Biomechanics and Modeling in Mechanobiology

, Volume 12, Issue 1, pp 137–150 | Cite as

Multi-scale mechanics of traumatic brain injury: predicting axonal strains from head loads

  • R. J. H. Cloots
  • J. A. W. van Dommelen
  • S. Kleiven
  • M. G. D. Geers
Open Access
Original Paper


The length scales involved in the development of diffuse axonal injury typically range from the head level (i.e., mechanical loading) to the cellular level. The parts of the brain that are vulnerable to this type of injury are mainly the brainstem and the corpus callosum, which are regions with highly anisotropically oriented axons. Within these parts, discrete axonal injuries occur mainly where the axons have to deviate from their main course due to the presence of an inclusion. The aim of this study is to predict axonal strains as a result of a mechanical load at the macroscopic head level. For this, a multi-scale finite element approach is adopted, in which a macro-level head model and a micro-level critical volume element are coupled. The results show that the axonal strains cannot be trivially correlated to the tissue strain without taking into account the axonal orientations, which indicates that the heterogeneities at the cellular level play an important role in brain injury and reliable predictions thereof. In addition to the multi-scale approach, it is shown that a novel anisotropic equivalent strain measure can be used to assess these micro-scale effects from head-level simulations only.


Traumatic brain injury TBI Diffuse axonal injury DAI Injury criteria Head model Finite element method Multi-scale 


Open Access

This article is distributed under the terms of the Creative Commons Attribution License which permits any use, distribution, and reproduction in any medium, provided the original author(s) and the source are credited.


