Contributions in Mathematical Oncology: When Theory Meets Reality

Accumulation of new biological and clinical data thanks to the development and generalization of novel measurement techniques (especially in imaging or molecular biology) is currently driving oncology towards a quantitative science. Meanwhile, mathematical models developed by theoreticians have often remained confined to qualitative conclusions and rarely been confronted to the observations. The work presented here aims to bridge this gap. Motivated by concrete biological or clinical questions, I have conducted combined experimental and theoretical studies with two main objectives: 1) better understand and 2) better predict. The contributions belong to three axis of research: tumor growth, metastasis and scheduling of anti-cancer treatments. The mathematical tools are mostly ordinary differential equations or physiologically structured partial differential equations. Statistical tools were also largely employed to fit the models to the data and test the hypotheses, with a major focus on nonlinear mixed-effects models. Together, these contributions represent a step forward towards the development of quantitative methods in cancer biology. They also set the basis for computational tools of clinical value to help defining the design of clinical trials (at the population level) but also to better assess the diagnosis and prognosis of a cancer disease in a personalized way, in order to individually tailor the therapeutic intervention