Relationships between diffusion tensor and q ‐space MRI †

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.