Head Injury Research: Computer Models of Head Impact

  • Albert I. King


The purpose of modeling head impact is to try to understand the effect of a blow to the brain. Thus, it is essential that the brain be modeled in as much detail as possible. Then, of course, it will be necessary to assess injury to the brain by computing its response. Based on what we know about brain injury, we hypothesize that strain in the axons is a likely cause of diffuse axonal injury (DAI) and intracranial pressure wave propagation can be a second parameter of interest. Because of the complexity of the geometry of the head and brain, the many different types of tissues involved, and the lack of data on their material properties under high strain rate conditions, the modeling task is far from being simple. In the pre-finite element era, simplifying assumptions were made to facilitate the formulation of equations that describe the impact event. For example, the first known model of head impact was proposed by Anzelius (1943) who assumed the head to be a rigid sphere and the brain to be a liquid. He solved the governing equations in closed form, and his model predicted coup and contrecoup pressures at the site of impact and at a site diametrically opposite to the site of impact, respectively.


  1. J.M. Abel, T.A. Gennarelli, H. Segawa, Incidence and severity of cerebral concussion in the rhesus monkey following sagittal plane angular acceleration, in 22nd Stapp Car Crash Conference, SAE Paper No. 780886, Ann Arbor, MI, 1978Google Scholar
  2. A.S. Al-Bsharat, W.N. Hardy, K.H. Yang, T.B. Khalil, S. Tashman, and A.I. King, Brain/skull relative displacement magnitude due to blunt head impact: new experimental data and model, in 43rd Stapp Car Crash Conference, SAE Paper No. 99SC22, San Diego, CA, 1999Google Scholar
  3. D. Allsop, C. Warner, M. Wille, D. Schneider, A. Nahum, Facial impact response—A comparison of the hybrid 3 dummy and human cadaver, in 32nd Stapp Car Crash Conference, SAE Paper No. 881719, Atlanta, GA, 1988Google Scholar
  4. A. Anzelius, The effect of an impact on a spherical liquid mass. Acta Pathol. Microbiol. Scand. 48(Suppl), 153–159 (1943)Google Scholar
  5. K.B. Arbogast, S.S. Margulies, Regional differences in mechanical properties of the porcine central nervous system, in 41st Stapp Car Crash Conference, SAE Paper No. 973336, Lake Buena Vista, FL, 1997Google Scholar
  6. A.E. Engin, The axisymmetric response of a fluid-filled spherical shell to a local radial impulse—a model for head injury. J. Biomech. 2, 325–341 (1969)CrossRefGoogle Scholar
  7. E. Giesen, T. Van Eijden, The three-dimensional cancellous bone architecture of the human mandibular condyle. J. Dent. Res. 79, 957–963 (2000)CrossRefGoogle Scholar
  8. E. Gurdjian, H. Lissner, J. Webster, F. Latimer, B. Haddad, Studies on experimental concussion: relation of physiologic effect to time duration of intracranial pressure increase at impact. Neurology 4, 674–681 (1954)CrossRefGoogle Scholar
  9. C. Hardy, P. Marcal, Elastic analysis of a skull, Technical Report No. 8, Office of Naval Research, Contract No. N00014-67-A-0191-0007, Division of Engineering, Brown University, 1971Google Scholar
  10. W.N. Hardy, C.D. Foster, M.J. Mason, K.H. Yang, A.I. King, S. Tashman, Investigation of head injury mechanisms using neutral density technology and high-speed biplanar X-ray. Stapp Car Crash J. 45, 337–368 (2001)Google Scholar
