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
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
P. Roca-Cusachs, V. Conte, X. Trepat, Nat. Cell Biol. 19, 742 (2017)
A.R. Bausch, W. Mller, E. Sackmann, Biophys. J. 76, 573 (1999)
J. Colombelli, S.W. Grill, E.H.K. Stelzer, Rev. Sci. Instrum. 75, 472 (2004)
F. Bosveld, I. Bonnet, B. Guirao, S. Tlili, Z. Wang, A. Petitalot, R. Marchand, P.-L. Bardet, P. Marcq, F. Graner, Y. Bellaïche, Science 336, 724 (2012)
R. Farhadifar, J.-C. Rper, B. Aigouy, S. Eaton, F. Jlicher, Curr. Biol. 17, 2095 (2007)
M.S. Hutson, Y. Tokutake, M.-S. Chang, J.W. Bloor, S. Venakides, D.P. Kiehart, G.S. Edwards, Science 300, 145 (2003)
K. Bambardekar, R. Clément, O. Blanc, C. Chardès, P.-F. Lenne, Proc. Natl. Acad. Sci. U.S.A. 112, 1416 (2015)
L. Selvaggi, L. Pasakarnis, D. Brunner, C.M. Aegerter, Rev. Sci. Instrum. 89, 045106 (2018)
K.K. Chiou, L. Hufnagel, B.I. Shraiman, PLoS Comput. Biol. 8, e1002512 (2012)
S. Ishihara, K. Sugimura, J. Theor. Biol. 313, 201 (2012)
G.W. Brodland, J.H. Veldhuis, S. Kim, M. Perrone, D. Mashburn, M.S. Hutson, PLoS ONE 9, e99116 (2014)
D. Eder, K. Basler, C.M. Aegerter, Sci. Rep. 7, 13692 (2017)
S.W. Moore, IEEE Trans. Biomed. Eng. 41, 45 (1994)
C. Wiebe, G.W. Brodland, J. Biomech. 38, 2087 (2005)
L.A. Davidson, R.E. Keller, Methods Cell Biol. 83, 425 (2007)
T. Schluck, C.M. Aegerter, Eur. Phys. J. E 33, 111 (2010)
A. Keller, F. Lanfranconi, C.M. Aegerter, Physica A 510, 208 (2018)
B.I. Shraiman, Proc. Natl. Acad. Sci. U.S.A. 102, 3318 (2005)
L. Hufnagel, A.a. Teleman, H. Rouault, S.M. Cohen, B.I. Shraiman, Proc. Natl. Acad. Sci. U.S.A. 104, 3835 (2007)
T. Aegerter-Wilmsen, C.M. Aegerter, E. Hafen, K. Basler, Mech. Dev. 124, 318 (2007)
T. Aegerter-Wilmsen, M.B. Heimlicher, A.C. Smith, P.B. de Reuille, R.S. Smith, C.M. Aegerter, K. Basler, Development 139, 3221 (2012)
T. Bittig, O. Wartlick, M. González-Gaitán, F. Jülicher, Eur. Phys. J. E 30, 93 (2009)
L. Sui, G.O. Pflugfelder, J. Shen, Development 139, 2773 (2012)
T. Schluck, U. Nienhaus, T. Aegerter-Wilmsen, C.M. Aegerter, PLoS ONE 8, 1 (2013)
U. Nienhaus, T. Aegerter-Wilmsen, C.M. Aegerter, Mech. Dev. 126, 942 (2009)
Y. Mao, A.L. Tournier, A. Hoppe, L. Kester, B.J. Thompson, N. Tapon, EMBO J. 32, 2790 (2013)
L. LeGoff, H. Rouault, T. Lecuit, Development 140, 4051 (2013)
C. Rauskolb, S. Sun, G. Sun, Y. Pan, K.D. Irvine, Cell 158, 143 (2014)
G.C. Fletcher, A. Elbediwy, I. Khanal, P.S. Ribeiro, N. Tapon, B.J. Thompson, EMBO J. 34, 940 (2015)
M. Duda, N.J. Kirkland, N. Khalilgharibi, M. Tozluoglu, A.C. Yuen, N. Carpi, A. Bove, M. Piel, G. Charras, B. Baum, Y. Mao, Dev. Cell 48, 245 (2019)
P. Domínguez-Giménez, N.H. Brown, M.D. Martín-Bermudo, J. Cell Sci. 120, 1061 (2007)
J.C. Pastor-Pareja, T. Xu, Dev. Cell 21, 245 (2011)
B.M. Glasheen, R.M. Robbins, C. Piette, G.J. Beitel, A. Page-McCaw, Dev. Biol. 344, 772 (2010)
M. Ma, X. Cao, J. Dai, J.C. Pastor-Pareja, Dev. Cell 42, 97 (2017)
S. Restrepo, J.J. Zartman, K. Basler, Cultivation and Live Imaging of Drosophila Imaginal Discs (Springer New York, New York, 2016) pp. 203--213
A. Guha, L. Lin, T.B. Kornberg, Dev. Biol. 335, 317 (2009)
C.M. Lye, H.W. Naylor, B. Sanson, Development 141, 4006 (2014)
Q. Fang, D.A. Boas, Tetrahedral mesh generation from volumetric binary and grayscale images, in 2009 IEEE International Symposium on Biomedical Imaging: From Nano to Macro (IEEE, 2009) pp. 1142--1145
Sven, interpmask - interpolate (tween) logical masks, https://ch.mathworks.com/matlabcentral/fileexchange/46429-interpmask-interpolate-tween-logical-masks (2004), accessed 18-06-2018
S.A. Maas, B.J. Ellis, G.A. Ateshian, J.A. Weiss, J. Biomech. Eng. 134, 011005 (2012)
R.S. Rivlin, Philos. Trans. R. Soc. London A: Math. Phys. Eng. Sci. 241, 379 (1948)
J. Bonet, R. D Wood, Nonlinear Continuum Mechanics for Finite Element Analysis (Cambridge University Press, 1998)
S.A. Maas, D. Rawlins, J.A. Weiss, G.A. Ateshian, Febio suite online manuals, http://help.mrl.sci.utah.edu/help/index.jsp (2016), accessed: 2018-06-18
M. Holmes, V. Mow, J. Biomech. 23, 1145 (1990)
N.T. Jacobs, D.H. Cortes, J.M. Peloquin, E.J. Vresilovic, D.M. Elliott, J. Biomech. 47, 2540 (2014)
M.A. Puso, J.A. Weiss, J. Biomech. Eng. 120, 62 (1998)
J.P. Winer, S. Oake, P.A. Janmey, PLoS ONE 4, 1 (2009)
Author information
Authors and Affiliations
Corresponding author
Additional information
Publisher’s Note
The EPJ Publishers remain neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
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.
About this article
Cite this article
Atzeni, F., Lanfranconi, F. & Aegerter, C.M. Disentangling geometrical, viscoelastic and hyperelastic effects in force-displacement relationships of folded biological tissues. Eur. Phys. J. E 42, 47 (2019). https://doi.org/10.1140/epje/i2019-11807-x
Received:
Accepted:
Published:
DOI: https://doi.org/10.1140/epje/i2019-11807-x