标题： 顶点模型中参数的退化性 显示英文标题

标题： Parameter degeneracy in the vertex model for tissues

摘要： 具有均匀细胞特性的顶点模型已知在系统动力学与目标面积无关的情况下表现出参数退化。 在这里，我们展示了在细胞大小和刚度不同的异质顶点模型中，退化现象也存在，平均目标面积与刚度的乘积在动力学上变得无关。 固定这一量等价于固定全局内部组织压力。 除非适当处理，这种退化会削弱关键可观测量的数值的物理相关性，例如形状指数、细胞压力和细胞应力张量。 我们提出了解决退化的方法，并通过应用于细胞目标面积的对称变换来正确设置参考压力。 我们进一步证明，在某些边界条件下，退化会被消除，而当使用局部平面近似对球形组织进行建模时，退化部分被解除，这在将模型参数拟合到实验数据时会产生数值后果。 该方法不仅适用于顶点模型，还提供了一个框架，用于测试其他物理模型的参数空间是否免受退化的影响。 显示英文摘要

摘要： The vertex model with homogeneous cell properties is known to exhibit a parameter degeneracy in which the system's dynamics is independent of the target area. Here, we show, for the heterogeneous vertex model where cells differ in size and stiffness, that degeneracy is also present with the average product of target areas and stiffness becoming dynamically irrelevant. Fixing this quantity is equivalent to fixing the global internal tissue pressure. Unless properly treated, this degeneracy undermines the physical relevance of key observables' numerical values, such as the shape index, cell pressure, and cell stress tensor. We present methods to resolve the degeneracy and to correctly set the gauge pressure via symmetry transformations applied to the cells' target areas. We further demonstrate that the degeneracy is removed under certain boundary conditions and partially lifted when spherical tissues are modeled using a locally planar approximation, leading to numerical consequences when fitting model parameters to experimental data. The approach extends beyond vertex models and provides a framework for testing whether the parameter spaces of other physical models are free from degeneracy.