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Relationships between diffusion tensor and q ‐space MRI †
Author(s) -
Basser Peter J.
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.10052
Subject(s) - diffusion mri , tensor (intrinsic definition) , space (punctuation) , displacement (psychology) , k space , physics , diffusion , nuclear magnetic resonance , scanner , dispersion (optics) , gaussian , distribution (mathematics) , mathematical analysis , mathematics , magnetic resonance imaging , geometry , optics , computer science , radiology , medicine , quantum mechanics , psychology , fourier transform , psychotherapist , operating system
Fundamental relationships between diffusion tensor (DT) and 3D q ‐space MRI are derived which establish conditions when these two complementary MR methods are equivalent. It is shown that the displacement distribution measured by q ‐space MRI in both the large displacement (i.e., large r) and the long‐wavelength (i.e., small q ) limits is the same 3D Gaussian displacement distribution assumed in DT‐MRI. In these limiting cases, q ‐space MR yields a dispersion tensor that is identical to the effective DT, D , measured in DT‐MRI. An experiment is then proposed to measure D using q ‐space methods. These findings establish that the effective DT, measured in DT‐MRI, characterizes molecule motions on a coarse length‐scale. Finally, the feasibility of and requirements for performing 3D q ‐space MRI on a clinical scanner are considered. Magn Reson Med 47:392–397, 2002. Published 2002 Wiley‐Liss, Inc.