’s head, body, limb, or the ground). Only video-confirmed impacts were selected for analysis in the present study. Spurious triggers such as body contact, device insertion/removal, and device manual manipulation were rejected. High speed (1300–2500 frames s−1) video was also recorded at select athletic events (Phantom Miro LC-320S, Vision Research, Wayne, NJ) to study head impacts with higher temporal resolution and for comparison to mouthguard measurements (Movies S1 and S2).

Mouthguard Deployment and Injury Monitoring

We instrumented subjects who are exposed to repeated athletic head impacts over a wide spectrum of conditions. Of 33 recruited subjects, 30 were collegiate American football players, 2 were professional boxers (1 male and 1 female), and 1 was a male professional mixed martial artist. Prototype devices were deployed at 19 select athletic events over 3 years. Human subject protocols were approved by the Stanford Institutional Review Board (IRB No. 21304) and we received informed consent from all subjects.

At data collection events, subjects experiencing injury symptoms were monitored for potential brain injury. At competitions, sideline/ringside clinicians monitored subjects throughout the event. When signs of injury were identified by the clinician or self-reported by the subject, the clinician/trainer conducted an immediate neurological evaluation. If injury was suspected, the subject was removed from competition to receive a detailed neurological evaluation. At practices and training events, clinical or research staff were present to identify signs of brain injury throughout each event. In cases of injury, the subject was removed from the event and taken to a clinician for a detailed evaluation. Detailed evaluation following competition and training event injuries was conducted within 24 h of injury and consisted of a 3 Tesla (3T) magnetic resonance imaging (MRI) scan and a neurological examination. During the neurological examination, the subject was asked to report the circumstances and symptoms relating to their injury. The neurological examination was repeated at 3 days and 3 months post-injury. In the absence of a clinically diagnosed concussion, recorded head impacts were categorized as “non-injury”.

Mouthguard Measurement Processing

Raw accelerometer measurements of translational acceleration and raw gyroscope measurements of rotational velocity were filtered using a second-order Butterworth low-pass filter with a cutoff frequency of 200 and 110 Hz, respectively.13 Accelerometer measurements were defined as the acceleration of the accelerometer origin in accelerometer reference frame. The gyroscope measurements were defined as the rotational velocity of gyroscope reference frame in ground inertial frame. Sensor origins were defined at the sensor location (Fig. 1) and their location relative to the center of gravity of the 50th percentile male (since MRI data was not available for all subjects) was determined using CAD drawings of the dummy head using for accuracy validation.13 Sensor measurements were transformed to express the translational acceleration of the head center of gravity and the rotational velocity and acceleration of a head anatomical reference frame (pointing in the anterior, left, and superior directions) using a previously published algorithm.13

Animations of the mouthguard measurements were generated in MATLAB (Mathworks, Natick, MA, USA) (Movies S1 and S2). The orientation and position of the head in the animation were generated by first estimating the head orientation in the first frame (t = 0 ms) of the video, and then integrating the accelerometer and gyroscope data from the mouthguards. This data was subsequently transformed to the center of gravity of the head to resolve the position and orientation of the head in future frames.

Kinematic Injury Criteria

Twelve existing kinematic injury criteria (Table 1) were calculated using the collected and processed 6DOF mouthguard measurement:

Peak Translational Acceleration Magnitude (a peak)18,30,50,62,63,71 was defined as the peak value of the translational acceleration vector magnitude time series,

$$a_{\text{peak}} = {\text{max }}\parallel \vec{\varvec{a}}(t)\parallel$$
(1)

where \(\vec{\varvec{a}}\) represents the translational acceleration vector (anterior, left, superior) and \(\parallel \vec{\varvec{a}}\parallel\) represents the magnitude (computed as L2 norm) of a vector \(\vec{\varvec{a}}\). The maximum is taken over the entire 100 ms window when sensor measurements are recorded.

Head Injury Criterion (HIC15 and HIC36)21,45,51,63,78 is the most widely used injury criteria and was calculated as,

$$HIC = \mathop {\hbox{max} }\limits_{{t_{1} ,t_{2} }} \left\{ {\left[ {\frac{1}{{t_{2} - t_{1} }}\mathop \int \limits_{{t_{1} }}^{{t_{2} }} \parallel \vec{\varvec{a}}(t)\parallel dt} \right]^{2.5} (t_{2} - t_{1} )} \right\}$$
(2)

where \(\parallel \vec{\varvec{a}}(t)\parallel\) is the magnitude of translational acceleration and the times t 1 and t 2 are chosen to maximize the value of HIC, bounded by t 2 − t 1 < 15 ms for HIC15 or t 2 − t 1 < 36 ms for HIC36.

