Sparse Multi-Shell Diffusion Imaging

Abstract. Diffusion magnetic resonance imaging (dMRI) is an impor-tant tool that allows non-invasive investigation of neural architecture of the brain. The data obtained from these in-vivo scans provides important information about the integrity and connectivity of neural fiber bundles in the brain. A multi-shell imaging (MSI) scan can be of great value in the study of several psychiatric and neurological disorders, yet its usabil-ity has been limited due to the long acquisition times required. A typical MSI scan involves acquiring a large number of gradient directions for the 2 (or more) spherical shells (several b-values), making the acquisition time significantly long for clinical application. In this work, we propose to use results from the theory of compressive sampling and determine the minimum number of gradient directions required to attain signal re-construction similar to a traditional MSI scan. In particular, we propose a generalization of the single shell spherical ridgelets basis for sparse rep-resentation of multi shell signals. We demonstrate its efficacy on several synthetic and in-vivo data sets and perform quantitative comparisons with solid spherical harmonics based representation. Our preliminary re-sults show that around 20-24 directions per shell are enough for robustly recovering the diffusion propagator.

Response to comment on "the geometric structure of the brain fiber pathways".

In response to Catani et al., we show that corticospinal pathways adhere via sharp turns to two local grid orientations; that our studies have three times the diffusion resolution of those compared; and that the noted technical concerns, including crossing angles, do not challenge the evidence of mathematically specific geometric structure. Thus, the geometric thesis gives the best account of the available evidence

Representing diffusion MRI in 5-D simplifies regularization and segmentation of white matter tracts.

We present a new five-dimensional (5-D) space representation of diffusion magnetic resonance imaging (dMRI) of high angular resolution. This 5-D space is basically a non-Euclidean space of position and orientation in which crossing fiber tracts can be clearly disentangled, that cannot be separated in three-dimensional position space. This new representation provides many possibilities for processing and analysis since classical methods for scalar images can be extended to higher dimensions even if the spaces are not Euclidean. In this paper, we show examples of how regularization and segmentation of dMRI is simplified with this new representation. The regularization is used with the purpose of denoising and but also to facilitate the segmentation task by using several scales, each scale representing a different level of resolution. We implement in five dimensions the Chan-Vese method combined with active contours without edges for the segmentation and the total variation functional for the regularization. The purpose of this paper is to explore the possibility of segmenting white matter structures directly as entirely separated bundles in this 5-D space. We will present results from a synthetic model and results on real data of a human brain acquired with diffusion spectrum magnetic resonance imaging (MRI), one of the dMRI of high angular resolution available. These results will lead us to the conclusion that this new high-dimensional representation indeed simplifies the problem of segmentation and regularization

Understanding diffusion MR imaging techniques: from scalar diffusion-weighted imaging to diffusion tensor imaging and beyond.

The complex structural organization of the white matter of the brain can be depicted in vivo in great detail with advanced diffusion magnetic resonance (MR) imaging schemes. Diffusion MR imaging techniques are increasingly varied, from the simplest and most commonly used technique-the mapping of apparent diffusion coefficient values-to the more complex, such as diffusion tensor imaging, q-ball imaging, diffusion spectrum imaging, and tractography. The type of structural information obtained differs according to the technique used. To fully understand how diffusion MR imaging works, it is helpful to be familiar with the physical principles of water diffusion in the brain and the conceptual basis of each imaging technique. Knowledge of the technique-specific requirements with regard to hardware and acquisition time, as well as the advantages, limitations, and potential interpretation pitfalls of each technique, is especially useful