A family of models of angiogenesis and anti-angiogenesis anti-cancer therapy

被引:50
|
作者
D'Onofrio, Alberto [1 ]
Gandolfi, Alberto [2 ]
机构
[1] European Inst Oncol, Epidemiol & Biostatist Div, I-20141 Milan, Italy
[2] CNR, Ist Anal Sistemi & Informat A Ruberti, I-00185 Rome, Italy
关键词
angiogenesis; anti-angiogenesis; tumour eradication; stability; delay differential equations; TUMOR-INDUCED ANGIOGENESIS; ANTIANGIOGENIC THERAPY; POINT ANALYSIS; GROWTH; CANCER; COMBINATION; STABILITY; DORMANCY; DRUGS; ODE;
D O I
10.1093/imammb/dqn024
中图分类号
Q [生物科学];
学科分类号
07 ; 0710 ; 09 ;
摘要
In this paper we propose a class of models that describe the mutual interaction between tumour growth and the development of tumour vasculature and that generalize existing models. The study is mainly focused on the effect of a therapy that induces tumour vessel loss (anti-angiogenic therapy), with the aim of finding conditions that asymptotically guarantee the eradication of the disease under constant infusion or periodic administration of the drug. Furthermore, if tumour and/or vessel dynamics exhibit time delays, we derive conditions for the existence of Hopf bifurcations. The destabilizing effect of delays on achieving the tumour eradication is also investigated. Finally, global conditions for stability and eradication in the presence of delays are given for some particular cases.
引用
收藏
页码:63 / 95
页数:33
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