Utilizing Principal Modes of d-PFG Measurements to Detect Local non-Gaussian Diffusion

Diffusion in porous media is known to be non-Gaussian. When conventional NMR diffusion measurements are applied to porous media, this non-Gaussian behavior can instead be dominated by the superposition of different Gaussian compartments arising from material heterogeneity. For example, a diffusion measurement of a vial of water and a vial of oil will lead to non-Gaussian behavior due to a superposition of their signals, not non-Gaussian diffusion. Similarly, restricted diffusion in individual pores of varying size can lead to the same effect, where the distribution of Gaussian moments obscures the presence of 'true' (compartmental) non-Gaussian diffusion. Correlating diffusive motion between successive periods of time with d-PFG has been shown to be capable of elucidating local features of diffusion otherwise obscured my sample heterogeneity [1], for example microscopic anisotropy due to the shape of individual pores in macroscopically isotropic samples. However, the relative motion between the encoding periods in d-PFG is in part inherently interrelated due to diffusion being a stationary process, hindering the design of these sequences.

Instead, we will show that there exist diffusion encoding modes that are not coupled by stationarity, providing a greatly simplified framework to design techniques to correlating and isolating features of diffusion. We identify these fundamental symmetries of diffusive motion and develop corresponding pairs of independent measures (gradient sequences), one of which consists of an alternative description of the principal gradient sequences applied in d-PFG. [2] As these measures independently encode for different aspects of diffusion motion, their use allows for the systematic design of a new class of NMR diffusion techniques wherein the sequences can be designed to either correlate or isolate certain features of diffusion. We present one implementation for MRI, Symmetrized Double PFG (sd-PFG) that can for the first time unambiguously identify local non-Gaussian restricted diffusion in the presence of an ensemble averaging of varying pore orientation and size. We experimentally demonstrate the measurement of the fourth moment (Kurtosis) of diffusion by its unique four-cycle oscillation and find it consistent with theoretical predictions.

[1] Mitra PP (1995) Multiple wave-vector extensions of the NMR pulsed-field-gradient spin-echo diffusion measurement. Phys Rev B 51:15074-15078.
[2] Paulsen JL, Song YQ (2014) Two-dimensional diffusion time correlation experiment using a single direction gradient. JMR 244:6-11.