NURBS in DT-MRI

S. Pajevic, P. J. Basser MSCL/CIT, National Institutes of Health, Bethesda, MD, United States, NICHD/STBB, NIH, Bethesda, MD, United States Introduction: Diffusion Tensor MRI (DTI) measures a diffusion tensor of water in tissue, fr om which useful micr ostructural information can be obtained [1]. DTI provides information about the local diffusion field from which one can attempt to reconstruct nerve fiber tracts (e.g., see [2]). One problem in white matter tractography has been that the diffusion tensor data from which these continuous tracts are constructed is actually discrete and noisy [3]. Several approaches have been proposed to provide a continuous tensor field approximation to the discrete, noisy tensor data so that the fiber tract trajectory can be followed continuously through the imaging volume. One such approach employs B-splines [4]. The problem with this approach is that it removes noise by sacrificing resolution. Also this method fails to provide reliable estimates of useful quantities that arise in differential geometry, like curvature and torsion, which provide descriptions of geometric features of the tract, because these quantities involve taking high-order derivatives of functions of the tensor field. Increasingly, we see differential geometric features as providing new and useful parameters to help us characterize different white matter pathways. We argue that a class of basis functions, known as Non-Unifor m Rational B-Splines (NURBS), provide a suitable tool to achieve such goal.