Byrne H M, Chaplain M A
School of Mathematical Sciences, University of Bath, U.K.
Bull Math Biol. 1995 May;57(3):461-86. doi: 10.1007/BF02460635.
To ensure its sustained growth, a tumour may secrete chemical compounds which cause neighbouring capillaries to form sprouts which then migrate towards it, furnishing the tumour with an increased supply of nutrients. In this paper a mathematical model is presented which describes the migration of capillary sprouts in response to a chemoattractant field set up by a tumour-released angiogenic factor, sometimes termed a tumour angiogenesis factor (TAF). The resulting model admits travelling wave solutions which correspond either to successful neovascularization of the tumour or failure of the tumour to secure a vascular network, and which exhibit many of the characteristic features of angiogenesis. For example, the increasing speed of the vascular front, and the evolution of an increasingly developed vascular network behind the leading capillary tip front (the brush-border effect) are both discernible from the numerical simulations. Through the development and analysis of a simplified caricature model, valuable insight is gained into how the balance between chemotaxis, tip proliferation and tip death affects the tumour's ability to induce a vascular response from neighbouring blood vessels. In particular, it is possible to define the success of angiogenesis in terms of known parameters, thereby providing a potential framework for assessing the viability of tumour neovascularization in terms of measurable quantities.
为确保持续生长，肿瘤可能会分泌一些化合物，这些化合物会促使邻近的毛细血管形成芽，然后芽向肿瘤迁移，从而为肿瘤提供更多的营养供应。本文提出了一个数学模型，该模型描述了毛细血管芽在肿瘤释放的血管生成因子（有时称为肿瘤血管生成因子，TAF）所建立的化学引诱剂场作用下的迁移。由此产生的模型允许行波解，这些解要么对应于肿瘤成功的新血管生成，要么对应于肿瘤未能建立血管网络，并且展现出血管生成的许多特征。例如，从数值模拟中可以看出血管前沿速度的增加以及在领先的毛细血管尖端前沿后面日益发达的血管网络的演变（刷状缘效应）。通过开发和分析一个简化的模型，我们深入了解了趋化性、尖端增殖和尖端死亡之间的平衡如何影响肿瘤诱导邻近血管产生血管反应的能力。特别是，可以根据已知参数来定义血管生成的成功与否，从而为根据可测量的量评估肿瘤新血管生成的可行性提供一个潜在的框架。
