Advertisement

Determining constitutive behavior of the brain tissue using digital image correlation and finite element modeling

  • Amir Mohammad Felfelian
  • Amirhosein Baradaran Najar
  • Reza Jafari NedoushanEmail author
  • Hossein Salehi
Original Paper
  • 58 Downloads

Abstract

Detailed knowledge about the mechanical properties of brain can improve numerical modeling of the brain under various loading conditions. The success of this modeling depends on constitutive model and reliable extraction of its material constants. The isotropy of the brain tissue is a key factor which affects the form of constitutive models. In this study, compression tests were performed on different parts of the sheep brain tissue. Also, the digital image correlation (DIC) method was utilized to investigate the direction dependency of brain parts considering their microstructures. To this aim, the DIC method was employed to measure the transverse strain of two lateral sides of the tissue samples. The results of DIC method revealed that the brain stem and corona radiata were isotropic, while the mixed white and gray matter showed an unrepeatable behavior depending on the extracted sample. To examine and validate DIC method, stress–strain diagrams were also used to investigate the isotropy. It could be concluded that axonal fibers had no reinforcing role in the brain tissue. Furthermore, the DIC method indicated incompressibility of the brain tissue. Then, the significance of using a correct method to extract the material constants of brain was discussed. In other words, the effect of the real boundary conditions in experiments, which was neglected in most previous studies, was taken into account here. Finally, the particle swarm optimization algorithm along with the finite element modeling was used to estimate the hyper-viscoelastic constants of different parts of the brain tissue.

Keywords

Brain tissue Mechanical characterization Reinforcing role of axons Digital image correlation Finite element modeling Particle swarm optimization 

Notes

Compliance with ethical standards

Conflict of interest

The authors declare that they have no conflict of interest.

