Skip to main content
Log in

Tension Strain-Softening and Compression Strain-Stiffening Behavior of Brain White Matter

  • Original Article
  • Published:
Annals of Biomedical Engineering Aims and scope Submit manuscript

Abstract

Brain, the most important component of the central nervous system (CNS), is a soft tissue with a complex structure. Understanding the role of brain tissue microstructure in mechanical properties is essential to have a more profound knowledge of how brain development, disease, and injury occur. While many studies have investigated the mechanical behavior of brain tissue under various loading conditions, there has not been a clear explanation for variation reported for material properties of brain tissue. The current study compares the ex-vivo mechanical properties of brain tissue under two loading modes, namely compression and tension, and aims to explain the differences observed by closely examining the microstructure under loading. We tested bovine brain samples under uniaxial tension and compression loading conditions, and fitted hyperelastic material parameters. At 20% strain, we observed that the shear modulus of brain tissue in compression is about 6 times higher than in tension. In addition, we observed that brain tissue exhibited strain-stiffening in compression and strain-softening in tension. In order to investigate the effect of loading modes on the tissue microstructure, we fixed the samples using a novel method that enabled keeping the samples at the loaded stage during the fixation process. Based on the results of histology, we hypothesize that during compressive loading, the strain-stiffening behavior of the tissue could be attributed to glial cell bodies being pushed against surroundings, contacting each other and resisting compression, while during tension, cell connections are detached and the tissue displays softening behavior.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Figure 1
Figure 2
Figure 3
Figure 4
Figure 5
Figure 6
Figure 7

Similar content being viewed by others

References

  1. Arbogast, K. B., and S. S. Margulies. Material characterization of the brainstem from oscillatory shear tests. J. Biomech. 31:801–807, 1998.

    CAS  PubMed  Google Scholar 

  2. Arbogast, K. B., and S. S. Margulies. A fiber-reinforced composite model of the viscoelastic behavior of the brainstem in shear. J. Biomech. 32:865–870, 1999.

    CAS  PubMed  Google Scholar 

  3. Badachhape, A. A., R. J. Okamoto, R. S. Durham, B. D. Efron, S. J. Nadell, C. L. Johnson, and P. V. Bayly. The relationship of three-dimensional human skull motion to brain tissue deformation in magnetic resonance elastography studies. J. Biomech. Eng. 2017. https://doi.org/10.1115/1.4036146.

    Article  PubMed  PubMed Central  Google Scholar 

  4. Bain, A. C., D. I. Shreiber, and D. F. Meaney. Modeling of microstructural kinematics during simple elongation of central nervous system tissue. J. Biomech. Eng. 125:798–804, 2003.

    PubMed  Google Scholar 

  5. Bayly, P. V., T. S. Cohen, E. P. Leister, D. Ajo, E. C. Leuthardt, and G. M. Genin. Deformation of the human brain induced by mild acceleration. J. Neurotrauma 22:845–856, 2005.

    CAS  PubMed  PubMed Central  Google Scholar 

  6. Begonia, M. T., R. Prabhu, J. Liao, M. F. Horstemeyer, and L. N. Williams. The influence of strain rate dependency on the structure-property relations of porcine brain. Ann. Biomed. Eng. 38:3043–3057, 2010.

    PubMed  Google Scholar 

  7. Bernick, K. B., T. P. Prevost, S. Suresh, and S. Socrate. Biomechanics of single cortical neurons. Acta Biomater. 7:1210–1219, 2011.

    PubMed  Google Scholar 

  8. Bilston, L. E., Z. Liu, and N. Phan-Thien. Large strain behaviour of brain tissue in shear: some experimental data and differential constitutive model. Biorheology 38:335–345, 2001.

    CAS  PubMed  Google Scholar 

  9. Budday, S., T. C. Ovaert, G. A. Holzapfel, P. Steinmann, and E. Kuhl. Fifty shades of brain: a review on the mechanical testing and modeling of brain tissue. Arch. Comput. Methods Eng. 2019. https://doi.org/10.1007/s11831-019-09352-w.

