Mesoscopic and continuum modelling of angiogenesis.
Mesoscopic and continuum modelling of angiogenesis.
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DOI：
10.1007/s00285-014-0771-1
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发表时间：
2015-02
影响因子：
1.9
通讯作者：
Byrne HM
中科院分区：
文献类型：
--
作者：
Spill F;Guerrero P;Alarcon T;Maini PK;Byrne HM
血管生成是响应于由例如伤口或肿瘤分泌的化学信号而从预先存在的血管形成新的血管。在本文中，我们提出了一个基于介观格子的血管生成模型，其中包括增殖和细胞运动的过程被认为是随机事件。通过研究的晶格间距和所涉及的细胞的数量的模型的依赖性，我们能够推导出我们的方程的确定性连续极限，并将其与现有的类似模型的血管生成。我们进一步确定的条件下，使用连续模型是合理的，和其他随机或离散效应占主导地位。我们还比较了不同的随机模型的内皮尖端细胞的运动具有相同的宏观，确定性的行为，但导致显着不同的行为方面的生产新的血管细胞。
Angiogenesis is the formation of new blood vessels from pre-existing ones in response to chemical signals secreted by, for example, a wound or a tumour. In this paper, we propose a mesoscopic lattice-based model of angiogenesis, in which processes that include proliferation and cell movement are considered as stochastic events. By studying the dependence of the model on the lattice spacing and the number of cells involved, we are able to derive the deterministic continuum limit of our equations and compare it to similar existing models of angiogenesis. We further identify conditions under which the use of continuum models is justified, and others for which stochastic or discrete effects dominate. We also compare different stochastic models for the movement of endothelial tip cells which have the same macroscopic, deterministic behaviour, but lead to markedly different behaviour in terms of production of new vessel cells.