Ubiquitous modeling for scales interaction. Application for tumor response prediction during radiotherapy

The work presented in this thesis focused on the mathematical modeling of tumor response during treatment by radiotherapy. The goal was to provide for doctors a digital tool to help cancer diagnose. For example, monitoring tumor volume during and after treatment, rehabilitating therapeutic strategies, etc. In a first step, we proposed a discrete stochastic model based on a multiscale approach. In this context, we focused on three different scales of tumor modeling: microscopic scale (cells in a voxel), mesoscopic scale (cell population in a voxel) and macroscopic scale (tumor tissue), with transitional interfaces between these three scales. At the cellular level, the description was based on probabilities of phase transfer in the cellular cycle. At the mesoscopic scale, we represented cell populations according to the different stages of a cell cycle. Finally, on a macroscopic scale, tumor description was based on the use of FDG PET medical images. These three scales naturally exist: the biological data were collected at the macroscopic level but the pathological behavior of the tumor is based on an abnormal cell cycle at the microscopic scale. Introduction of a mesoscopic scale was essential to reduce the gap between the two extremes, in terms of transition between them. We used the discrete multiscale model to predict the temporal evolution of the tumor cells number. On the other hand, this model was not well adapted to predict the tumor volume evolution. Thus, we had proposed a second model which was biomechanical and based on an advection reaction equation. Finally, the discrete multiscale and the biomechanical models had been combined to form an hybrid model. Indeed, the discrete model was used to estimate the oxygen partial pressures trajectories, in the tumor environment. These pressures were then input to the continuous (biomechanical) model for the tumor volume evolution prediction. (author)