Angiogenesis is the process wherein endothelial cells (ECs) form sprouts that elongate from the pre-existing vasculature to create new vascular networks. In addition to its essential role in normal development, angiogenesis plays a vital role in pathologies such as cancer, diabetes and atherosclerosis. Mathematical and computational modeling has contributed to unraveling its complexity. Many existing theoretical models of angiogenic sprouting are based on the “snail-trail” hypothesis. This framework assumes that leading ECs positioned at sprout tips migrate toward low-oxygen regions while other ECs in the sprout passively follow the leaders' trails and proliferate to maintain sprout integrity. However, experimental results indicate that, contrary to the snail-trail assumption, ECs exchange positions within developing vessels, and the elongation of sprouts is primarily driven by directed migration of ECs. The functional role of cell rearrangements remains unclear. This review of the theoretical modeling of angiogenesis is the first to focus on the phenomenon of cell mixing during early sprouting. We start by describing the biological processes that occur during early angiogenesis, such as phenotype specification, cell rearrangements and cell interactions with the microenvironment. Next, we provide an overview of various theoretical approaches that have been employed to model angiogenesis, with particular emphasis on recent in silico models that account for the phenomenon of cell mixing. Finally, we discuss when cell mixing should be incorporated into theoretical models and what essential modeling components such models should include in order to investigate its functional role.

中文翻译：

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血管生成的计算模型：血管生长过程中细胞重排的重要性

血管生成是内皮细胞 (EC) 形成芽的过程，这些芽从预先存在的脉管系统中延伸出来，形成新的血管网络。血管生成除了在正常发育中发挥重要作用外，还在癌症、糖尿病和动脉粥样硬化等病理学中发挥着至关重要的作用。数学和计算模型有助于揭示其复杂性。许多现有的血管生成萌芽理论模型都是基于“蜗牛轨迹”假说。该框架假设位于芽尖的领先 EC 向低氧区域迁移，而芽中的其他 EC 被动地跟随领导者的踪迹并增殖以维持芽的完整性。然而，实验结果表明，与蜗牛轨迹假设相反，ECs 在发育中的血管内交换位置，并且芽的伸长主要是由 ECs 的定向迁移驱动的。细胞重排的功能作用仍不清楚。这篇对血管生成理论模型的综述首次关注早期萌芽过程中的细胞混合现象。我们首先描述早期血管生成过程中发生的生物过程，例如表型规范、细胞重排以及细胞与微环境的相互作用。接下来，我们概述了用于模拟血管生成的各种理论方法，特别强调了最近解释细胞混合现象的计算机模型。最后，我们讨论何时应将细胞混合纳入理论模型中，以及这些模型应包含哪些基本建模组件以研究其功能作用。