Advertisement

Identification of the visco-hyperelastic properties of brain white matter based on the combination of inverse method and experiment

  • Qiming Liu
  • Jie LiuEmail author
  • Fengjiao Guan
  • Xu HanEmail author
  • Lixiong Cao
  • Kezhen Shan
Original Article
  • 88 Downloads

Abstract

To fully understand the brain injury mechanism and develop effective protective approaches, an accurate constitutive model of brain tissue is firstly required. Generally, the brain tissue is regarded as a kind of viscoelastic material and is simply used in the simulation of brain injury. In fact, the brain tissue has the behavior of the visco-hyperelastic property. Therefore, this paper presents an effective computational inverse method to determine the material parameters of visco-hyperelastic constitutive model of brain white matter through compression experiments. First, with the help of 3D hand scanner, 3D geometries of brain white matter specimens are obtained to make it possible to establish the accurate simulation models of the specific specimens. Then, the global sensitivity analysis is adopted to evaluate the importance of the material parameters and further determine the parameters which may be identified. Subsequently, based on the genetic algorithm, the optimal material parameters of brain white matter can be identified by minimizing the match error between the experimental and simulated responses. Finally, by comparing the experiment and simulation results on the other specific specimen, and the simulation results with the material parameters from the references, respectively, the accuracy and reliability of the constitutive model parameters of brain white matter are demonstrated.

Graphical abstract

The main flowchart of the computational inverse technique for determining the material parameters of specimen-specific on brain white matter. Generalization: Combining the computational inverse method and unconfined uniaxial compression experiment of the specific specimen, an effective identification method is presented to accurately determine the hyperelastic and viscoelastic parameters of brain white matter in this paper.

Keywords

Brain white matter Material parameter identification Visco-hyperelastic Computational inverse method Global sensitivity analysis 

Notes

Funding information

This work is supported by the National Science Foundation of China (Grant Nos. 51621004 and 11572115) and an independent research project of the State Key Laboratory of Reliability and Intelligence Electrical Equipment, Hebei University of Technology (EERIZZ2018001).

Compliance with ethical standards

Conflict of interest

The authors declare that they have no conflict of interest.

Ethical approval

All procedures performed in studies involving animals were in accordance with the ethical standards of the institution or practice at which the studies were conducted.

