Mathematical model of cancer growth controled by metronomic chemotherapies

Nicolas Andre (1, 2) , Dominique Barbolosi (2) , Frédérique Billy (3, 4) , Guillemette Chapuisat (5) , Florence Hubert (5) , Emmanuel Grenier (6) , Amandine Rovini (2)

1 TIMONE - Hôpital de la Timone [CHU - APHM]
2 CRO2 - Centre de Recherches en Oncologie biologique et Oncopharmacologie
3 LJLL - Laboratoire Jacques-Louis Lions
4 BANG - Nonlinear Analysis for Biology and Geophysical flows
5 LATP - Laboratoire d'Analyse, Topologie, Probabilités
6 NUMED - Numerical Medicine

We propose in this article to compare the efficiency of two chemotherapeutic schedules: the traditional and the metronomic. For this, we develop a new mathematical model describing the growth dynamics of tumor and endothelial cells as well as the impact of molecules as oxygen or vascular endothelial growth factor on this dynamics. The model construction: biological assumptions, description of the equations and their discretization, constitutes the core of the article. Numerical experiments illustrate the expected behavior of the disease under the two chemotherapeutic schedules.

Mots clés: mathematical modeling; tumor growth; angiogenesis; metronomic chemotherapy

Domaines: Equations aux dérivées partielles [math.AP]; Cancer; Modélisation et simulation; Bio-Informatique, Biologie Systémique [q-bio.QM]; Bio-informatique [q-bio.QM]

Nicolas Andre, Dominique Barbolosi, Frédérique Billy, Guillemette Chapuisat, Florence Hubert, et al.. Mathematical model of cancer growth controled by metronomic chemotherapies. CANUM 2012, 41e Congrès National d'Analyse Numérique, 2012, France. pp.77-94, ⟨10.1051/proc/201341004⟩. ⟨hal-00751645v1⟩