Severity Index (SI),7,8,23,51,63 also known as Gadd Severity Index (GSI), is given by,

$$SI = \mathop \int \nolimits \parallel \vec{\varvec{a}}(t)\parallel^{2.5} dt$$
(3)

The integral is evaluated over the period of time from when the signal first exceeds 4g to when it returns to 4g after the largest peak.51

Peak Rotational Acceleration Magnitude (α peak)37,48,59,63,72 was defined as the peak value of the rotational acceleration vector magnitude time series,

$$\alpha_{\text{peak}} = {\text{max }}\parallel \vec{\varvec{\alpha}}(t)\parallel$$
(4)

where \(\vec{\varvec{\alpha }}\) represents the rotational acceleration vector (coronal, sagittal, horizontal). The maximum is taken over the entire 100 ms window when sensor measurements are recorded.

Rotational Injury Criterion (RIC)12,42 is the rotational acceleration equivalent of HIC and is defined as,

$$RIC = \mathop {\hbox{max} }\limits_{{t_{1} ,t_{2} }} \left\{ {\left[ {\frac{1}{{t_{2} - t_{1} }}\mathop \int \limits_{{t_{1} }}^{{t_{2} }} \parallel \vec{\varvec{\alpha }}(t)\parallel dt} \right]^{2.5} (t_{2} - t_{1} )} \right\}$$
(5)

where the times t 1 and t 2 are chosen to maximize the value of RIC, bounded by t 2 − t 1 < 36.

Peak Change in Rotational Velocity Magnitude (∆ω peak)48,61,72 was defined as the largest change in rotational velocity magnitude,

$$\Delta \omega_{\text{peak}} = \hbox{max} \parallel \overrightarrow {\varvec{\omega}} (t)\parallel - \hbox{min} \parallel \overrightarrow {\varvec{\omega}} (t)\parallel$$
(6)

where \(\vec{\varvec{\omega }}\) represents the rotational velocity vector (coronal, sagittal, horizontal). The maximum and minimum is taken over the entire 100 ms window when sensor measurements are recorded.

Brain Injury Criterion (BrIC)75 was developed by National Highway Traffic Safety Administration to account for diffuse axonal injury. It is based on Cumulative Strain Damage Measure (CSDM) values and uses critical values derived from finite element simulations:

$$BrIC = \frac{{\vec{\varvec{\omega }}_{\text{peaks}} }}{{\vec{\varvec{\omega }}_{\text{cr}} }}$$
(7)

where \(\vec{\varvec{\omega }}_{\text{peaks}}\) is a vector of the peak values for rotational velocity in each anatomical direction over time, and \(\vec{\varvec{\omega }}_{\text{cr}}\) = [ω cr,x , ω cr,y , ω cr,z ] = [66.2, 59.1, 44.2] rad/s are the corresponding critical values determined from experimental data of frontal dummy impacts.

Head Impact Power (HIP)49,57 is computed including translational and rotational components of acceleration at the head center of gravity, assuming rigid body motion, as shown below:

$$\begin{array}{*{20}l} {HIP = {\text{max }}(ma_{x} (t)\mathop \int \nolimits a_{x} (t)dt + ma_{y} (t)\mathop \int \nolimits a_{y} (t)dt} \hfill \\ { + ma_{z} (t)\mathop \int \nolimits a_{z} (t)dt + I_{xx} \alpha_{x} (t)\mathop \int \nolimits \alpha_{x} (t)dt} \hfill \\ { + I_{yy} \alpha_{y} (t)\mathop \int \nolimits \alpha_{y} (t)dt + I_{zz} \alpha_{z} (t)\mathop \int \nolimits \alpha_{z} (t)dt)} \hfill \\ \end{array}$$
(8)

where x, y, z respectively correspond to anterior, left, superior for translation acceleration, and to coronal, sagittal, horizontal for rotational acceleration, m = 4.5 kg equals the mass of the human head, and I xx , I yy , I zz  = [0.016, 0.024, 0.022] kg m2 equal the appropriate mass moments of inertia of the human head. The maximum is taken over the entire 100 ms window when sensor measurements are recorded.

