We examine the consequences of long-range effects on tumour cell migration. Our starting point are previous results of ours where we have shown that the migration patterns of glioma cells are best interpreted if one assumes attractive interactions between cells. Here we complement the cellular automaton model previously introduced by the assumption of the existence of a chemorepellent produced by the main bulk of large spheroids (in the hypoxic/necrotic areas). Visible effects due to the presence of such a substance can be found in the density profiles of cells migrating out of a single spheroid as well as in the angular distribution of cells coming from two close-lying spheroids. These effects depend crucially on the diffusion speed of the chemorepellent. A comparison of the simulation results to experimental data of Werbowetski et al. allows to draw (tentative) conclusions on the existence of a chemorepellent and its properties.

中文翻译：

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迁移肿瘤细胞的短程和长程相互作用模型

我们研究了对肿瘤细胞迁移的长期影响的后果。我们的出发点是我们之前的结果，我们已经表明，如果假设细胞之间具有吸引力的相互作用，则可以最好地解释神经胶质瘤细胞的迁移模式。在这里，我们补充了先前引入的元胞自动机模型，假设存在由大部分大球体（在缺氧/坏死区域）产生的化学驱虫剂。由于这种物质的存在，可以在从单个球体迁移出的细胞的密度分布中以及在来自两个靠近的球体的细胞的角分布中找到由于这种物质的存在而产生的可见影响。这些效果主要取决于化学驱虫剂的扩散速度。模拟结果与 Werbowetski 等人的实验数据的比较。