%0 Journal Article
%T Mathematical model of cancer growth controled by metronomic chemotherapies
%+ Hôpital de la Timone [CHU - APHM] (TIMONE)
%+ Centre de Recherches en Oncologie biologique et Oncopharmacologie (CRO2)
%+ Laboratoire Jacques-Louis Lions (LJLL)
%+ Nonlinear Analysis for Biology and Geophysical flows (BANG)
%+ Laboratoire d'Analyse, Topologie, Probabilités (LATP)
%+ Numerical Medicine (NUMED)
%A Andre, Nicolas
%A Barbolosi, Dominique
%A Billy, Frédérique
%A Chapuisat, Guillemette
%A Hubert, Florence
%A Grenier, Emmanuel
%A Rovini, Amandine
%< avec comité de lecture
%@ 2267-3059
%J ESAIM: Proceedings and Surveys
%3 CANUM 2012, 41e Congrès National d'Analyse Numérique
%B CANUM 2012, 41e Congrès National d'Analyse Numérique
%C Superbesse, France
%I EDP Sciences
%V 41
%P 77-94
%8 2013-12-09
%D 2013
%R 10.1051/proc/201341004
%K mathematical modeling
%K tumor growth
%K angiogenesis
%K metronomic chemotherapy
%Z Mathematics [math]/Analysis of PDEs [math.AP]
%Z Life Sciences [q-bio]/Cancer
%Z Computer Science [cs]/Modeling and Simulation
%Z Life Sciences [q-bio]/Quantitative Methods [q-bio.QM]
%Z Computer Science [cs]/Bioinformatics [q-bio.QM]Journal articles
%X 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.
%G English
%2 https://hal.science/hal-00751645v2/document
%2 https://hal.science/hal-00751645v2/file/proceeding_angio_rev.pdf
%L hal-00751645
%U https://hal.science/hal-00751645
%~ ENS-LYON
%~ UNIV-PARIS7
%~ UPMC
%~ CNRS
%~ INRIA
%~ UNIV-AMU
%~ INRIA-RHA
%~ INRIA-ROCQ
%~ EC-MARSEILLE
%~ LJLL
%~ INRIA_TEST
%~ TESTALAIN1
%~ I2M
%~ INRIA2
%~ TDS-MACS
%~ UPMC_POLE_1
%~ INRIA-RENGRE
%~ SORBONNE-UNIVERSITE
%~ SU-SCIENCES
%~ UDL
%~ UNIV-LYON
%~ UNIV-PARIS
%~ SU-TI
%~ ALLIANCE-SU