Nonparametric tests of structure for high angular resolution diffusion imaging in Q-space

TL;DR

This paper introduces nonparametric statistical methods to analyze high angular resolution diffusion imaging data, enabling detailed characterization of water molecule diffusion structures in brain tissue without relying on parametric models.

Contribution

The paper proposes novel nonparametric scalar measures and hypothesis tests for diffusion data, allowing direct analysis of microstructural features in Fourier space without parametric assumptions.

Findings

Effective characterization of local diffusion properties in simulations

Detection of complex white-matter structures in MRI data

Nonparametric tests distinguish diffusion modalities

Abstract

High angular resolution diffusion imaging data is the observed characteristic function for the local diffusion of water molecules in tissue. This data is used to infer structural information in brain imaging. Nonparametric scalar measures are proposed to summarize such data, and to locally characterize spatial features of the diffusion probability density function (PDF), relying on the geometry of the characteristic function. Summary statistics are defined so that their distributions are, to first-order, both independent of nuisance parameters and also analytically tractable. The dominant direction of the diffusion at a spatial location (voxel) is determined, and a new set of axes are introduced in Fourier space. Variation quantified in these axes determines the local spatial properties of the diffusion density. Nonparametric hypothesis tests for determining whether the diffusion is unimodal, isotropic or multi-modal are proposed. More subtle characteristics of white-matter microstructure, such as the degree of anisotropy of the PDF and symmetry compared with a variety of asymmetric PDF alternatives, may be ascertained directly in the Fourier domain without parametric assumptions on the form of the diffusion PDF. We simulate a set of diffusion processes and characterize their local properties using the newly introduced summaries. We show how complex white-matter structures across multiple voxels exhibit clear ellipsoidal and asymmetric structure in simulation, and assess the performance of the statistics in clinically-acquired magnetic resonance imaging data.