  11. R.R. Hosey, Y.K. Liu, A homeomorphic finite element model of the human head and neck, in Finite Elements in Biomechanics, ed. by R.H. Gallagher, P. Simon, T. Johbnson, J. Gross (Wiley, New York), pp. 379–401 (1982)Google Scholar
  12. T. Igarashi, M.B. Potts, L.J. Noble-Haeusslein, Injury severity determines Purkinje cell loss and microglial activation in the cerebellum after cortical contusion injury. Exp. Neurol. 203, 258–268 (2007)CrossRefGoogle Scholar
  13. V. Kenner, W. Goldsmith, Dynamic loading of a fluid-filled spherical shell. Int. J. Mech. Sci. 14, 557–568 (1972)CrossRefGoogle Scholar
  14. V. Kenner, W. Goldsmith, Impact on a simple physical model of the head. J. Biomech. 6, 1–11 (1973)CrossRefGoogle Scholar
  15. T.B. Khalil, R.P. Hubbard, Parametric study of head response by finite element modeling. J. Biomech. 10, 119–132 (1977)CrossRefGoogle Scholar
  16. T.B. Khalil, W. Goldsmith, J. Sackman, Impact on a model head-helmet system. Int. J. Mech. Sci. 16, 609–625 (1974)CrossRefGoogle Scholar
  17. A.I. King, C.C. Chou, Mathematical modelling, simulation and experimental testing of biomechanical system crash response. J. Biomech. 9, 301–317 (1976)CrossRefGoogle Scholar
  18. H. Mao, Computational analysis of in vivo brain trauma. Ph.D. Dissertation, Wayne State University, Detroit, MI (2009)Google Scholar
  19. H. Mao, L. Zhang, K.H. Yang, A.I. King, Application of a finite element model of the brain to study traumatic brain injury mechanisms in the rat. Stapp Car Crash J. 50, 583–600 (2006)Google Scholar
  20. H. Mao, X. Jin, L. Zhang, K.H. Yang, T. Igarashi, L.J. Noble-Haeusslein, A.I. King, Finite element analysis of controlled cortical impact-induced cell loss. J. Neurotrauma 27, 877–888 (2010)CrossRefGoogle Scholar
  21. D. Meaney, D. Smith, D. Ross, T. Gennarelli, Diffuse axonal injury in the miniature pig: biomechanical development and injury threshold, in Crashworthiness Occupant Protection, vol. 25 (ASME Applied Mechanics Division/Bioengineering Division, New York, NY, 1993), pp. 169–175Google Scholar
  22. K. Mendis, Finite element modeling of the brain to establish diffuse axonal injury criteria, PhD Dissertation, Ohio State University, Columbus, OH, 1992Google Scholar
  23. R. Miller, S. Margulies, M. Leoni, M. Nonaka, X. Chen, D. Smith, D. Meaney, Finite element modeling approaches for predicting injury in an experimental model of severe diffuse axonal injury, in 42nd Stapp Car Crash Conference, SAE Paper No. 983154, Tempe, AZ, 1998Google Scholar
  24. K.L. Monson, N. Barbaro, W. Goldsmith, G. Manley, Static and dynamic mechanical and failure properties of human cerebral vessels, in Crashworthiness, Occupant Protection and Biomechanics in Transportation Systems, ed. by H.F. Mahmood, S.D. Barbat, M.R. Baccouche, vol 49 (American Society of Mechanical Engineers, New York), pp. 255–266 (2000)Google Scholar
  25. A.M. Nahum, R. Smith, C.C. Ward, Intracranial pressure dynamics during head impact, in 21th Stapp Car Crash Conference, SAE Paper No. 770922, New Orleans, LA, 1977Google Scholar
  26. G.W. Nyquist, J.M. Cavanaugh, S.J. Goldberg, A.I. King, Facial impact tolerance and response, in 30th Stapp Car Crash Conference, SAE Paper No. 861896 (San Diego, CA, 1986)Google Scholar
  27. G. Paxinos, C. Watson, The Rat Brain in Stereotactic Coordinates (Elsevier Academic Press, New York, 2005)Google Scholar
  28. D.T. Ross, D.F. Meaney, M.K. Sabol, D.H. Smith, T.A. Gennarelli, Distribution of forebrain diffuse axonal injury following inertial closed head injury in miniature swine. Exp. Neurol. 126, 291–298 (1994)CrossRefGoogle Scholar
