Extraction and validation of correlation lengths from interstitial velocity fields using diffusion-weighted MRI

Magnetic Resonance Imaging methods sensitive to individual molecular displacements (q-space MRI) provide a convenient means of measuring dispersion in complex interstitial spaces. Pressure-driven flow experiments through a water-saturated packed bed phantom have been conducted to prove the feasibility of using q-space MRI to measure the coherence length associated with the interstitial velocity field. The method involves measuring the dependence of the apparent dispersion coefficient on the distance along the mean flow by repeating a small number of pulsed-gradient stimulated-echo experiments with increasing gradient pulse separation times. Assuming homogeneous interstitial flow statistics inside the averaging volume, an integral spatial scale characterizing the Eulerian velocity auto-correlation coefficient is extracted via a stochastic convective model. The validity of the a priori statistical description of interstitial flow is verified by comparing with an independent MRI measurement of the Eulerian velocity field using phase contrast methods in the same phantom with pore-level resolution. The integral length scale obtained via q-space MRI agrees with the mean pore size in the present as well as in similar phantoms found in the literature. This method has direct applicability in the quantification of the interstitial morphology of fluid-saturated porous media with resolution independent of voxel size, assuming "perfectly reflecting pore walls" (no surface relaxation) and no contribution to the MR signal from outside the pore space.