In cancer treatment, understanding the aggressiveness of the tumor is essential in therapy planning and patient follow-up. In this article, we present a novel method for quantifying the speed of invasion of gliomas in white and grey matter from time series of magnetic resonance (MR) images. The proposed approach is based on mathematical tumor growth models using the reaction-diffusion formalism. The quantification process is formulated by an inverse problem and solved using anisotropic fast marching method yielding an efficient algorithm. It is tested on a few images to get a first proof of concept with promising new results.