Journal
MATHEMATICAL BIOSCIENCES
Volume 191, Issue 2, Pages 159-184Publisher
ELSEVIER SCIENCE INC
DOI: 10.1016/j.mbs.2004.06.003
Keywords
tumour growth models; angiogenesis; periodic anticancer therapy; global stability; forced oscillators
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The model proposed by Hahnfeldt et al. (1999) describes the growth of a tumour assuming that tumour growth is strictly controlled by the evolution of the vascular network that supplies oxygen and nutrients to tumour cells. Consequently, it provides a framework to represent the effects of antiangiogenic therapies. In this paper, some possible modifications of that model are proposed, and conditions that guarantee the eradication of the tumour under a regimen of periodic antiangiogenic therapy are derived. The model variants considered assume the potential doubling time of the vasculature to be constant, and subdivide the endothelial cell pool, which is involved in angiogenesis, in resting and proliferating cells allowing for a more detailed description of drug effects. (C) 2004 Elsevier Inc. All rights reserved.
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