  29. J.S. Ruan, Impact biomechanics of head injury by mathematical modeling. PhD Dissertation, Wayne State University, Detroit, Michigan, 1994Google Scholar
  30. J. Ruan, T. Khalil, A. King, Human head dynamic response to side impact by finite element modeling. J. Biomech. Eng. 113, 276–283 (1991)CrossRefGoogle Scholar
  31. J. Ruan, T. Khalil, A. King, Finite element modeling of direct head impact, in 37th Stapp Car Crash Conference. SAE Paper No. 933114, San Antonio, TX, 1993Google Scholar
  32. J. Ruan, T. Khalil, A.I. King, Dynamic response of the human head to impact by three-dimensional finite element analysis. J. Biomech. Eng. 116, 44–50 (1994)CrossRefGoogle Scholar
  33. D.I. Shreiber, A.C. Bain, D.F. Meaney, In vivo thresholds for mechanical injury to the blood–brain barrier, in 41st Stapp Car Crash Conference, SAE Paper No. 973335, Lake Buena Vista, FL, 1997Google Scholar
  34. L.Z. Shuck, S.H. Advani, A mathematical model for the determination of viscoelastic behavior of brain in vivo—I oscillatory response. J. Biomech. 5, 431–446 (1972)CrossRefGoogle Scholar
  35. T.A. Shugar, M.G. Katona, Development of finite element head injury model. J .Eng. Mech. Div. 101, 223–239 (1975)Google Scholar
  36. X. Trosseille, C. Tarriere, F. Lavaste, F. Guillon, A. Domont, Development of a FEM of the human head according to a specific test protocol, in 36th Stapp Car Crash Conference, SAE Paper No. 922527, Seattle, WA, 1992Google Scholar
  37. F. Turquier, H. Kang, X. Trosseille, R. Willinger, F. Lavaste, C. Tarriere, A. Domont, Validation study of a 3D finite element head model against experimental data, in 40th Stapp Car Crash Conference, SAE Paper No. 962431, Albuquerque, NM, 1996Google Scholar
  38. C.C. Ward, R.B. Thompson, The development of a detailed finite element brain model, in 19th Stapp Car Crash Conference, SAE Paper No. 751163, San Diego, CA, 1975Google Scholar
  39. C. Ward, M. Chan, A. Nahum, Intracranial pressure–a brain injury criterion, in 24th Stapp Car Crash Conference, SAE Paper No. 801304, Troy, MI, 1980Google Scholar
  40. H. Yamada, F.G. Evans, Strength of biological materials (Williams and Wilkins, Baltimore, 1970)Google Scholar
  41. L. Zhang, K.H. Yang, R. Dwarampudi, K. Omori, T. Li, K. Chang, W.N. Hardy, T.B. Khalil, A.I. King, Recent advances in brain injury research: a new human head model development and validation. Stapp Car Crash J. 45, 369–394 (2001)Google Scholar
  42. L. Zhang, J. Bae, W.N. Hardy, K.L. Monson, G.T. Manley, W. Goldsmith, K.H. Yang, A.I. King, Computational study of the contribution of the vasculature on the dynamic response of the brain. Stapp Car Crash J. 46, 145–164 (2002)Google Scholar
  43. C. Zhou, T.B. Khalil, A.I. King, Shear stress distribution in the porcine brain due to rotational impact, in 38th Stapp Car Crash Conference, SAE Paper No. 942314, Ft. Lauderdale, FL, 1994Google Scholar
  44. C. Zhou, Finite element modeling of impact response of an inhomogeneous brain. Ph.D. Dissertation, Wayne State University, Detroit, MI, 1995Google Scholar
  45. C. Zhou, A.I. King, T.B. Khalil, A new model comparing impact responses of the homogeneous and inhomogeneous human brain, in 39th Stapp Car Crash Conference, SAE Paper No. 952714, San Diego, CA, 1995Google Scholar

Copyright information

© Springer International Publishing AG 2018

Authors and Affiliations

  • Albert I. King
    • 1
  1. 1.Department of Biomedical EngineeringWayne State UniversityDetroitUSA

Personalised recommendations