Power Rotational Head Injury Criterion (PRHIC)12,43 is similar HIC and RIC, and is defined as,

$$PRHIC = \mathop {\hbox{max} }\limits_{{t_{1} ,t_{2} }} \left\{ {\left[ {\frac{1}{{t_{2} - t_{1} }}\mathop \int \limits_{{t_{1} }}^{{t_{2} }} HIP_{rot} (t)\,dt} \right]^{2.5} (t_{2} - t_{1} )} \right\}$$
(9)

where HIP rot(t) is the rotational acceleration contribution to Head Impact Power (HIP).

Generalized Acceleration Model for Brain Injury Threshold (GAMBIT)54 is a generalized acceleration model for brain injury threshold that was previously proposed combining rotational and translational components of head acceleration and is calculated from the equation below,

$$GAMBIT = { \hbox{max} }\left\{ {\left[ {\left( {\frac{{\parallel \vec{\varvec{a}}(t)\parallel }}{{a_{c} }}} \right)^{n} + \left( {\frac{{\parallel \vec{\varvec{\alpha }}(t)\parallel }}{{\alpha_{c} }}} \right)^{m} } \right]^{1/s} } \right\}$$
(10)

where a c and α c are the thresholds for the corresponding acceleration mode, and n, m and s are empirical values. The proposed values for above constants are n = m = s = 2, a c = 250g, and α c = 25000 rad/s2.54 The maximum is taken over the entire 100 ms window when sensor measurements are recorded.

Principal Component Score (PCS)29 is a weighted sum of translation and rotational accelerations, HIC, and SI with empirically determined weights, as shown below,

$$\begin{array}{*{20}l} {PCS = 10((0.4336\overline{{a_{\text{peak}} }} + 0.2164\overline{{\alpha_{\text{peak}} }} (13)} \hfill \\ { + 0.4718\overline{SI} + 0.4742\overline{HIC} ) + 2)} \hfill \\ \end{array}$$
(11)

where \(\overline{X}\) is a standardized value defined as \(\overline{X}\) = (X − µ)/σ, µ is the population mean, and σ is the population standard deviation.

Brain Finite Element (FE) Criteria

To understand how head kinematics produce brain stress and strain, we simulated head impacts using a finite element (FE) head model developed at the KTH Royal Institute of Technology in Stockholm, Sweden,47 which represents an average adult male human head. This model, developed in LS-DYNA (LSTC, Livermore, CA), incorporates the scalp, skull, brain, meninges, cerebral spinal fluid, and eleven pairs of parasagittal bridging veins, differentiating between white matter, gray matter, and the ventricles. It models CNS tissues using an Ogden hyperelastic constitutive law (to account for large deformations of the tissue) with additional linear viscoelastic terms (to account for the rate dependence of the tissue). Also, the brain-skull interface is modeled by tied-node contact. The FE model was validated against displacement data from cadaver head impact experiments performed by Hardy et al.,32 where neutral density targets were inserted inside cadaver brains and tracked using high-speed biplanar X-ray during impacts.

A subset of impacts were chosen for the computationally intense FE simulations (approximate 4 h run-time for a single 100 ms impact on a high end workstation): all impacts resulting in clinically diagnosed injury, a random sample of 10% of non-injury impacts, and all remaining impacts that exceeded any injury impact in at least one translational or rotational acceleration component. This subset of impacts is biased to include a greater percentage of non-injury impacts that would be most difficult to classify. For each simulation, 6DOF translational and rotational measurements over 100 ms were used as inputs to the model. Six existing brain deformation criteria (Table 1) were calculated using the results of the finite element simulations:

Peak Principal Strain (ε peak and ε peak,CC )16,47 in the entire brain and in the corpus callosum was given by the first principal Green–Lagrange strain. This criteria describes the maximum longitudinal tensile strain in the tissue and was calculated throughout the volume of the brain (and corpus callosum) over time. The peak was selected by taking the maximum over time across all individual model elements (in the whole brain and just in the corpus callosum) during a 100 ms interval.

Cumulative Strain Damage Measure (CSDM15 and CSDM25)76 is a criteria describing the total volume fraction of brain tissue that undergoes strain values larger than a prescribed threshold (0.15 and 0.25 in our study).

Minimum/Maximum Pressure (P min and P max)79 are the minimum and maximum values for pressure inside brain. In the present study, absolute value of each criteria was used before performing statistical analysis.

