A Visco‑hyperelastic Model for Prediction of the Brain Tissue Response and the Traumatic Brain Injuries

Document Type : Original Article


1 Department of Applied Design, Faculty of Mechanical Engineering, University of Kashan

2 Department of Applied Design, Faculty of Mechanical Engineering, K. N. Toosi University of Technology, Tehran, Iran



Introduction: Numerous geometrically simplified models may be found in the literature on simulation of the traumatic brain injuries due to the
increased intracranial pressure induced by severe translational accelerations of the brain inside the cranium following the impact waves. While
numerous researchers have utilized viscoelastic models, some have employed specific hyperelastic models for behavior analysis of the brain
tissue. No research has been presented so far based on the more realistic visco‑hyperelastic model. Materials and Methods: In the present
research, a realistic finite element model and four visco‑hyperelastic constitutive models (viscoelastic models on the basis of the polynomial,
Yeoh, Arruda‑Boyce, and Ogden hyperelastic models) are employed to accomplish the outlined task. Therefore, the main motivation of the
present research is checking the accuracy of the modeling procedure rather than presenting clinical results. In this regard, a realistic skull‑brain
model is constructed in CATIA computer code based on the magnetic resonance imaging scans and optimized in the HYPERMESH finite element
software. Results: Influence of the contact and nonlinear characteristics of the brain tissue are considered in the simulation of the relative motions
in LS‑DYNA software to predict time histories of the acceleration and the coup and countercoup pressures by means of ANSYS finite element
analysis software. Discussion: Comparing results of the four proposed visco‑hyperelastic constitutive models with the available experimental
reveals that employing Arruda–Boyce or Ogden‑type viscoelastic models may lead to inaccurate or even erroneous results.


