Imaging the Brain Neuronal Network with Diffusion MRI: A Way to Understand Its Global Architecture

In order to better understand the high complexity of the brain, the detailed study of its individual components clearly seems insufficient. The backbone of complexity in the nervous system is composed of the large scale architectural characteristics of the neuronal network. Newly, by the advent of MR tractography, its investigation is accessible. We report on two important network characteristics that were already guessed from functional investigations and animal ex vivo studies, but never directly addressed in the human subject, ie the small world and hierarchical architecture of the human long-range brain axonal network

Sparse image reconstruction on the sphere: implications of a new sampling theorem

We study the impact of sampling theorems on the fidelity of sparse image reconstruction on the sphere. We discuss how a reduction in the number of samples required to represent all information content of a band-limited signal acts to improve the fidelity of sparse image reconstruction, through both the dimensionality and sparsity of signals. To demonstrate this result we consider a simple inpainting problem on the sphere and consider images sparse in the magnitude of their gradient. We develop a framework for total variation (TV) inpainting on the sphere, including fast methods to render the inpainting problem computationally feasible at high-resolution. Recently a new sampling theorem on the sphere was developed, reducing the required number of samples by a factor of two for equiangular sampling schemes. Through numerical simulations we verify the enhanced fidelity of sparse image reconstruction due to the more efficient sampling of the sphere provided by the new sampling theorem.Comment: 11 pages, 5 figure

Implications for compressed sensing of a new sampling theorem on the sphere

A sampling theorem on the sphere has been developed recently, requiring half as many samples as alternative equiangular sampling theorems on the sphere. A reduction by a factor of two in the number of samples required to represent a band-limited signal on the sphere exactly has important implications for compressed sensing, both in terms of the dimensionality and sparsity of signals. We illustrate the impact of this property with an inpainting problem on the sphere, where we show the superior reconstruction performance when adopting the new sampling theorem compared to the alternative.Comment: 1 page, 2 figures, Signal Processing with Adaptive Sparse Structured Representations (SPARS) 201

Statistical DSI Brain Tractography: A Way to Handle the Kiss-Cross Uncertainty.

Despite the advent of diffusion magnetic resonance imaging and tractography algorithms, the accurate mapping of complex fiber kiss-crossings areas of the brain remains out of reach. In this study, we present a statistical DSI-based tractography algorithm which explores all possible paths in the brain white matter. We also introduce a cortex connectivity graph whose weighted edges correspond to the connection likelihood. The tests performed on the centrum semi-ovale have shown that a simple thresholding applied to the edges of this graph allows us to image the connectivity of any part of the brain to the desired level of complexity

A Method to Study Alterations in Networks of Structural Connectivity

The global structural connectivity of the brain can be explored in vivo with a connectivity matrix derived from diffusion MRI tractography [1]. In such a matrix, M, every index i or j represents a small region of interest (ROI) at the white-gray matter (WGM) interface and every entry M(i,j) provides a measure of connectivity derived from tractography. Once the matrix computed, it is easy to obtain connectional information betwee

How Much Confidence Do We Have in a MRI Tractography Experiment?

When performing a tractography experiment it is essential to know whether a reconstructed tract results from the diffusion signal itself or from some random effect or noise. In this study, we introduce a way to associate to every connection a confidence level. The reason why the latter greatly varies with the length of the tract is analyzed. We use this method to filter out the connections likely to be the result of noise and show the effect on the connectivity of the human visual system

Fast-Marching Tractography for Connection Matrix (Fast-TraC)

Although high angular resolution diffusion MRI techniques are able to solve multiple intra-voxel fiber orientations, the usual streamline Diffusion Spectrum Imaging (DSI) tractography algorithms present some limitations in their ability to map complex fiber-crossings in the brain white matter because they select locally only the most linear trajectories. In this work, we present a fast marching tractography algorithm for DSI, called Fast-TraC, which 1) is able to efficiently address this issue, 2) creates fiber trajectories between 1000 small cortical ROIs covering the entire brain and 3) builds a whole brain connection matrix. We also see selected tracts that are accurately reconstructed