Skip to main content
SpringerLink
Log in

A model for the compressible, viscoelastic behavior of human amnion addressing tissue variability through a single parameter

  • Original Paper
  • Published:
Biomechanics and Modeling in Mechanobiology Aims and scope Submit manuscript

Abstract

A viscoelastic, compressible model is proposed to rationalize the recently reported response of human amnion in multiaxial relaxation and creep experiments. The theory includes two viscoelastic contributions responsible for the short- and long-term time-dependent response of the material. These two contributions can be related to physical processes: water flow through the tissue and dissipative characteristics of the collagen fibers, respectively. An accurate agreement of the model with the mean tension and kinematic response of amnion in uniaxial relaxation tests was achieved. By variation of a single linear factor that accounts for the variability among tissue samples, the model provides very sound predictions not only of the uniaxial relaxation but also of the uniaxial creep and strip-biaxial relaxation behavior of individual samples. This suggests that a wide range of viscoelastic behaviors due to patient-specific variations in tissue composition can be represented by the model without the need of recalibration and parameter identification.

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

Similar content being viewed by others

Notes

  1. In Rubin’s work (Rubin 1994a, b, 1996), this is satisfied by dissipative rates of the form \(\varvec{ {a} }=\mathbf {{L}}_{\mathrm{p}}\varvec{ {m} }_{\mathrm{e}}\), where the second-order tensor \(\mathbf {{L}}_{\mathrm{p}}\) transforms as \(\mathbf {{L}}_{\mathrm{p}}^+=\mathbf {{Q}}\mathbf {{L}}_{\mathrm{p}}\mathbf {{Q}}^{\mathrm T}\) under superposed rigid body motions. The approach in Eq. (11) is consistent with the particular choice \(\mathbf {{L}}_{\mathrm{p}}={\varGamma }_{\mathrm{F}}\mathbf {{I}}\).

References

  • Anssari-Benam A, Gupta HS, Screen HRC (2012) Strain transfer through the aortic valve. J Biomech Eng 134(6):061003

    Article  Google Scholar 

  • Ateshian GA, Chahine NO, Basalo IM, Hung CT (2004) The correspondence between equilibrium biphasic and triphasic material properties in mixture models of articular cartilage. J Biomech 37(3):391–400

    Article  Google Scholar 

  • Atkinson TS, Haut RC, Altiero NJ (1997) A poroelastic model that predicts some phenomenological responses of ligaments and tendons. J Biomech Eng 119(4):400–405

    Article  Google Scholar 

  • Barbarino GG, Jabareen M, Mazza E (2011) Experimental and numerical study on the mechanical behavior of the superficial layers of the face. Skin Res Technol 17(4):434–444

    Article  Google Scholar 

  • Beck V, Lewi P, Gucciardo L, Devlieger R (2012) Preterm prelabor rupture of membranes and fetal survival after minimally invasive fetal surgery: A systematic review of the literature. Fetal Diagn Ther 31(1):1–9

    Article  Google Scholar 

  • Bourne G (1962) The foetal membranes. Postgrad Med J 38:193–201

    Article  Google Scholar 

  • Bürzle W, Haller CM, Jabareen M, Egger J, Mallik AS, Ochsenbein-Kölble N, Ehrbar M, Mazza E (2013) Multiaxial mechanical behavior of human fetal membranes and its relationship to microstructure. Biomech Model Mechanobiol 12:747–762

    Article  Google Scholar 

  • Bürzle W, Mazza E (2013) On the deformation behavior of human amnion. J Biomech 46(11):1777–1783

    Article  Google Scholar 

  • Coleman BD, Gurtin ME (1967) Thermodynamics with internal state variables. J Chem Phys 47(2):597–613

    Article  Google Scholar 

  • de Boer R (2000) Current state of porous media theory. Springer, Berlin

    Book  MATH  Google Scholar 

  • Devlieger R, Millar L, Bryant-Greenwood G, Lewi L, Deprest J (2006) Fetal membrane healing after spontaneous and iatrogenic membrane rupture: a review of current evidence. Am J Obstet Gynecol 195(6):1512–1520

