Skip to main content
SpringerLink
Log in

Hyperelastic Models for Anisotropic Tissue Characterization

  • Chapter
  • First Online:
Mechanical Properties of Human Tissues

Part of the book series: Materials Horizons: From Nature to Nanomaterials ((MHFNN))

Abstract

Soft tissues typically exhibit nonlinear mechanical properties, which can be described using hyperelastic constitutive material models. Also, due to presence of multiple layers of differently oriented fibers in soft tissues, they are highly anisotropic in properties. In literature, a range of isotropic hyperelastic material models has been employed to characterize a wide range of soft tissues. This chapter reviews all such models in detail. Also, state-of-the-art anisotropic hyperelastic model formulation, incorporating multiple tissue layer interactions with varying fiber volume fractions and orientations, is discussed in depth. These hyperelastic models will be indispensable for characterization of nonlinear experimental stress–strain responses of soft tissues and their use in a wide range of computational models across disciplines.

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

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 139.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 179.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Free shipping worldwide - see info
Hardcover Book
USD 179.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. Picinbono G, Delingette H, Ayache N (2001) Nonlinear and anisotropic elastic soft tissue models for medical simulation. Proc 2001 ICRA. IEEE Int Conf Robot Autom (Cat. No. 01CH37164), IEEE. https://doi.org/10.1109/ROBOT.2001.932801

  2. Chanda A, Unnikrishnan V, Roy S, Richter HE (2015) Computational modeling of the female pelvic support structures and organs to understand the mechanism of pelvic organ prolapse: a review. Appl Mech Rev 67. https://doi.org/10.1115/1.4030967/370016

  3. Chanda A, Ghoneim H (2015) Pumping potential of a two-layer left-ventricle-like flexible-matrix-composite structure. Compos Struct 122:570–575. https://doi.org/10.1016/J.COMPSTRUCT.2014.11.069

    Article  Google Scholar 

  4. Lowry OH, Gilligan DR, Katersky EM (1941) The determination of collagen and elastin in tissues, with results obtained in various normal tissues from different species. J Biol Chem 139:795–804. https://doi.org/10.1016/s0021-9258(18)72951-7

    Article  CAS  Google Scholar 

  5. Neuman RE, Logan MA (1950) The determination of collagen and elastin in tissues. J Biol Chem 186:549–556. https://doi.org/10.1016/s0021-9258(18)56248-7

    Article  CAS  PubMed  Google Scholar 

  6. Basser PJ, Pajevic S, Pierpaoli C, Duda J, Aldroubi A (2000) In vivo fiber tractography using DT-MRI data. Magn Reson Med 44:625–632. https://doi.org/10.1002/1522-2594(200010)44:4

    Article  CAS  PubMed  Google Scholar 

  7. Wang Y, Haynor DR, Kim Y (2001) An investigation of the importance of myocardial anisotropy in finite-element modeling of the heart: methodology and application to the estimation of defibrillation efficacy. IEEE Trans Biomed Eng 48:1377–1389. https://doi.org/10.1109/10.966597

    Article  CAS  PubMed  Google Scholar 

  8. Colli Franzone P, Guerri L, Pennacchio M, Taccardi B (1998) Spread of excitation in 3-D models of the anisotropic cardiac tissue. II. Effects of fiber architecture and ventricular geometry. Math Biosci 147:131–71. https://doi.org/10.1016/S0025-5564(97)00093-X

  9. Chanda A, Graeter R, Unnikrishnan V (2015) Effect of blasts on subject-specific computational models of skin and bone sections at various locations on the human body. AIMS Mater Sci 2:425–447. https://doi.org/10.3934/matersci.2015.4.425

    Article  CAS  Google Scholar 

  10. Martins PALS, Jorge RMN, Ferreira AJM (2006) A comparative study of several material models for prediction of hyperelastic properties: Application to silicone-rubber and soft tissues. Strain 42:135–147. https://doi.org/10.1111/j.1475-1305.2006.00257.x

    Article  Google Scholar 

  11. Beatty MF (1987) Topics in finite elasticity: hyperelasticity of rubber, elastomers, and biological tissues—with examples. Appl Mech Rev 40:1699–1734. https://doi.org/10.1115/1.3149545

