A methodology is presented for estimation of a probability density function of cerebral fibre orientations when one or two fibres are present in a voxel. All data are acquired on a clinical MR scanner, using widely available acquisition techniques. The method models measurements of water diffusion in a single fibre by a Gaussian density function and in multiple fibres by a mixture of Gaussian d...

Laminar dispersion in a serpentine microchannel with a Y-shape inlet was investigated using optical coherence tomography (OCT) and optical Doppler tomography (ODT). Dimensionless analysis was performed to understand the complex convective diffusion phenomena. It was shown that OCT/ODT is not only a visualization method but also a methodology to characterize important physics: streamwise velocit...

We introduce a fibre tractography framework based on a particle filter which estimates a local geometrical model of the underlying white matter tract, formulated as a 'streamline flow' using generalized helicoids. The method is not dependent on the diffusion model, and is applicable to diffusion tensor (DT) data as well as to high angular resolution reconstructions. The geometrical model allows...

In this paper, we study the stability and accuracy of adaptive finite element methods for the convection-dominated convection-diffusion-reaction problem in the twodimension space. Through various numerical examples on a type of layer-adapted grids (Shishkin grids), we show that the mesh adaptivity driven by accuracy alone cannot stabilize the scheme in all cases. Furthermore the numerical appro...

In this paper we prove a posteriori L2(L2) and L∞(H−1) residual based error estimates for a finite element method for the one-dimensional time dependent coupling equations of two scalar conservation laws. The underlying discretization scheme is Characteristic Galerkin method which is the particular variant of the Streamline diffusion finite element method for δ = 0. Our estimate contains certai...

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...

Diffusion MRI tractography is often used to estimate structural connections between brain areas and there is a fast-growing interest in quantifying these connections based on their position, shape, size and length. However, a portion of the connections reconstructed with tractography is biased by their position, shape, size and length. Thus, connections reconstructed are not equally distributed...

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...

We consider a space-time finite element discretization of a time-dependent nonlinear hyperbolic conservation law in one space dimension (Burgers' equation). The finite element method is higher-order accurate and is a Petrov-Galerkin method based on the so-called streamline diffusion modification of the test functions giving added stability. We first prove that if a sequence of finite element so...