https://doi.org/10.1140/epje/i2012-12046-5
Regular Article
Tissue dynamics with permeation
1
Institut Curie (UMR 168: Institut Curie, CNRS, Université Paris VI), 26 rue d’Ulm, 75248, Paris Cedex 05, France
2
Max-Planck-Institut für Physik komplexer Systeme, Nöthnitzer Str. 38, 01187, Dresden, Germany
3
ESPCI, 10 rue Vauquelin, 75231, Paris Cedex 05, France
* e-mail: jean-francois.joanny@curie.fr
Received:
28
October
2011
Accepted:
25
May
2012
Published online:
15
June
2012
Animal tissues are complex assemblies of cells, extracellular matrix (ECM), and permeating interstitial fluid. Whereas key aspects of the multicellular dynamics can be captured by a one-component continuum description, cell division and apoptosis imply material turnover between different components that can lead to additional mechanical conditions on the tissue dynamics. We extend our previous description of tissues in order to account for a cell/ECM phase and the permeating interstitial fluid independently. In line with our earlier work, we consider the cell/ECM phase to behave as an elastic solid in the absence of cell division and apoptosis. In addition, we consider the interstitial fluid as ideal on the relevant length scales, i.e., we ignore viscous stresses in the interstitial fluid. Friction between the fluid and the cell/ECM phase leads to a Darcy-like relation for the interstitial fluid velocity and introduces a new characteristic length scale. We discuss the dynamics of a tissue confined in a chamber with a permeable piston close to the homeostatic state where cell division and apoptosis balance, and we calculate the rescaled effective diffusion coefficient for cells. For different mass densities of the cell/ECM component and the interstitial fluid, a treadmilling steady state due to gravitational forces can be found.
Key words: Biological Physics: Multicellular Systems
© EDP Sciences, SIF, Springer-Verlag Berlin Heidelberg, 2012