Diffusion magnetic resonance imaging (dMRI) is a compelling tool for investigating the structure and geometry of brain tissue based on indirect measurement of the diffusion anisotropy of water. Recent developments in global top-down tractogram optimizations enable the estimation of streamline weights, which characterize the connection between gray matter areas. In this work, the intra-axonal cr...

Abstract Several useful tractography-derived maps have recently been introduced, such as track density imaging (TDI) and the average pathlength map (APM). Here, an extension to these techniques is introduced by sampling diffusion indices along streamline trajectories (DIST). With this approach, voxels contain summary information of diffusivity measures within streamlines. The diffusion metric...

Introduction: Diffusion Tensor Imaging (DTI) is now a well-established scheme for analyzing neural pathways in the brain by means of streamline or probabilistic tractography. But DTI models the diffusion of water molecules by a Gaussian process, while the data captured by the diffusionweighted MRI (DW-MRI) could very well be non-Gaussian. To overcome this limitation, a High Angular Resolution D...

This paper présents a stabilization technique for approximating transport équations. The key idea consists in introducing an artificial diffusion based on a two-level décomposition of the approximation space. The technique is proved to have stability and convergence properties that are similar to that of the streamline diffusion method. AMS Subject Classification. 35L50, 65N30. Received: Februa...

In this paper we analyze local properties of the Continuous Interior Penalty (CIP) Method for a model convection-dominated singularly perturbed convection-diffusion problem. We show weighted a priori error estimates, where the weight function exponentially decays outside the subdomain of interest. This result shows that locally, the CIP method is comparable to the Streamline Diffusion (SD) or t...