    Article  Google Scholar 

  10. Budday, S., M. Sarem, L. Starck, G. Sommer, J. Pfefferle, N. Phunchago, E. Kuhl, F. Paulsen, P. Steinmann, V. P. Shastri, and G. A. Holzapfel. Towards microstructure-informed material models for human brain tissue. Acta Biomater. 104:53–65, 2020.

    CAS  PubMed  Google Scholar 

  11. Budday, S., G. Sommer, C. Birkl, C. Langkammer, J. Haybaeck, J. Kohnert, M. Bauer, F. Paulsen, P. Steinmann, E. Kuhl, and G. A. Holzapfel. Mechanical characterization of human brain tissue. Acta Biomater. 48:319–340, 2017.

    CAS  PubMed  Google Scholar 

  12. Cheng, S., and L. E. Bilston. Unconfined compression of white matter. J. Biomech. 40:117–124, 2007.

    PubMed  Google Scholar 

  13. Christ, A. F., K. Franze, H. Gautier, P. Moshayedi, J. Fawcett, R. J. M. Franklin, R. T. Karadottir, and J. Guck. Mechanical difference between white and gray matter in the rat cerebellum measured by scanning force microscopy. J. Biomech. 43:2986–2992, 2010.

    PubMed  Google Scholar 

  14. Darvish, K. K., and J. R. Crandall. Nonlinear viscoelastic effects in oscillatory shear deformation of brain tissue. Med. Eng. Phys. 23:633–645, 2001.

    CAS  PubMed  Google Scholar 

  15. Destrade, M., M. D. Gilchrist, J. G. Murphy, B. Rashid, and G. Saccomandi. Extreme softness of brain matter in simple shear. Int. J. Non. Linear. Mech. 75:54–58, 2015.

    Google Scholar 

  16. Efremov, Y. M., E. V. Dzyubenko, D. V. Bagrov, G. V. Maksimov, S. I. Shram, and K. V. Shaitan. Atomic force microscopy study of the arrangement and mechanical properties of astrocytic cytoskeleton in growth medium. Acta Naturae 3:93–99, 2011.

    PubMed  PubMed Central  Google Scholar 

  17. El Sayed, T., A. Mota, F. Fraternali, and M. Ortiz. A variational constitutive model for soft biological tissues. J. Biomech. 41:1458–1466, 2008.

    PubMed  Google Scholar 

  18. 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. 64:49–57, 2019.

    Google Scholar 

  19. Feng, Y., Y. Gao, T. Wang, L. Tao, S. Qiu, and X. Zhao. A longitudinal study of the mechanical properties of injured brain tissue in a mouse model. J. Mech. Behav. Biomed. Mater. 71:407–415, 2017.

    PubMed  Google Scholar 

  20. Feng, Y., C. H. Lee, L. Sun, S. Ji, and X. Zhao. Characterizing white matter tissue in large strain via asymmetric indentation and inverse finite element modeling. J. Mech. Behav. Biomed. Mater. 65:490–501, 2017.

    PubMed  Google Scholar 

  21. Gefen, A., and S. S. Margulies. Are in vivo and in situ brain tissues mechanically similar? J. Biomech. 37:1339–1352, 2004.

    PubMed  Google Scholar 

  22. Guertler, C. A., R. J. Okamoto, J. L. Schmidt, A. A. Badachhape, C. L. Johnson, and P. V. Bayly. Mechanical properties of porcine brain tissue in vivo and ex vivo estimated by MR elastography. J. Biomech. 69:10–18, 2018.

    PubMed  PubMed Central  Google Scholar 

  23. 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.

    PubMed  Google Scholar 

  24. Iwashita, M., N. Kataoka, K. Toida, and Y. Kosodo. Systematic profiling of spatiotemporal tissue and cellular stiffness in the developing brain. Development 141:3793–3798, 2014.

