Mathematical modeling of the stretching-induced elongation of the embryonic epithelium layer in the absence of an external load

Abstract

A clue to understanding the deformation of a plane embryonic epithelium layer unloaded after a short time uniaxial stretch and fixation in a stretched state over different time periods is found. The first steps in the understanding of this process come from the knowledge about the uniform stretching of the tissue fragment (explantate) with the subsequent stretching at a fixed length. In this study we used the earlier developed continuum model that describes the stress-strain state of the epithelial tissue taking into account the parameters that characterize the shape of the cells and their stress state, and also the active stresses they exert when interact with one another. The experimentally observed continuation of deformation of the stretched tissue after the cessation of action of the external force is described theoretically as a result of active cell reactions to the mechanical stress. The strong effect of the duration of explantate fixation on its further elongation and the cell activity pattern is demonstrated.