Institut Jean le Rond d'Alembert, CNRS UMR 7190, Université Pierre et Marie Curie, Paris, France.
J R Soc Interface. 2013 Mar 13;10(82):20130109. doi: 10.1098/rsif.2013.0109. Print 2013 May 6.
Villi are ubiquitous structures in the intestine of all vertebrates, originating from the embryonic development of the epithelial mucosa. Their morphogenesis has similar stages in living organisms but different forming mechanisms. In this work, we model the emergence of the bi-dimensional undulated patterns in the intestinal mucosa from which villi start to elongate. The embryonic mucosa is modelled as a growing thick-walled cylinder, and its mechanical behaviour is described using an hyperelastic constitutive model, which also accounts for the anisotropic characteristics of the reinforcing fibres at the microstructural 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 are finally discussed with respect to different growth and materials properties. In conclusion, we demonstrate that the emergence of intestinal villi in embryos is triggered by a differential growth between the mucosa and the mesenchymal tissues. The proposed model quantifies how both the geometrical and the mechanical properties of the mucosa drive the formation of previllous structures in embryos.
绒毛是所有脊椎动物肠道中普遍存在的结构，起源于胚胎发育中的上皮黏膜。它们的形态发生在生物体内具有相似的阶段，但形成机制不同。在这项工作中，我们模拟了从肠道黏膜开始延伸的二维波浪状图案的出现。胚胎黏膜被建模为一个生长的厚壁圆柱体，其力学行为使用超弹性本构模型来描述，该模型还考虑了微观结构水平上增强纤维的各向异性特征。使用基于增量变形叠加在有限变形上的理论的线性稳定性分析来研究表面波动的发生。推导出了增量边值问题的 Stroh 公式，并实现了一种数值求解程序来计算不稳定性的增长阈值。最后，根据不同的生长和材料特性讨论了数值结果。总之，我们证明了胚胎中肠绒毛的出现是由黏膜和间充质组织之间的差异生长引发的。所提出的模型量化了黏膜的几何和力学特性如何驱动胚胎中绒毛前结构的形成。
