Diffusion tensor imaging measures diffusion of water in tissue. Within structured tissue, such as neural fiber tracts of the human brain, anisotropic diffusion is observed since the cell membranes of the long cylindric nerves restrict diffusion. Diffusion tensor imaging thus provides information about neural fiber tracts within the human brain which is of major interest for neurosurgery. However, the visualization is a challenging task due to noise and limited resolution of the data. A common visualization strategy of white matter is fiber tracking which utilizes techniques known from flow visualization. The resulting streamlines provide a good impression of the spatial relation of fibers and anatomy. Therefore, they are a valuable supplement for neurosurgical planning. As a drawback, fibers may diverge from the exact path due to numerical inaccuracies during streamline propagation even if higher order integration is used. To overcome this problem, a novel strategy for directional volume growing is presented which enables the extraction of separate tract systems and thus allows to compare and estimate the quality of fiber tracking algorithms. Furthermore, the presented approach is suited to get a more precise representation of the volume encompassing white matter tracts. Thereby, the entire volume potentially containing fibers is provided in contrast to fiber tracking which only shows a more restricted representation of the actual volume of interest. This is of major importance in brain tumor cases where white matter tracts are in the close vicinity of brain tumors. Overall, the presented strategy contributes to make surgical planning safer and more reliable.