Geodesic
A mathematical model of systemic inhibition of angiogenesis in metastatic development
Sébastien Benzekry1 ; Alberto Gandolfi2 ; Philip Hahnfeldt3
1 Inria team MC2, Institut de Mathématiques de Bordeaux, Bordeaux, France
2 Istituto di Analisi dei Sistemi ed Informatica “Antonio Ruberti” - CNR, Roma, Italy
3 Center of Cancer Systems Biology, GRI, Tufts University School of Medicine, Boston, 02142, USA
ESAIM. Proceedings, Tome 45 (2014), pp. 75-87.

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We present a mathematical model describing the time development of a population of tumors subject to mutual angiogenic inhibitory signaling. Based on biophysical derivations, it describes organism-scale population dynamics under the influence of three processes: birth (dissemination of secondary tumors), growth and inhibition (through angiogenesis). The resulting model is a nonlinear partial differential transport equation with nonlocal boundary condition. The nonlinearity stands in the velocity through a nonlocal quantity of the model (the total metastatic volume). The asymptotic behavior of the model is numerically investigated and reveals interesting dynamics ranging from convergence to a steady state to bounded non-periodic or periodic behaviors, possibly with complex repeated patterns. Numerical simulations are performed with the intent to theoretically study the relative impact of potentiation or impairment of each process of the birth/growth/inhibition balance. Biological insights on possible implications for the phenomenon of “cancer without disease” are also discussed.
DOI : 10.1051/proc/201445008

Sébastien Benzekry 1 ; Alberto Gandolfi 2 ; Philip Hahnfeldt 3

1 Inria team MC2, Institut de Mathématiques de Bordeaux, Bordeaux, France
2 Istituto di Analisi dei Sistemi ed Informatica “Antonio Ruberti” - CNR, Roma, Italy
3 Center of Cancer Systems Biology, GRI, Tufts University School of Medicine, Boston, 02142, USA 
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     title = {A mathematical model of systemic inhibition of angiogenesis in metastatic development},
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Sébastien Benzekry; Alberto Gandolfi; Philip Hahnfeldt. A mathematical model of systemic inhibition of angiogenesis in metastatic development. ESAIM. Proceedings, Tome 45 (2014), pp. 75-87. doi : 10.1051/proc/201445008. http://geodesic.mathdoc.fr/articles/10.1051/proc/201445008/

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