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A large deformation theory for coupled swelling and growth with application to growing tumors and bacterial biofilms
Journal of the Mechanics and Physics of Solids ( IF 5.3 ) Pub Date : 2024-03-26 , DOI: 10.1016/j.jmps.2024.105627
S. Chockalingam , T. Cohen

There is significant interest in modeling the mechanics and physics of growth of soft biological systems such as tumors and bacterial biofilms. Solid tumors account for more than 85% of cancer mortality and bacterial biofilms account for a significant part of all human microbial infections. These growing biological systems are a mixture of fluid and solid components and increase their mass by intake of diffusing species such as fluids and nutrients (swelling) and subsequent conversion of some of the diffusing species into solid material (growth). Experiments indicate that these systems swell by large amounts and that the swelling and growth are intrinsically coupled, with the swelling being an important driver of growth. However, many existing theories for swelling coupled growth employ linear poroelasticity, which is limited to small swelling deformations, and employ phenomenological prescriptions for the dependence of growth rate on concentration of diffusing species and the stress-state in the system. In particular, the termination of growth is enforced through the prescription of a critical concentration of diffusing species and a homeostatic stress. In contrast, by developing a fully coupled swelling-growth theory that accounts for large swelling through nonlinear poroelasticity, we show that the emergent driving stress for growth automatically captures all the above phenomena. Further, we show that for the soft growing systems considered here, the effects of the homeostatic stress and critical concentration can be encapsulated under a single notion of a critical swelling ratio. The applicability of the theory is shown by its ability to capture experimental observations of growing tumors and biofilms under various mechanical and diffusion–consumption constraints. Additionally, compared to generalized mixture theories, our theory is amenable to relatively easy numerical implementation with a minimal physically motivated parameter space.

中文翻译:

耦合膨胀和生长的大变形理论及其在生长肿瘤和细菌生物膜中的应用

人们对肿瘤和细菌生物膜等软生物系统生长的力学和物理建模非常感兴趣。实体瘤占癌症死亡率的 85% 以上,细菌生物膜占所有人类微生物感染的重要组成部分。这些生长的生物系统是流体和固体成分的混合物,并通过吸收扩散物质(例如流体和营养物)(膨胀)以及随后将一些扩散物质转化为固体材料(生长)来增加其质量。实验表明,这些系统会大量膨胀,并且膨胀和生长本质上是耦合的,膨胀是生长的重要驱动力。然而,许多现有的膨胀耦合生长理论采用线性孔隙弹性,其仅限于小的膨胀变形,并采用现象学方法来描述生长速率对扩散物质浓度和系统中应力状态的依赖性。特别是,通过规定扩散物质的临界浓度和稳态应激来强制终止生长。相比之下,通过发展完全耦合的膨胀-生长理论,通过非线性孔隙弹性解释大膨胀,我们表明,生长的新兴驱动应力自动捕获了所有上述现象。此外,我们表明,对于此处考虑的软生长系统,稳态应力​​和临界浓度的影响可以封装在临界膨胀比的单一概念下。该理论的适用性体现在它能够捕获在各种机械和扩散消耗约束下生长的肿瘤和生物膜的实验观察结果。此外,与广义混合理论相比,我们的理论适合于相对容易的数值实现,具有最小的物理驱动参数空间。
更新日期:2024-03-26
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