细胞侵入周围组织的行波分析
Travelling wave analysis of cellular invasion into surrounding tissues
摘要：
单物种反应扩散方程，如Fisher-KPP和Porous-Fisher方程，支持行波解，通常被解释为生物入侵的简单数学模型。这样的行波解决方案被认为在包括发育、伤口愈合和恶性侵袭的各种应用中发挥作用。对这些单物种方程的一个批评是，它们没有明确描述入侵种群与周围环境之间的相互作用。在这项工作中，我们研究了一个反应扩散方程，描述了恶性肿瘤的侵袭已被用来解释实验测量描述恶性黑色素瘤细胞侵入周围的人体皮肤组织。该模型明确描述了癌细胞群如何降解周围组织，从而创造自由空间，癌细胞在其中迁移和增殖，形成恶性组织的入侵波，并与皮肤组织的撤退波耦合。我们分析行波解的数值模拟，相平面分析和微扰技术相结合，这个模型。我们的分析表明，行波解涉及一系列非常有趣的性质，类似于Fisher-KPP和Porous-Fisher方程的某些既定特征，以及一系列新的性质，可以被认为是这些研究良好的单物种方程的扩展。特别令人感兴趣的是，行波解的入侵模型是非常好的近似的轨迹，通常被忽视的费舍尔-KPP相平面。这一观察建立了一个以前未被注意的联系耦合多物种反应扩散模型的入侵和不同类别的模型，涉及移动边界问题的入侵。
英文摘要：
Single-species reaction-diffusion equations, such as the Fisher-KPP and Porous-Fisher equations, support travelling wave solutions that are often interpreted as simple mathematical models of biological invasion. Such travelling wave solutions are thought to play a role in various applications including development, wound healing and malignant invasion. One criticism of these single-species equations is that they do not explicitly describe interactions between the invading population and the surrounding environment. In this work we study a reaction-diffusion equation that describes malignant invasion which has been used to interpret experimental measurements describing the invasion of malignant melanoma cells into surrounding human skin tissues. This model explicitly describes how the population of cancer cells degrade the surrounding tissues, thereby creating free space into which the cancer cells migrate and proliferate to form an invasion wave of malignant tissue that is coupled to a retreating wave of skin tissue. We analyse travelling wave solutions of this model using a combination of numerical simulation, phase plane analysis and perturbation techniques. Our analysis shows that the travelling wave solutions involve a range of very interesting properties that resemble certain well-established features of both the Fisher-KPP and Porous-Fisher equations, as well as a range of novel properties that can be thought of as extensions of these well-studied single-species equations. Of particular interest is that travelling wave solutions of the invasion model are very well approximated by trajectories in the Fisher-KPP phase plane that are normally disregarded. This observation establishes a previously unnoticed link between coupled multi-species reaction diffusion models of invasion and a different class of models of invasion that involve moving boundary problems.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