References

  1. 1.
    World Health Organization (2015) Global status report on road safety 2015. World Health OrganizationGoogle Scholar
  2. 2.
    Golman AJ, Danelson KA, Miller LE, Stitzel JD (2014) Injury prediction in a side impact crash using human body model simulation. Accid Anal Prev 64(2):1–8CrossRefGoogle Scholar
  3. 3.
    Gabler LF, Crandall JR, Panzer MB (2016) Assessment of kinematic brain injury metrics for predicting strain responses in diverse automotive impact conditions. Ann Biomed Eng 44(12):3705–3718CrossRefGoogle Scholar
  4. 4.
    Candefjord S, Winges J, Malik AA, Yu YN, Rylander T, McKelvey T, Fhager A, Elam M, Persson M (2016) Microwave technology for detecting traumatic intracranial bleedings: tests on phantom of subdural hematoma and numerical simulations. Med Biol Eng Comput 55(8):1–12Google Scholar
  5. 5.
    Cui S, Li H, Li X, Ruan J (2015) Effects of the variation in brain tissue mechanical properties on the intracranial response of a 6-year-old child. Comput Math Method M.  https://doi.org/10.1155/2015/529729
  6. 6.
    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 Mater 4(8):1905–1919CrossRefGoogle Scholar
  7. 7.
    Chatelin S, Deck C, Willinger R (2013) An anisotropic viscous hyperelastic constitutive law for brain material finite-element modeling. J Biorheol 27(1):26–37CrossRefGoogle Scholar
  8. 8.
    Miller K, Chinzei K (1997) Constitutive modelling of brain tissue: experiment and theory. J Biomech 30(11–12):1115–1121CrossRefGoogle Scholar
  9. 9.
    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
  10. 10.
    Li Y, Deng J, Zhou J, Li X (2016) Elastic and viscoelastic mechanical properties of brain tissues on the implanting trajectory of sub-thalamic nucleus stimulation. J Mater Sci Mater Med 27(11):163CrossRefGoogle Scholar
  11. 11.
    Bilston LE, Liu Z, Phan-Thien N (2001) Large strain behaviour of brain tissue in shear: some experimental data and differential constitutive model. Biorheology 38(4):335–345PubMedGoogle Scholar
  12. 12.
    Tamura A, Hayashi S, Nagayama K, Matsumoto T (2008) Mechanical characterization of brain tissue in high-rate extension. J Biomech Sci Eng 3(2):263–274CrossRefGoogle Scholar
  13. 13.
    Wu JZ, Dong RG, Schopper AW (2004) Analysis of effects of friction on the deformation behavior of soft tissues in unconfined compression tests. J Biomech 37(1):147–155CrossRefGoogle Scholar
  14. 14.
    Hrapko M, Van Dommelen JAW, Peters GWM, Wismans JSHM (2006) The mechanical behaviour of brain tissue: large strain response and constitutive modelling. Biorheology 43(5):623–636PubMedGoogle Scholar
  15. 15.
    Hrapko M, Van Dommelen JAAW, Peters GWM, Wismans JSHM (2008) The influence of test conditions on characterization of the mechanical properties of brain tissue. J Biomech Eng 130(3):031003CrossRefGoogle Scholar
  16. 16.
    Pervin F, Chen WW (2011) Effect of inter-species, gender, and breeding on the mechanical behavior of brain tissue. NeuroImage 54:S98–S102CrossRefGoogle Scholar
  17. 17.
    Antona-Makoshi J, Davidsson J, Ejima S, Ono K, Brolin K, Anata K (2013) Correlation of global head and brain tissue injury criteria to experimental concussion derived from monkey head trauma experiments. In IRCOBI Conference (No. IRC-13-55, pp. 509–522)Google Scholar
  18. 18.
    Yue H, Deng J, Zhou J, Li Y, Chen F, Li L (2017) Biomechanics of porcine brain tissue under finite compression. J Mech Med Biol 17(01):1750001CrossRefGoogle Scholar
  19. 19.
    Parkinson CM, O'Brien A, Albers TM, Simon MA, Clifford CB, Pritchett-Corning KR (2011) Diagnostic necropsy and selected tissue and sample collection in rats and mice. J Vis Exp 54:e2966Google Scholar
  20. 20.
    Laksari K, Shafieian M, Darvish K (2012) Constitutive model for brain tissue under finite compression. J Biomech 45(4):642–646CrossRefGoogle Scholar
  21. 21.
    Ruan JS, Khalil T, King AI (1991) Human head dynamic response to side impact by finite element modeling. J Biomech Eng 113(3):276–283CrossRefGoogle Scholar
  22. 22.
    Claessens MHA (1997) Finite element modeling of the human head under impact conditions. Eindhoven University of Technology, EindhovenGoogle Scholar
  23. 23.
    Takhounts EG, Crandall JR, Darvish K (2003) On the importance of nonlinearity of brain tissue under large deformations (No. 2003-22-0005). SAE Technical PaperGoogle Scholar
  24. 24.
    Takhounts EG, Eppinger RH, Campbell JQ, Tannous RE, Power ED, Shook LS (2003) On the development of the SIMon finite element head model. In Sae Conference Proceedings P (pp. 107-134). SAE; 1999Google Scholar
  25. 25.
    Kleiven S, Hardy WN (2002) Correlation of an FE model of the human head with local brain motion—consequences for injury prediction. Stapp Car Crash J 46(2):123–144PubMedGoogle Scholar
  26. 26.
    Ho J, Holst H, Kleiven S (2009) Automatic generation and validation of patient-specific finite element head models suitable for crashworthiness analysis. Int J Crashworthiness 14(6):555–563CrossRefGoogle Scholar
  27. 27.
    Shafiee A, Ahmadian MT, & Hoviattalab M (2016) Mechanical characterization of brain tissue in compression. In ASME 2016 International Design Engineering Technical Conferences and Computers and Information in Engineering ConferenceGoogle Scholar