    CAS  PubMed  Google Scholar 

  25. Ji, S., W. Zhao, Z. Li, and T. W. McAllister. Head impact accelerations for brain strain-related responses in contact sports: a model-based investigation. Biomech. Model. Mechanobiol. 13:1121–1136, 2014.

    PubMed  PubMed Central  Google Scholar 

  26. Jin, X., F. Zhu, H. Mao, M. Shen, and K. H. Yang. A comprehensive experimental study on material properties of human brain tissue. J. Biomech. 46:2795–2801, 2013.

    PubMed  Google Scholar 

  27. Koser, D. E., E. Moeendarbary, J. Hanne, S. Kuerten, and K. Franze. CNS cell distribution and axon orientation determine local spinal cord mechanical properties. Biophys. J. 108:2137–2147, 2015.

    CAS  PubMed  PubMed Central  Google Scholar 

  28. Labus, K. M., and C. M. Puttlitz. An anisotropic hyperelastic constitutive model of brain white matter in biaxial tension and structural-mechanical relationships. J. Mech. Behav. Biomed. Mater. 62:195–208, 2016.

    PubMed  Google Scholar 

  29. Laksari, K., S. Assari, B. Seibold, K. Sadeghipour, and K. Darvish. Computational simulation of the mechanical response of brain tissue under blast loading. Biomech. Model. Mechanobiol. 14:459–472, 2015.

    PubMed  Google Scholar 

  30. 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.

    CAS  PubMed  Google Scholar 

  31. Laksari, K., K. Sadeghipour, and K. Darvish. Mechanical response of brain tissue under blast loading. J. Mech. Behav. Biomed. Mater. 32:132–144, 2014.

    PubMed  Google Scholar 

  32. Laksari, K., M. Shafieian, and K. Darvish. Constitutive model for brain tissue under finite compression. J. Biomech. 45:642–646, 2012.

    PubMed  Google Scholar 

  33. Li, W., D. E. T. Shepherd, and D. M. Espino. Frequency dependent viscoelastic properties of porcine brain tissue. J. Mech. Behav. Biomed. Mater. 102:103460, 2020.

    CAS  PubMed  Google Scholar 

  34. Lu, Y. B., K. Franze, G. Seifert, C. Steinhäuser, F. Kirchhoff, H. Wolburg, J. Guck, P. Janmey, E. Q. Wei, J. Käs, and A. Reichenbach. Viscoelastic properties of individual glial cells and neurons in the CNS. Proc. Natl. Acad. Sci. USA 103:17759–17764, 2006.

    CAS  PubMed  Google Scholar 

  35. Mihai, L. A., L. Chin, P. A. Janmey, and A. Goriely. A comparison of hyperelastic constitutive models applicable to brain and fat tissues. J. R. Soc. Interface 12:0486, 2015.

    PubMed  Google Scholar 

  36. Miller, K. Method of testing very soft biological tissues in compression. J. Biomech. 38:153–158, 2005.

    PubMed  Google Scholar 

  37. Miller, K., and K. Chinzei. Constitutive modelling of brain tissue: experiment and theory. J. Biomech. 30:1115–1121, 1997.

    CAS  PubMed  Google Scholar 

  38. Miller, K., and K. Chinzei. Mechanical properties of brain tissue in tension. J. Biomech. 35:483–490, 2002.

    PubMed  Google Scholar 

  39. Miller, K., K. Chinzei, G. Orssengo, and P. Bednarz. Mechanical properties of brain tissue in-vivo: experiment and computer simulation. J. Biomech. 33:1369–1376, 2000.

    CAS  PubMed  Google Scholar 

  40. Perepelyuk, M., L. Chin, X. Cao, A. van Oosten, V. B. Shenoy, P. A. Janmey, and R. G. Wells. Normal and fibrotic rat livers demonstrate shear strain softening and compression stiffening: a model for soft tissue mechanics. PLoS ONE 11:e0146588, 2016.

