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

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.

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Notes

  1. 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 \(\mathbf {{L}}_{\mathrm{p}}={\varGamma }_{\mathrm{F}}\mathbf {{I}}\).

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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.

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Correspondence to Arabella Mauri.

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

Appendix

Appendix

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.

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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

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Keywords

  • Biological membrane
  • Compressible viscoelastic model
  • Specimen variability
  • Human amnion
  • Creep
  • Stress relaxation