Colloquium: Mechanical formalisms for tissue dynamics

  • Sham Tlili
  • Cyprien Gay
  • François Graner
  • Philippe Marcq
  • François Molino
  • Pierre Saramito
Colloquium

Abstract

The understanding of morphogenesis in living organisms has been renewed by tremendous progress in experimental techniques that provide access to cell scale, quantitative information both on the shapes of cells within tissues and on the genes being expressed. This information suggests that our understanding of the respective contributions of gene expression and mechanics, and of their crucial entanglement, will soon leap forward. Biomechanics increasingly benefits from models, which assist the design and interpretation of experiments, point out the main ingredients and assumptions, and ultimately lead to predictions. The newly accessible local information thus calls for a reflection on how to select suitable classes of mechanical models. We review both mechanical ingredients suggested by the current knowledge of tissue behaviour, and modelling methods that can help generate a rheological diagram or a constitutive equation. We distinguish cell scale (“intra-cell”) and tissue scale (“inter-cell”) contributions. We recall the mathematical framework developed for continuum materials and explain how to transform a constitutive equation into a set of partial differential equations amenable to numerical resolution. We show that when plastic behaviour is relevant, the dissipation function formalism appears appropriate to generate constitutive equations; its variational nature facilitates numerical implementation, and we discuss adaptations needed in the case of large deformations. The present article gathers theoretical methods that can readily enhance the significance of the data to be extracted from recent or future high throughput biomechanical experiments.

Graphical abstract

Keywords

Living systems: Biological Matter 

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Copyright information

© EDP Sciences, SIF, Springer-Verlag Berlin Heidelberg 2015

Authors and Affiliations

  • Sham Tlili
    • 1
  • Cyprien Gay
    • 1
    • 6
  • François Graner
    • 1
    • 6
  • Philippe Marcq
    • 2
  • François Molino
    • 3
    • 4
    • 6
  • Pierre Saramito
    • 5
    • 6
  1. 1.Laboratoire Matière et Systèmes ComplexesUniversité Denis Diderot - Paris 7, CNRS UMR 7057Paris Cedex 13France
  2. 2.Laboratoire Physico-Chimie Curie, Institut CurieUniversité Marie et Pierre Curie - Paris 6, CNRS UMR 168Paris Cedex 05France
  3. 3.Laboratoire Charles CoulombUniv. Montpellier II, CNRS UMR 5221Montpellier Cedex 5France
  4. 4.Institut de Génomique FonctionnelleUniv. Montpellier I, Univ. Montpellier IIMontpellier Cedex 05France
  5. 5.Laboratoire Jean KuntzmannUniversité Joseph Fourier - Grenoble I, CNRS UMR 5524Grenoble CedexFrance
  6. 6.Academy of BradylogistsParis Cedex 13France

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