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June 2011 Nonparametric tests of structure for high angular resolution diffusion imaging in Q-space
Sofia C. Olhede, Brandon Whitcher
Ann. Appl. Stat. 5(2B): 1293-1327 (June 2011). DOI: 10.1214/10-AOAS441


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.


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Sofia C. Olhede. Brandon Whitcher. "Nonparametric tests of structure for high angular resolution diffusion imaging in Q-space." Ann. Appl. Stat. 5 (2B) 1293 - 1327, June 2011.


Published: June 2011
First available in Project Euclid: 13 July 2011

zbMATH: 1223.62066
MathSciNet: MR2849775
Digital Object Identifier: 10.1214/10-AOAS441

Keywords: Anisotropy , asymmetry , diffusion weighted imaging , magnetic resonance imaging , nonparametric

Rights: Copyright © 2011 Institute of Mathematical Statistics


Vol.5 • No. 2B • June 2011
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