  28. 28.
    Kim B, Lee SB, Lee J, Sehyun C, Hyungmin P, Sanghoon Y, Sung HP (2012) A comparison among neo-Hookean model, Mooney-Rivlin model, and Ogden model for chloroprene rubber. Int J Precis Eng Manuf 13(5):759–764CrossRefGoogle Scholar
  29. 29.
    Ahsanizadeh S, Li L (2015) Visco-hyperelastic constitutive modeling of soft tissues based on short and long-term internal variables. Biomed Eng Online 14(1):29CrossRefGoogle Scholar
  30. 30.
    Budday S, Sommer G, Birkl C, Langkammer C, Haybaeck J, Kohnert J, Bauer M, Paulsen F, Steinmann P, Kuhl E, Holzapfel GA (2017) Mechanical characterization of human brain tissue. Acta Biomater 48:319–340CrossRefGoogle Scholar
  31. 31.
    de Rooij R, Kuhl E (2016) Constitutive modeling of brain tissue: current perspectives. Appl Mech Rev 68(1):010801CrossRefGoogle Scholar
  32. 32.
    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
  33. 33.
    Rashid B, Destrade M, Gilchrist MD (2012) Mechanical characterization of brain tissue in compression at dynamic strain rates. J Mech Behav Biomed 10:23–38CrossRefGoogle Scholar
  34. 34.
    Brands DWA, Peters GWM, Bovendeerd PHM (2004) Design and numerical implementation of a 3-D non-linear viscoelastic constitutive model for brain tissue during impact. J Biomech 37(1):127–134CrossRefGoogle Scholar
  35. 35.
    Finan JD, Sundaresh SN, Elkin BS, McKhann GM II, Morrison B III (2017) Regional mechanical properties of human brain tissue for computational models of traumatic brain injury. Acta Biomater 55:333–339CrossRefGoogle Scholar
  36. 36.
    Jiang Y, Li G, Qian LX, Destrade M, Cao Y (2015) Measuring the linear and nonlinear elastic properties of brain tissue with shear waves and inverse analysis. Biomech Model Mechanobiol 14(5):1119–1128CrossRefGoogle Scholar
  37. 37.
    Harb N, Labed N, Domaszewski M, Peyraut F (2014) Optimization of material parameter identification in biomechanics. Struct Multidiscip Optim 49(2):337–349CrossRefGoogle Scholar
  38. 38.
    Zhang W, Liu J, Cho C, Han X (2015) A hybrid parameter identification method based on Bayesian approach and interval analysis for uncertain structures. Mech Syst Signal Process 60-61:853–865CrossRefGoogle Scholar
  39. 39.
    Liu J, Hu Y, Xu C, Jiang C, Han X (2016) Probability assessments of identified parameters for stochastic structures using point estimation method. Reliab Eng Syst Saf 156:51–58CrossRefGoogle Scholar
  40. 40.
    Liu J, Cai H, Jiang C, Han X, Zhang Z (2018) An interval inverse method based on high dimensional model representation and affine arithmetic. Appl Math Model 63:732–743CrossRefGoogle Scholar
  41. 41.
    Ahn B, Kim Y, Kim J (2008) Biomechanical characterization with inverse FE model parameter estimation. Trans Korean Soc Mech Eng A 33(11):1202–1208CrossRefGoogle Scholar
  42. 42.
    Chawla A, Mukherjee S, Karthikeyan B (2009) Characterization of human passive muscles for impact loads using genetic algorithm and inverse finite element methods. Biomech Model Mechanobiol 8(1):67–76CrossRefGoogle Scholar
  43. 43.
    Guan F, Zhang G, Liu J, Wang S, Luo X, Zhu F (2017) Study on material parameters identification of brain tissue considering uncertainty of friction coefficient. In IOP Conference Series: Materials Science and Engineering (Vol. 250, No. 1, p. 012049). IOP PublishingGoogle Scholar
  44. 44.
    Nicolle S, Lounis M, Willinger R (2004) Shear properties of brain tissue over a frequency range relevant for automotive impact situations: new experimental results (No. 2004-22-0011). SAE Technical PaperGoogle Scholar
  45. 45.
    Mooney M (1940) A theory of large elastic deformation. J Appl Phys 11(9):582–592CrossRefGoogle Scholar
  46. 46.
    Rivlin RS (1948) Large elastic deformations of isotropic materials IV. Further developments of the general theory. Phil Trans R Soc Lond A 241(835):379–397CrossRefGoogle Scholar
  47. 47.
    Mendis KK, Stalnaker RL, Advani SH (1995) A constitutive relationship for large deformation finite element modeling of brain tissue. J Biomech Eng 117(3):279–285CrossRefGoogle Scholar
  48. 48.
    Elhage H, Mallick PK, Zamani N (2004) Numerical modeling of quasi-static axial crush of square aluminium-composite hybrid tubes. Int J Crashworthiness 9(6):653–664CrossRefGoogle Scholar
  49. 49.
    Sobol IM (1993) Sensitivity estimates for nonlinear mathematical models. Math Model Comput Exp 1(4):407–414Google Scholar
  50. 50.
    Liu J, Tu L, Liu G, Jiang C, Zhang Z (2018) An analytical structural global sensitivity analysis method based on direct integral. Inverse Probl Sci En.  https://doi.org/10.1080/17415977.2018.1531856

Copyright information

© International Federation for Medical and Biological Engineering 2019

Authors and Affiliations

  1. 1.State Key Laboratory of Reliability and Intelligence of Electrical Equipment, School of Electrical EngineeringHebei University of TechnologyTianjinPeople’s Republic of China
  2. 2.State Key Laboratory of Advanced Design and Manufacturing for Vehicle Body, College of Mechanical and Vehicle EngineeringHunan UniversityChangshaPeople’s Republic of China
  3. 3.Science and Technology on Integrated Logistics Support LaboratoryNational University of Defense TechnologyChangshaPeople’s Republic of China

Personalised recommendations