Hopf point analysis for angiogenesis models
The authors present several ODE systems encoding the most essential observations and assumption on the complex hierarchical interactive processes of tumor neo-vascularization. From experimental results they 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, they perform a Hopf-point analysis of the angiogenesis models and obtain the result that Hopf points appear if and only if a nontrivial set of time-delays is introduced into the tumor proliferation or the neo-vascularization process.
scientific article; zbMATH DE number 2069698