This paper studies the error in, the efficient implementation of and time stepping methods for a variational multiscale method (VMS) for solving convectiondominated problems. The VMS studied uses a fine mesh C 0 finite element space Xh to approximate the concentration and a coarse mesh discontinuous vector finite element space LH for the large scales of the flux in the two scale discretization....

Diffusion tensor MRI tractography aims to reconstruct noninvasively the 3D trajectories of white matter fasciculi within the brain, providing neuroscientists and clinicians with a potentially useful tool for mapping brain architecture. While this technique is widely used to visualize white matter pathways, the associated uncertainty in fiber orientation and artifacts have, to date, not been vis...

We introduce a framework for population analysis of white matter tracts in diffusion weighted images. Our pipeline computes fibers from high angular resolution diffusion imaging (HARDI) images; it clusters the fibers incorporating prior knowledge from an atlas; the method then represents each fiber bundle compactly using a path following points of highest density (maximum density path; MDP); an...

We study numerically the solutions of the steady advection-diffusion problem in bounded domains with prescribed boundary conditions when the Péclet number Pe is large. We approximate the solution at high, but finite Péclet numbers by the solution to a certain asymptotic problem in the limit Pe → ∞. The asymptotic problem is a system of coupled 1-dimensional heat equations on the graph of stream...

Fibre tractography using diffusion tensor imaging is a promising method for estimating the pathways of white matter tracts in the human brain. The success of fibre tracking methods ultimately depends upon the accuracy of the fibre tracking algorithms and the quality of the data. Uncertainty and its representation have an important role to play in fibre tractography methods to infer useful infor...

In this paper, a coupled radiative transfer equation and diffusion approximation model is extended for light propagation in turbid medium with low-scattering and non-scattering regions. The light propagation is modelled with the radiative transfer equation in sub-domains in which the assumptions of the diffusion approximation are not valid. The diffusion approximation is used elsewhere in the d...

Diffusion tensor imaging allows to investigate white matter structures in vivo which is of particular interest for neurosurgery. However, due to the restricted resolution of the data and due to noise artifacts the analysis of this kind of data is a challenging task. A promising approach for the reconstruction of neural pathways are streamline based approaches commonly referred to as fiber track...

Diffusion tensor imaging (DTI) allows investigating white matter structures in vivo which is of particular interest for neurosurgery. A promising approach for the reconstruction of neural pathways are streamline techniques, which are commonly referred to as fiber tracking. However, the resulting visualization of fibers within the whole brain may be complex and difficult to interpret. For this r...

In this work, sparse linear systems obtained from the streamline diffusion finite element discretization of the convection-diffusion equations are solved by a multigrid method and the generalized minimal residule method. Adaptive mesh refinement process is considered as an integral part of the solution process. We propose some stopping criteria for iterative solvers to ensure the iterative erro...

Abstract. For solving the non-linear equations governing force-free fields, an iterative methodology based on the splitting of the problem is described. On the basis of this splitting, three families of subproblems have to be solved numerically. The first problem consists to find a potential field. A mixed hybrid method is used to solve it. The second problem, which is a curl-div system, is sol...