Injury Prediction Using Logistic Regression

For each of the 18 kinematic and brain FE criteria, univariate logistic regression was performed to predict mTBI. For each impact, the criteria value was used as the predictor, and the clinical diagnosis of injury was used as a binary yes/no response. A generalized linear model regression (MATLAB’s glmfit routine) of the responses, y, on the predictors, x, using a binomial distribution was performed in MATLAB for the following logistic model:

$$E(Y|x) = \frac{1}{{(1 + e^{{ - \beta_{0} - \beta_{1} x}} )}}$$
(12)

where β 0 and β 1 are the intercept and slope coefficients, respectively. E(Y|x) is the expected value of response Y given the predictor value x, or rather, the probability of injury for a given criteria value.38 Logistic regression was performed on the subset of impacts for which finite element simulations were performed.

A Kolmogorov–Smirnov (KS) test of normality was performed on the natural log transform of each criteria, x’. For those criteria with log-normal distributions, the logistic model was also fit to standardized criteria values, \(\widehat{x}\), where,

$$\widehat{x} = \frac{{x^{\prime } - \overline{{x^{\prime } }} }}{{s^{\prime } }}$$
(13)

with \(\overline{{x^{\prime } }}\) and s′ corresponding to the mean and standard deviation of the natural log transformed criteria values, x′. The corresponding intercept and slope coefficients, \(\widehat{\beta }_{0}\) and \(\widehat{\beta }_{1}\), describe the change in injury risk for a one standard deviation change in a given criteria.

The deviance (D) statistic assesses the quality of fit of a logistic regression (analogous to r 2 in linear regression)38 and has been used to assess mTBI prediction (also known as −2LLR).44,55,58,63 The statistic is given by,

$$D = - 2\ln \left( {\frac{{{\text{Likelihood}}\;{\text{of}}\;{\text{the}}\;{\text{fitted}}\;{\text{model}}}}{{{\text{Likelihood}}\;{\text{of}}\;{\text{the}}\;{\text{saturated}}\;{\text{model}}}}} \right)$$
(14)

where the predicted injury risk from a fitted model is that which is predicted by a given criteria, and predicted injury risk from a saturated model is equal to the observed injury risk (a perfectly predictive model). For a binary prediction, the likelihood of the saturated model is equal to 1. As deviance approaches 0, the fitted model more closely approximates a perfectly predictive model (the ratio of likelihoods inside the natural logarithm approaches 1). Zero deviance is expected for a criteria that perfectly classifies injury and non-injury impacts.

We computed the difference in deviance between each fitted model and a null model (predicted injury risk without using the criteria, that is, with only a β 0 term). This difference in deviance follows a χ 2 distribution; a low corresponding p value suggested that a criteria significantly improved injury prediction.38 A p value is computed for the β 1 and \(\widehat{\beta }_{1}\) coefficients, with a low value indicating higher confidence that the β 1 parameter is not 0.

Injury Prediction Using Machine Learning

We investigated a novel approach to injury prediction using multivariate machine learning on kinematic measurements. Using the Support Vector Machine (SVM) classification routine defined in MATLAB’s svmtrain and svmclassify functions, we determined an example multidimensional linear classifier separating the injury and non-injury impacts. Twelve input features were used in the routine: three direction components and magnitude of translational acceleration, rotational acceleration, and rotational velocity. Using the fewest features necessary, the routine finds a classification boundary (separating hyperplane) that maximizes the margins between the injury and non-injury classes.

Results

Injury Diagnosis

Two subjects suffered a concussion during competitive play. The first patient was a 21-year-old male NCAA collegiate football player who sustained a concussion from a head impact while being tackled (Fig. 2a and Movie S1). The patient was witnessed to have brief extensor posturing of his upper extremities and loss of consciousness (LOC) lasting approximately 2 min. The patient continued to have an altered mental status with post concussive symptoms for 3 days post injury. His detailed neurological examination was normal. A 3T brain MRI was obtained within 24 h and was normal. It was noted that this was his fourth overall concussion, and the second in 3 weeks. He did not return to play for the remaining two games of the season but ultimately made a complete recovery and now plays professionally. Follow up comprehensive neurological testing performed at 3 months post injury was normal.