    Article  Google Scholar 

  12. Chabanas M, Payan Y, Marécaux C, Swider P, Boutault F (2004) Comparison of linear and non-linear soft tissue models with post-operative CT scan in maxillofacial surgery. Lect Notes Comput Sci (Including Subser Lect Notes Artif Intell Lect Notes Bioinformatics) 3078:19–27. https://doi.org/10.1007/978-3-540-25968-8_3/COVER

    Article  Google Scholar 

  13. Guerin HL, Elliott DM (2007) Quantifying the contributions of structure to annulus fibrosus mechanical function using a nonlinear, anisotropic, hyperelastic model. J Orthop Res 25:508–516. https://doi.org/10.1002/JOR.20324

    Article  PubMed  Google Scholar 

  14. Hirokawa S, Tsuruno R (2000) Three-dimensional deformation and stress distribution in an analytical/computational model of the anterior cruciate ligament. J Biomech 33:1069–1077. https://doi.org/10.1016/S0021-9290(00)00073-7

    Article  CAS  PubMed  Google Scholar 

  15. Kaster T, Sack I, Samani A (2011) Measurement of the hyperelastic properties of ex vivo brain tissue slices. J Biomech 44:1158–1163. https://doi.org/10.1016/j.jbiomech.2011.01.019

    Article  CAS  PubMed  Google Scholar 

  16. O’Hagan JJ, Samani A (2009) Measurement of the hyperelastic properties of 44 pathological ex vivo breast tissue samples. Phys Med Biol 54:2557–2569. https://doi.org/10.1088/0031-9155/54/8/020

    Article  PubMed  Google Scholar 

  17. Miller K (2005) Method of testing very soft biological tissues in compression. J Biomech 38:153–158. https://doi.org/10.1016/J.JBIOMECH.2004.03.004

    Article  PubMed  Google Scholar 

  18. Velardi F, Fraternali F, Angelillo M (2006) Anisotropic constitutive equations and experimental tensile behavior of brain tissue. Biomech Model Mechanobiol 5:53–61. https://doi.org/10.1007/S10237-005-0007-9/METRICS

    Article  CAS  PubMed  Google Scholar 

  19. El Sayed T, Mota A, Fraternali F, Ortiz M (2008) A variational constitutive model for soft biological tissues. J Biomech 41:1458–1466. https://doi.org/10.1016/J.JBIOMECH.2008.02.023

    Article  PubMed  Google Scholar 

  20. Gao Z, Lister K, Desai JP (2010) Constitutive modeling of liver tissue: experiment and theory. Ann Biomed Eng 38:505–516. https://doi.org/10.1007/s10439-009-9812-0

    Article  PubMed  Google Scholar 

  21. Holzapfel GA, Gasser TC, Ogden RW (2000) A new constitutive framework for arterial wall mechanics and a comparative study of material models. J Elast 61:1–48. https://doi.org/10.1023/A:1010835316564/METRICS

    Article  Google Scholar 

  22. Humphrey JD, Yin FCP (1987) On constitutive relations and finite deformations of passive cardiac tissue: I a pseudostrain-energy foundation. J Biomech Eng 109:298–304. https://doi.org/10.1115/1.3138684

    Article  CAS  PubMed  Google Scholar 

  23. Humphrey JD, Yin FC (1987) A new constitutive formulation for characterizing the mechanical behavior of soft tissues. Biophys J 52:563–570. https://doi.org/10.1016/S0006-3495(87)83245-9

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  24. Seshaiyer P, Humphrey JD (2003) a sub-domain inverse finite element characterization of hyperelastic membranes including soft tissues. J Biomech Eng 125:363–371. https://doi.org/10.1115/1.1574333

    Article  PubMed  Google Scholar 

  25. Van Loocke M, Lyons CG, Simms CK (2006) A validated model of passive muscle in compression. J Biomech 39:2999–3009. https://doi.org/10.1016/j.jbiomech.2005.10.016

    Article  PubMed  Google Scholar 

  26. Wang DHJ, Makaroun M, Webster MW, Vorp DA (2001) Mechanical properties and microstructure of intraluminal thrombus from abdominal aortic aneurysm. J Biomech Eng 123:536–539. https://doi.org/10.1115/1.1411971

