We introduce a hybrid two-dimensional multiscale model of angiogenesis, the process by which endothelial cells (ECs) migrate from a pre-existing vascular bed in response to local environmental cues and cell-cell interactions, to create a new vascular network. Recent experimental studies have highlighted a central role of cell rearrangements in the formation of angiogenic networks. Our model accounts for this phenomenon via the heterogeneous response of ECs to their microenvironment. These cell rearrangements, in turn, dynamically remodel the local environment. The model reproduces characteristic features of angiogenic sprouting that include branching, chemotactic sensitivity, the brush border effect, and cell mixing. These properties, rather than being hardwired into the model, emerge naturally from the gene expression patterns of individual cells. After calibrating and validating our model against experimental data, we use it to predict how the structure of the vascular network changes as the baseline gene expression levels of the VEGF-Delta-Notch pathway, and the composition of the extracellular environment, vary. In order to investigate the impact of cell rearrangements on the vascular network structure, we introduce the mixing measure, a scalar metric that quantifies cell mixing as the vascular network grows. We calculate the mixing measure for the simulated vascular networks generated by ECs of different lineages (wild type cells and mutant cells with impaired expression of a specific receptor). Our results show that the time evolution of the mixing measure is directly correlated to the generic features of the vascular branching pattern, thus, supporting the hypothesis that cell rearrangements play an essential role in sprouting angiogenesis. Furthermore, we predict that lower cell rearrangement leads to an imbalance between branching and sprout elongation. Since the computation of this statistic requires only individual cell trajectories, it can be computed for networks generated in biological experiments, making it a potential biomarker for pathological angiogenesis.

我们介绍了一种血管生成的混合二维多尺度模型，该过程是内皮细胞（EC）通过响应局部环境提示和细胞间相互作用从先前存在的血管床迁移而创建新的血管网络的过程。最近的实验研究强调了细胞重排在血管生成网络形成中的核心作用。我们的模型通过EC对其微环境的异质响应来解释这种现象。这些单元的重新排列又动态地重塑了本地环境。该模型再现了血管新生的特征，包括分支，趋化敏感性，刷状边界效应和细胞混合。这些特性，而不是硬性连接到模型中，自然是从单个细胞的基因表达模式中显现出来的。在根据实验数据校准并验证我们的模型后，我们将其用于预测血管网络的结构如何随着VEGF-Delta-Notch途径的基线基因表达水平以及细胞外环境的组成而变化。为了研究细胞重排对血管网络结构的影响，我们引入了混合量度，这是一种标量度量，用于量化随着血管网络增长而发生的细胞混合。我们计算由不同谱系（野生型细胞和具有特定受体表达受损的突变细胞）的EC产生的模拟血管网络的混合量度。我们的结果表明，混合量度的时间演变与血管分支模式的一般特征直接相关，因此，支持细胞重排在发芽血管生成中起重要作用的假说。此外，我们预测较低的细胞重排会导致分支和芽伸长之间的不平衡。由于此统计信息的计算仅需要单个细胞轨迹，因此可以针对生物学实验中生成的网络进行计算，使其成为病理性血管生成的潜在生物标记。