Advertisement

Medical & Biological Engineering & Computing

, Volume 49, Issue 4, pp 497–506 | Cite as

Strain rate-dependent viscohyperelastic constitutive modeling of bovine liver tissue

  • Esra RoanEmail author
  • Kumar Vemaganti
Original Article

Abstract

The mechanical response of most soft tissue is considered to be viscohyperelastic, making the development of accurate constitutive models a challenging task. In this article, we present a constitutive model for bovine liver tissue that utilizes a viscous dissipation potential, and use it to model the response of bovine liver tissue at strain rates ranging from 0.001 to 0.04 s−1. On the material modeling front of this study, the free energy is assumed to depend on the right Cauchy–Green deformation tensor, whereas a separate rate-dependent viscous potential is posited to characterize viscoelasticity. This viscous dissipation component is a function of the time rate of change of the right Cauchy–Green deformation tensor. On the experimental front, no-slip uniaxial compression experiments are conducted on bovine liver tissue at various strain rates. A numerical correction approach is used to account for the no-slip edge conditions, and the constitutive model is fit to the resulting corrected stress–strain data. The complete derivation of the material model, its implementation in the finite element software package ABAQUS, and a validation study are presented in this article. The results show that bovine liver tissue exhibits a strong strain-rate dependence even at the low strain rates considered here and that the proposed constitutive model is able to accurately describe this response.

Keywords

Soft tissue Liver Viscohyperelastic Uniaxial compression Friction 

Notes

Acknowledgments

We would like to acknowledge Honda R&D Americas for their support of this project. In addition, we would like to recognize and thank the help Dr. Shawn Hunter has extended in the course of this study.

