Abstract
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.
Original language | English |
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Pages (from-to) | 29-38 |
Number of pages | 10 |
Journal | Discrete and Continuous Dynamical Systems - Series B |
Volume | 4 |
Issue number | 1 |
DOIs | |
State | Published - Feb 2004 |
Externally published | Yes |
Keywords
- Angiogenesis
- Hopf points
- Time-delay differential equations
ASJC Scopus subject areas
- Discrete Mathematics and Combinatorics
- Applied Mathematics