    Article  Google Scholar 

  • Doehring TC, Freed AD, Carew EO, Vesely I (2005) Fractional order viscoelasticity of the aortic valve cusp: an alternative to quasilinear viscoelasticity. J Biomech Eng 127(4):700–708

    Article  Google Scholar 

  • Eckart C (1948) The thermodynamics of irreversible processes. IV. The theory of elasticity and anelasticity. Phys Rev 73(4):373–382

  • Ehlers W, Karajan N, Markert B (2006) A porous media model describing the inhomogeneous behaviour of the human intervertebral disc. Materialwissenschaft und Werkstrofftechnik 37(6):546–551

    Article  Google Scholar 

  • Ehlers W, Eipper G (1999) Finite elastic deformations in liquid-saturated and empty porous solids. Transp Porous Media 34(1–3):179–191

    Article  MathSciNet  Google Scholar 

  • Ehret AE (2011) Generalised concepts for constitutive modelling of soft biological tissues. Dissertation RWTH Aachen University, Lehr-und Forschungsgebiet Kontinuumsmechanik

  • Ehret A, Itskov M, Weinhold G (2010) A viscoelastic anisotropic model for soft collageneous tissues based on distributed fiber-matrix units. IUTAM Bookseries 16:55–65

    Article  Google Scholar 

  • Ehret AE, Itskov M (2007) A polyconvex hyperelastic model for fiber-reinforced materials in application to soft tissues. J Mater Sci 42(21):8853–8863

    Article  Google Scholar 

  • El Khwad M, Stetzer B, Moore RM, Kumar D, Mercer B, Arikat S, Redline RW, Mansour JM, Moore JJ (2005) Term human fetal membranes have a weak zone overlying the lower uterine pole and cervix before onset of labor. Biol Reprod 72(3):720–726

    Article  Google Scholar 

  • Flory P (1961) Thermodynamic relations for high elastic materials. Trans Faraday Soc 57:829–838

    Article  MathSciNet  Google Scholar 

  • Flynn C, Rubin M (2014) An anisotropic discrete fiber model with dissipation for soft biological tissues. Mech Mater 68:217–227

    Article  Google Scholar 

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

    Book  Google Scholar 

  • Grashow JS, Sacks MS, Liao J, Yoganathan AP (2006) Planar biaxial creep and stress relaxation of the mitral valve anterior leaflet. Ann Biomed Eng 34(10):1509–1518

    Article  Google Scholar 

  • Haslach HWJ (2005) Nonlinear viscoelastic, thermodynamically consistent, models for biological soft tissue. Biomech Model Mechanobiol 3(3):172–189

    Article  Google Scholar 

  • Helfenstein J, Jabareen M, Mazza E, Govindjee S (2010) On non-physical response in models for fiber-reinforced hyperelastic materials. Int J Solids Struct 47(16):2056–2061

    Article  MATH  Google Scholar 

  • Hingorani RV, Provenzano PP, Lakes RS, Escarcega A, Ray Vanderby J (2004) Nonlinear viscoelasticity in rabbit medial collateral ligament. Ann Biomed Eng 32(2):306–312

    Article  Google Scholar 

  • Hollenstein M, Jabareen M, Rubin M (2013) Modeling a smooth elastic–inelastic transition with a strongly objective numerical integrator needing no iteration. Comput Mech 52(3):649–667

    Article  MathSciNet  MATH  Google Scholar 

  • Holzapfel GA (2000) Nonlinear solid mechanics: a continuum approach for engineering. Wiley, West Sussex

    MATH  Google Scholar 

  • Holzapfel GA, Gasser TC (2001) A viscoelastic model for fiber-reinforced composites at finite strains: continuum basis, computational aspects and applications. Comput Methods Appl Mech Eng 190(34):4379–4403

    Article  Google Scholar 

  • Huber N, Tsakmakis C (2000) Finite deformation viscoelasticity laws. Mech Mater 32(1):1–18

    Article  MATH  Google Scholar 

  • Jabareen M, Mallik AS, Bilic G, Zisch AH, Mazza E (2009) Relation between mechanical properties and microstructure of human fetal membranes: an attempt towards a quantitative analysis. Eur J Obstet Gynecol Reprod Biol 144:S134–S141

