The mechanism by which cells measure the dimension of the organ in which they are embedded, and slow down their growth when the final size is reached, is a long-standing problem of developmental biology. The role of mechanics in this feedback is considered important. Morphoelasticity is a standard continuum framework for modeling growing elastic tissues. However, in this theory, in the absence of additional variables, the feedback between growth and mechanical stress leads to either a collapse or unbounded growth of the tissue, but usually prohibits reaching a finite asymptotic size (‘size control’). In this article, we modify this classical setting to include an energetic cost associated with growth, leading to the physical effect of size control. The present model simultaneously provides a qualitatively correct residual stress profile and has a naturally emerging necrotic core, all of which have previously been experimentally established in multicellular spheroids. This is achieved through a local feedback mechanism derived from a thermodynamical framework. The model delivers testable predictions for experimental systems and could be a step towards the understanding of the role of mechanics in the multifaceted question of how growing organs attain their final size.

细胞测量它们所嵌入的器官的尺寸并在达到最终尺寸时减慢其生长的机制是发育生物学的一个长期存在的问题。机械师在这种反馈中的作用被认为很重要。形态弹性是用于模拟生长弹性组织的标准连续体框架。然而，在该理论中，在没有其他变量的情况下，生长和机械应力之间的反馈会导致组织崩溃或无限制生长，但通常会阻止达到有限的渐近尺寸（“尺寸控制”）。在本文中，我们修改了这种经典设置，以包含与生长相关的能量成本，从而产生尺寸控制的物理效应。本模型同时提供了定性上正确的残余应力分布并具有自然出现的坏死核心，所有这些先前都已在多细胞球体中通过实验建立。这是通过源自热力学框架的局部反馈机制来实现的。该模型为实验系统提供了可测试的预测，并且可能是理解力学在生长器官如何达到最终尺寸这一多方面问题中的作用的一步。