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Abstract: Although the same simple laws govern cancer outcome (cell division repeated again and again), each tumour has a different outcome before as well as after irradiation therapy. The linear-quadratic radiosensitivity model allows an assessment of tumor sensitivity to radiotherapy. This model presents some limitations in clinical practice because it does not take into account the interactions between tumour cells and non-tumoral bystander cells (such as endothelial cells, fibroblasts, immune cells…) that modulate radiosensitivity and tumor growth dynamics. These interactions can lead to non-linear and complex tumor growth which appears to be random but that is not since there is not so many tumors spontaneously regressing. In this paper we propose to develop a deterministic approach for tumour growth dynamics using chaos theory. Various characteristics of cancer dynamics and tumor radiosensitivity can be explained using mathematical models of competing cell species. [Copyright &y& Elsevier]

Abstract: The oncologist is confronted daily by questions related to the fact that any patient presents a specific evolution for his cancer: he is challenged by very different, unexpected and often unpredictable outcomes, in some of his patients. The mathematical approach used today to describe this evolution has recourse to statistics and probability laws: such an approach does not ultimately apply to one particular patient, but to a given more or less heterogeneous population. This approach therefore poorly characterizes the dynamics of this disease and does not allow to state whether a patient is cured, to predict if he will relapse and when this could occur, and in what form, nor to predict the response to treatment and, in particular, to radiation therapy. Chaos theory, not well known by oncologists, could allow a better understanding of these issues. Developed to investigate complex systems producing behaviours that cannot be predicted due to a great sensitivity to initial conditions, chaos theory is rich of suitable concepts for a new approach of cancer dynamics. This article is three-fold: to provide a brief introduction to chaos theory, to clarify the main connecting points between chaos and carcinogenesis and to point out few promising research perspectives, especially in radiotherapy. [Copyright &y& Elsevier]