肿瘤球体中由表面张力驱动的边界生长
Surface tension-driven boundary growth in tumour spheroids
AI总结：
该研究建立超弹性边界增生模型，揭示弹性毛细作用驱动肿瘤球体切割后张开，并可据此估算表面张力。
摘要：
越来越多的实验证据强调，力学在实体肿瘤的生理过程中发挥着重要作用，即使在其早期阶段也是如此。虽然大多数数学模型将肿瘤生长描述为整体内部质量的体积增加，但关于肿瘤球体的体外实验表明，细胞增殖发生在细胞聚集体边界处的一薄层中。在本工作中，我们研究弹性和表面张力在肿瘤球体发育过程中如何相互作用。我们将球体建模为经历边界增生的超弹性材料，其中新生成的细胞在表面张力作用下发生变形。这种生长导致受挫参考构型，并产生残余应力。我们利用文献中的实验结果验证了该理论框架。与完全发育的肿瘤一样，球体在受到径向切割时会张开。值得注意的是，即使在缺乏残余应力的新形成球体中，也观察到这种行为。通过解析解和数值模拟，我们表明该现象由弹性毛细相互作用驱动，而在已生长球体中形成的残余应力会放大肿瘤的张开。我们模型的结果与实验观察一致，并使我们能够估算作用于肿瘤球体的表面张力。
英文摘要：
Growing experimental evidence highlights the relevant role of mechanics in the physiology of solid tumours, even in their early stages. While most of the mathematical models describe tumour growth as a volumetric increase of mass in the bulk, in vitro experiments on tumour spheroids have demonstrated that cell proliferation occurs in a thin layer at the boundary of the cellular aggregate. In this work, we investigate how elasticity and surface tension interact during the development of tumour spheroids. We model the spheroid as a hyperelastic material undergoing boundary accretion, where the newly created cells are deformed by the action of surface tension. This growth leads to a frustrated reference configuration, resulting in the appearance of residual stress. Our theoretical framework is validated using experimental results from the literature. Like fully developed tumours, spheroids open when subjected to radial cuts. Remarkably, this behaviour is observed even in newly formed spheroids, which lack residual stress. Through both analytical solutions and numerical simulations, we show that this phenomenon is driven by elastocapillary interactions, where the residual stress developed in grown spheroids amplifies the tumour opening. Our model's outcomes align with experimental observations and allow us to estimate the surface tension acting on tumour spheroids.
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