Carter Paul, Doelman Arjen, van Heijster Peter, Levy Daniel, Maini Philip, Okey Erin, Yeung Paige
Department of Mathematics, University of California, Irvine, CA, USA.
Mathematical Institute, Leiden University, Leiden, Netherlands.
J Math Biol. 2025 May 5;90(6):55. doi: 10.1007/s00285-025-02209-w.
We consider a Gatenby-Gawlinski-type model of invasive tumors in the presence of an Allee effect. We describe the construction of bistable one-dimensional traveling fronts using singular perturbation techniques in different parameter regimes corresponding to tumor interfaces with, or without, an acellular gap. By extending the front as a planar interface, we perform a stability analysis to long wavelength perturbations transverse to the direction of front propagation and derive a simple stability criterion for the front in two spatial dimensions. In particular we find that in general the presence of the acellular gap indicates transversal instability of the associated planar front, which can lead to complex interfacial dynamics such as the development of finger-like protrusions and/or different invasion speeds.
我们考虑存在阿利效应时侵袭性肿瘤的加滕比 - 高林斯基型模型。我们描述了在不同参数区域中使用奇异摄动技术构建双稳一维行波前沿，这些区域对应有或无细胞间隙的肿瘤界面。通过将前沿扩展为平面界面，我们对垂直于前沿传播方向的长波长扰动进行稳定性分析，并推导二维空间中前沿的简单稳定性判据。特别地，我们发现一般来说，细胞间隙的存在表明相关平面前沿的横向不稳定性，这可能导致复杂的界面动力学，如指状突起的形成和/或不同的侵袭速度。
