The effect of the rotational angle on MR diffusion indices in nerves: is the rms displacement of the slow-diffusing component a good measure of fiber orientation?

From single-pulsed field gradient to double-pulsed field gradient MR: gleaning new microstructural information and developing new forms of contrast in MRI

One of the hallmarks of diffusion NMR and MRI is its ability to utilize restricted diffusion to probe compartments much smaller than the excited volume or the MRI voxel, respectively, and to extract microstructural information from them. Single-pulsed field gradient (s-PFG) MR methodologies have been employed with great success to probe microstructures in various disciplines, ranging from chemistry to neuroscience. However, s-PFG MR also suffers from inherent shortcomings, especially when specimens are characterized by orientation or size distributions: in such cases, the microstructural information available from s-PFG experiments is limited or lost. Double-pulsed field gradient (d-PFG) MR methodology, an extension of s-PFG MR, has attracted attention owing to recent theoretical studies predicting that it can overcome certain inherent limitations of s-PFG MR. In this review, we survey the microstructural features that can be obtained from conventional s-PFG methods in the different q regimes, and highlight its limitations. The experimental aspects of d-PFG methodology are then presented, together with an overview of its theoretical underpinnings and a general framework for relating the MR signal decay and material microstructure, affording new microstructural parameters. We then discuss recent studies that have validated the theory using phantoms in which the ground truth is well known a priori, a crucial step prior to the application of d-PFG methodology in neuronal tissue. The experimental findings are in excellent agreement with the theoretical predictions and reveal, inter alia, zero-crossings of the signal decay, robustness towards size distributions and angular dependences of the signal decay from which accurate microstructural parameters, such as compartment size and even shape, can be extracted. Finally, we show some initial findings in d-PFG MR imaging. This review lays the foundation for future studies, in which accurate and novel microstructural information could be extracted from complex biological specimens, eventually leading to new forms of contrast in MRI.

Detecting diffusion-diffraction patterns in size distribution phantoms using double-pulsed field gradient NMR: Theory and experiments

NMR observable nuclei undergoing restricted diffusion within confining pores are important reporters for microstructural features of porous media including, inter-alia, biological tissues, emulsions and rocks. Diffusion NMR, and especially the single-pulsed field gradient (s-PFG) methodology, is one of the most important noninvasive tools for studying such opaque samples, enabling extraction of important microstructural information from diffusion-diffraction phenomena. However, when the pores are not monodisperse and are characterized by a size distribution, the diffusion-diffraction patterns disappear from the signal decay, and the relevant microstructural information is mostly lost. A recent theoretical study predicted that the diffusion-diffraction patterns in double-PFG (d-PFG) experiments have unique characteristics, such as zero-crossings, that make them more robust with respect to size distributions. In this study, we theoretically compared the signal decay arising from diffusion in isolated cylindrical pores characterized by lognormal size distributions in both s-PFG and d-PFG methodologies using a recently presented general framework for treating diffusion in NMR experiments. We showed the gradual loss of diffusion-diffraction patterns in broadening size distributions in s-PFG and the robustness of the zero-crossings in d-PFG even for very large standard deviations of the size distribution. We then performed s-PFG and d-PFG experiments on well-controlled size distribution phantoms in which the ground-truth is well-known a priori. We showed that the microstructural information, as manifested in the diffusion-diffraction patterns, is lost in the s-PFG experiments, whereas in d-PFG experiments the zero-crossings of the signal persist from which relevant microstructural information can be extracted. This study provides a proof of concept that d-PFG may be useful in obtaining important microstructural features in samples characterized by size distributions.

Observation of restricted diffusion in the presence of a free diffusion compartment: single- and double-PFG experiments

Theoretical and experimental studies of restricted diffusion have been conducted for decades using single pulsed field gradient (s-PFG) diffusion experiments. In homogenous samples, the diffusion-diffraction phenomenon arising from a single population of diffusing species has been observed experimentally and predicted theoretically. In this study, we introduce a composite bi-compartmental model which superposes restricted diffusion in microcapillaries with free diffusion in an unconfined compartment, leading to fast and slow diffusing components in the NMR signal decay. Although simplified (no exchange), the superposed diffusion modes in this model may exhibit features seen in more complex porous materials and biological tissues. We find that at low q-values the freely diffusing component masks the restricted diffusion component, and that prolongation of the diffusion time shifts the transition from free to restricted profiles to lower q-values. The effect of increasing the volume fraction of freely diffusing water was also studied; we find that the transition in the signal decay from the free mode to the restricted mode occurs at higher q-values when the volume fraction of the freely diffusing water is increased. These findings were then applied to a phantom consisting of crossing fibers, which demonstrated the same qualitative trends in the signal decay. The angular d-PGSE experiment, which has been recently shown to be able to measure small compartmental dimensions even at low q-values, revealed that microscopic anisotropy is lost at low q-values where the fast diffusing component is prominent. Our findings may be of importance in studying realistic systems which exhibit compartmentation.

Measuring small compartmental dimensions with low-q angular double-PGSE NMR: The effect of experimental parameters on signal decay

In confined geometries, the MR signal attenuation obtained from single pulsed gradient spin echo (s-PGSE) experiments reflects the dimension of the compartment, and in some cases, its geometry. However, to measure compartment size, high q-values must be applied, requiring high gradient strengths and/or long pulse durations and diffusion times. The angular double PGSE (d-PGSE) experiment has been proposed as a means to extract dimensions of confined geometries using low q-values. In one realization of the d-PGSE experiment, the first gradient pair is fixed along the x-axis, and the orientation of the second gradient pair is varied in the X-Y plane. Such a measurement is sensitive to microscopic anisotropy induced by the boundaries of the restricting compartment, and allows extraction of the compartment dimension. In this study, we have juxtaposed angular d-PGSE experiments and simulations to extract sizes from well-characterized NMR phantoms consisting of water filled microcapillaries. We are able to accurately extract sizes of small compartments (5mum) using the angular d-PGSE experiment even when the short gradient pulse (SGP) approximation is violated and over a range of mixing and diffusion times. We conclude that the angular d-PGSE experiment may fill an important niche in characterizing compartment sizes in which restricted diffusion occurs.