Bulletin of Mathematical Biology

, Volume 66, Issue 6, pp 1785–1819 | Cite as

Lattice and non-lattice models of tumour angiogenesis

  • M. J. PlankEmail author
  • B. D. Sleeman


In order to progress from the relatively harmless avascular state to the potentially lethal vascular state, solid tumours must induce the growth of new blood vessels from existing ones, a process called angiogenesis. The capillary growth centres around endothelial cells: there are several cell-based models of this process in the literature and these have reproduced some of the key microscopic features of capillary growth. The most common approach is to simulate the movement of leading endothelial cells on a regular lattice. Here, we apply a circular random walk model to the process of angiogenesis, and thus allow the cells to move independently of a lattice; the results display good agreement with empirical observations. We also run simulations of two lattice-based models in order to make a critical comparison of the different modelling approaches. Finally, non-lattice simulations are carried out in the context of a realistic model of tumour angiogenesis, and potential anti-angiogenic strategies are evaluated.


Prefer Direction Capillary Network Rotational Diffusivity Random Walk Model Parent Vessel 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Society for Mathematical Biology 2004

Authors and Affiliations

  1. 1.School of MathematicsUniversity of LeedsLeedsUK

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