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Development of a Second-Order System for Rapid Estimation of Maximum Brain Strain

  • State-of-the-Art Modeling and Simulation of the Brain's Response to Mechanical Loads
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Abstract

Diffuse brain injuries are assessed with deformation-based criteria that utilize metrics based on rotational head kinematics to estimate brain injury severity. Although numerous metrics have been proposed, many are based on empirically-derived models that use peak kinematics, which often limit their applicability to a narrow range of head impact conditions. However, over a broad range of impact conditions, brain deformation response to rotational head motion behaves similarly to a second-order mechanical system, which utilizes the full kinematic time history of a head impact. This study describes a new brain injury metric called Diffuse Axonal Multi-Axis General Evaluation (DAMAGE). DAMAGE is based on the equations of motion of a three-degree-of-freedom, coupled 2nd-order system, and predicts maximum brain strain using the directionally dependent angular acceleration time-histories from a head impact. Parameters for the effective mass, stiffness, and damping were determined using simplified rotational pulses which were applied multiaxially to a 50th percentile adult human male finite element model. DAMAGE was then validated with a separate database of 1747 head impacts including helmet, crash, and sled tests and human volunteer responses. Relative to existing rotational brain injury metrics that were evaluated in this study, DAMAGE was found to be the best predictor of maximum brain strain.

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References

  1. Alshareef, A., J. S. Giudice, J. Forman, R. S. Salzar, and M. B. Panzer. A novel method for quantifying human in situ whole brain deformation under rotational loading using sonomicrometry. J. Neurotrauma 35(5):780–789, 2018.

    Article  Google Scholar 

  2. Antona-Makoshi, J., K. Mikami, M. Lindkvist, J. Davidsson, and S. Schick. Accident analysis to support the development of strategies for the prevention of brain injuries in car crashes. Accid. Anal. Prev. 117:98–105, 2018.

    Article  Google Scholar 

  3. Bandak, F. A. On the mechanics of impact neurotrauma: a review and critical synthesis. J. Neurotrauma 12:635–649, 1995.

    Article  CAS  Google Scholar 

  4. Cullen, D. K., C. M. Simon, and M. C. LaPlaca. Strain rate-dependent induction of reactive astrogliosis and cell death in three-dimensional neuronal–astrocytic co-cultures. Brain Res. 1158:103–115, 2007.

    Article  CAS  Google Scholar 

  5. Deck, C., and R. Willinger. The current state of the human head finite element modelling. Int. J. Veh. Saf. 4:85–112, 2009.

    Article  Google Scholar 

  6. Elkin, B. S., L. F. Gabler, M. B. Panzer, and G. P. Siegmund. Brain tissue strains vary with head impact location: a possible explanation for increased concussion risk in struck versus striking football players. Clin. Biomech. 2018. https://doi.org/10.1016/j.clinbiomech.2018.03.021.

    Article  Google Scholar 

  7. Gabler, L. F., J. R. Crandall, and M. B. Panzer. Assessment of kinematic brain injury metrics for predicting strain responses in diverse automotive impact conditions. Ann. Biomed. Eng. 2016. https://doi.org/10.1007/s10439-016-1697-0.

    Article  PubMed  Google Scholar 

  8. Gabler, L. F., J. R. Crandall, M. B. Panzer, N. Praxl, P. Wernicke. Development of Improved Brain Injury Predictors for Diverse Impacts. In: 61st Stapp Car Crash Conference 2017.

  9. Gabler, L. F., J. R. Crandall, and M. B. Panzer. Development of a metric for predicting brain strain responses using head kinematics. Ann. Biomed. Eng. 46(7):972–985, 2018.

    Article  Google Scholar 

  10. Gabler, L. F., H. Joodaki, J. R. Crandall, and M. B. Panzer. Development of a single-degree-of-freedom mechanical model for predicting strain-based brain injury responses. J. Biomech. Eng. 140:031002, 2018.

    Article  Google Scholar 

  11. Gadd, C. W. Use of a weighted-impulse criterion for estimating injury hazard. SAE Technical Paper, 1966. http://papers.sae.org/660793/.

  12. Gennarelli, T. A., L. E. Thibault, and D. I. Graham. Diffuse axonal injury: an important form of traumatic brain damage. Neuroscientist 4:202–215, 1998.

    Article  Google Scholar 

  13. Goldsmith, W. Biomechanics of Head Injury. Englewood Cliffs: Prentice-Hall, pp. 585–634, 1972.

    Google Scholar 

  14. Harmon, K. G., J. A. Drezner, M. Gammons, K. M. Guskiewicz, M. Halstead, S. A. Herring, J. S. Kutcher, A. Pana, M. Putukian, and W. O. Roberts. American Medical Society for Sports Medicine position statement: concussion in sport. Br. J. Sports Med. 47:15–26, 2013.

    Article  Google Scholar 

  15. Hernandez, F., L. C. Wu, M. C. Yip, K. Laksari, A. R. Hoffman, J. R. Lopez, G. A. Grant, S. Kleiven, and D. B. Camarillo. Six degree-of-freedom measurements of human mild traumatic brain injury. Ann. Biomed. Eng. 43:1918–1934, 2015.

    Article  Google Scholar 

  16. Holbourn, A. H. S. Mechanics of head injuries. Lancet 242:438–441, 1943.

    Article  Google Scholar 

  17. J211/1: Instrumentation for Impact Test—Part 1—Electronic Instrumentation—SAE International. http://standards.sae.org/j211/1_201403/.