    Article  Google Scholar 

  • Jacobs NT, Cortes DH, Peloquin JM, Vresilovic EJ, Elliott DM (2014) Validation and application of an intervertebral disc finite element model utilizing independently constructed tissue-level constitutive formulations that are nonlinear, anisotropic, and time-dependent. J Biomech 47(11):2540–2546

    Article  Google Scholar 

  • Kumar D, Schatz F, Moore R, Mercer B, Rangaswamy N, Mansour J, Lockwood C, Moore J (2011) The effects of thrombin and cytokines upon the biomechanics and remodeling of isolated amnion membrane, in vitro. Placenta 32(3):206–213

    Article  Google Scholar 

  • Lakes RS, Vanderby R (1999) Interrelation of creep and relaxation: a modeling approach for ligaments. J Biomech Eng 121(6):612–615

    Article  Google Scholar 

  • Lavery JP, Miller CE (1977) The viscoelastic nature of chorioamniotic membranes. Obstet Gynecol 50(4):467–472

    Google Scholar 

  • Limbert G, Middleton J (2004) A transversely isotropic viscohyperelastic material: application to the modeling of biological soft connective tissues. Int J Solids Struct 41(15):4237–4260

    Article  MATH  Google Scholar 

  • Mauri A, Perrini M, Mateos J, Maake C, Ochsenbein-Kölble N, Zimmermann R, Ehrbar M, Mazza E (2013) Second harmonic generation microscopy of fetal membranes under deformation: normal and altered morphology. Placenta 34(11):1020–1026

    Article  Google Scholar 

  • Mauri A, Ehret AE, Perrini M, Maake C, Ochsenbein-Kölble N, Ehrbar M, Oyen ML, Mazza E (2015b) Deformation mechanisms of human amnion: quantitative studies based on second harmonic generation microscopy. J Biomech 48(9):1606–1613

    Article  Google Scholar 

  • Mauri A, Perrini M, Ehret AE, Focatiis DSD, Mazza E (2015c) Time-dependent mechanical behavior of human amnion: macroscopic and microscopic characterization. Acta Biomater 11:314–323

    Article  Google Scholar 

  • Mauri A, Ehret A, De Focatiis D, Mazza E (2015a) Characterization and modeling of the mechanical behavior of human amnion. In: Proceedings of the 16th international conference on deformation, yield and fracture of polymers, Kerkrade, NL

  • Mazza E, Papes O, Rubin M, Bodner S, Binur N (2005) Nonlinear elastic-viscoplastic constitutive equations for aging facial tissues. Biomech Model Mechanobiol 4(2–3):178–189

    Article  Google Scholar 

  • Mazza E, Nava A, Hahnloser D, Jochum W, Bajka M (2007) The mechanical response of human liver and its relation to histology: an in vivo study. Med Image Anal 11(6):663–672

    Article  Google Scholar 

  • Menon R, Nicolau N, Bredson S, Polettini J (2015) Fetal membranes: potential source of preterm birth biomarkers. In: Preedy VR, Patel VB (eds) General methods in biomarker research and their applications, biomarkers in disease: methods, discoveries and applications. Springer, Netherlands, pp 483–529

    Chapter  Google Scholar 

  • Moore R, Mansour J, Redline R, Mercer B, Moore J (2006) The physiology of fetal membrane rupture: insight gained from the determination of physical properties. Placenta 27(11–12):1037–1051

    Article  Google Scholar 

  • Nguyen T, Jones R, Boyce B (2007) Modeling the anisotropic finite-deformation viscoelastic behavior of soft fiber-reinforced composites. Int J Solids Struct 44(25–26):8366–8389

    Article  MATH  Google Scholar 

  • Oxlund H, Helmig R, Halaburt J, Uldbjerg N (1990) Biomechanical analysis of human chorioamniotic membranes. Eur J Obstet Gynecol Reprod Biol 34(3):247–255

    Article  Google Scholar 

  • Oyen ML, Calvin SE, Cook RF (2004) Uniaxial stress-relaxation and stress–strain responses of human amnion. J Mater Sci Mater Med 15(5):619–624

    Article  Google Scholar 

  • Oyen ML, Cook RF, Stylianopoulos T, Barocas VH, Calvin SE, Landers DV (2005) Uniaxial and biaxial mechanical behavior of human amnion. J Mater Res 20(11):2902–2909

