Low-rank representation of head impact kinematics: A data-driven emulator

Head motion induced by impacts has been deemed as one of the most important measures in brain injury prediction, given that the majority of brain injury metrics use head kinematics as input. Recently, researchers have focused on using fast approaches, such as machine learning, to approximate brain deformation in real-time for early brain injury diagnosis. However, those requires large number of kinematic measurements, and therefore data augmentation is required given the limited on-field measured data available. In this study we present a principal component analysis-based method that emulates an empirical low-rank substitution for head impact kinematics, while requiring low computational cost. In characterizing our existing data set of 537 head impacts, consisting of 6 degrees of freedom measurements, we found that only a few modes, e.g. 15 in the case of angular velocity, is sufficient for accurate reconstruction of the entire data set. Furthermore, these modes are predominantly low frequency since over 70% to 90% of the angular velocity response can be captured by modes that have frequencies under 40Hz. We compared our proposed method against existing impact parametrization methods and showed significantly better performance in injury prediction using a range of kinematic-based metrics -- such as head injury criterion and rotational injury criterion (RIC) -- and brain tissue deformation-metrics -- such as brain angle metric, maximum principal strain (MPS) and axonal fiber strains (FS). In all cases, our approach reproduced injury metrics similar to the ground truth measurements with no significant difference, whereas the existing methods obtained significantly different (p<0.01) values as well as poor injury classification sensitivity and specificity. This emulator will enable us to provide the necessary data augmentation to build a head impact kinematic data set of any size.