1. Dawodu ST. Traumatic brain injury: Definition, epidemiology,
pathophysiology, E Medicine from WebMD; 2007. Available form:
https://emedicine.medscape.com/article/326510-overview. [Last
Retrieved on 2017 Aug 16].
2. El Sayed T, Mota A, Fraternali F, Ortiz M. Biomechanics of traumatic
brain injury. Comput Methods Appl Mech Eng 2008;197:4692‑701.
3. Johnson E, Young P. The Analysis of Pressure Response in Head Injury.
SAE Technical Paper; 2006.
4. Yue X, Wang L, Sun S, Tong L. Viscoelastic finite‑element analysis of
human skull‑dura mater system as intracranial pressure changing. Afr J
Biotechnol 2008;7: 689-95.
5. Yue X, Wang L, Zhou F. Finite Element Analysis on Strains of
Viscoelastic Human Skull and Duramater. Croatia: INTECH Open
Access Publisher; 2010.
6. Odgaard A. Three‑dimensional methods for quantification of cancellous
bone architecture. Bone 1997;20:315‑28.
7. van Noort R, Black MM, Martin TR, Meanley S. A study of the uniaxial
mechanical properties of human dura mater preserved in glycerol.
Biomaterials 1981;2:41‑5.
8. Willinger R, Kang H, Diaw B. Development and validation of a human
head mechanical model. Comptes Rendus de I Académie des Sciences -
Series IIB - Mechanics-Physics-Astronomy 1999;327:125‑31.
9. Ding Z, Song D, Li S. Creep behavior of dura and substitutes. J Shanghai
Jiaotong Univ Chin Ed 1998;32:93‑6.
10. Zhang L, Yang KH, Dwarampudi R, Omori K, Li T, Chang K, et al.
Recent advances in brain injury research: A new human head model
development and validation. Stapp Car Crash J 2001;45:369‑94.
11. Willinger R, Kang HS, Diaw B. Three‑dimensional human head
finite‑element model validation against two experimental impacts. Ann
Biomed Eng 1999;27:403‑10.
12. Kleiven S, von Holst H. Consequences of head size following trauma to
the human head. J Biomech 2002;35:153‑60.
13. Horgan TJ, Gilchrist MD. Influence of FE model variability in
predicting brain motion and intracranial pressure changes in head
impact simulations. Int J Crashworthiness 2004;9:401‑18.
14. Liu S, Yin Z, Zhao H, Yang G. Investigation of the cavitation and
pressure change of brain tissue based on a transparent head model in its
decelerating impact. J Mech Med Biol 2010;10:361‑72.
15. Chen Y, Ostoja‑Starzewski M. MRI‑based finite element modeling
of head trauma: Spherically focusing shear waves. Acta Mech
16. Bergström J, Boyce M. Constitutive modeling of the time‑dependent
and cyclic loading of elastomers and application to soft biological
tissues. Mech Mater 2001;33:523‑30.
17. Brands DW, Peters GW, Bovendeerd PH. Design and numerical
implementation of a 3‑D non‑linear viscoelastic constitutive model for
brain tissue during impact. J Biomech 2004;37:127‑34.
18. Franceschini G, Bigoni D, Regitnig P, Holzapfel GA. Brain tissue
deforms similarly to filled elastomers and follows consolidation theory.
J Mech Phys Solids 2006;54:2592‑620.
19. Gasser TC, Holzapfel GA. A rate‑independent elastoplastic constitutive
model for biological fiber‑reinforced composites at finite strains:
Continuum basis, algorithmic formulation and finite element
implementation. Comput Mech 2002;29:340‑60.
20. Meaney DF. Relationship between structural modeling and hyperelastic
material behavior: Application to CNS white matter. Biomech Model
Mechanobiol 2003;1:279‑93.
21. Miller K, Chinzei K. Mechanical properties of brain tissue in tension.
J Biomech 2002;35:483‑90.
22. Velardi F, Fraternali F, Angelillo M. Anisotropic constitutive equations
and experimental tensile behavior of brain tissue. Biomech Model
Mechanobiol 2006;5:53‑61.
23. Kaster T, Sack I, Samani A. Measurement of the hyperelastic properties
of ex vivo brain tissue slices. J Biomech 2011;44:1158‑63.
24. Post A, Hoshizaki B, Gilchrist MD. Finite element analysis of the
effect of loading curve shape on brain injury predictors. J Biomech
25. Zhou C, Khalif T, King AI, editors. New Model Comparing Impact
Responses of the Homogeneous and Inhomogeneous Human Brain.
Proceedings: Stapp Car Crash Conference; Society of Automotive
Engineers SAE; 1995.
26. Johnson K, Becker J. The Whole Brain Atlas. Available form: http://
www.med.harvard.edu/aanlib, 2017.
27. Saba L. Image Principles, Neck and the Brain. Boca Raton: CRC Press;
28. Yeoh O. Some forms of the strain energy function for rubber. Rubber
Chemistry and Technology. 1993; 66:754-71.
29. Liu Y, Kerdok AE, Howe RD. A nonlinear finite element model of
soft tissue indentation. Medical Simulation. Berlin: Springer; 2004.
p. 67‑76.
30. Shariyat M. A double‑superposition global‑local theory for vibration and
dynamic buckling analyses of viscoelastic composite/sandwich plates:
A complex modulus approach. Arch Appl Mech 2011;81:1253‑68.
31. Shariyat M. A nonlinear double‑superposition global‑local theory for
dynamic buckling of imperfect viscoelastic composite/sandwich plates:
A hierarchical constitutive model. Compos Struct 2011;93:1890‑9.
32. Shariyat M. Nonlinear thermomechanical dynamic buckling
analysis of imperfect viscoelastic composite/sandwich shells by a
double‑superposition global‑local theory and various constitutive
models. Compos Struct 2011;93:2833‑43.
33. Ashrafi H, Shariyat M. A nano-indentation identification technique
for viscoelastic constitutive characteristics of periodontal ligaments. J
Biomed Phys Eng 2016;6:109-18.
34. Shariyat M, Hosseini SH. Eccentric impact analysis of pre‑stressed
composite sandwich plates with viscoelastic cores: A novel global‑local
theory and a refined contact law. Compos Struct 2014:117:333‑45.
35. Nahum AM, Smith R, Ward CC. Intracranial Pressure Dynamics During
Head Impact. SAE Technical Paper; 1977.
36. Trosseille X, Tarriere C, Lavaste F, Guillon F, Domont A. Development
of a FEM of the Human Head According to a Specific Test Protocol.
SAE Technical Paper; 1992.
37. Available form: https://www.brocku.ca/abieducation/binder/English/
chap2.html. [Last Retrieved on 2015 Feb 09].
38. Hardy WN, Mason MJ, Foster CD, Shah CS, Kopacz JM, Yang KH,
et al. A study of the response of the human cadaver head to impact.
Stapp Car Crash J 2007;51:17‑80.
39. Takhounts EG, Ridella SA, Hasija V, Tannous RE, Campbell JQ,
Malone D, et al. Investigation of traumatic brain injuries using the next
generation of simulated injury monitor (SIMon) finite element head
model. Stapp Car Crash J 2008;52:1‑31.
40. Zhou C, Kahlil T, Dragovic L. Head Injury Assessment of a Real World
Crash by Finite Element Modelling. AGARD; 1996.
41. Baumgartner D, Willinger R. Numerical modeling of the human
head under impact: New injury mechanisms and tolerance limits. In:
Gilchrist MD, editor. IUTAM Symposium on Impact Biomechanics:
From Fundamental Insights to Applications. Netherlands: Springer; 2005.