This study introduces a new injury metric, the combined probability of concussion, which computes the overall risk of concussion based on the peak linear and rotational accelerations experienced by the head during impact. The combined probability of concussion is unique in that it determines the likelihood of sustaining a concussion for a given impact, regardless of whether the athlete would report the injury or not. This was accomplished by adjusting the HITS dataset to account for an estimated underreporting rate during development of the risk curve. To side with conservatism, a greater underreporting rate was used in this analysis than previous independent linear and rotational acceleration risk curves that considered underreporting.51
Linear and rotational acceleration are considered because they both likely contribute to concussion risk and are thought to be associated with different injury mechanisms.30
Linear acceleration of the head is associated with a transient intracranial pressure gradient, while rotational acceleration of the head is associated with a strain response. Experiments designed to induce brain injury in animals have produced injury through isolated linear acceleration and isolated rotational acceleration events. Furthermore, Hardy et al
measured the pressure and strain response of the human cadaver head to impact. Impacts similar in severity to those experienced in football were modeled, and kinematic parameters were related to the pressure and strain response of the brain. Peak pressure increased with increasing linear acceleration of the head. Peak strains were less than 9% and brain motion correlated with rotational speed. For these reasons, both linear and rotational acceleration are considered in the combined probability of concussion.
Data from two different methodologies used to investigate the biomechanics of concussions were analyzed in this study. The HITS dataset was comprised of data collected from instrumented football players, while the NFL dataset was generated through laboratory reconstructions using crash test dummies. Even though data were generated from two different methodologies, the peak linear and rotational accelerations associated with concussion are similar. The primary difference between the two datasets is the sub-concussive subset. The HIT System allowed for the recording of every head impact a player experienced during games and practices while he was instrumented. As a result, the HITS dataset includes a vast number of impacts that did not result in concussion, and is more representative of the total head impact exposure that football players experience.17
The NFL dataset was generated from laboratory reconstructions that made it impractical to consider the thousands of head impacts experienced by NFL players, and instead only modeled some of the more severe impacts that could be characterized from video analysis.48
Both datasets are valuable tools for evaluating injury predictors, but it is important to understand these differences between the HITS and NFL data.
Concussive impacts are well-characterized by peak biomechanical measures, and as acceleration magnitude increases, injury risk also increases.2
For this reason, all predictors were very sensitive to identifying concussive impacts within datasets. However, because the datasets had varying distributions of sub-concussive impacts, the specificity of the predictors varied greatly (Table ). For true positive rates of 75 and 90%, the small number of low magnitude sub-concussive impacts in the NFL dataset resulted in much greater false positive rates than the HITS datasets. In contrast, the high number of low-magnitude sub-concussive impacts in the HITS dataset resulted in very low false positive rates. As the HITS dataset was parsed into the top 50% and top 25% of impacts, false positive rates increased. Given the vast number of impacts in the HITS datasets, the number of false positives was greater than the number of concussions. This lack of specificity can be partially attributed the underreporting of concussion. It is possible that some of the impacts labeled as sub-concussive impacts in the HITS dataset and the NFL dataset resulted in a concussion that was not reported, even after the HITS dataset was adjusted to account for underreporting. While concussive impacts could be characterized using these biomechanical measures, other factors such as impact location, impact duration, muscle factors, and genetic predispositions likely affect concussion risk.22
For all datasets, the combined probability of concussion produced the greatest AUC, suggesting it was the best predictor of concussion of the parameters investigated. However, linear acceleration was not significantly different than the combined probability of concussion, suggesting it can predict concussion as well as the combined probability of concussion in the datasets analyzed in this study. With the exception of the NFL data, where there were no differences among parameters, rotational acceleration was a significantly worse predictor of concussion than the combined probability of concussion and linear acceleration. This is due to most head impacts in football being inherently similar to one another, in that they are linearly driven. Rotational acceleration of the head is a function of the linear acceleration and direction of force acting on the head. The relationships between linear acceleration and rotational acceleration are similar for impacts to the front, side, and back of the helmet.53
However, impacts to the top of the helmet result in a much different relationship, where for a given linear acceleration, rotational accelerations are much lower.53
In these datasets, concussive impacts to the top of the helmet resulted in high linear accelerations and relatively low rotational accelerations that reduced the predictive capability of peak rotational acceleration. The combined probability of concussion method accounted for this because it considered both linear and rotational accelerations for each impact.
The acceleration response of real-world head impacts consists of linear and rotational acceleration components. Depending on the impact location and direction of force, the respective contribution of linear and rotational acceleration will vary. For head impacts in football, the profile and duration of the head acceleration response are similar, and rotational acceleration is correlated to linear acceleration.53
As new helmet designs begin to incorporate mechanisms to manage rotational acceleration independently of linear acceleration, this relationship will likely vary. The combined probability of concussion will be a useful tool in evaluating such designs. While only football head impact datasets were analyzed in this study, the combined probability of concussion has applications beyond football, considering impacts are similar in impact duration. The combined probability of concussion could be a valuable method to assess brain injury risk in a laboratory setting for evaluating product safety, including head protection and automobile restraint design, considering that the impact characteristics are similar to those analyzed here. With an improved ability to assess concussion risk, engineering analyses can be used to evaluate and influence product design to reduce injury incidence.54
This study has several limitations. First, ROC analysis is dependent on the dataset that is being characterized. A specific type of impact mode (football helmet impacts) was analyzed in this study using 2 different datasets. Neither dataset included impacts that were predominantly comprised of rotational acceleration, as this impact mode is very rare in football. Further work is needed to assess to the predictive capability of the combined probability of concussion for impacts that are predominantly comprised of rotational acceleration. Second, the underreporting of concussion may have affected the ROC analysis, even though the HITS dataset was adjusted to account for underreporting rates. Unreported concussions in the HITS and NFL datasets would result in conservative estimates of specificity, where the true value of the false positive rates would be lower. While these datasets may be limited by the presence of unreported concussions, these are currently the best datasets that are available for analyzing the biomechanics of concussion in humans. Third, the combined probability of concussion only considers peak linear and rotational acceleration. While risk curves are commonly used to relate mechanical stimuli to injury, other factors can affect injury risk.7
Impact location, impact duration, muscle factors, and genetic predispositions likely affect concussion risk. When using the combined probability of concussion to evaluate injury risk, one should be aware of impact duration and these other factors that may affect risk. With that said, peak linear and rotational acceleration characterize concussion well and are good predictors of injury.