Advances in computational and statistical diffusion MRI

Abstract

Computational methods are crucial for the analysis of diffusion magnetic resonance imaging (MRI) of the brain. Computational diffusion MRI can provide rich information at many size scales, including local microstructure measures such as diffusion anisotropies or apparent axon diameters, whole-brain connectivity information that describes the brain's wiring diagram and population-based studies in health and disease. Many of the diffusion MRI analyses performed today were not possible five, ten or twenty years ago, due to the requirements for large amounts of computer memory or processor time. In addition, mathematical frameworks had to be developed or adapted from other fields to create new ways to analyze diffusion MRI data. The purpose of this review is to highlight recent computational and statistical advances in diffusion MRI and to put these advances into context by comparison with the more traditional computational methods that are in popular clinical and scientific use. We aim to provide a high-level overview of interest to diffusion MRI researchers, with a more in-depth treatment to illustrate selected computational advances.

Keywords: diffusion MRI; registration; statistics; tractography.

Figure 1

Computational methods for diffusion MRI are needed to analyze input diffusion-weighted image (DWI) data to enable visualization or quantitation. At left, coronal images show DWIs acquired using several gradient directions. The yellow box indicates the zoomed region shown in the images at the right, which result from computational analysis of the DWIs. Colors encode fiber orientation such that left-right is red, inferior-superior is blue, and anterior-posterior is green. The traditional single diffusion tensor model (DTI, top right) is shown using ellipsoids for tensor visualization. DTI analysis has led to important findings, but it cannot represent anatomical fiber tract crossings (bottom right image, arrows) that can be seen with a multi-fiber model such as the two-tensor (2-T) [10, 11] tractography shown here. These images were created using the first dataset from the Human Connectome Project [12] using the SlicerDMRI package in 3D Slicer [13, 14].

Figure 2

Computational demands and benefits for quantifying the connectivity of notable formulations proposed to date for tractography: line propagation ( a, deterministic; b, probabilistic), global inverse problem ( c, bottom-up), microstructure informed tractography ( d, top-down; e, dictionary-based).

Figure 3

Two rotation transformations applied to the dMRI field on the left. The one on the top right does not include the warping of diffusivity information; the one on the bottom right does.