Anisotropic growth shapes intestinal tissues during embryogenesis

Abstract

Embryogenesis offers a real laboratory for pattern formation, buckling, and postbuckling induced by growth of soft tissues. Each part of our body is structured in multiple adjacent layers: the skin, the brain, and the interior of organs. Each layer has a complex biological composition presenting different elasticity. Generated during fetal life, these layers will experience growth and remodeling in the early postfertilization stages. Here, we focus on a herringbone pattern occurring in fetal intestinal tissues. Common to many mammalians, this instability is a precursor of the villi, finger-like projections into the lumen. For avians (chicks' and turkeys' embryos), it has been shown that, a few days after fertilization, the mucosal epithelium of the duodenum is smooth, and then folds emerge, which present 2 d later a pronounced zigzag instability. Many debates and biological studies are devoted to this specific morphology, which regulates the cell renewal in the intestine. After reviewing experimental results about duodenum morphogenesis, we show that a model based on simplified hypothesis for the growth of the mesenchyme can explain buckling and postbuckling instabilities. Being completely analytical, it is based on biaxial compressive stresses due to differential growth between layers and it predicts quantitatively the morphological changes. The growth anisotropy increasing with time, the competition between folds and zigzags, is proved to occur as a secondary instability. The model is compared with available experimental data on chick's duodenum and can be applied to other intestinal tissues, the zigzag being a common and spectacular microstructural pattern of intestine embryogenesis.bifurcation | bilayer | neo-Hookean elasticity

Towards a quantitative understanding of period-doubling wrinkling patterns occurring in film/substrate bilayer systems

“…Understanding the unusual wrinkling modes at compressive strains well above the bifurcation strain such as period-doubling and folding is a challenging issue [5,11,16,34]. In this paper, we have studied the occurrence of a period-doubling mode in the plane strain compression of film/substrate bilayer systems.…”

Mimicking Cortex Convolutions Through the Wrinkling of Growing Soft Bilayers

“…This will reflect the structure of the grey matter and its tendency to proliferate more in the direction parallel to the cranium. This growth anisotropy is not known experimentally but may have some consequences on final patterns at large strains, as shown for villi [8]. For the white matter, there is no reason to introduce such difference and we will choose an isotropic growth modeling, to limit the number of parameters.…”

“…These hypotheses can appear rather restrictive to fully represent the biological complexity of growth during morphogenesis or embryogenesis, however a growing number of independent parameters obscures the wrinkling results, changing the threshold value for existence without always changing the physical reality. Here we mostly focus on the ratio between both shear moduli which is often smaller than one in biological systems [19,8,56] contrary to material sciences [66,36,65]. Capital letters (X,Y ) represent the cartesian coordinates of a point in the reference configuration, assumed free of stresses at initial time, and, small letters (x, y) are devoted to the current configuration, at time t. Both samples are assumed incompressible.…”

“…Such ideal situation is known to generate buckling, folding, creases [57,31,60] and even other more complex patterns [2,60,8], especiallly in three dimensions, as soon as the growth differs in the two layers. Complex patterns are out of reach of the linear analysis presented here and they require sophisticated numerical treatments.…”

“…This situation of an infinite soft substrate falls in the domain of long wavelengths while the Biot's singularity of a neo-Hookean monolayer concerns the short-wavelength limit. Morphogenesis and embryogenesis reveal a lot of examples of bilayer wrinkling due to growth such as our fingerprints [37,4,19], intestine villi [29,8], esophagus [39] and brain convolutions [56,5,28]. Occurring in fetal life, at a rather precise stage post fertilization, these instabilities are common to most mammals, but not only, and concern differential growth of bilayers, with a bottom layer, in most cases, stiffer than the upper layer.…”