    Article  Google Scholar 

  • Oyen ML, Calvin SE, Landers DV (2006) Premature rupture of the fetal membranes: Is the amnion the major determinant? Am J Obstet Gynecol 195(2):510–515

    Article  Google Scholar 

  • Perrini M, Mauri A, Ehret AE, Ochsenbein-Kölble N, Zimmermann R, Ehrbar M, Mazza E (2015) Mechanical and microstructural investigation of the cyclic behavior of human amnion. J Biomech Eng 137(6):061010

    Article  Google Scholar 

  • Pierce DM, Maier F, Weisbecker H, Viertler C, Verbrugghe P, Famaey N, Fourneau I, Herijgers P, Holzapfel GA (2015) Human thoracic and abdominal aortic aneurysmal tissues: damage experiments, statistical analysis and constitutive modeling. J Mech Behav Biomed Mater 41:92–107

    Article  Google Scholar 

  • Prévost TP (2006) Biomechanics of the human chorioamnion. Master’s thesis, Massachusetts Institute of Technology

  • Reeps C, Bundschuh RA, Pellise kJ, Herz M, van Marwick S, Schwaiger M, Eckstein HH, Nekolla SG, Essler M (2013) Quantitative assessment of glucose metabolism in the vessel wall of abdominal aortic aneurysms: correlation with histology and role of partial volume correction. Int J Cardiovasc Imaging 29(2):505–512

    Article  Google Scholar 

  • Reese S, Govindjee S (1998) A theory of finite viscoelasticity and numerical aspects. Int J Solids Struct 35(26–27):3455–3482

    Article  MATH  Google Scholar 

  • Rubin M (1989) A time integration procedure for plastic deformation in elastic-viscoplastic metals. Zeitschrift für angewandte Mathematik und Physik ZAMP 40(6):846–871

    Article  MathSciNet  MATH  Google Scholar 

  • Rubin M (1994a) Plasticity theory formulated in terms of physically based microstructural variables—Part I. Theory. Int J Solids Struct 31(19):2615–2634

    Article  MATH  Google Scholar 

  • Rubin M (1994b) Plasticity theory formulated in terms of physically based microstructural variables—Part II. Examples. Int J Solids Struct 31(19):2635–2652

    Article  MATH  Google Scholar 

  • Rubin M (1996) On the treatment of elastic deformation in finite elastic-viscoplastic theory. Int J Plast 12(7):951–965

    Article  MATH  Google Scholar 

  • Rubin M, Bodner S (2002) A three-dimensional nonlinear model for dissipative response of soft tissue. Int J Solids Struct 39(19):5081–5099

    Article  MATH  Google Scholar 

  • Rubin M, Papes O (2011) Advantages of formulating evolution equations for elastic-viscoplastic materials in terms of the velocity gradient instead of the spin tensor. J Mech Mater Struct 6(1):529–543

    Article  Google Scholar 

  • Safadi M, Rubin M (2014) Modeling rate-independent hysteresis in large deformations of preconditioned soft tissues. Int J Solids Struct 51(18):3265–3272

    Article  Google Scholar 

  • Schriefl AJ, Schmidt T, Balzani D, Sommer G, Holzapfel GA (2015) Selective enzymatic removal of elastin and collagen from human abdominal aortas: Uniaxial mechanical response and constitutive modeling. Acta Biomater 17:125–136

    Article  Google Scholar 

  • Simo J (1992) Algorithms for static and dynamic multiplicative plasticity that preserve the classical return mapping schemes of the infinitesimal theory. Comput Methods Appl Mech Eng 99(1):61–112

    Article  MathSciNet  MATH  Google Scholar 

  • Simo JC, Hughes TJ (2000) Computational inelasticity, interdisciplinary applied mathematics, vol 7. Springer, Berlin

    Google Scholar 

  • Simo J, Taylor R (1982) Penalty function formulations for incompressible nonlinear elastostatics. Comput Methods Appl Mech Eng 35(1):107–118

    Article  MathSciNet  MATH  Google Scholar 

  • Sopakayang R, De Vita R (2011) A mathematical model for creep, relaxation and strain stiffening in parallel-fibered collagenous tissues. Med Eng Phys 33(9):1056–1063

