In this work, we obtain the numerical solutions of a 2D mathematical model of tumor angiogenesis originally presented in [Pamuk S, ÇAY İ, Sazci A, A 2D mathematical model for tumor angiogenesis: The roles of certain cells in the extra cellular matrix, Math Biosci 306:32–48, 2018] to numerically prove that the certain cells, the endothelials (EC), pericytes (PC) and macrophages (MC) follow the trails of the diffusions of some chemicals in the extracellular matrix (ECM) which is, in fact, inhomogeneous. This leads to branching, the sprouting of a new neovessel from an existing vessel. Therefore, anastomosis occurs between these sprouts. In our figures we do see these branching and anastomosis, which show the fact that the cells diffuse according to the structure of the ECM. As a result, one sees that our results are in good agreement with the biological facts about the movements of certain cells in the Matrix.

中文翻译：

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某些细胞遵循某些化学物质在细胞外基质中的扩散轨迹的数值证明

在这项工作中，我们获得了最初在 [Pamuk S, ÇAY İ, Sazci A, 肿瘤血管生成的二维数学模型：某些细胞在细胞外基质中的作用，数学生物科学 306:32–48, 2018] 以数值证明某些细胞、内皮细胞 (EC)、周细胞 (PC) 和巨噬细胞 (MC) 遵循某些化学物质在细胞外基质 (ECM) 中的扩散轨迹，即在事实上，不均匀。这会导致分支，即从现有血管中长出新血管。因此，这些芽之间发生吻合。在我们的图中，我们确实看到了这些分支和吻合，这表明细胞根据 ECM 的结构扩散。结果，人们看到我们的结果与关于矩阵中某些细胞运动的生物学事实非常吻合。