    PubMed  PubMed Central  Google Scholar 

  41. Pervin, F., and W. W. Chen. Dynamic mechanical response of bovine gray matter and white matter brain tissues under compression. J. Biomech. 42:731–735, 2009.

    PubMed  Google Scholar 

  42. Prevost, T. P., G. Jin, M. A. De Moya, H. B. Alam, S. Suresh, and S. Socrate. Dynamic mechanical response of brain tissue in indentation in vivo, in situ and in vitro. Acta Biomater. 7:4090–4101, 2011.

    PubMed  Google Scholar 

  43. Rashid, B., M. Destrade, and M. D. Gilchrist. Mechanical characterization of brain tissue in tension at dynamic strain rates. J. Mech. Behav. Biomed. Mater. 33:43–54, 2014.

    PubMed  Google Scholar 

  44. Raul, J. S., D. Baumgartner, R. Willinger, and B. Ludes. Finite element modelling of human head injuries caused by a fall. Int. J. Legal Med. 120:212–218, 2006.

    PubMed  Google Scholar 

  45. Sahoo, D., C. Deck, and R. Willinger. Brain injury tolerance limit based on computation of axonal strain. Accid. Anal. Prev. 92:53–70, 2016.

    PubMed  Google Scholar 

  46. Samadi-Dooki, A., G. Z. Voyiadjis, and R. W. Stout. An indirect indentation method for evaluating the linear viscoelastic properties of the brain tissue. J. Biomech. Eng. 139:061007, 2017.

    Google Scholar 

  47. Sawyer, T. W., T. Josey, Y. Wang, M. Villanueva, D. V. Ritzel, P. Nelson, and J. J. Lee. Investigations of primary blast-induced traumatic brain injury. Shock Waves 28:85–99, 2018.

    Google Scholar 

  48. Shafieian, M., K. K. Darvish, and J. R. Stone. Changes to the viscoelastic properties of brain tissue after traumatic axonal injury. J. Biomech. 42:2136–2142, 2009.

    PubMed  Google Scholar 

  49. Shiga, H., Y. Yamane, E. Ito, K. Abe, K. Kawabata, and H. Haga. Mechanical properties of membrane surface of cultured astrocyte revealed by atomic force microscopy. Jpn. J. Appl. Phys. Part 1 Regul. Pap. Short Notes Rev. Pap. 39:3711–3716, 2000.

    CAS  Google Scholar 

  50. Shreiber, D. I., H. Hao, and R. A. Elias. Probing the influence of myelin and glia on the tensile properties of the spinal cord. Biomech. Model. Mechanobiol. 8:311–321, 2009.

    PubMed  Google Scholar 

  51. Shuck, L. Z., and S. H. Advani. Rheological response of human brain tissue in shear. J. Basic Eng. 94:905, 2010.

    Google Scholar 

  52. Spedden, E., and C. Staii. Neuron biomechanics probed by atomic force microscopy. Int. J. Mol. Sci. 14:16124–16140, 2013.

    PubMed  PubMed Central  Google Scholar 

  53. Szczesny, S. E., J. M. Peloquin, D. H. Cortes, J. Kadlowec, L. J. Soslowsky, and D. M. Elliott. Biaxial tensile testing and constitutive modeling of human supraspinatus tendon. J. Biomech. Eng. 134:021004, 2012.

    PubMed  Google Scholar 

  54. Takhounts, E. G., J. R. Crandall, and K. Darvish. On the importance of nonlinearity of brain tissue under large deformations. Stapp Car Crash J. 47:79–92, 2003.

    PubMed  Google Scholar 

  55. Takhounts, E. G., R. H. Eppinger, J. Q. Campbell, R. E. Tannous, E. D. Power, and L. S. Shook. On the development of the SIMon finite element head model. Stapp Car Crash J. 47:107–133, 2003.

