## Modeling of the metastatic variability in cancer disease.

F. Verga (1) (2), B. You (3), A. Benabdallah (2), F. Hubert (2), C Faivre (1), D. Barbolosi (1)

(1) Faculty of Pharmacy-Pharmacokinetics Department UMR MD3, Marseille, France (2) LATP UMR 6632, University of Provence, Marseille, France, (3) MD, Oncology Department, Lyon Sud Hospital, France

Objectives: In cancer diseases the appearence of metastases is a very pejorative forecast. In a first time we shall show how  our work could help to precise the stage of disease for each patient with respect of their metastatic risk. In a second time we aim to find the optimal number of chemotherapy cycles in order to minimize  the occurence of new metastases on the long term.

Methods: We have developed a mathematical model [1] based on partial differential equations, governed by four parameters: two for describing the tumoral aggressiveness and two in order to take into account the metastatic colonization. This model permits to compute the evolution of the total metastases number produced from a given primary tumor, with respect to the time. We call this number the Metastatic Index (MI).

Results: At first we shall present the impact of the parameters variability on the metastatic distribution. In a retrospective tri al Koscielny et al. have defined in [2] the risk to develop metastases with respect to the initial tumor mass. These data have been compared to those computed by the model. The similarity of the computed results and the observed ones could confirm the ability of the model in predicting the risk of metastatic extension.
In a second time we shall include in this modeling a chemotherapy treatment in the case of the metastatic breast cancer and we shall describe the variability of the total metastases number with respect to the variability of the chemotherapy cycles number.

Conclusions: The previous results show that the computation of the MI could be a useful tool in order to precise the tumoral classification and moreover it could help to target the best treatment for each patient.

References:
[1] D.Barbolosi, A.Benabdallah, F.Hubert, F.Verga, "Mathematical and numerical analysis for a model of growing metastatic tumors", Mathematical Biosciences, 2009, 218, pages 1-14.
[2] S.Koscielny, M.Tubiana, MG Le, "Breast cancer: a relationship between the size of the primary tumor and the probabilty of metastatic  dissemination". British Journal of Cancer, 1984,; 49, pages 709-715.

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