Microscopic anisotropy revealed by NMR double pulsed field gradient experiments with arbitrary timing parameters

Abstract

We consider a general double pulsed field gradient experiment with arbitrary experimental parameters and calculate an exact expression for the NMR signal attenuation from restricted geometries, which is valid at long wavelengths, i.e., when the product of the gyromagnetic ratio of the spins, the pulsed gradients' duration, and their magnitude is small compared to the reciprocal of the pore size. It is possible to observe microscopic anisotropy within the pore space induced by the boundaries of the pore, which can be used to differentiate restricted from free or multicompartmental diffusion and to estimate a characteristic pore dimension in the former case. Explicit solutions for diffusion taking place between parallel plates as well as in cylindrical and spherical pores are provided. In coherently packed cylindrical pores, it is possible to measure simultaneously the cylinders' orientation and diameter using small gradient strengths. The presence of orientational heterogeneity of cylinders is addressed, and a scheme for differentiating microscopic from ensemble anisotropy is proposed.

A general framework to quantify the effect of restricted diffusion on the NMR signal with applications to double pulsed field gradient NMR experiments

“…Note that the eigenfunctions, u k ͑r͒, are the same functions used in the eigenfunction expansion of the diffusion propagator whose long time asymptotic demands one of the eigenvalues to vanish. 22 If this eigenvalue is assigned the index 0, i.e., 0 = 0, then u 0 ͑r͒ = V −1/2 , where V denotes the pore volume.…”

“…Experiments performed on well-controlled NMR phantoms consisting of cylindrical tubes suggested that the predictions of Ref. 22 can be employed to obtain accurate estimates of small compartmental dimensions. 23 In a different study, it was predicted that when all gradient orientations were kept parallel to each other in a multi-PFG acquisition with an even number of gradient pulse pairs, increasing the gradient strength would yield peculiar features such as zero crossings that are robust to the heterogeneity of the specimen.…”

“…1͑b͔͒ in which the dependence of the signal on the angle between the two gradient vectors reflects features of restricted diffusion that can be used to obtain estimates of compartment size. 21,22 The theory in Ref. 22 provided explicit solutions for the double-PFG NMR signal intensity with arbitrary gradient timing parameters when the long wavelength assumption is satisfied, i.e., at small gradient strengths.…”

Experimental validation of a bias in apparent exchange rate measurement

“…Computer simulations [13,14] corroborated that at parallel diffusion gradients a decrease in signal is expected when increasing due to the decreasing restriction effect described by Mitra [2,15].…”

Pore size estimation from double diffusion encoding

“…Recent advances in the analytical description of the diffusion MRI signal [14], as well as its numerical prediction [15,16], make it now conceivable to study and optimize the sensitivity of this experimental protocol. Previous work [17] has shown that the parallelantiparallel difference in signal attenuation in DDE decays exponentially with an increase of delay between diffusion encodings -the mixing time (τ m ).…”