PULSED-GRADIENT SPIN-ECHO DIFFUSION STUDIES IN NMR IMAGING - EFFECTS OF THE IMAGING GRADIENTS ON THE DETERMINATION OF DIFFUSION-COEFFICIENTS

Studies of self-diffusion by magnetic resonance imaging using variations of the pulsed-gradient spin-echo experiment are complicated by the presence of the imaging-gradient pulses. This problem is particularly severe in NMR microscopy, where the diffusion gradients are of the same order or even smaller than the imaging gradients. Due to cross terms between the diffusion gradient and parallel imaging gradients, the Stejskal-Tanner relation no longer applies. This commonly used equation could result in significant overestimation of the self-diffusion coefficient when used in such instances. The effect of diffusion on signal attenuation in a number of spin-echo diffusion imaging sequences has been analyzed, and analytical expressions including the cross terms with the imaging gradients have been derived. The equations derived were verified experimentally through measurements of the self-diffusion coefficient of water, using high-resolution microimaging (imaging gradients of 10-15 G/cm, pixel size of 23 μm) at 400 MHz. Including the cross terms in the data analysis yields values within the literature range (2.6 × 10-5 cm2/s) for the self-diffusion coefficient of water. Neglecting the cross terms is demonstrated to result in a tenfold over-estimation of the diffusion coefficient. When imaging gradients which are larger than the incremented diffusion gradient are used, the experiment becomes significantly more sensitive to diffusion effects, due to the cross terms between the gradients. This predicted and observed result improves the accuracy of imaging diffusion experiments and may also be applicable in spectroscopic diffusion measurements. © 1990.