In the present report, we propose a new model to simulate the growth of glioblastomas multiforma (GBM), the most aggressive glial tumors. Because the GBM shows a preferential growth in the white fibers and have a distinct invasion speed with respect to the nature of the invaded tissue, we rely on an anatomical atlas to introduce this information into the model. This atlas includes a white fibers diffusion tensor information and the delineation of cerebral structures having a distinct response to the tumor aggression. We use the finite element method (FEM) to simulate both the invasion of the GBM in the brain parenchyma and its mechanical interaction (mass effect) with the invaded structures. The former effect is modeled with either a reaction-diffusion or a Gompertz equation depending on the considered tissue, while the latter is based on a linear elastic brain constitutive equation. In addition, we propose a new coupling equation taking into account the mechanical influence of the tumor cells on the invaded tissues. This tumor growth model is assessed by comparing the \textit{in-silico} GBM growth with the real GBM growth observed between two magnetic resonance images (MRIs) of a patient acquired with six months difference. The quality of the results shows the feasibility of modeling the complex behavior of brain tumors and will justify a further validation of this new conceptual approach.