1 Laboratoire de Physique de l'Ecole normale supérieure, ENS , Université PSL , CNRS, Sorbonne Université, 24 rue Lhomond, 75005 Paris , France.
2 Faculté de médecine, Institut Universitaire de Cancérologie , Sorbonne Université , 91 Bd de l'Hôpital, 75013 Paris , France.
Philos Trans A Math Phys Eng Sci. 2019 May 6;377(2144):20180070. doi: 10.1098/rsta.2018.0070.
For many organisms, shapes emerge from growth, which generates stresses, which in turn can feedback on growth. In this review, theoretical methods to analyse various aspects of morphogenesis are discussed with the aim to determine the most adapted method for tissue mechanics. We discuss the need to work at scales intermediate between cells and tissues and emphasize the use of finite elasticity for this. We detail the application of these ideas to four systems: active cells embedded in tissues, brain cortical convolutions, the cortex of Caenorhabditis elegans during elongation and finally the proliferation of epithelia on extracellular matrix. Numerical models well adapted to inhomogeneities are also presented. This article is part of the theme issue 'Rivlin's legacy in continuum mechanics and applied mathematics'.
对于许多生物体来说，形状是由生长产生的，而生长会产生应力，反过来，这些应力又会对生长产生反馈。在这篇综述中，我们讨论了分析形态发生各个方面的理论方法，目的是确定最适合组织力学的方法。我们讨论了在细胞和组织之间的中间尺度上工作的必要性，并强调了有限弹性的使用。我们详细介绍了这些想法在四个系统中的应用：嵌入组织中的活性细胞、大脑皮质脑回、伸长过程中的秀丽隐杆线虫皮层，以及最后是细胞外基质上的上皮细胞增殖。我们还提出了非常适合非均匀性的数值模型。本文是主题为“Rivlin 在连续介质力学和应用数学中的遗产”的一部分。
