论文标题
上皮组织的自由边界机械生物学模型中的行进波
Travelling waves in a free boundary mechanobiological model of an epithelial tissue
论文作者
论文摘要
我们考虑了上皮细胞迁移的自由边界模型，并由机械相互作用引起的逻辑生长和非线性扩散。使用数值模拟，相位平面和扰动分析，我们发现并分析了具有负，零和正波的行驶波解决方案。与反应扩散方程的经典行进波解不同，我们探索的行驶波解决方案具有明确的前部，并且在相位平面中与杂斜轨道无关。我们发现自由边界处波动和密度的领先顺序表达式。有趣的是，波动溶液是否入侵还是退缩仅取决于承载能力密度是否对应于处于压缩或延伸的细胞。
We consider a free boundary model of epithelial cell migration with logistic growth and nonlinear diffusion induced by mechanical interactions. Using numerical simulations, phase plane and perturbation analysis, we find and analyse travelling wave solutions with negative, zero, and positive wavespeeds. Unlike classical travelling wave solutions of reaction-diffusion equations, the travelling wave solutions that we explore have a well-defined front and are not associated with a heteroclinic orbit in the phase plane. We find leading order expressions for both the wavespeed and the density at the free boundary. Interestingly, whether the travelling wave solution invades or retreats depends only on whether the carrying capacity density corresponds to cells being in compression or extension.