Figure 2
figure 2

Measurement of human mild traumatic brain injury. A collegiate American football player lost consciousness after sustaining a head impact during a regular season game. (a) Broadcast footage at 40 frames s−1 are compared with an (b) animation of head position and orientation during the impact calculated by integrating (c) device measurements of translational acceleration and (d) rotational acceleration

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The second patient was a 20-year-old male NCAA collegiate football player who sustained a concussion during practice. Although he did not lose consciousness, he self-reported several post concussive symptoms immediately following the impact including headache, poor concentration, and slowed reaction time. These symptoms persisted for 12 h and then dissipated. Detailed neurological examination and 3T brain MRI at 18 h post injury were normal. In retrospect, the patient reported suffering a mild head injury 48 h prior to this impact, but he did not report his symptoms at the time. He ultimately made a full recovery and returned to football after a stepwise return to play.

Mouthguard Measurements and Kinematic Criteria

Mouthguards were evaluated on a dummy head in the lab using a published validation protocol13 (Table 3). Linear regression slopes (m) between mouthguard and dummy head peak magnitude measures were in the range 0.94–1.09 for all designs. The one-to-one linear model fit (quantified by r 2) was strongest for rotational velocity, followed by translational acceleration, then rotational acceleration. In field deployment, we collected data on volunteer subjects with each of the mouthguard designs. We measured a total of 513 video-confirmed head impacts: 421 from American football including two clinically diagnosed injuries, 73 from boxing, and 19 from mixed martial arts (MMA). All three contact sports had similar distributions of kinematic measurements across all 513 impacts (Fig. S1). The 513 impacts were 1% of all mouthguard measurements recorded in the study, the rest being spurious triggers that were not included in the present analysis.

We collected 6DOF kinematic measurements of the clinically diagnosed LOC injury (Fig. 2). The six acceleration time series were not simple impulses; the components reached local extrema, changed direction, and inflected many times in 100 ms, highlighting the complexity of forces acting on the subject’s helmet, skull, and brain during the head impact. For the LOC injury, translational acceleration magnitude of the head (Fig. 2c) peaked at 106g, rotational acceleration magnitude at 12,900 rad s−2 (Fig. 2d), and change in rotational velocity magnitude at 34 rad s−1. The self-reported injury was characterized by milder kinematics: 85g, 7040, and 23 rad s−1.

These complex 6DOF measurements are traditionally reduced to 3DOF kinematic criteria such as peak translational acceleration (purple diamond) and HIC (gray shaded region) (Fig. 2c) to predict mTBI. We calculated these and ten other existing kinematic injury criteria (Table 1) for a subset of 110 head impacts: two injuries, 50 randomly selected, and 58 with at least one translational or rotational acceleration component that exceeded either injury (Fig. 3); neither of the injured players had non-injury impacts in this group (accelerations exceeding their injury impacts). The log-normal median (µ) and interquartile range for peak translational acceleration magnitude was 33g (21–53g), for peak rotational acceleration magnitude was 2730 rad s−2 (1520–4880 rad s−2), and for peak change in rotational velocity magnitude was 14 rad s−1 (9–22 rad s−1), (Figs. 3a, 3e, and 3g). The back-transformed (multiplicative) standard deviations (σ*) for these statistics were 2.00, 2.37, and 1.90.

Figure 3
figure 3

Kinematic injury criteria. Injury and non-injury values for each kinematic criteria are given for a subset of 110 impacts (2 injuries, 58 high acceleration, and 50 randomly selected). All but PCS passed a Kolmogorov–Smirnov test of log-normality with statistical significance. The region that lies within one standard deviation, σ*, of the log-normal median, µ*, is indicated

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For the most widely used injury criteria, HIC15 and HIC36, 3 and 4% of non-injury impacts exceeded the LOC injury, while 6% exceeded the self-reported injury (Figs. 3b and 3c, Eq. 2). Video analysis of these non-injury impacts revealed no remarkable incident. For peak rotational acceleration magnitude, 2% of the non-injury impacts exceeded the LOC injury, while 13% exceeded the self-reported injury. HIP (Fig. 3j, Eq. 8) considers both translation and rotation but had a similar distribution to peak rotational acceleration magnitude: 1% of non-injuries exceeded the LOC injury, while 9% exceeded the self-reported injury. More non-injury impacts exceeded the LOC in rotational acceleration than in HIP, however, the margin by which these impacts exceeded the LOC was greater in HIP than in rotational acceleration. The highest non-injury HIP (43 kW) was 48% above the LOC injury (29 kW), while the highest peak rotational acceleration (14300 rad s−1) was 11% above the LOC (12,900 rad s−1).

