Conventions and nomenclature for double diffusion encoding NMR and MRI

Stejskal and Tanner's ingenious pulsed field gradient design from 1965 has made diffusion NMR and MRI the mainstay of most studies seeking to resolve microstructural information in porous systems in general and biological systems in particular. Methods extending beyond Stejskal and Tanner's design, such as double diffusion encoding (DDE) NMR and MRI, may provide novel quantifiable metrics that are less easily inferred from conventional diffusion acquisitions. Despite the growing interest on the topic, the terminology for the pulse sequences, their parameters, and the metrics that can be derived from them remains inconsistent and disparate among groups active in DDE. Here, we present a consensus of those groups on terminology for DDE sequences and associated concepts. Furthermore, the regimes in which DDE metrics appear to provide microstructural information that cannot be achieved using more conventional counterparts (in a model‐free fashion) are elucidated. We highlight in particular DDE's potential for determining microscopic diffusion anisotropy and microscopic fractional anisotropy, which offer metrics of microscopic features independent of orientation dispersion and thus provide information complementary to the standard, macroscopic, fractional anisotropy conventionally obtained by diffusion MR. Finally, we discuss future vistas and perspectives for DDE. Magn Reson Med 75:82–87, 2016. © 2015 Wiley Periodicals, Inc.     

Anisotropic noise propagation in diffusion tensor MRI sampling schemes.

The subject of this study is the controversial choice of directions in diffusion tensor MRI (DT-MRI); specifically, the numerical algebra related to this choice. In DT-MRI, apparent diffusivities are sampled in six or more directions and a least-squares equation is solved to reconstruct the diffusion tensor. Numerical characteristics of the system are considered, in particular the condition number and normal matrix, and are shown to be dependent on the relative orientation of the tensor with respect to the laboratory frame. As a consequence, noise propagation can be anisotropic. However, the class of icosahedral direction schemes is an exception, and icosahedral directions have the same condition number and normal matrix for direction encoding as the ideal scheme with an infinite number of directions. This normal matrix and its condition number are rotationally invariant. Numerical simulations show that for icosahedral schemes with 30 directions the standard deviation of the fractional anisotropy is both low and nearly independent of fiber orientation. The recommended choice of directions for a DT-MRI experiment is therefore the icosahedral set of directions with the highest number of directions achievable in the available time.     

Diffusion tensor imaging of in vivo and excised rat spinal cord at 7 T with an icosahedral encoding scheme.

Regional values of fractional anisotropy (FA) and mean diffusivity (D(av)) of in vivo and excised rat spinal cords were measured using an iscosahedral encoding scheme that is based on 21 uniformly distributed and alternating gradient directions with an echo planar imaging (EPI) readout. Based on the water phantom studies, this scheme was shown to provide unbiased estimation of FA. The stability of the scanner during the acquisition of diffusion tensor imaging (DTI) data was evaluated. Repeated measurements of the FA values demonstrated excellent reproducibility, as assessed by the Bland-Altman analysis. These studies demonstrated a reduced anisotropy in excised samples relative to in vivo cords. Diffusion in the spinal cord gray matter was shown to be anisotropic. The FA value in the dorsal white matter (WM) was found to be higher relative to the ventral WM. Results from these studies should provide the necessary baseline data for serial in vivo DTI of injured spinal cord.     

Computation of the fractional anisotropy and mean diffusivity maps without tensor decoding and diagonalization: Theoretical analysis and validation.

Diffusion tensor MRI (DT-MRI) is a promising modality for in vivo mapping of the organization of deep tissues. The most commonly used DT-MRI invariant maps are the mean diffusivity, mu(D), relative anisotropy (RA), and fractional anisotropy (FA). Because of the computational burden, anisotropy maps are generally computed offline. The availability of a simple procedure to compute RA, FA, and mu(D) online would make DT-MRI more useful in clinical applications that require immediate feedback. In this study, analytical expressions that relate the commonly used tensor anisotropy measures obtained from the decoded and diagonalized DT with those obtained from the first and second moments of the measured diffusion-weighted (DW) data are derived. Specifically, it is shown that for the principal icosahedron encoding scheme, RA is related to the mean and standard deviation (SD) of the DW measurements that can be computed online. Since FA is commonly used as an anisotropy measure, an analytical expression relating RA and FA was derived from the tensor invariants. These results were validated using both Monte Carlo simulations and high-resolution, normal whole-brain DT-MRI measurements acquired with different b-factors, encoding schemes, and signal-to-noise ratio (SNR) levels. The bias introduced by the rotationally variant encoding schemes into the diffusion measures is also investigated.