Skip to main content
SpringerLink
Log in

Strain rate-dependent viscohyperelastic constitutive modeling of bovine liver tissue

  • Original Article
  • Published:
Medical & Biological Engineering & Computing Aims and scope Submit manuscript

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.

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

Access this article

Log in via an institution

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

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8

Similar content being viewed by others

References

  1. Armstrong CG, Lai WM, Mow VC (1984) An analysis of the unconfined compression of articular cartilage. J Biomech 106(2):165–173

    Article  CAS  Google Scholar 

  2. Beatty M, Usmani S (1975) On the indentation of a highly elastic half-space. Q J Mech Appl Math 28:47–62

    Article  Google Scholar 

  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, CA

  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 5:231–236

    Article  PubMed  CAS  Google Scholar 

  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):191–194

    Article  Google Scholar 

  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 42:787–798

    Article  CAS  Google Scholar 

  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 45:99–106

    Article  CAS  Google Scholar 

  8. Criscione JC (2003) Rivlin’s representation formula is ill-conceived for the determination of response functions via biaxial testing. J Elast 70:129–147

    Article  Google Scholar 

  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 48:2445–2465

    Article  Google Scholar 

  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 32:417–425

    Article  PubMed  CAS  Google Scholar 

  11. Fung Y (1973) Biorheology of soft tissues. Biorheology 10:139–155

    PubMed  CAS  Google Scholar 

  12. Fung YC (1993) Biomechanics: mechanical properties of living tissues. Springer, New York

    Google Scholar 

  13. Holzapfel GA (2000) Nonlinear solid mechanics; a continuum approach for engineers. Wiley, New York

    Google Scholar 

  14. Hu T, Desai JP (2004) Characterization of soft tissue material properties: Large deformation analysis. ISMS-LNCS 3078:28–37

    Google Scholar 

  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):192–201

    Article  PubMed  CAS  Google Scholar 

  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 46:628–634

    Article  PubMed  Google Scholar 

  17. Ledoux WR, Blevins JJ (2007) The compressive material properties of the plantar soft tissue. J Biomech 40:2975–2981

    Article  PubMed  Google Scholar 

  18. Limbert G, Middleton J (2004) A transversely isotropic viscohyperelastic material application to modeling of biological soft connective tissues. Int J Solids Struct 41:4237–4260

    Article  Google Scholar 

  19. Limbert G, Middleton J (2006) A constitutive model of the posterior cruciate ligament. Med Eng Phys 28:99–113

    Article  PubMed  Google Scholar 

  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. Miller K (2000) Constitutive modelling of abdominal organs. J Biomech 33:367–373

    Article  PubMed  CAS  Google Scholar 

  22. Miller K, Kiyoyuki C (1997) Constitutive modeling of brain tissue. J Biomech 30:1115–1121

    Article  PubMed  CAS  Google Scholar 

  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 12:269–280

    Google Scholar 

  24. Parks RW, Chrysos E, Diamond T (1999) Management of liver trauma. Br J Surg 86:1121−1135

    Article  PubMed  CAS  Google Scholar 

  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 31:753–757

    Article  PubMed  CAS  Google Scholar 

  26. Prange MT, Margulies SS (2002) Regional, directional, and age-dependent properties of the brain undergoing large deformation. J Biomech Eng 124:244–252

    Article  PubMed  Google Scholar 

  27. Roan E (2007) Experimental and multiscale computational approaches to the nonlinear characterization of liver tissue. PhD thesis, University of Cincinnati

  28. Roan E, Vemaganti K (2007) The nonlinear material properties of liver tissue determined from no-slip uniaxial compression experiments. J Biomech Eng 129:450–456

    Article  PubMed  Google Scholar 

  29. Simulia, Inc. (2009) ABAQUS/Standard User Manual, 6.8, Providence, RI

  30. The MathWorks, Inc. (2004) MATLAB: Version 7.0.1 Documentation

  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 5:269–279

    Article  CAS  Google Scholar 

  32. Toms SR, Dakin GJ, Lemons JE, Eberhardt AW (2002) Quasi-linear viscoelastic behavior of the human periodontal ligament. J Biomech 35(10):1411–1415

    Article  PubMed  Google Scholar 

  33. Vemaganti K, Roan E (2010) A compressible formulation for strain rate-dependent viscohyperelasticity and its FE implementation. CAE Lab Technical Report, University of Cincinnati

  34. Veronda DR, Westmann RA (1970) Mechanical characterization of skin-finite deformation. J Biomech 3:111–124

    Article  PubMed  CAS  Google Scholar 

  35. Yang W, Fung TC, Chian KS, Chong CK (2006) Viscoelasticity of esophageal tissue and application of a qlv model. J Biomech Eng 128:909–916

    Article  PubMed  CAS  Google Scholar 

  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):467–474

    Article  PubMed  Google Scholar 

  37. Yin L, Elliott DM (2005) A homogenization model of the annulus fibrosus. J Biomech 38:1674–1684

    Article  PubMed  Google Scholar 

Download references

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.

Author information

Authors and Affiliations

  1. Department of Biomedical Engineering, University of Memphis, 330 Engineering Technology Building, Memphis, TN, 38152, USA

    Esra Roan

  2. School of Dynamic Systems, University of Cincinnati, P.O. Box 210072, Cincinnati, OH, 45221-0072, USA

    Kumar Vemaganti

Authors
  1. Esra Roan
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Kumar Vemaganti
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Esra Roan.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Roan, E., Vemaganti, K. Strain rate-dependent viscohyperelastic constitutive modeling of bovine liver tissue. Med Biol Eng Comput 49, 497–506 (2011). https://doi.org/10.1007/s11517-010-0702-2

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11517-010-0702-2

Keywords

Search

Navigation