    Article  Google Scholar 

  • Taber LA, Puleo AM (1996) Poroelastic plate and shell theories. In: Selvadurai A (ed) Mechanics of poroelastic media, solid mechanics and its applications, vol 35. Springer, Netherlands, pp 323–337

    Chapter  Google Scholar 

  • Thornton GM, Oliynyk A, Frank CB, Shrive NG (1997) Ligament creep cannot be predicted from stress relaxation at low stress: a biomechanical study of the rabbit medial collateral ligament. J Orthop Res 15(5):652–656

    Article  Google Scholar 

  • Thornton GM, Frank CB, Shrive NG (2001) Ligament creep behavior can be predicted from stress relaxation by incorporating fiber recruitment. J Rheol (1978-present) 45(2):493–507

    Article  Google Scholar 

  • Weickenmeier J, Jabareen M (2014) Elastic-viscoplastic modeling of soft biological tissues using a mixed finite element formulation based on the relative deformation gradient. Int J Numer Methods Biomed Eng 30(11):1238–1262

    Article  MathSciNet  Google Scholar 

  • Yarpuzlu B, Ayyildiz M, Tok OE, Aktas RG, Basdogan C (2014) Correlation between the mechanical and histological properties of liver tissue. J Mech Behav Biomed Mater 29:403–416

    Article  Google Scholar 

Download references

Acknowledgments

The authors are grateful to the team of Prof. Zimmermann at the University Hospital Zurich for providing FM samples and to the Swiss National Science Foundation (SNSF) for financial support (Project Number: 205321 134803/1). AEE gratefully acknowledges the support within the ETH Zurich Postdoctoral Fellowship (FEL13-12-2) and Marie Curie Actions for People COFUND programs. DSADF gratefully acknowledges financial support from the Faculty of Engineering at the University of Nottingham that enabled a 3-month visiting professorship at the ETH Zurich during the first half of 2013.

Author information

Authors and Affiliations

  1. Department of Mechanical and Process Engineering, Institute of Mechanical Systems, ETH Zurich, Zurich, 8092, Switzerland

    Arabella Mauri, Alexander E. Ehret & Edoardo Mazza

  2. Division of Materials, Mechanics and Structures, Faculty of Engineering, University of Nottingham, Nottingham, NG7 2RD, UK

    Davide S. A. De Focatiis

  3. Empa. Swiss Federal Laboratories for Materials Science and Technology, Dübendorf, 8600, Switzerland

    Alexander E. Ehret & Edoardo Mazza

Authors
  1. Arabella Mauri
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Alexander E. Ehret
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Davide S. A. De Focatiis
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Edoardo Mazza
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Arabella Mauri.

Additional information

Arabella Mauri and Alexander E. Ehret share first authorship of this article.

Appendix

Appendix

1.1 Experimental materials and methods

The experimental data published in Mauri et al. (2015c) were used to calibrate and validate the proposed model. Additional tests were performed to increase the number of R–U specimens from different membranes to better evaluate the model. For these additional amnion samples, after informed written consent of the patients was given (Ethical Committee of the District of Zurich Stv22/2006 and Stv07/07), preparation, testing and post-processing were performed as described in Mauri et al. (2015c). All membranes were collected from term elective cesarean sections. The model response under different multiaxial relaxation and creep configurations was computed with the time, force and local strain histories of all experiments. The local in-plane stretches were extracted from the images recorded with 4 Hz through the video extensometer system, similarly to Perrini et al. (2015). The holding stretch in relaxation tests was defined by a target force (cf. Mauri et al. 2015c), which resulted in different values for the stretch due to the variability of the specimen properties. Therefore, the mean relaxation curve was calculated after synchronizing the times for which the target force was reached (times at peak). To simulate the complete deformation history of the experiment, an according representative loading ramp with constant rate was generated from the average local stretch and the average time at the peak.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Mauri, A., Ehret, A.E., De Focatiis, D.S.A. et al. A model for the compressible, viscoelastic behavior of human amnion addressing tissue variability through a single parameter. Biomech Model Mechanobiol 15, 1005–1017 (2016). https://doi.org/10.1007/s10237-015-0739-0

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10237-015-0739-0

Keywords

Search

Navigation