Several non-injury impacts exceed the translational and rotational peak translational acceleration magnitude vectors (Figs. 3a and 4) of the LOC and self-reported injuries (7 and 13% of non-injury impacts, respectively). However, the injury accelerations occurred in unique directions (Fig. S2). The LOC injury was the largest peak translational acceleration vector (Figs. 4a, 4b, 4c) within a 70° cone, and the self-reported injury was largest within 20°. The peak rotational acceleration vector of the LOC injury was even more unique, occurring largely in the coronal plane with no non-injuries of the same magnitude within a 150° cone (Figs. 4d, 4e, and 4f). Direction components are weighted differently for only a few of the kinematic injury criteria evaluated here (Table 1), but are inherently factored into finite element analysis which models material and geometric asymmetries of the skull and brain.

Figure 4
figure 4

Direction of head acceleration. The direction of (a–c) peak translational acceleration, and (d–f) peak rotational acceleration distinguishes injury from non-injury. Most impacts resulted in posterior translation and sagittal plane rotation of the head

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Brain Finite Element (FE) Criteria

For the same subset of 110 impacts, we estimated brain deformation using finite element (FE) simulations (Fig. 5, Movies S1 and S3). Peak principal strains for the LOC (49.8%) and self-reported (17.7%) injuries were higher than the non-injury median (16.4, 10–27% interquartile range) over the entire brain (Fig. 5a). Maximum pressures for the LOC (83.7 kPa) and self-reported (40.0 kPa) injuries were also higher than the non-injury median (32.5, 20–54 kPa interquartile range) (Fig. 5e). Minimum pressure (absolute value) for the LOC (−91.2 kPa) and self-reported (−32.9 kPa) injuries exhibited the same trend compared to the non-injury median (24.5 kPa, –51 to –12 kPa interquartile range) (Fig. 5f).

Figure 5
figure 5

Brain deformation injury criteria. Injury and non-injury values for each (a–f) brain deformation criteria are given for the subset of 110 impacts. Multiplicative standard deviation, σ*, and log-normal median, µ*, are indicated (all criteria except CSDM passed a test of log-normality). Fringe plots of (g–h) principal strain and (i–j) pressure indicate regions of greatest brain deformation. (K) Peak principal strain in both injuries uniquely occurred in the corpus callosum

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The spatial distribution of strain for the LOC and self-reported injuries (Figs. 5g and 5h) indicated strain concentrations in the corpus callosum. Peak strains in non-injury impacts occurred more peripherally (Fig. 5k). The LOC (49.8%) and self-reported (17.7%,) injury strains in the corpus callosum were also higher the non-injury median (9.3%, 6–16% interquartile range). The LOC injury peak principal strain was among the highest in the subset of simulated impacts (top 6% for the whole brain and the highest in corpus callosum), while the self-reported injury was in the top 49 and 25% for the whole brain and corpus callosum, respectively. Although a few non-injury impacts produced strains in the corpus callosum that exceeded the self-reported injury (none exceeded the LOC injury), the injuries were the only impacts where the peak principal strain occurred in the corpus callosum (Fig. 5k). For both injuries, the largest pressure differential occurred between opposite sides of the brain, indicating the coup and contrecoup injury mechanism (Figs. 5i and 5j).

Injury Prediction

Univariate logistic regression was used to predict injury for kinematic and FE criteria (Fig. 6), with a lower deviance statistic indicating a closer approximation to a perfectly predictive model. The predictor with the lowest deviance was peak strain in the corpus callosum (13.5), a 6DOF FE criteria, followed by peak rotational acceleration magnitude (14.9), HIP (15.7), and GAMBIT (15.8), all criteria that include rotation measurements. These four criteria had deviance that were significantly (α = 0.05) lower than the deviance of the null model (20.0). Among the translation-only criteria (red bars), peak acceleration had the lowest deviance (16.4); all groups that included rotation measures had at least one criteria with lower deviance. For this limited injury dataset, rotational kinematics (whether alone or combined with translation) generally had lower deviance than translation-only criteria. Peak strain in the corpus callosum, peak rotational acceleration, and HIP also had the largest standardized regression coefficients, \(\widehat{\beta }_{0}\) and \(\widehat{\beta }_{1}\). That is, a standard deviation change in these criteria had the greatest effect on predicted injury risk (Fig. 6).