References

  1. Aimedieu P, Grebe R, Idy-Peretti I (2001) Study of brain white matter anisotropy. In: Engineering in medicine and biology society. Proceedings of the 23rd annual international conference of the IEEE, IEEE, vol 2, pp 1009–1011Google Scholar
  2. Anderson RW, Brown CJ, Blumbergs PC, McLean AJ, Jones NR (2003) Impact mechanics and axonal injury in a sheep model. J Neurotrauma 20(10):961–974CrossRefGoogle Scholar
  3. Annaidh AN, Bruyère K, Destrade M, Gilchrist MD, Otténio M (2012) Characterization of the anisotropic mechanical properties of excised human skin. J Mech Behav Biomed Mater 5(1):139–148CrossRefGoogle Scholar
  4. Arbogast KB, Margulies SS (1999) A fiber-reinforced composite model of the viscoelastic behavior of the brainstem in shear. J Biomech 32(8):865–870CrossRefGoogle Scholar
  5. Bilston LE, Liu Z, Phan-Thien N (2001) Large strain behavior of brain tissue in shear: some experimental data and differential constitutive model. Biorheology 38(4):335–345Google Scholar
  6. Brunon A, Bruyere-Garnier K, Coret M (2010) Mechanical characterization of liver capsule through uniaxial quasi-static tensile tests until failure. J Biomech 43(11):2221–2227CrossRefGoogle Scholar
  7. Budday S et al (2015) Mechanical properties of gray and white matter brain tissue by indentation. J Mech Behav Biomed Mater 46:318–330CrossRefGoogle Scholar
  8. Budday S et al (2017a) Mechanical characterization of human brain tissue. Acta Biomater 48:319–340CrossRefGoogle Scholar
  9. Budday S, Sommer G, Holzapfel G, Steinmann P, Kuhl E (2017b) Viscoelastic parameter identification of human brain tissue. J Mech Behav Biomed Mater 74:463–476CrossRefGoogle Scholar
  10. Chatelin S et al (2011) Computation of axonal elongation in head trauma finite element simulation. J Mech Behav Biomed Mater 4(8):1905–1919CrossRefGoogle Scholar
  11. Chatelin S, Vappou J, Roth S, Raul J-S, Willinger R (2012) Towards child versus adult brain mechanical properties. J Mech Behav Biomed Mater 6:166–173CrossRefGoogle Scholar
  12. Christ AF et al (2010) Mechanical difference between white and gray matter in the rat cerebellum measured by scanning force microscopy. J Biomech 43(15):2986–2992CrossRefGoogle Scholar
  13. Cloots R, Van Dommelen J, Nyberg T, Kleiven S, Geers M (2011) Micromechanics of diffuse axonal injury: influence of axonal orientation and anisotropy. Biomech Model Mechanobiol 10(3):413–422CrossRefGoogle Scholar
  14. Cloots R, Van Dommelen J, Geers M (2012) A tissue-level anisotropic criterion for brain injury based on microstructural axonal deformation. J Mech Behav Biomed Mater 5(1):41–52CrossRefGoogle Scholar
  15. Cloots RJ, Van Dommelen J, Kleiven S, Geers M (2013) Multi-scale mechanics of traumatic brain injury: predicting axonal strains from head loads. Biomech Model Mechanobiol 12(1):137–150CrossRefGoogle Scholar
  16. Darvish K, Crandall J (2001) Nonlinear viscoelastic effects in oscillatory shear deformation of brain tissue. Med Eng Phys 23(9):633–645CrossRefGoogle Scholar
  17. Donnelly B, Medige J (1997) Shear properties of human brain tissue. J Biomech Eng 119(4):423–432CrossRefGoogle Scholar
  18. Elkin BS, Ilankovan A, Morrison B (2010) Age-dependent regional mechanical properties of the rat hippocampus and cortex. J Biomech Eng 132(1):011010CrossRefGoogle Scholar
  19. Estes MS, McElhaney JH (1970) Response of brain tissue to compressive loading. Mech Eng 92:58–61Google Scholar
  20. Fallenstein G, Hulce VD, Melvin JW (1969) Dynamic mechanical properties of human brain tissue. J Biomech 2(3):217–226CrossRefGoogle Scholar
  21. Feng Y, Okamoto RJ, Namani R, Genin GM, Bayly PV (2013) Measurements of mechanical anisotropy in brain tissue and implications for transversely isotropic material models of white matter. J Mech Behav Biomed Mater 23(117):132Google Scholar
  22. Feng Y, Lee C-H, Sun L, Ji S, Zhao X (2017) Characterizing white matter tissue in large strain via asymmetric indentation and inverse finite element modeling. J Mech Behav Biomed Mater 65:490–501CrossRefGoogle Scholar
