In this paper, we present a tractography paradigm that addresses the challenge of tracking through edema as well as regions of complex white matter. It involves the fitting of a multi-compartment model to a multi-shell acquisition, with one compartment pertaining to free water that characterizes the edema, and the second compartment, a higher order diffusion model that captures the underlying fiber structure. This is then incorporated into a probabilistic streamline tracking algorithm. This paradigm has been validated using cortical stimulation data acquired on patients. We applied the tracking paradigm to the datasets of the MICCAI Tractography Challenge. As the data comprised four shells, b = 200, 500, 1000 and 3000 s/mm2 respectively, we were able to successfully fit a two-compartment model to the data that combines edema correction with a fiber orientation distribution (FOD) scheme to create a new higher order diffusion model. We then used this higher order diffusion model for tracking the cortico-spinal tract (CST) in the two patients with brain tumor. The tract was reconstructed using inclusion regions in the cerebral peduncle provided with the Challenge data, as well as regions defining the motor cortex segmented in the two subjects using an atlas. The results of fiber tracking showed that we were able to track through the edema, as well as complex white matter to reconstruct the CST, obtaining not only the main trunk of the CST, but also the lateral fibers to the hand and face regions. The results on the Challenge data were evaluated for anatomical correctness by two neurosurgeons, as well as for overlap with the motor strip provided with the Challenge data.