Diffusion Tensor Magnetic Resonance Imaging (DT-MRI) is a non invasive method for brain neuronal fibers delineation. Here we show a modification for DT-MRI that allows delineation of neuronal fibers which are infiltrated by edema. We use the Muliple Tensor Variational (MTV) framework which replaces the diffusion model of DT-MRI with a multiple component model and fits it to the signal attenuation with a variational regularization mechanism. In order to reduce free water contamination we estimate the free water compartment volume fraction in each voxel, remove it, and then calculate the anisotropy of the remaining compartment. The variational framework was applied on data collected with conventional clinical parameters, containing only six diffusion directions. By using the variational framework we were able to overcome the highly ill posed fitting. The results show that we were able to find fibers that were not found by DT-MRI.