  23. Finan JD, Elkin BS, Pearson EM, Kalbian IL, Morrison B (2012) Viscoelastic properties of the rat brain in the sagittal plane: effects of anatomical structure and age. Ann Biomed Eng 40(1):70–78CrossRefGoogle Scholar
  24. Franceschini G, Bigoni D, Regitnig P, Holzapfel GA (2006) Brain tissue deforms similarly to filled elastomers and follows consolidation theory. J Mech Phys Solids 54(12):2592–2620CrossRefzbMATHGoogle Scholar
  25. Galford JE, McElhaney JH (1970) A viscoelastic study of scalp, brain, and dura. J Biomech 3(2):211–221CrossRefGoogle Scholar
  26. Garcia-Gonzalez D, Jérusalem A, Garzon-Hernandez S, Zaera R, Arias A (2018) A continuum mechanics constitutive framework for transverse isotropic soft tissues. J Mech Phys Solids 112:209–224MathSciNetCrossRefGoogle Scholar
  27. Giordano C, Kleiven S (2014) Evaluation of axonal strain as a predictor for mild traumatic brain injuries using finite element modeling. SAE technical paperGoogle Scholar
  28. Giordano C, Cloots R, Van Dommelen J, Kleiven S (2014) The influence of anisotropy on brain injury prediction. J Biomech 47(5):1052–1059CrossRefGoogle Scholar
  29. Goriely A et al (2015) Mechanics of the brain: perspectives, challenges, and opportunities. Biomech Model Mechanobiol 14(5):931–965CrossRefGoogle Scholar
  30. Hrapko M, Van Dommelen J, Peters G, Wismans J (2008a) Characterisation of the mechanical behavior of brain tissue in compression and shear. Biorheology 45(6):663–676Google Scholar
  31. Hrapko M, Van Dommelen J, Peters G, Wismans J (2008b) The influence of test conditions on characterization of the mechanical properties of brain tissue. J Biomech Eng 130(3):031003CrossRefGoogle Scholar
  32. Javid S, Rezaei A, Karami G (2014) A micromechanical procedure for viscoelastic characterization of the axons and ECM of the brainstem. J Mech Behav Biomed Mater 30:290–299CrossRefGoogle Scholar
  33. Jin X, Zhu F, Mao H, Shen M, Yang KH (2013) A comprehensive experimental study on material properties of human brain tissue. J Biomech 46(16):2795–2801CrossRefGoogle Scholar
  34. Karimi A, Navidbakhsh M (2014) An experimental study on the mechanical properties of rat brain tissue using different stress–strain definitions. J Mater Sci Mater Med 25(7):1623–1630CrossRefGoogle Scholar
  35. Karimi A, Navidbakhsh M, Yousefi H, Haghi AM, Sadati SA (2014) RETRACTED: experimental and numerical study on the mechanical behavior of rat brain tissue. Perfusion 29(4):307–314CrossRefGoogle Scholar
  36. Lauret C, Hrapko M, Van Dommelen J, Peters G, Wismans J (2009) Optical characterization of acceleration-induced strain fields in inhomogeneous brain slices. Med Eng Phys 31(3):392–399CrossRefGoogle Scholar
  37. Lee W, Lee SD, Park MY, Foley L, Purcell-Estabrook E, Kim H et al (2015) Functional and diffusion tensor magnetic resonance imaging of the sheep brain. BMC Vet Res 11(1):262CrossRefGoogle Scholar
  38. Lewis SB et al (1996) A head impact model of early axonal injury in the sheep. J Neurotrauma 13(9):505–514CrossRefGoogle Scholar
  39. Libertiaux V, Pascon F, Cescotto S (2011) Experimental verification of brain tissue incompressibility using digital image correlation. J Mech Behav Biomed Mater 4(7):1177–1185CrossRefGoogle Scholar
  40. Mihai LA, Chin L, Janmey PA, Goriely A (2015) A comparison of hyperelastic constitutive models applicable to brain and fat tissues. J R Soc Interface 12(110):20150486CrossRefGoogle Scholar
  41. Mihai LA, Budday S, Holzapfel GA, Kuhl E, Goriely A (2017) A family of hyperelastic models for human brain tissue. J Mech Phys Solids 106(60):79MathSciNetGoogle Scholar
  42. Miller K (1999) Constitutive model of brain tissue suitable for finite element analysis of surgical procedures. J Biomech 32(5):531–537CrossRefGoogle Scholar
  43. Miller K, Chinzei K (1997) Constitutive modelling of brain tissue: experiment and theory. J Biomech 30(11):1115–1121CrossRefGoogle Scholar
  44. Miller K, Chinzei K (2002) Mechanical properties of brain tissue in tension. J Biomech 35(4):483–490CrossRefGoogle Scholar
