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Characterization of anisotropy in high angular resolution diffusion‐weighted MRI
Author(s) -
Frank Lawrence R.
Publication year - 2002
Publication title -
magnetic resonance in medicine
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.696
H-Index - 225
eISSN - 1522-2594
pISSN - 0740-3194
DOI - 10.1002/mrm.10156
Subject(s) - spherical harmonics , anisotropy , diffusion , diffusion mri , anisotropic diffusion , isotropy , angular resolution (graph drawing) , physics , resolution (logic) , nuclear magnetic resonance , tensor (intrinsic definition) , mathematical analysis , optics , computational physics , mathematics , computer science , geometry , artificial intelligence , magnetic resonance imaging , medicine , radiology , combinatorics , thermodynamics
The methods of group theory are applied to the problem of characterizing the diffusion measured in high angular resolution MR experiments. This leads to a natural representation of the local diffusion in terms of spherical harmonics. In this representation, it is shown that isotropic diffusion, anisotropic diffusion from a single fiber, and anisotropic diffusion from multiple fiber directions fall into distinct and separable channels. This decomposition can be determined for any voxel without any prior information by a spherical harmonic transform, and for special cases the magnitude and orientation of the local diffusion may be determined. Moreover, non‐diffusion–related asymmetries produced by experimental artifacts fall into channels distinct from the fiber channels, thereby allowing their separation and a subsequent reduction in noise from the reconstructed fibers. In the case of a single fiber, the method reduces identically to the standard diffusion tensor method. The method is applied to normal volunteer brain data collected with a stimulated echo spiral high angular resolution diffusion‐weighted (HARD) acquisition. Magn Reson Med 47:1083–1099, 2002. Published 2002 Wiley‐Liss, Inc.