Effects of equilibrium exchange on diffusion‐weighted NMR signals: The diffusigraphic “shutter‐speed”

Abstract

A general picture is presented of the implications for diffusion-weighted NMR signals of the parsimonious two-site-exchange (2SX) paradigm. In particular, it is shown that the diffusigraphic "shutter-speed," tau(-1) identical with |q(2)(D(A) - D(B))|, is a useful concept. The "wave-number" q has its standard definition (given in the text), and D(A) and D(B) are the apparent diffusion coefficients (ADCs) of molecules in the two "sites," A and B, if there is no exchange between them. At low gradient strengths (center of q-space), tau(-1) is less than rate constants for intercompartmental water molecule exchange in most tissue cases. Thus, the exchange reaction appears fast. However, q is increased during the course of most experiments and, as it is, the shutter-speed becomes "faster" and the exchange reaction, the kinetics of which do not change, appears to slow down. This causes a multiexponential behavior in the diffusion-weighting dimension, b, which also has its standard definition. This picture is found to be in substantial agreement with a number of different experimental observations. It is applied here to literature (1)H(2)O data from a yeast cell suspension and from the human and the rat brain. Since the equilibrium transcytolemmal water exchange reaction appears to be in the fast-exchange-limit at small b, the initial slope represents the weighted-average of the ADCs of intra- and extracellular water. Of course, in tissue the former is in the significant majority. Furthermore, a consideration of reasonable values for the other 2SX parameters suggests that, for resting brain tissue, the intracellular water ADC may be larger than the extracellular water ADC. There are some independent inferences of this, which would have ramifications for many applications of diffusion-weighted MRI.