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A Pre-computed Brain Response Atlas for Instantaneous Strain Estimation in Contact Sports


Finite element models of the human head play an important role in investigating the mechanisms of traumatic brain injury, including sports concussion. A critical limitation, however, is that they incur a substantial computational cost to simulate even a single impact. Therefore, current simulation schemes significantly hamper brain injury studies based on model-estimated tissue-level responses. In this study, we present a pre-computed brain response atlas (pcBRA) to substantially increase the simulation efficiency in estimating brain strains using isolated rotational acceleration impulses parameterized with four independent variables (peak magnitude and duration, and rotational axis azimuth and elevation angles) with values determined from on-field measurements. Using randomly generated testing datasets, the partially established pcBRA achieved a 100% success rate in interpolation based on element-wise differences in accumulated peak strain (\(\varepsilon^{p}\)) according to a “double-10%” criterion or average regional \(\varepsilon^{p}\) in generic regions and the corpus callosum. A similar performance was maintained in extrapolation. The pcBRA performance was further successfully validated against directly simulated responses from two independently measured typical real-world rotational profiles. The computational cost to estimate element-wise whole-brain or regional \(\varepsilon^{p}\) was 6 s and <0.01 s, respectively, vs. ~50 min directly simulating a 40 ms impulse. These findings suggest the pcBRA could substantially increase the throughput in impact simulation without significant loss of accuracy from the estimation itself and, thus, its potential to accelerate the exploration of the mechanisms of sports concussion in general. If successful, the pcBRA may also become a diagnostic adjunct in conjunction with sensors that measure head impact kinematics on the field to objectively monitor and identify tissue-level brain trauma in real-time for “return-to-play” decision-making on the sideline.

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This work was sponsored, in part, by the NIH Grant R21 NS078607 and the Dartmouth Hitchcock Foundation.


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Correspondence to Songbai Ji.

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Associate Editor Joel D. Stitzel oversaw the review of this article.

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Ji, S., Zhao, W. A Pre-computed Brain Response Atlas for Instantaneous Strain Estimation in Contact Sports. Ann Biomed Eng 43, 1877–1895 (2015).

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  • Traumatic brain injury
  • Sports concussion
  • Rotational acceleration
  • Pre-computation
  • Dartmouth Head Injury Model