具有基底摩擦的延迟粘弹性流变模型的稳定性界
Stability bounds of a delay visco-elastic rheological model with substrate friction
摘要：
细胞和组织在重塑、迁移或胚胎发生过程中表现出振荡变形。虽然已经表明这些振荡与细胞生化信号相关，但尚不清楚这些振荡在触发剧烈的细胞重组事件或不稳定性中的作用，以及这种振荡响应与测试的粘弹性性质的耦合。我们在这里提出了一个流变模型，它结合了弹性，粘性和摩擦组件，并能够产生振荡响应，通过延迟自适应过程的休息长度。我们分析了它的稳定性作为模型参数的函数，并推导出稳定域的解析界。虽然延迟和重塑率的增加值使模型不稳定，我们也表明，增加摩擦与基板不稳定的振荡响应。此外，我们在数值上验证了该模型的扩展到非线性应变措施能够产生持续的振荡，稳定和不稳定的区域之间交替。
英文摘要：
Cells and tissues exhibit oscillatory deformations during remodelling, migration or embryogenesis. Although it has been shown that these oscillations correlate with cell biochemical signalling, it is yet unclear the role of these oscillations in triggering drastic cell reorganisation events or instabilities, and the coupling of this oscillatory response with tested visco-elastic properties. We here present a rheological model that incorporates elastic, viscous and frictional components, and that is able to generate oscillatory response through a delay adaptive process of the rest-length. We analyse its stability properties as a function of the model parameters and deduce analytical bounds of the stable domain. While increasing values of the delay and remodelling rate render the model unstable, we also show that increasing friction with the substrate destabilise the oscillatory response. Furthermore, we numerically verify that the extension of the model to non-linear strain measures is able to generate sustained oscillations that alternate between stable and unstable regions.
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