References

  1. 1.
    Armstrong CG, Lai WM, Mow VC (1984) An analysis of the unconfined compression of articular cartilage. J Biomech 106(2):165–173CrossRefGoogle Scholar
  2. 2.
    Beatty M, Usmani S (1975) On the indentation of a highly elastic half-space. Q J Mech Appl Math 28:47–62CrossRefGoogle Scholar
  3. 3.
    Brown J, Rosen J, Kim Y, Chang L, Sinanan M, Hannaford B (2003) In-vivo and in-situ compressive properties of porcine abdominal soft tissues. In: Medicine meets virtual reality, Newport Beach, CAGoogle Scholar
  4. 4.
    Carter FJ, Frank TG, Davies PJ, McLean D, Cuschieri A (2001) Measurements and modelling of the complience of human and porcine organs. Med Image Anal 5:231–236PubMedCrossRefGoogle Scholar
  5. 5.
    Chen EJ, Novakofski J, Jenkins WK, O’Brien WDJ (1996) Young’s modulus measurements of soft tissues with application to elasticity imaging. IEEE Trans Ultrason Ferroelectr Freq Control 43(1):191–194CrossRefGoogle Scholar
  6. 6.
    Chui C, Kobayashi E, Chen X, Hisada T, Sakuma I (2004) Combined compression and elongation experiments and non-linear modelling of liver tissue for surgical simulation. Med Eng Biol Eng Comput 42:787–798CrossRefGoogle Scholar
  7. 7.
    Chui C, Kobayashi E, Chen X, Hisada T, Sakuma I (2007) Transversely isotropic properties of porcine liver tissue: experiments and constitutive modelling. Med Eng Biol Eng Comput 45:99–106CrossRefGoogle Scholar
  8. 8.
    Criscione JC (2003) Rivlin’s representation formula is ill-conceived for the determination of response functions via biaxial testing. J Elast 70:129–147CrossRefGoogle Scholar
  9. 9.
    Criscione JC, Humphrey JD, Douglas AS, Hunter WC (2000) An invariant basis for natural strain which yields orthogonal stress response terms in isotropic hyperelasticity. J Mech Phys Solids 48:2445–2465CrossRefGoogle Scholar
  10. 10.
    Farshad M, Barbezat M, Flüeler P, Schmidlin F, Graber P, Niederer P (1999) Material characterization of the pig kidney in relation with the biomechanical analysis of renal trauma. J Biomech 32:417–425PubMedCrossRefGoogle Scholar
  11. 11.
    Fung Y (1973) Biorheology of soft tissues. Biorheology 10:139–155PubMedGoogle Scholar
  12. 12.
    Fung YC (1993) Biomechanics: mechanical properties of living tissues. Springer, New YorkGoogle Scholar
  13. 13.
    Holzapfel GA (2000) Nonlinear solid mechanics; a continuum approach for engineers. Wiley, New YorkGoogle Scholar
  14. 14.
    Hu T, Desai JP (2004) Characterization of soft tissue material properties: Large deformation analysis. ISMS-LNCS 3078:28–37Google Scholar
  15. 15.
    Jordan P, Socrate S, Zickler TE, Howe RD (2009) Constitutive modeling of porcine liver in indentation using 3d ultrasound imaging. J Mech Behav Biomed Mater 2(2):192–201PubMedCrossRefGoogle Scholar
  16. 16.
    Kettaneh A, Marcellin P, Douvin C, Poupon R, Ziol M, Beatty M, de Ledinghen V (2007) Features associated with success rate and performance of fibroscan measurements for the diagnosis of cirrhosis in HCV patients: a prospective study of 935 patients. J Hepatol 46:628–634PubMedCrossRefGoogle Scholar
  17. 17.
    Ledoux WR, Blevins JJ (2007) The compressive material properties of the plantar soft tissue. J Biomech 40:2975–2981PubMedCrossRefGoogle Scholar
  18. 18.
    Limbert G, Middleton J (2004) A transversely isotropic viscohyperelastic material application to modeling of biological soft connective tissues. Int J Solids Struct 41:4237–4260CrossRefGoogle Scholar
  19. 19.
    Limbert G, Middleton J (2006) A constitutive model of the posterior cruciate ligament. Med Eng Phys 28:99–113PubMedCrossRefGoogle Scholar
  20. 20.
    Liu Y, Kerdok A, Howe RD (2004) A nonlinear finite element model of soft tissue indentation. ISMS-LNCS 3078:67−76.Google Scholar
  21. 21.
    Miller K (2000) Constitutive modelling of abdominal organs. J Biomech 33:367–373PubMedCrossRefGoogle Scholar
  22. 22.
    Miller K, Kiyoyuki C (1997) Constitutive modeling of brain tissue. J Biomech 30:1115–1121PubMedCrossRefGoogle Scholar
  23. 23.
    Nava A, Mazza E, Kleinermann F, Avis NJ (2004) Evaluation of the mechanical properties of human liver and kidney through aspiration experiments. Technol Healthc 12:269–280Google Scholar
  24. 24.
    Parks RW, Chrysos E, Diamond T (1999) Management of liver trauma. Br J Surg 86:1121−1135PubMedCrossRefGoogle Scholar
  25. 25.
    Pioletti D, Rakotomanana L, Benvenuti J, Leyvraz PF (1998) Viscoelastic constitutive law in large deformations application to human knee ligaments and tendons. J Biomech 31:753–757PubMedCrossRefGoogle Scholar
  26. 26.
    Prange MT, Margulies SS (2002) Regional, directional, and age-dependent properties of the brain undergoing large deformation. J Biomech Eng 124:244–252PubMedCrossRefGoogle Scholar
  27. 27.
    Roan E (2007) Experimental and multiscale computational approaches to the nonlinear characterization of liver tissue. PhD thesis, University of CincinnatiGoogle Scholar
  28. 28.
    Roan E, Vemaganti K (2007) The nonlinear material properties of liver tissue determined from no-slip uniaxial compression experiments. J Biomech Eng 129:450–456PubMedCrossRefGoogle Scholar
  29. 29.
    Simulia, Inc. (2009) ABAQUS/Standard User Manual, 6.8, Providence, RIGoogle Scholar
  30. 30.
    The MathWorks, Inc. (2004) MATLAB: Version 7.0.1 DocumentationGoogle Scholar
  31. 31.
    Ticker J, Bigliani L, Soslowsky L, Pawluk R, Flatow E, Mow V (1996) Inferior glenohumeral ligament: geometric and strain-rate dependent properties. J Should Elb Surg 5:269–279CrossRefGoogle Scholar
  32. 32.
    Toms SR, Dakin GJ, Lemons JE, Eberhardt AW (2002) Quasi-linear viscoelastic behavior of the human periodontal ligament. J Biomech 35(10):1411–1415PubMedCrossRefGoogle Scholar
  33. 33.
    Vemaganti K, Roan E (2010) A compressible formulation for strain rate-dependent viscohyperelasticity and its FE implementation. CAE Lab Technical Report, University of CincinnatiGoogle Scholar
  34. 34.
    Veronda DR, Westmann RA (1970) Mechanical characterization of skin-finite deformation. J Biomech 3:111–124PubMedCrossRefGoogle Scholar
  35. 35.
    Yang W, Fung TC, Chian KS, Chong CK (2006) Viscoelasticity of esophageal tissue and application of a qlv model. J Biomech Eng 128:909–916PubMedCrossRefGoogle Scholar
  36. 36.
    Yeh W, Li P, Jeng Y, Hsu H, Kuo P, Li M, Yang P, Lee PH (2002) Elastic modulus measurements of human liver and correlation with pathology. Ultrasound Med Biol 28(4):467–474PubMedCrossRefGoogle Scholar
  37. 37.
    Yin L, Elliott DM (2005) A homogenization model of the annulus fibrosus. J Biomech 38:1674–1684PubMedCrossRefGoogle Scholar

Copyright information

© International Federation for Medical and Biological Engineering 2010

Authors and Affiliations

  1. 1.Department of Biomedical EngineeringUniversity of MemphisMemphisUSA
  2. 2.School of Dynamic SystemsUniversity of CincinnatiCincinnatiUSA

Personalised recommendations