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Disentangling geometrical, viscoelastic and hyperelastic effects in force-displacement relationships of folded biological tissues

  • Francesco Atzeni
  • Flavio Lanfranconi
  • Christof M. AegerterEmail author
Open Access
Regular Article

Abstract.

Drosophila wing discs show a remarkable variability when subject to mechanical perturbation. We developed a stretching bench that allows accurate measurements of instantaneous and time-dependent material behaviour of the disc as a whole, while determining the exact three-dimensional structure of the disc during stretching. Our experiments reveal force relaxation dynamics on timescales that are significant for development, along with a surprisingly nonlinear force-displacement relationship. Concurrently our imaging indicates that the disc is a highly heterogeneous tissue with a complex geometry. Using image-based 3D finite element modelling we are able to identify the contributions of size, shape and materials parameters to the measured force-displacement relations. In particular, we find that simulating the stretching of a disc with stiffness patterns in the extra-cellular matrix (ECM) recapitulates the experimentally found stretched geometries. In our simulations, linear hyperelasticity explains the measured nonlinearity to a surprising extent. To fully match the experimental force-displacement curves, we use an exponentially elastic material, which, when coupled to material relaxation also explains time-dependent experiments. Our simulations predict that as the disc develops, two counteracting effects, namely the discs foldedness and the hardening of the ECM lead to force-relative displacement curves that are nearly conserved during development.

Graphical abstract

Keywords

Living systems: Multicellular Systems 

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Copyright information

© The Author(s) 2019

Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 License (http://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Authors and Affiliations

  • Francesco Atzeni
    • 1
    • 2
    • 3
  • Flavio Lanfranconi
    • 1
  • Christof M. Aegerter
    • 1
    • 2
    Email author
  1. 1.Physics InstituteUniversity of ZurichZurichSwitzerland
  2. 2.Institute of Molecular Life SciencesUniversity of ZurichZurichSwitzerland
  3. 3.Life Science Zurich Graduate SchoolETH Zurich and University of ZurichZurichSwitzerland

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