Morpho-elasticity of intestinal villi
Résumé
In the context of morphogenetic processes in animal biology, in particular for those related to soft tissues, a morpho-elastic model for the embryonal development of intestinal villi, is presented. Villi originate from the embryonic development of the epithelial layer in the intestinal mucosa. Since the first stages of development, a bi-dimensional pattern starts to affect the intestinal epithelium, as a consequence of growth and residual stresses inside the tissue. It's from this undulated pattern, that villi will start to elongate. The embryonic mucosa is modeled as a growing thick-walled cylinder, and its mechanical behavior is described using an hyperelastic constitutive model, which also accounts for the anisotropic characteristics of the reinforcing fibers at the micro-structural level. The occurrence of surface undulations is investigated using a linear stability analysis based on the theory of incremental deformations superimposed on a finite deformation. The Stroh formulation of the incremental boundary value problem is derived and a numerical solution procedure is implemented for calculating the growth thresholds of instability. The numerical results, obtained from different growth scenarios are finally compared with the existing experimental results, showing that the geometrical and mechanical properties of the tissue and the differential growth between epithelium and mesenchyma, can drive the formation of intestinal villi in embryos.
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