Lattice and non-lattice models of tumour angiogenesis |
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Authors: | Plank M J Sleeman B D |
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Institution: | (1) School of Mathematics, University of Leeds, Leeds, LS2 9JT, UK;(2) Department of Mathematics and Statistics, University of Canterbury, Private Bag 4800, Christchurch, New Zealand |
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Abstract: | 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. |
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Keywords: | |
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