  45. Miller K, Chinzei K, Orssengo G, Bednarz P (2000) Mechanical properties of brain tissue in vivo: experiment and computer simulation. J Biomech 33(11):1369–1376CrossRefGoogle Scholar
  46. Ning X, Zhu Q, Lanir Y, Margulies SS (2006) A transversely isotropic viscoelastic constitutive equation for brainstem undergoing finite deformation. J Biomech Eng 128(6):925–933CrossRefGoogle Scholar
  47. Ogden RW (1972) Large deformation isotropic elasticity—on the correlation of theory and experiment for incompressible rubberlike solids. Proc R Soc Lond A 326(1567):565–584CrossRefzbMATHGoogle Scholar
  48. Pamiljans V, Krishnaswamy P, Dumville G, Meister A (1962) Studies on the mechanism of glutamine synthesis; isolation and properties of the enzyme from sheep brain. Biochemistry 1(1):153–158CrossRefGoogle Scholar
  49. Pan B, Qian K, Xie H, Asundi A (2009) Two-dimensional digital image correlation for in-plane displacement and strain measurement: a review. Meas Sci Technol 20(6):062001CrossRefGoogle Scholar
  50. Prange M, Meaney DF (2000) Defining brain mechanical properties: effects of region, direction, and species (no 2000-01-SC15). SAE technical paper extraction of brain stem sampleGoogle Scholar
  51. Prange MT, Margulies SS (2002) Regional, directional, and age-dependent properties of the brain undergoing large deformation. J Biomech Eng 124(2):244–252CrossRefGoogle Scholar
  52. Rashid B, Destrade M, Gilchrist MD (2012) Mechanical characterization of brain tissue in compression at dynamic strain rates. J Mech Behav Biomed Mater 10:23–38CrossRefGoogle Scholar
  53. Rashid B, Destrade M, Gilchrist MD (2013) Mechanical characterization of brain tissue in simple shear at dynamic strain rates. J Mech Behav Biomed Mater 28:71–85CrossRefGoogle Scholar
  54. Rashid B, Destrade M, Gilchrist MD (2014) Mechanical characterization of brain tissue in tension at dynamic strain rates. J Mech Behav Biomed Mater 33:43–54CrossRefGoogle Scholar
  55. Shuck L, Advani S (1972) Rheological response of human brain tissue in shear. J Basic Eng 94(4):905–911CrossRefGoogle Scholar
  56. Thibault KL, Margulies SS (1998) Age-dependent material properties of the porcine cerebrum: effect on pediatric inertial head injury criteria. J Biomech 31(12):1119–1126CrossRefGoogle Scholar
  57. Tse KM, Tan LB, Lee SJ, Lim SP, Lee HP (2014) Development and validation of two subject-specific finite element models of human head against three cadaveric experiments. Int J Numer Methods Biomed Eng 30(3):397–415CrossRefGoogle Scholar
  58. Van Dommelen J, Van der Sande T, Hrapko M, Peters G (2010) Mechanical properties of brain tissue by indentation: interregional variation. J Mech Behav Biomed Mater 3(2):158–166CrossRefGoogle Scholar
  59. Velardi F, Fraternali F, Angelillo M (2006) Anisotropic constitutive equations and experimental tensile behavior of brain tissue. Biomech Model Mechanobiol 5(1):53–61CrossRefGoogle Scholar
  60. Voyiadjis GZ, Samadi-Dooki A (2018) Hyperelastic modeling of the human brain tissue: effects of no-slip boundary condition and compressibility on the uniaxial deformation. J Mech Behav Biomed Mater 83:63–78CrossRefGoogle Scholar
  61. Wright RM, Post A, Hoshizaki B, Ramesh KT (2013) A multiscale computational approach to estimating axonal damage under inertial loading of the head. J Neurotrauma 30(2):102–118CrossRefGoogle Scholar
  62. Wu LC et al (2016) In vivo evaluation of wearable head impact sensors. Ann Biomed Eng 44(4):1234–1245CrossRefGoogle Scholar
  63. Zhang DS, Arola DD (2004) Applications of digital image correlation to biological tissues. J Biomed Opt 9(4):691–700CrossRefGoogle Scholar

Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  • Amir Mohammad Felfelian
    • 1
  • Amirhosein Baradaran Najar
    • 1
  • Reza Jafari Nedoushan
    • 1
    Email author
  • Hossein Salehi
    • 2
  1. 1.Department of Mechanical EngineeringIsfahan University of TechnologyIsfahanIran
  2. 2.Department of Anatomical Sciences, School of MedicineIsfahan University of Medical SciencesIsfahanIran

Personalised recommendations