Mathematical model of cancer growth controled by metronomic chemotherapies

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...

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Bibliographic Details
Published in:ESAIM. Proceedings 2013-12, Vol.41, p.77-94
Main Authors: André, N., Barbolosi, D., Billy, F., Chapuisat, G., Hubert, F., Grenier, E., Rovini, A.
Format: Article
Language:English
Subjects:
Analysis of PDEs
Bioinformatics
Cancer
Computational efficiency
Computer Science
Discretization
Dynamics
Endothelial cells
Growth factors
Life Sciences
Mathematical analysis
Mathematical models
Mathematics
Modeling and Simulation
Quantitative Methods
Schedules
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Summary: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. Nous proposons dans cet article de comparer l’action de deux protocoles d’administration de chimiothérapie. Pour cela, nous développons un nouveau modèle mathématique décrivant la dynamique de croissance de diverses cellules tumorales et endothéliales et l’impact sur cette dynamique de molécules comme l’oxygène et de facteurs de croissances endothéliales. La construction du modèle, à savoir les hypothèses biologiques sous-jacentes, la description des équations et leur discrétisation constitue le coeur de cet article. Nous donnons quelques illustrations numériques de l’évolution de la maladie sous l’action des deux protocoles thérapeutiques et retrouvons les résultats attendus par les oncologues.
ISSN:1270-900X
2267-3059
1270-900X
2267-3059
DOI:10.1051/proc/201341004