Morphoelastic control of gastro-intestinal organogenesis: Theoretical predictions and numerical insights

Abstract

Cite this article as: V. Balbi, E. Kuhl and P. Ciarletta, Morphoelastic control of gastro-intestinal organogenesis: Theoretical predictions and numerical insights, AbstractWith nine meters in length, the gastrointestinal tract is not only our longest, but also our structurally most diverse organ. During embryonic development, it evolves as a bilayered tube with an inner endodermal lining and an outer mesodermal layer. Its inner surface displays a wide variety of morphological patterns, which are closely correlated to digestive function. However, the evolution of these intestinal patterns remains poorly understood. Here we show that geometric and mechanical factors can explain intestinal pattern formation. Using the nonlinear field theories of mechanics, we model surface morphogenesis as the instability problem of constrained differential growth. To allow for internal and external expansion, we model the gastrointestinal tract with homogeneous Neumann boundary conditions. To establish estimates for the folding pattern at the onset of folding, we perform a linear stability analysis supplemented by the perturbation theory. To predict pattern evolution in the post-buckling regime, we perform a series of nonlinear finite element simulations. Our model explains why longitudinal folds emerge in the esophagus with a thick and stiff outer layer, whereas circumferential folds emerge in the jejunum with a thinner and softer outer layer. In intermediate regions like the feline esophagus, longitudinal and circumferential folds emerge simultaneously. Our model could serve as a valuable tool to explain and predict alterations in esophageal morphology as a result of developmental disorders or certain digestive pathologies including food allergies.

Elastosis during airway wall remodeling explains multiple co-existing instability patterns

“…This trend is clinically relevant: If a patient’s health swiftly declines and there is more deterioration of elastin fibers in the airway wall, few-fold configurations with a higher potential of collapse become the more likely failure mode. While two-fold failure modes are not observed in linear buckling analysis of previous studies [7, 45, 68], the airway’s ability to form secondary long-wavelength buckling modes to obstruct the lumen, similar to the ones seen in elastosis, sheds light on the potential dangers of airway wall remodeling.…”

“…For both, we assume incompressibility using a Poisson’s ratio of 0.4995 and chose the boundary conditions to mimic a plane strain state. While plane strain conditions appear natural for long cylindrical structures, they remain a simplification and might neglect important longitudinal effects, which could affect the overall folding pattern [7, 20]. However, our previous simulations with three-dimensional, personalized airway wall segments predict comparable folding patterns for different geometries and suggest that our analysis is rather insensitive to the effects of the third dimension [23].…”

Finite bending and pattern evolution of the associated instability for a dielectric elastomer slab

“…where the positive integers q and m give the numbers of circumferential and axial wrinkles of the sector, respectively (Destrade et al, 2009b;Balbi et al, 2015). It should be noticed that they cannot be zero simultaneously.…”

Systems biology and mechanics of growth

“…In the example of the intestines, embryonic growth is sectioned into three main stages during development . To model the formation of realistic intestinal structures, the inner layer of the intestine is grown radially and circumferentially . Figure illustrates a two‐dimensional view of the circular cross section, where the innermost layer grows thicker eventually buckling inwards and creating folds characteristic of the gut.…”

“…40 To model the formation of realistic intestinal structures, the inner layer of the intestine is grown radially and circumferentially. 41 Figure 6 illustrates a twodimensional view of the circular cross section, where the innermost layer grows thicker eventually buckling inwards and creating folds characteristic of the gut. During this temporal evolution, we see folds appearing throughout the length of intestines.…”