Eur. Phys. J. E (2013) 36: 45
https://doi.org/10.1140/epje/i2013-13045-8

Regular Article

Comparative study of non-invasive force and stress inference methods in tissue

¹⁹⁸⁵⁹ Graduate School of Arts and Sciences, The University of Tokyo, Komaba 3-8-1, Meguro-ku, Tokyo, Japan
²⁹⁸⁵⁹ Institute for Integrated Cell-Material Sciences (WPI-iCeMS), Kyoto University, Yoshida Honmachi, Sakyo-ku, Kyoto, Japan
³⁹⁸⁵⁹ RIKEN Brain Science Institute, Wako, Saitama, 351-0198, Japan
⁴⁹⁸⁵⁹ Institute of Mathematics and Physics, Aberystwyth University, Ceredigion, SY23 3BZ, UK
⁵⁹⁸⁵⁹ Genetics and Developmental Biology, Team “Polarity, division and morphogenesis”, Institut Curie, UMR3215 CNRS, U934 Inserm, Paris, France
⁶⁹⁸⁵⁹ Physico-Chimie Curie, Institut Curie, UMR168 CNRS, UPMC, 26 rue d’Ulm, F-75248, Paris Cedex 05, France
⁷⁹⁸⁵⁹ Laboratoire Matière et Systèmes Complexes, UMR 7057 CNRS and Université Paris Diderot, 10 rue Alice Domon et Léonie Duquet, F-75205, Paris Cedex 13, France

^* e-mail: shuji@complex.c.u-tokyo.jp

Received: 14 November 2012
Revised: 1 February 2013
Accepted: 19 March 2013
Published online: 26 April 2013

Abstract

In the course of animal development, the shape of tissue emerges in part from mechanical and biochemical interactions between cells. Measuring stress in tissue is essential for studying morphogenesis and its physical constraints. For that purpose, a possible new approach is force inference (up to a single prefactor) from cell shapes and connectivity. It is non-invasive and can provide space-time maps of stress in a whole tissue, unlike existing methods. To validate this approach, three force-inference methods, which differ in their approach of treating indefiniteness in an inverse problem between cell shapes and forces, were compared. Tests using two artificial and two experimental data sets consistently indicate that our Bayesian force inference, by which cell-junction tensions and cell pressures are simultaneously estimated, performs best in terms of accuracy and robustness. Moreover, by measuring the stress anisotropy and relaxation, we cross-validated the force inference and the global annular ablation of tissue, each of which relies on different prefactors. A practical choice of force-inference methods in different systems of interest is discussed.