Stress-dependent morphogenesis: continuum mechanics and truss systems

Author (s): Muñoz, J; Conte, V and Miodownik, M
Journal: Biomechanics and Modeling in Mechanobiology

Volume: 9, Issue 4
Pages: 451 – 467
Date: 2010

A set of equilibrium equations is derived for the stress-controlled shape change of cells due to the remodelling
and growth of their internal architecture. The approach involves the decomposition of the deformation gradient
into an active and a passive component; the former is allowed to include a growth process, while the latter is
assumed to be hyperelastic and mass-preserving. The two components are coupled with a control function
that provides the required feedback mechanism. The balance equations for general continua are derived and,
using a variational approach, we deduce the equilibrium equations and study the effects of the control function
on these equations. The results are applied to a truss system whose function is to simulate the cytoskeletal
network constituted by myosin microfilaments and microtubules, which are found experimentally to control
shape change in cells. Special attention is paid to the conditions that a thermodynamically consistent
formulation should satisfy. The model is used to simulate the multicellular shape changes observed during
ventral furrow invagination of the Drosophila melanogaster embryo. The results confirm that ventral furrow
invagination can be achieved through stress control alone, without the need for other regulatory or signalling
mechanisms. The model also reveals that the yolk plays a distinct role in the process, which is different to its
role during invagination with externally imposed strains. In stress control, the incompressibility constraint of
the yolk leads, via feedback, to the generation of a pressure in the ventral zone of the epithelium that eventually
eases its rise and internalisation.



author="Mu{\~{n}}oz, J.J.; Conte, V. and Miodownik, M.",
title="Stress-dependent morphogenesis: continuum mechanics and truss systems",
journal="Biomechanics and Modeling in Mechanobiology",