Mathematical model of cancer growth controled by metronomic chemotherapies

Abstract

Abstract. 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.Résumé. 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, a savoir les hypothèses biologiques sous-jacentes, la description deséquations 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.

Physiologically Based Mathematical Models to Optimize Therapies Against Metastatic Colorectal Cancer: A Mini-Review

“…The biological rationale for this therapeutic strategy [64] is usually (and has initially been) presented as efficiently limiting tumor neoangiogenesis, which thrives during treatment interruptions, allowing tumors to regrow even stronger, which leads treat-ments to failures. Note that metronomic therapies are also supported by another recent model [94] based on a previous multiscale physiological model of tumor growth with angiogenesis [55]. It is also noteworthy that on different bases, without involving neoangiogenesis, but in a chronotherapeutic setting, other theoretical studies [59,74] have also led to the conclusion that avoiding treatment interruptions during long time intervals, but on the contrary administering a chemotherapy on a 24 hour-periodic basis with a short actual drug infusion time during this 24 hour-period, is an optimal (in fact only suboptimal, in as much as in its principle it searches for necessary, but not sufficient, conditions of optimality) strategy.…”

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“…schedules consisting of many, equally spaced and generally low doses of chemotherapeutic drugs without extended rest periods (see e.g. [80,81]).…”

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“…Atualmente a modelagem matemática em cânceré uma linha de pesquisa em pleno desenvolvimento que permite descrever os mecanismos de surgimento e tratamento da doença [1]. Se o cálculo de ordem não inteira munido com equações diferenciais que descrevam fenômenos físicosúteis já assume grande importância na obtenção de novos resultados, quando ligado a equações referente a crescimento tumoral essa relevânciaé ainda maior.…”