Currently, most research in oncology involve genetic mutations potentially responsible for cancer initiation. Since the identification of a large number of genes involved in carcinogenesis is not correlated to an increase in number of patients in remission, investigating a cancer as a pure genetic process was not effecient as initially expected. Although genetic mutations have a key role in tumorigenesis, some other factors such as the micro-environment should be also considered. In daily practice, the oncologist must address the question of his ability to predict (or not) the evolution of the cancer his patient has. He is thus challenged by too often unpredictable outcomes, which can be explained by the too large number of parameters influencing the cancer evolution and the technology available to evaluate them. The nonlinear dynamical systems theory could be helpful to better understand this disease.
Thus, the aim of this thesis is to investigate tumor dynamics, thanks to chaos theory, by taking into account the role of the micro-environment. After a description of the biology involved in carcinogenesis, a model having the advantage of involving the host cells, the tumor micro-environment, in addition to effector immune and tumor cells, was analyzed. We found that an action on host cells is more efficient than an action on the tumor mass. In order to reproduce the tumor neo-angiogenesis, a fourth equation was added to describe the evolution of endothelial cells. This new model was able to reproduce the angiogenic switch occurring between the avascular and vascular stages of tumorigenesis. This four-dimensional model (limited to a single tumor site) was then extended to a regular grid to simulate the spatial growth of tumors. Avascular phase simulations of tumor growth were performed and the obtained dynamic was analyzed.