    Article  CAS  PubMed  Google Scholar 

  27. Weiss JA, Maker BN, Govindjee S (1996) Finite element implementation of incompressible, transversely isotropic hyperelasticity. Comput Methods Appl Mech Eng 135:107–128. https://doi.org/10.1016/0045-7825(96)01035-3

    Article  Google Scholar 

  28. Martins P, Peña E, Calvo B, Doblaré M, Mascarenhas T, Jorge RN et al (2010) Prediction of nonlinear elastic behaviour of vaginal tissue: experimental results and model formulation, vol 13, pp 327–37. https://doi.org/10.1080/10255840903208197

  29. Martins PALS, Filho ALS, Fonseca AMRMI, Santos A, Santos L, Mascarenhas T et al (2011) Uniaxial mechanical behavior of the human female bladder. Int Urogynecol J 22:991–5. https://doi.org/10.1007/S00192-011-1409-0/TABLES/1

  30. Peña E, Calvo B, Martínez MA, Martins P, Mascarenhas T, Jorge RMN et al (2010) Experimental study and constitutive modeling of the viscoelastic mechanical properties of the human prolapsed vaginal tissue. Biomech Model Mechanobiol 9:35–44. https://doi.org/10.1007/S10237-009-0157-2/METRICS

    Article  PubMed  Google Scholar 

  31. Peña E, Martins P, Mascarenhas T, Natal Jorge RM, Ferreira A, Doblaré M et al (2011) Mechanical characterization of the softening behavior of human vaginal tissue. J Mech Behav Biomed Mater 4:275–283. https://doi.org/10.1016/J.JMBBM.2010.10.006

    Article  PubMed  Google Scholar 

  32. Veronda DR, Westmann RA (1970) Mechanical characterization of skin—finite deformations. J Biomech 3:111–124. https://doi.org/10.1016/0021-9290(70)90055-2

    Article  CAS  PubMed  Google Scholar 

  33. Groves RB, Coulman SA, Birchall JC, Evans SL (2013) An anisotropic, hyperelastic model for skin: experimental measurements, finite element modelling and identification of parameters for human and murine skin. J Mech Behav Biomed Mater 18:167–180. https://doi.org/10.1016/j.jmbbm.2012.10.021

    Article  PubMed  Google Scholar 

  34. Mehrabian H, Campbell G, Samani A (2010) A constrained reconstruction technique of hyperelasticity parameters for breast cancer assessment. Phys Med Biol 55. https://doi.org/10.1088/0031-9155/55/24/007

  35. Pavan TZ, Madsen EL, Frank GR, Adilton O Carneiro A, Hall TJ (2010) Nonlinear elastic behavior of phantom materials for elastography. Phys Med Biol 55:2679. https://doi.org/10.1088/0031-9155/55/9/017

  36. Holzapfel GA, Ogden RW, Holzapfel GA, Ogden RW (2010) Constitutive modelling of arteries. Proc R Soc A Math Phys Eng Sci 466:1551–1597. https://doi.org/10.1098/RSPA.2010.0058

    Article  Google Scholar 

  37. Brown LW, Smith LM (2011) A simple transversely isotropic hyperelastic constitutive model suitable for finite element analysis of fiber reinforced elastomers. J Eng Mater Technol 133. https://doi.org/10.1115/1.4003517/475345

Download references

Author information

Authors and Affiliations

  1. Centre for Biomedical Engineering, Indian Institute of Technology Delhi, New Delhi, India

    Arnab Chanda & Gurpreet Singh

Authors
  1. Arnab Chanda
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Gurpreet Singh
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Arnab Chanda .

Rights and permissions

Reprints and permissions

Copyright information

© 2023 The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd.

About this chapter

Check for updates. Verify currency and authenticity via CrossMark

Cite this chapter

Chanda, A., Singh, G. (2023). Hyperelastic Models for Anisotropic Tissue Characterization. In: Mechanical Properties of Human Tissues. Materials Horizons: From Nature to Nanomaterials. Springer, Singapore. https://doi.org/10.1007/978-981-99-2225-3_7

Download citation

Publish with us

Policies and ethics

Search

Navigation