Diffusion tensor imaging (DTI) is a recent magnetic resonance (MR) technique that provides comprehensive information about water diffusivity. Since diffusivity correlates with tissue structure at the microscopic level DTI reveals fibrous structures such as white matter (WM) pathways in the field of neurosurgery. WM tracts are thereby of major interest and the ability to distinguish between diff...

We compare numerically the performance of a new continuous-discontinuous finite element method (CDFEM) for linear convection-diffusion equations with three well-known upwind finite element formulations, namely with the streamline upwind Petrov-Galerkin finite element method, the residualfree bubble method and the discontinuous Galerkin finite element method. The defining feature of the CDFEM is...

A single diffusion MRI streamline fiber tracking dataset may contain hundreds of thousands, and often millions of streamlines and can take up to several gigabytes of memory. This amount of data is not only heavy to compute, but also difficult to visualize and hard to store on disk (especially when dealing with a collection of brains). These problems call for a fiber-specific compression format ...

Considering a simple model transport problem, we present a new finite element method. While the new method fits in the class of discontinuous Galerkin (DG) methods, it differs from standard DG and streamline diffusion methods, in that it uses a space of discontinuous trial functions tailored for stability. The new method, unlike the older approaches, yields optimal estimates for the primal vari...

In this paper local discontinuous Galerkin method (LDG) was analyzed for solving 1-D convection-diffusion equations with a boundary layer near the outflow boundary. Local error estimates are established on quasi-uniform meshes with maximum mesh size h. On a subdomain with O(h ln(1/h)) distance away from the outflow boundary, the L error of the approximations to the solution and its derivative c...

We present a stabilized finite element method for the scalar advection-diffusion equation, which does not require tunable mesh-dependent parameters. Stabilization is achieved by using diffusive fluxes extracted from an edge element lifting of Scharfetter-Gummel edge fluxes into the elements. Although the method is formally first-order accurate, qualitative numerical studies suggest that it occu...

A finite element based level set method is proposed for structural topology optimization. Because both the level set equation and the reinitialization equation are advection dominated partial differential equations, the standard Galerkin finite element method may produce oscillating results. In this paper, both equations are solved using a streamline diffusion finite element method (SDFEM). The...

Methods– Data acquisition. We scanned 9 healthy subjects (3F/6M, 31.25 ± 4.2y) at three time points separated by a 2 weeks interval. Diffusion-weighted EPI were acquired on a Siemens 3T Verio scanner, b = 1000 s/mm2, on 64 evenly distributed directions plus 2 b = 0 images. Pre-processing. The diffusion-weighted images were regularized and corrected for Rician noise. The diffusion tensor was est...