Tumor growth parameters estimation and source localization from a unique time point: Application to low-grade gliomas

Coupling time series of MR Images with reaction-diffusion-based models has provided interesting ways to better understand the proliferative-invasive aspect of glial cells in tumors. In this paper, we address a different formulation of the inverse problem: from a single time point image of a non-swollen brain tumor, estimate the tumor source location and the diffusivity ratio between white and grey matter, while exploring the possibility to predict the further extent of the observed tumor at later time points in low-grade gliomas. The synthetic and clinical results show the stability of the located source and its varying distance from the tumor barycenter and how the estimated ratio controls the spikiness of the tumor.