February  2004, 4(1): 29-38. doi: 10.3934/dcdsb.2004.4.29

Hopf point analysis for angiogenesis models

1. 

Institute for Medical Biomathematics (IMBM), 10 Hate'ena St., P.O. Box 282, 60991, Bene Ataroth, Israel

2. 

Institute for Medical Biomathematics (IMBM), Hate'ena St. 10, POB 282, 60991, Bene Ataroth, Israel, Israel, Israel

Received  December 2002 Revised  September 2003 Published  November 2003

In this paper we present several ODE systems encoding the most essential observations and assumptions about the complex hierarchical interactive processes of tumor neo-vascularization (angiogenesis). From experimental results we infer that a significant marker of tumor aggressiveness is the oscillatory behavior of tumor size, which is driven by its vascularization dynamics. To study the forces underlying these oscillations we perform a Hopf point analysis of the angiogenesis models. In the analyzed models Hopf points appear if and only if a nontrivial set of time-delays is introduced into the tumor proliferation or the neo-vascularization process. We suggest to examine in laboratory experiments how to employ these results for containing cancer growth.
Citation: Zvia Agur, L. Arakelyan, P. Daugulis, Y. Ginosar. Hopf point analysis for angiogenesis models. Discrete & Continuous Dynamical Systems - B, 2004, 4 (1) : 29-38. doi: 10.3934/dcdsb.2004.4.29
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