Figure 6
figure 6

Injury prediction using logistic regression. Logistic model coefficients, 0 and β 1 (\(\widehat{\beta }_{0}\) and \(\widehat{\beta }_{1}\) for standardized values), are given for 18 injury criteria. Decreasing deviance, D, suggests a criteria logistic regression more closely approximates a perfectly predictive model. Criteria with deviance that significantly differed from the null model deviance are indicated by asterisks over their bar

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Multivariate machine learning and Support Vector Machine (SVM) classification provided an alternative approach to injury prediction. Of the 12 kinematic features used to train the SVM classifier, a minimum of three were required to produce a dichotomous hyperplane boundary between injury and non-injury (Fig. 7). Two of these kinematic features, inferior-superior and anterior-posterior translational acceleration, defined a plane in which the LOC and self-reported injuries were nearly unique. A few non-injury impacts were higher magnitude in this plane, but the addition of coronal rotational acceleration was sufficient to unambiguously classify the injuries. With only two injuries to train the classifier, this plane should in no way be viewed as describing an injury threshold boundary. Rather, this plane illustrates a different approach to binary injury prediction allowing for optimally solved directional weightings of acceleration components.

Figure 7
figure 7

Example injury classification using machine learning. The LOC and self-reported injuries were separable from non-injury data using a three-dimensional hyperplane defined by two translational acceleration quantities and one rotational acceleration quantity. With few injury data points, this plane should not be interpreted to represent injury tolerance—additional injury data will certainly reveal injury classification bounds defined with more dimensions

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Discussion

The objective of this study was to investigate whether direct measurement of head rotation improves mTBI prediction. Using an instrumented mouthguard, we reported the first direct six degree-of-freedom (6DOF) measurements of clinically diagnosed mTBI and assessed predictive deviance of several existing injury criteria using univariate logistic regression. Criteria that included rotation gave the lowest deviance, principal strain in the corpus callosum (6DOF), α peak (3DOF), HIP (6DOF), and GAMBIT (6DOF), lower than any translation-only criteria. While prior studies have included 2DOF head rotation estimates (inferior-superior axis excluded),8,19,72 these are not directly measured, but rather, determined empirically as a function of translational measurements by assuming rotation about a fixed point in the neck.72 In the current study, only four criteria significantly improved prediction over a null model without any criteria, and they all use full 3DOF rotation measurements. Brain strain has been attributed to head rotation,40,46 which is consistent with our observation that principal strain in the corpus callosum had the greatest predictive accuracy, followed by peak rotational acceleration. Brain pressure has been attributed to head translation40,46,80 and we observed maximum and minimum pressure to have some of the lowest predictive accuracies. FE criteria, rotational acceleration, and HIP have in common that they all have a physical basis in torque, power, and deformation. Given the small injury sample size, we did not attempt to determine absolute injury risk, or suggest any injury thresholds. That is, we did not use our regression parameters to propose criteria values associated with any specific likelihood of injury.

The criteria with the highest deviance were PRHIC, BrIC and the whole brain finite element (FE) values. PRHIC is a rotational kinematic criterion adapted from HIC that also assumes a power exponent of 2.5. However unlike the HIC exponent, the PRHIC exponent was not empirically determined since 6DOF injury data was not available at the time PRHIC was proposed,43 potentially explaining the higher deviance. BrIC was developed based on correlation with the FE outputs CSDM and peak strain. We found that CSDM and peak strain outputs of the KTH FE model had a similarly low predictive accuracy as BrIC. CSDM was originally developed using the SIMon FE model, but it was proposed as a model-independent measure of whole brain deformation75,76 and has been previously estimated using the KTH FE model.47 Although the KTH and SIMon models have been validated against the same datasets, their prediction of brain deformation may differ.40 The KTH FE model was used for all simulations in the present study and is expected to provide consistent relative responses across subjects.

Strain in the corpus callosum resulted in lower deviance than whole brain FE criteria but was still an imperfect injury predictor. However, the two injuries were the only impacts analyzed whose peak strain occurred in the corpus callosum. The injuries had large coronal rotation components that may have produced a wave down the falx that gave rise to stress where it meets the corpus callosum. These findings are consistent with the critical function of the corpus callosum to transmit information between cerebral hemispheres. Callosal damage disrupts this communication, affecting perception24 and causing traditional symptoms of mTBI such as disorientation, amnesia, and impaired visual judgment.77 Recently, diffusion tensor imaging found that disruption in the corpus callosum impaired performance after brain trauma, both in cognitive tasks and reaction time.4 The axonal fibers in the corpus callosum responsible for this interhemispheric communication are highly organized directionally left–right. Fiber orientation results in material property anisotropy3,22 but this was not modeled here, nor was the direction of the strain considered which certainly would have altered our results.27 FE is a promising tool for predicting injury but may need to be specific in terms of tissue orientations and anatomical structures that cause the symptoms of injury. A validated FE model that utilizes the 6DOF data is important to derive tissue-level responses that kinematics data alone could not provide otherwise.