  1. Abaqus: (2010) Abaqus 6.10 manual. Simulia, ProvidenceGoogle Scholar
  2. Alberts B, Bray D, Lewis J, Raff M, Roberts K, Watson JD (1994) Molecular biology of the cell, 3rd edn. Garland Publishing, New YorkGoogle Scholar
  3. Arbogast KB, Margulies SS (1998) Material characterization of the brainstem from oscillatory shear tests. J Biomech 31: 801–807CrossRefGoogle Scholar
  4. Arbogast KB, Margulies SS (1999) A fiber-reinforced composite model of the viscoelastic behavior of the brainstem in shear. J Biomech 32: 865–870CrossRefGoogle Scholar
  5. Arbogast KB, Meaney DF, Thibault LE (1995) Biomechanical characterization of the constitutive relationship for the brainstem. In: Proceedings of the 39th Stapp car crash conference SAE, vol 952716, pp 153–159Google Scholar
  6. Bain AC, Meaney DF (2000) Tissue-level thresholds for axonal damage in an experimental model of central nervous system white matter injury. J Biomech Eng 122: 615–622CrossRefGoogle Scholar
  7. Bain AC, Raghupathi R, Meaney DF (2001) Dynamic stretch correlates to both morphological abnormalities and electrophysiological impairment in a model of traumatical axonal injury. J Neurotrauma 18: 499–511CrossRefGoogle Scholar
  8. Cater H, Sundstrom L, Morrison III B (2006) Temporal development of hippocampal cell death is dependent on tissue strain but not strain rate. J Biomech 39: 2810–2818CrossRefGoogle Scholar
  9. Chatelin S, Deck C, Renard F, Kremer S, Heinrich C, Armspach JP, Willinger R (2011) Computation of axonal elongation in head trauma finite element simulation. J Mech Behav Biomed 4: 1905–1919CrossRefGoogle Scholar
  10. Chen Y, Ostoja-Starzewski M (2010) Mri-based finite element modeling of head trauma: spherically focusing shear waves. Acta Mech 213: 155–167zbMATHCrossRefGoogle Scholar
  11. Cloots RJH, Nyberg T, Kleiven S, van Dommelen JAW, Geers MGD (2011) Micromechanics of diffuse axonal injury: influence of axonal orientation and anisotropy. Biomech Model Mechanobiol 10: 413–422CrossRefGoogle Scholar
  12. Cloots RJH, van Dommelen JAW, Geers MGD (2012) A tissue-level anisotropic criterion for brain injury based on microstructural axonal deformation. J Mech Behav Biomed 5: 41–52CrossRefGoogle Scholar
  13. Cotter D, Mackay D, Chana G, Beasley C, Landau S, Everall IP (2002) Reduced neuronal size and glial cell density in area 9 of the dorsolateral prefrontal cortex in subjects with major depressive disorder. Cereb Cortex 12: 386–394CrossRefGoogle Scholar
  14. Elkin B, Morrison III B (2007) Region-specific tolerance criteria for the living brain. Stapp Car Crash J 51: 127–138Google Scholar
  15. Elkin BS, Azeloglu EU, Costa KD, Morrison III B (2007) Mechanical heterogeneity of the rat hippocampus measured by atomic force microscope indentation. J Neurotrauma 24: 812–822CrossRefGoogle Scholar
  16. Engel DC, Slemmer JE, Vlug AS, Maas AIR, Weber JT (2005) Combined effects of mechanical and ischemic injury to cortical cells: secondary ischemia increases damage and decreases effects of neuroprotective agents. Neuropharmacology 49: 985–995CrossRefGoogle Scholar
  17. Floyd CL, Gorin FA, Lyeth BG (2005) Mechanical strain injury increases intracellular sodium and reverses Na+/Ca2+ exchange in cortical astrocytes. Glia 51: 35–46CrossRefGoogle Scholar
  18. Gaetz M (2004) The neurophysiology of brain injury. Clin Neurophysiol 115: 4–18CrossRefGoogle Scholar
  19. Gasser TC, Ogden RW, Holzapfel GA (2006) Hyperelastic modelling of arterial layers with distributed collagen fibre orientations. J R Soc Interface 3: 15–35CrossRefGoogle Scholar
  20. Gennarelli TA, Spielman GM, Langfitt TW, Gildenberg PL, Harrington T, Jane JA, Marshall LF, Miller JD, Pitts LH (1982) Influence of the type of intracranial lesion on outcome from severe head injury. J Neurosurg 56: 26–32CrossRefGoogle Scholar
  21. Gentleman SM, Roberts GW, Gennarelli TA, Maxwell WL, Adams JH, Kerr S, Graham DI (1995) Axonal injury: a universal consequence of fatal closed head injury. Acta Neuropathol 89: 537–543CrossRefGoogle Scholar
  22. Hardy WN, Foster CD, Mason MJ, Yang KH, King AI, Tashman S (2001) Investigation of head injury mechanisms using neutral density technology and high-speed biplanar x-ray. Stapp Car Crash J 45: 337–368Google Scholar
  23. Highley JR, Walker MA, McDonald B, Crow TJ, Esiri MM (2003) Size of hippocampal pyramidal neurons in schizophrenia. Br J Psychiatry 183: 414–417CrossRefGoogle Scholar
  24. Ho J, von Holst H, Kleiven S (2009) An automatic method to generate a patient specific finite element head model. Int J Crashworthines 14: 555–563CrossRefGoogle Scholar
  25. Hrapko M, van Dommelen JAW, Peters GWM, Wismans JSHM (2008) The influence of test conditions on characterization of the mechanical properties of brain tissue. J Biomech Eng 130:031003-1-10Google Scholar
  26. Hutsler JJ (2003) The specialized structure of human language cortex: Pyramidal cell size asymmetries within auditory and language-associated regions of the temporal lobes. Brain Lang 86: 226–242CrossRefGoogle Scholar
