Angiogenesis, the growth of a network of blood vessels, is a crucial component of solid tumor growth, linking the relatively harmless avascular and the potentially fatal vascular growth phases of the tumor. As a process, angiogenesis is a well-orchestrated sequence of events involving endothelial cell migration and proliferation; degradation of tissue; new capillary vessel formation; loop formation (anastomosis) and, crucially, blood flow through the network. Once there is flow associated with the nascent network, subsequent growth evolves both temporally and spatially in response to the combined effects of angiogenic factors, migratory cues via the extracellular matrix, and perfusion-related hemodynamic forces in a manner that may be described as both adaptive and dynamic. In this article, we first present a review of previous theoretical and computational models of angiogenesis and then indicate how recent developments in flow models are providing insight into antiangiogenic and chemotherapeutic drug treatment of solid tumors.

中文翻译：

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肿瘤诱导的血管生成的数学模型。

血管生成是血管网络的生长，是实体瘤生长的重要组成部分，将相对无害的无血管和可能致命的血管生长阶段联系在一起。作为一个过程，血管生成是一系列精心策划的事件，涉及内皮细胞的迁移和增殖。组织降解；新的毛细血管形成；回路形成（解剖），并且至关重要的是，血液通过网络流动。一旦存在与新生网络相关的血流，随后的生长将响应血管生成因子，通过细胞外基质的迁徙提示以及与灌注相关的血流动力学力的综合作用而在时间和空间上演化，这可以描述为适应性的。充满活力 在这篇文章中，