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Two-dimensional froths and the dynamics of biological tissues B. Dubertret,* T. Aste,
 

Summary: Two-dimensional froths and the dynamics of biological tissues
B. Dubertret,* T. Aste,
H. M. Ohlenbusch,
and N. Rivier§
Laboratoire de Dynamique des Fluides Complexes, Universite´ Louis Pasteur, 3 rue de l'Universite´, Strasbourg 67084, France
Received 12 November 1997; revised manuscript received 26 May 1998
Two-dimensional foams are used to model the evolution and the steady state of biological tissues. When
only cell division occurs, we deduce the mode of division simply from the stationary distribution of the number
of sides per cells, by inverting a system of coupled rate equations. Comparisons with experimental data confirm
the method. We then discuss the time evolution of tissues evolving both through cell division and cell
disappearance, theoretically and by topological simulations. Simulations reproduce realistically the steady state
of the innermost layer of the human epidermis. We conclude that short-ranged topological information is
sufficient to explain the evolution and stability of biological tissues. S1063-651X 98 08111-2
PACS number s : 87.10. e, 87.22. q
I. INTRODUCTION
Random cellular structures form the basic frame of many
natural or engineered materials 1 . Among the many mate-
rials that have already been studied, epithelial tissues the
human epidermis, the epithelium of the cucumber, or the
cork epithelium are most striking for their ability to remain

  

Source: Aste, Tomaso - Department of Applied Mathematics, Australian National University

 

Collections: Physics