The experimental evidence that a feedback exists between growth and stress in tumors poses challenging questions. First, the rheological properties (the “constitutive equations”) of aggregates of malignant cells are still a matter of debate. Secondly, the feedback law (the “growth law”) that relates stress and mitotic–apoptotic rate is far to be identified. We address these questions on the basis of a theoretical analysis of in vitro and in vivo experiments that involve the growth of tumor spheroids. We show that solid tumors exhibit several mechanical features of a poroelastic material, where the cellular component behaves like an elastic solid. When the solid component of the spheroid is loaded at the boundary, the cellular aggregate grows up to an asymptotic volume that depends on the exerted compression. Residual stress shows up when solid tumors are radially cut, highlighting a peculiar tensional pattern. By a novel numerical approach we correlate the measured opening angle and the underlying residual stress in a sphere. The features of the mechanobiological system can be explained in terms of a feedback of mechanics on the cell proliferation rate as modulated by the availability of nutrient, that is radially damped by the balance between diffusion and consumption. The volumetric growth profiles and the pattern of residual stress can be theoretically reproduced assuming a dependence of the target stress on the concentration of nutrient which is specific of the malignant tissue.

中文翻译：

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实体瘤是具有化学机械反馈生长的多孔弹性固体

肿瘤生长和压力之间存在反馈的实验证据提出了具有挑战性的问题。首先，恶性细胞聚集体的流变特性（“本构方程”）仍然存在争议。其次，与压力和有丝分裂 - 凋亡率相关的反馈定律（“生长定律”）还有待确定。我们基于对涉及肿瘤球体生长的体外和体内实验的理论分析来解决这些问题。我们表明实体瘤表现出多孔弹性材料的几个机械特征，其中细胞成分表现得像弹性固体。当球体的固体成分加载在边界处时，细胞聚集体增长到取决于施加的压缩的渐近体积。当实体瘤被径向切割时，会出现残余应力，突出一种特殊的张力模式。通过一种新颖的数值方法，我们将测量的张角与球体中的潜在残余应力相关联。机械生物学系统的特征可以用力学对细胞增殖速率的反馈来解释，该反馈由营养物质的可用性调节，扩散和消耗之间的平衡径向阻尼。假设目标应力依赖于恶性组织特有的营养物浓度，理论上可以再现体积生长曲线和残余应力模式。通过一种新颖的数值方法，我们将测量的张角与球体中的潜在残余应力相关联。机械生物学系统的特征可以用力学对细胞增殖速率的反馈来解释，该反馈由营养物质的可用性调节，扩散和消耗之间的平衡径向阻尼。假设目标应力依赖于恶性组织特有的营养物浓度，理论上可以再现体积生长曲线和残余应力模式。通过一种新颖的数值方法，我们将测量的张角与球体中的潜在残余应力相关联。机械生物学系统的特征可以用力学对细胞增殖速率的反馈来解释，该反馈由营养物质的可用性调节，扩散和消耗之间的平衡径向阻尼。假设目标应力依赖于恶性组织特有的营养物浓度，理论上可以再现体积生长曲线和残余应力模式。