Although 3DOF translation-only criteria had higher deviance than those that included rotation, rotational criteria predictions could still be improved. It is important to note that these criteria were developed in the absence of human 6DOF direct measurements of injury. New criteria may be possible with the availability of more 6DOF data that could improve injury prediction. In addition to evaluating the effect of rotation, 6DOF data allows for the traumatic effects of rotation and translation in different directions to be evaluated. Animal research has shown that injury susceptibility can vary substantially depending on rotational direction.20,26,46,74 Among the criteria we evaluated in this study, only PRHIC, BrIC, HIP, and the FE values differentiate among directions. These criteria, and their directional sensitivities, are physically based; PRHIC and HIP compute rotational power which varies in directions based on moment of inertia, while BrIC and FE vary in direction based on geometrical and material property asymmetries. It is indeed possible that refinement of the physics of these criteria will improve prediction when provided 6DOF measurements as input. However, the relationship between physical forces and cognitive symptoms is complex and can also be investigated from a data mining approach that learns directional sensitivity based on training data.29

We explored a new machine learning approach to injury prediction by training an SVM binary classifier on kinematic measurements. SVM classification has been used previously to detect injury through video,66 CT image features,65 MRI image features,10 and electroencephalography features.14 The machine learning classification algorithm presented here optimizes a combination of 12 kinematic measurements to best predict clinically diagnosed injury, agnostic of the underlying physics. This approach is clinically relevant as field decisions to triage the injured is a yes–no binary decision. The two injuries could be divided from the non-injury with a plane with three linearly weighted kinematic measurements. Given the small sample size of this study, this plane certainly does not suggest an injury tolerance. To define injury tolerance, SVM requires a larger sample of impacts that lie on the “boundary” between injury and non-injury (that is, SVM may not select certain injury impacts to define a classifier if they are obviously removed from the non-injury group, and vice versa). More injury data points will almost certainly require a higher dimensional hyperplane and possibly non-linear surface. Furthermore, temporal measures may be important as well since the brain is a dynamic system which may be more sensitive to pulses of certain durations. However, a statistical approach like this that factors in 6DOF spatiotemporal data independently may allow for new predictors to be developed that can more clearly distinguish injury. More 6DOF data will be required for such machine learning approaches to have more predictive value than (or with) physical approaches.

This study has several limitations to mention. The greatest limitation is small sample size of injury data making our findings only preliminary. For the injuries that were recorded, recent history of injury for both subjects could have reduced their tolerance to the injury that was measured.1,9,31 Unfortunately, this type of patient history is very common in football. Similarly, concussive symptoms may have been experienced but not reported for other subjects on impacts labeled as non-injury. Furthermore, the instrumented mouthguard used in this study has been evaluated for accuracy in a laboratory setting with an anthropomorphic test device that has a fixed jaw.13 While the design of the mouthguard is intended to fit tightly to the upper dentition, it is possible that mouthguard dislocation could occur leading to over- or under-estimation of acceleration signals that is beyond the bounds of the laboratory study. It is not possible to know with total certainty whether the injuries (or non-injury impacts) are direct measurement of skull accelerations, however, the signals were consistent with other experimental data from dummy head-mounted reference sensors. While the FE model used has been validated on cadaver data, it may not represent general in vivo properties or subject specific anatomy of those evaluated in this study. Only a subset of the recorded impacts were simulated in FE, including those with the highest level of acceleration. Finally, there was selection bias for the non-injury dataset given the time-intensive nature of video analysis; this dataset is enriched for injuries and therefore a subset of non-injury impacts was used in logistic regression to suggest injury probabilities.

Despite these limitations, this preliminary study of direct 6DOF measurements of mTBI suggests that rotational measurement does improve injury prediction using existing injury criteria. However, the predictive deviance of rotational measures was imperfect and may be improved by building/refining physical and/or statistical injury criteria. The importance of head translation and rotation in specific directions will not have consensus until more data is collected and tested on existing and new criteria.