  27. Kleiven S (2007) Predictors for traumatic brain injuries evaluated through accident reconstruction. Stapp Car Crash J 51: 81–114Google Scholar
  28. Kouznetsova VG, Brekelmans WAM, Baaijens FPT (2001) An approach to micro-macro modeling of heterogenous materials. Comp Mech 27: 37–48zbMATHCrossRefGoogle Scholar
  29. Marieb EN (1998) Human anatomy and physiology, 4th edn. Benjamin/Cummings Science Publishing, Menlo ParkGoogle Scholar
  30. Marjoux D, Baumgartner D, Deck C, Willinger R (2008) Head injury prediction of the HIC, HIP, SIMon and ULP criteria. Accident Anal Prev 40: 1135–1148CrossRefGoogle Scholar
  31. McCracken P, Manduca A, Felmlee J, Ehman R (2005) Mechanical transient-based magnetic resonance elastography. Magn Reson Med 53: 628–639CrossRefGoogle Scholar
  32. McElhany JH, Roberts VL, Hilyard JF (1976) Handbook of human tolerance, 2nd edn. Japan Automobile Research Institute Inc., TokyoGoogle Scholar
  33. Miller RT, Margulies SS, Leoni M, Nonaka M, Chen X, Smith DH, Meaney DF (1998) Finite element modeling approaches for predicting injury in an experimental model of severe diffuse axonal injury. In: Stapp car crash conference proceedings, vol 42. The Stapp Association, pp 155–166Google Scholar
  34. Morrison III B, Cater HL, Benham CD, Sundstrom LE (2006) An in vitro model of traumatic brain injury utilising two-dimensional stretch of organotypic hippocampal slice cultures. J Neurosci Methods 150: 192–201CrossRefGoogle Scholar
  35. NHTSA: (1972) Occupant crash protection—head injury criterion, S6.2 of FMVSS 571.208. NHTSA, WashingtonGoogle Scholar
  36. Nicolle S, Lounis M, Willinger R (2004) Shear properties of brain tissue over a frequency range relevant for automotive impact situations: new experimental results. Stapp Car Crash J 48: 239–258Google Scholar
  37. Nicolle S, Lounis M, Willinger R, Palierne JF (2005) Shear linear behavior of brain tissue over a large frequency range. Biorheology 42: 209–223Google Scholar
  38. Ning X, Zhu Q, Lanir Y, Margulies SS (2006) A transversely isotropic viscoelastic constitutive equation for brainstem undergoing finite deformation. J Biomech Eng 128: 925–933CrossRefGoogle Scholar
  39. Nolte J (2002) The human brain: an introduction to its functional anatomy, 5th edn. Mosby, Inc., St. LouisGoogle Scholar
  40. Pierri JN, Volk CLE, Auh S, Sampson A, Lewis DA (2001) Decreased somal size of deep layer 3 pyramidal neurons in the prefrontal cortex of subjects with schizophrenia. Arch Gen Psychiatry 58: 466–473CrossRefGoogle Scholar
  41. Povlishock JT (1993) Pathobiology of traumatically induced axonal injury in animals and man. Ann Emerg Med 22: 980–986CrossRefGoogle Scholar
  42. Prange MT, Margulies SS (2002) Regional, directional, and age-dependent properties of the brain undergoing large deformation. J Biomech Eng 124: 244–252CrossRefGoogle Scholar
  43. Prange MT, Meaney DF, Margulies SS (2000) Defining brain mechanical properties: Effects of region, direction, and species. Stapp Car Crash J 44: 205–213Google Scholar
  44. Rajkowska G, Goldman-Rakic PS (1995) Cytoarchitectonic definition of prefrontal areas in the normal human cortex: I. Remapping of areas 9 and 46 using quantitative criteria. Cereb Cortex 5: 307–322CrossRefGoogle Scholar
  45. Rajkowska G, Selemon LD, Goldman-Rakic PS (1998) Neuronal and glial somal size in the prefrontal cortex. Arch Gen Psychiatry 55: 215–224CrossRefGoogle Scholar
  46. Shaw NA (2002) The neurophysiology of concussion. Prog Neurobiol 67: 281–344CrossRefGoogle Scholar
  47. Smith DH, Meaney DF, Shull WH (2003) Diffuse axonal injury in head trauma. J Head Trauma Rehabil 18: 307–316CrossRefGoogle Scholar
  48. Tagliaferri F, Compagnone C, Korsic M, Servadei F, Kraus J (2006) A systematic review of brain injury epidemiology in Europe. Acta Neurochir 148: 255–268CrossRefGoogle Scholar
  49. Takhounts EG, Eppinger RH, Campbell JQ, Tannous RE, Power ED, Shook LS (2003) On the development of the SIMon finite element head model. Stapp Car Crash J 47: 51–57Google Scholar
  50. Viano DC, Casson IR, Pellman EJ, Zhang L, King AI, Yang KH (2005) Concussion in professional football: brain responses by finite element analysis: part 9. Neurosurgery 57: 891–916CrossRefGoogle Scholar
  51. Wright R, Ramesh K (2011) An axonal strain injury criterion for traumatic brain injury. Biomech Model Mechanobiol (in press). doi: 10.1007/s10,237-011-0307-1
  52. Zhang L, Yang KH, King AI (2004) A proposed injury threshold for mild traumatic brain injury. J Biomech Eng 126: 226–236CrossRefGoogle Scholar

Copyright information

© The Author(s) 2012

Authors and Affiliations

  • R. J. H. Cloots
    • 1
  • J. A. W. van Dommelen
    • 1
  • S. Kleiven
    • 2
  • M. G. D. Geers
    • 1
  1. 1.Materials Technology InstituteEindhoven University of TechnologyEindhovenThe Netherlands
  2. 2.Division of Neuronic Engineering, School of Technology and HealthRoyal Institute of TechnologyHuddingeSweden

Personalised recommendations