    PubMed  Google Scholar 

  56. Tan, X. G., A. J. Przekwas, and R. K. Gupta. Computational modeling of blast wave interaction with a human body and assessment of traumatic brain injury. Shock Waves 27:889–904, 2017.

    Google Scholar 

  57. van Oosten, A. S. G., X. Chen, L. Chin, K. Cruz, A. E. Patteson, K. Pogoda, V. B. Shenoy, and P. A. Janmey. Emergence of tissue-like mechanics from fibrous networks confined by close-packed cells. Nature 573:96–101, 2019.

    PubMed  Google Scholar 

  58. Velardi, F., F. Fraternali, and M. Angelillo. Anisotropic constitutive equations and experimental tensile behavior of brain tissue. Biomech. Model. Mechanobiol. 5:53–61, 2006.

    CAS  PubMed  Google Scholar 

  59. Vink, R. Large animal models of traumatic brain injury. J. Neurosci. Res. 96:527–535, 2018.

    CAS  PubMed  Google Scholar 

  60. von Bartheld, C. S., J. Bahney, and S. Herculano-houzel. The search for true numbers of neurons and glial cells in the human brain: a review of 150 years of cell counting. J. Comp. Neurol. 524:3865–3895, 2016.

    Google Scholar 

  61. Weickenmeier, J., R. de Rooij, S. Budday, P. Steinmann, T. C. Ovaert, and E. Kuhl. Brain stiffness increases with myelin content. Acta Biomater. 42:265–272, 2016.

    CAS  PubMed  Google Scholar 

  62. Weickenmeier, J., M. Kurt, E. Ozkaya, M. Wintermark, K. B. Pauly, and E. Kuhl. Magnetic resonance elastography of the brain: a comparison between pigs and humans. J. Mech. Behav. Biomed. Mater. 77:702–710, 2018.

    PubMed  Google Scholar 

  63. Wu, J. Z., R. G. Dong, and A. W. Schopper. Analysis of effects of friction on the deformation behavior of soft tissues in unconfined compression tests. J. Biomech. 37:147–155, 2004.

    PubMed  Google Scholar 

  64. Yang, J. Investigation of brain trauma biomechanics in vehicle traffic accidents using human body computational models. In: Computational Biomechanics for Medicine, edited by K. Miller, and P. M. F. Nielsen. New York: Springer, 2011, pp. 5–14. https://doi.org/10.1007/978-1-4419-9619-0_2.

    Chapter  Google Scholar 

  65. Yue, H., J. Deng, J. Zhou, Y. Li, F. Chen, and L. Li. Biomechanics of porcine brain tissue under finite compression. J. Mech. Med. Biol. 17:1750001, 2017.

    Google Scholar 

  66. Zhang, W., R. Run Zhang, F. Wu, L. Liang Feng, S. B. Yu, and C. Wei Wu. Differences in the viscoelastic features of white and grey matter in tension. J. Biomech. 49:3990–3995, 2016.

    PubMed  Google Scholar 

  67. Zhu, Z., C. Jiang, and H. Jiang. A visco-hyperelastic model of brain tissue incorporating both tension/compression asymmetry and volume compressibility. Acta Mech. 230:2125–2135, 2019.

    Google Scholar 

Download references

Acknowledgements

Authors have not received any funding for this research.

Conflict of interest

The authors declare that they have no conflict of interest.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Mehdi Shafieian.

Additional information

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

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Electronic supplementary material

Below is the link to the electronic supplementary material.

Supplementary material 1 (PDF 605 kb)

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Eskandari, F., Shafieian, M., Aghdam, M.M. et al. Tension Strain-Softening and Compression Strain-Stiffening Behavior of Brain White Matter. Ann Biomed Eng 49, 276–286 (2021). https://doi.org/10.1007/s10439-020-02541-w

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10439-020-02541-w

Keywords

Navigation