  18. Kim, T., J. Shin, X. Ye, J. Crandall, C. Knospe, and J. Funk. Evaluation of methods for the development of representative responses and corridors from biomechanical data using mechanical models. Int. J. Crashworthiness 18:633–646, 2013.

    Article  Google Scholar 

  19. Kimpara, H., and M. Iwamoto. Mild traumatic brain injury predictors based on angular accelerations during impacts. Ann. Biomed. Eng. 40:114–126, 2012.

    Article  Google Scholar 

  20. King, A. I., K. H. Yang, L. Zhang, W. Hardy, and D. C. Viano. Is head injury caused by linear or angular acceleration., 2003. http://snell-helmets.org/docs/articles/hic/King_IRCOBI_2003.pdf.

  21. Kleiven, S. Predictors for traumatic brain injuries evaluated through accident reconstructions. Stapp Car Crash J 51:81–114, 2007.

    PubMed  Google Scholar 

  22. Laksari, K., M. Kurt, H. Babaee, S. Kleiven, and D. Camarillo. Mechanistic insights into human brain impact dynamics through modal analysis. Phys. Rev. Lett. 120:138101, 2018.

    Article  CAS  Google Scholar 

  23. Langlois, J. A., W. Rutland-Brown, and M. M. Wald. The epidemiology and impact of traumatic brain injury: a brief overview. J. Head Trauma Rehabil. 21:375–378, 2006.

    Article  Google Scholar 

  24. Mao, H., L. Zhang, B. Jiang, V. V. Genthikatti, X. Jin, F. Zhu, R. Makwana, A. Gill, G. Jandir, A. Singh, et al. Development of a finite element human head model partially validated with thirty five experimental cases. J. Biomech. Eng. 135:111002, 2013.

    Article  Google Scholar 

  25. Newman, J. A., N. Shewchenko, and E. Welbourne. A proposed new biomechanical head injury assessment function—the maximum power index. Stapp Car Crash J. 44:215–247, 2000.

    CAS  PubMed  Google Scholar 

  26. Panzer, M. B., B. S. Myers, B. P. Capehart, and C. R. Bass. Development of a finite element model for blast brain injury and the effects of CSF cavitation. Ann. Biomed. Eng. 40:1530–1544, 2012.

    Article  Google Scholar 

  27. Rao, S. S., and F. F. Yap. Mechanical Vibrations. New York: Addison-Wesley, 1995.

    Google Scholar 

  28. Stalnaker, R. L., J. L. Fogle, and J. H. McElhaney. Driving point impedance characteristics of the head. J. Biomech. 4:127–139, 1971.

    Article  CAS  Google Scholar 

  29. Sullivan, S., S. A. Eucker, D. Gabrieli, C. Bradfield, B. Coats, M. R. Maltese, J. Lee, C. Smith, and S. S. Margulies. White matter tract-oriented deformation predicts traumatic axonal brain injury and reveals rotational direction-specific vulnerabilities. Biomech. Model. Mechanobiol. 14:877–896, 2015.

    Article  Google Scholar 

  30. Takahashi, Y., and T. Yanaoka. A Study of Injury Criteria for Brain Injuries in Traffic Accidents, 2017.

  31. Takhounts, E. G., M. J. Craig, K. Moorhouse, J. McFadden, and V. Hasija. Development of brain injury criteria (Br IC). Stapp Car Crash J. 57:243–266, 2013.

    PubMed  Google Scholar 

  32. Takhounts, E. G., V. Hasija, S. A. Ridella, S. Rowson, and S. M. Duma. Kinematic rotational brain injury criterion (BRIC), 2011. http://www-nrd.nhtsa.dot.gov/Pdf/esv/esv22/22ESV-000263.pdf.

  33. Taylor, C. A. Traumatic brain injury-related emergency department visits, hospitalizations, and deaths—United States, 2007 and 2013. MMWR Surveill. Summ. 66:1–16, 2017.

    Article  Google Scholar 

  34. Versace, J. A Review of the Severity Index. Warrendale: SAE International, 1971.

    Google Scholar 

  35. Willinger, R., L. Taleb, and C. M. Kopp. Modal and temporal analysis of head mathematical models. J. Neurotrauma 12:743–754, 1995.

    Article  CAS  Google Scholar 

  36. Yanaoka, T., Y. Dokko, and Y. Takahashi. Investigation on an Injury Criterion Related to Traumatic Brain Injury Primarily Induced by Head Rotation. SAE Technical Paper, 2015. http://papers.sae.org/2015-01-1439/.

  37. Zhao, W., Y. Cai, Z. Li, and S. Ji. Injury prediction and vulnerability assessment using strain and susceptibility measures of the deep white matter. Biomech. Model. Mechanobiol. 16(5):1709–1727, 2017.

    Article  Google Scholar 

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Correspondence to Matthew B. Panzer.

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Associate Editor Stefan M. Duma oversaw the review of this article.

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Gabler, L.F., Crandall, J.R. & Panzer, M.B. Development of a Second-Order System for Rapid Estimation of Maximum Brain Strain. Ann Biomed Eng 47, 1971–1981 (2019). https://doi.org/10.1007/s10439-018-02179-9

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  • DOI: https://doi.org/10.1007/s10439-018-02179-9

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