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Traumatic brain injury (TBI) is a complex injury that is hard to predict and diagnose, with many studies focused on associating head kinematics to brain injury risk. Recently, there has been a push towards using computationally expensive finite element (FE) models of the brain to create tissue deformation metrics of brain injury. Here, we develop a new brain injury metric, the Brain Angle Metric (BAM), based on the dynamics of a 3 degree-of-freedom lumped parameter brain model. The brain model is built based on the measured natural frequencies of a FE brain model simulated with live human impact data. We show it can be used to rapidly estimate peak brain strains experienced during head rotational accelerations. On our dataset, the simplified model highly correlates with peak principal FE strain (R 2 =0.80). Further, coronal and axial model displacement correlated with fiber-oriented peak strain in the corpus callosum (R 2 =0.77). Our proposed injury metric BAM uses the maximum angle predicted by our brain model, and is compared against a number of existing rotational and translational kinematic injury metrics on a dataset of head kinematics from 27 clinically diagnosed injuries and 887 non-injuries. We found that BAM performed comparably to peak angular acceleration, linear acceleration, and angular velocity in classifying injury and non-injury events. Metrics which separated time traces into their directional components had improved model deviance to those which combined components into a single time trace magnitude. Our brain model can be used in future work both as a computationally efficient alternative to FE models and for classifying injuries over a wide range of loading conditions. Key words:Brain injury, injury criterion, injury prediction, concussion 159.32, 131.53, and 132.02 respectively. Further, metrics such as HIC and SI which analyze acceleration magnitudes performed with lower sensitivity to those which treated each direction separately. Similarly, the VTCP, which takes into account peak linear and angular acceleration magnitude, had lower model deviance and higher AUCPR and AUCROC than metrics which treated each anatomical direction separately. Peak linear acceleration ( ⃗) had lower deviance, AUCPR, and AUCROC to peak angular kinematics and BAM but still outperformed many other metrics. While many previous studies suggest rotation is a primary cause of brain injury 16,17,56 , the results shown here indicate that linear acceleration still has predictive value in classifying brain injuries. This could be because in our dataset, with the majority of injuries taken from laboratory reconstruction data, the linear and angular acceleration values may be coupled more so than in-vivo data.However, single variate injury criteria, based on linear acceleration, had extremely low sensitivity in our dataset. We see that both HIC15 and SI predict only a single event with >50% risk of injury on our dataset due to a few non-injury events with high HIC15 and SI values. Surprisingly, many existing metrics had hig...

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Computer modeling and simulation are the cornerstones of product design and development in the automotive industry. Computer-aided engineering tools have improved to the extent that virtual testing may lead to significant reduction in prototype building and testing of vehicle designs. In order to make this a reality, we need to assess our confidence in the predictive capabilities of simulation models. As a first step in this direction, this paper deals with developing a metric to compare time histories that are outputs of simulation models to time histories from experimental tests with emphasis on vehicle safety applications. We focus on quantifying discrepancy between time histories as the latter constitute the predominant form of responses of interest in vehicle safety considerations. First we evaluate popular measures used to quantify discrepancy between time histories in fields such as statistics, computational mechanics, signal processing, and data mining. Then we propose a structured combination of some of these measures and define a comprehensive metric that encapsulates the important aspects of time history comparison. The new metric classifies error components associated with three physically meaningful characteristics (phase, magnitude and topology), and utilizes norms, cross-correlation measures and algorithms such as dynamic time warping to quantify discrepancies. Two case studies demonstrate that the proposed metric seems to be more consistent than existing metrics. It is also shown how the metric can be used in conjunction with ratings from subject matter experts to build regression-based val- * Corresponding author, Phone/Fax: (734) 615-8991/647-8403 idation models.