Approches mathématiques multi-niveaux pour l'étude de la croissance des tumeurs : Application à la morphogenèse du cancer du sein et ciblage thérapeutique de l'angiogenèse du cancer du côlon

Floriane Lignet 1, 2
2 NUMED - Numerical Medicine
Inria Grenoble - Rhône-Alpes, UMPA-ENSL - Unité de Mathématiques Pures et Appliquées
Abstract : Cancer is one of the leading causes of death in Europe. The mechanisms involved in tumour growth are qualitatively known, but we are still unable to precisely predict how a given tumour will evolve, nor estimate with certainty the optimal therapeutic protocol for each patient.It is well understood that mathematical modelling could give part of the answer to these questions. That is why during this thesis we considered the building of mathematical formalisms to describe tumour growth and the action of anti-cancer treatments. In particular, we investigated the molecular to tissular mechanisms of cancer development and angiogenesis through the building of a continuous multi-scale model. We were able to reproduce the effect of anti- angiogenesis treatments on tumour growth, and qualitatively study an optimal therapeutic protocol of anti-angiogenic combined with cytotoxic drugs. This multi-scale model integrates a mathematical representation of the signalling pathways of VEGF (Vascular Endothelial Growth Factor). We detail the development of this model which is based solely on information available in the literature and dedicated databases. In another approach, we considered a discrete, cell-based model to reproduce the development of spheroid structures of mammary epithelial cells. This model considers the behaviour of these cells when observed while grown in vitro in an appropriate medium. We were able to highlight the different mechanisms involved in the morphogenesis of wild and mutated cells structures.This work shows the importance of the multi-scale formalism we used to integrate the knowledge and data related to the study of cancer treatment.
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Floriane Lignet. Approches mathématiques multi-niveaux pour l'étude de la croissance des tumeurs : Application à la morphogenèse du cancer du sein et ciblage thérapeutique de l'angiogenèse du cancer du côlon. Mathématiques générales [math.GM]. Ecole normale supérieure de lyon - ENS LYON, 2012. Français. ⟨NNT : 2012ENSL0771⟩. ⟨tel-00844807⟩

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