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...

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...

The stability and accuracy of a streamline diffusion finite element method (SDFEM) on arbitrary grids applied to a linear 1-d singularly perturbed problem are studied in this paper. With a special choice of the stabilization quadratic bubble function, the SDFEM is shown to have an optimal second order in the sense that ‖u − uh‖∞ ≤ C infvh∈V h ‖u − vh‖∞, where uh is the SDFEM approximation of th...

The radiative transfer equation can be utilized in optical tomography in situations in which the more commonly applied diffusion approximation is not valid. In this paper, an image reconstruction method based on a frequency domain radiative transfer equation is developed. The approach is based on a total variation output regularized least squares method which is solved with a Gauss–Newton algor...

We consider a nonconforming streamline-diiusion nite element method for solving convection-diiusion problems. The theoretical and numerical investigation for triangular and tetrahedral meshes recently given by John, Maubach and Tobiska has shown that the usual application of the SDFEM gives not a suucient stabilization. Additional parameter dependent jump terms have been proposed which preserve...

In this paper, we propose to improve the stabilized POD-ROM introduced in [48] deal with numerical simulation of advection-dominated advection-diffusion-reaction equations. particular, a three-stage stabilizing strategy that will be very useful when considering low diffusion coefficients, i.e. strongly regime. This approach mainly consists three ingredients: (1) addition “streamline diffusion” ...

Optical tomography has a wide range of biomedical applications. Accurate prediction of photon transport in media is critical, as it directly affects the accuracy of the reconstructions. The radiative transfer equation (RTE) is the most accurate deterministic forward model, yet it has not been widely employed in practice due to the challenges in robust and efficient numerical implementations in ...

In this study, we aimed to identify major fiber pathways and their spatiotemporal relationships within transient fetal zones in the human fetal brain by comparing postmortem high-angular resolution diffusion MR imaging (HARDI) in combination with deterministic streamline tractography and histology. Diffusion weighted imaging was performed on postmortem human fetal brains [N = 9, age = 18-34 pos...

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....