Purpose: Diffusion Tensor Imaging (DTI) is a powerful imaging technique that has led to improvements in the diagnosis and prognosis of cerebral lesions and neurosurgical guidance for tumor resection. Traditional tensor modeling, however, has difficulties in differentiating tumor-infiltrated regions and peritumoral edema. Here, we describe the supertoroidal model, which incorporates an increase in surface genus and a continuum of toroidal shapes to improve upon the characterization of Glioblastoma multiforme (GBM). Materials and Methods: DTI brain datasets of 18 individuals with GBM and 18 normal subjects were acquired using a 3T scanner. A supertoroidal model of the diffusion tensor and two new diffusion tensor invariants, one to evaluate diffusivity, the toroidal volume (TV), and one to evaluate anisotropy, the toroidal curvature (TC), were applied and evaluated in the characterization of GBM brain tumors. TV and TC were compared with the mean diffusivity (MD) and fractional anisotropy (FA) indices inside the tumor, surrounding edema, as well as contralateral to the lesions, in the white matter (WM) and gray matter (GM). Results: The supertoroidal model enhanced the borders between tumors and surrounding structures, refined the boundaries between WM and GM, and revealed the heterogeneity inherent to tumor-infiltrated tissue. Both MD and TV demonstrated high intensities in the tumor, with lower values in the surrounding edema, which in turn were higher than those of unaffected brain parenchyma. Both TC and FA were effective in revealing the structural degradation of WM tracts. Conclusions: Our findings indicate that the supertoroidal model enables effective tensor visualization as well as quantitative scalar maps that improve the understanding of the underlying tissue structure properties. Hence, this approach has the potential to enhance diagnosis, preoperative planning, and intraoperative image guidance during surgical management of brain lesions.