Mesoscopic and continuum modelling of angiogenesis
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- 作者：F. Spill (1)
P. Guerrero (2) (3)
T. Alarcon (2) (4)
P. K. Maini (5)
H. M. Byrne (1) (6)
1. OCCAM ; Mathematical Institute ; University of Oxford ; Oxford ; OX2 6GG ; UK
2. Centre de Recerca Matematica ; Campus de Bellaterra ; Edifici C ; 08193聽 ; Bellaterra ; Barcelona ; Spain
3. Department of Mathematics ; University College London ; Gower Street ; London ; WC1E 6BT ; UK
4. Departament de Matem脿tiques ; Universitat Aton貌ma de Barcelona ; 08193聽 ; Bellaterra ; Barcelona ; Spain
5. Wolfson Centre for Mathematical Biology ; Mathematical Institute ; University of Oxford ; Oxford ; OX2 6GG ; UK
6. Department of Computer Science ; University of Oxford ; Oxford ; OX1聽3QD聽 ; UK - 关键词：Angiogenesis ; Stochastic models ; Master equation ; Mesoscopic models ; Reaction鈥揹iffusion system ; 92C17 Cell movement (chemotaxis ; etc.) ; 60J70 Applications of Brownian motions ; 35Q92 PDEs in connection with biology and other natural sciences
- 刊名：Journal of Mathematical Biology
- 出版年：2015
- 出版时间：February 2015
- 年：2015
- 卷：70
- 期：3
- 页码：485-532
- 全文大小：1,256 KB
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- 刊物主题：Mathematics
Mathematical Biology
Applications of Mathematics - 出版者：Springer Berlin / Heidelberg
- ISSN：1432-1416
文摘
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.