A tensor approach to double wave vector diffusion-weighting experiments on restricted diffusion
ABSTRACT Previously, it has been shown theoretically that in case of restricted diffusion, e.g. within isolated pores or cells, a measure of the pore size, the mean radius of gyration, can be estimated from double wave vector diffusion-weighting experiments. However, these results are based on the assumption of an isotropic orientation distribution of the pores or cells which hampers the applicability to samples with anisotropic or unknown orientation distributions, such as biological tissue. Here, the theoretical considerations are re-investigated and generalized in order to describe the signal dependency for arbitrary orientation distributions. The second-order Taylor expansion of the signal delivers a symmetric rank-2 tensor with six independent elements if the two wave vectors are concatenated to a single six-element vector. With this tensor approach the signal behavior for arbitrary wave vectors and orientation distributions can be described as is demonstrated by numerical simulations. The rotationally invariant trace of the tensor represents a pore size measure and can be determined from three orthogonal directions with parallel and antiparallel orientation of the two wave vectors. Thus, the presented tensor approach may help to improve the applicability of double wave vector diffusion-weighting experiments to determine pore or cell sizes, in particular in biological tissue.
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ABSTRACT: When PGSE NMR is applied to water in microheterogeneous materials such as liquid crystals, foodstuffs, porous rocks, and biological tissues, the signal attenuation is often multi-exponential, indicating the presence of pores having a range of sizes or anisotropic domains having a spread of orientations. Here we modify the standard PGSE experiment by introducing low-amplitude harmonically modulated gradients, which effectively make the q-vector perform magic-angle spinning (MAS) about an axis fixed in the laboratory frame. With this new technique, denoted q-MAS PGSE, the signal attenuation depends on the isotropic average of the local diffusion tensor. The capability of q-MAS PGSE to distinguish between pore size and domain orientation dispersion is demonstrated by experiments on a yeast cell suspension and a polydomain anisotropic liquid crystal. In the latter case, the broad distribution of apparent diffusivities observed with PGSE is narrowed to its isotropic average with q-MAS PGSE in a manner that is analogous to the narrowing of chemical shift anisotropy powder patterns using magic-angle sample spinning in solid-state NMR. The new q-MAS PGSE technique could be useful for resolving size/orientation ambiguities in the interpretation of PGSE data from, e.g., water confined within the axons of human brain tissue.Journal of Magnetic Resonance 11/2012; 226C:13-18. · 2.30 Impact Factor
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ABSTRACT: Pulsed field gradient diffusion sequences (PFG) with multiple diffusion encoding blocks have been indicated to offer new microstructural tissue information, such as the ability to detect nonspherical compartment shapes in macroscopically isotropic samples, i.e. samples with negligible directional signal dependence on diffusion gradients in standard diffusion experiments. However, current acquisition schemes are not rotationally invariant in the sense that the derived metrics depend on the orientation of the sample, and are affected by the interplay of sampling directions and compartment orientation dispersion when applied to macroscopically anisotropic systems. Here we propose a new framework, the d-PFG 5-design, to enable rotationally invariant estimation of double wave vector diffusion metrics (d-PFG). The method is based on the idea that an appropriate orientational average of the signal emulates the signal from a powder preparation of the same sample, where macroscopic anisotropy is absent by construction. Our approach exploits the theory of exact numerical integration (quadrature) of polynomials on the rotation group, and we exemplify the general procedure with a set consisting of 60 pairs of diffusion wave vectors (the d-PFG 5-design) facilitating a theoretically exact determination of the fourth order Taylor or cumulant expansion of the orientationally averaged signal. The d-PFG 5-design is evaluated with numerical simulations and ex vivo high field diffusion MRI experiments in a nonhuman primate brain. Specifically, we demonstrate rotational invariance when estimating compartment eccentricity, which we show offers new microstructural information, complementary to that of fractional anisotropy (FA) from diffusion tensor imaging (DTI). The imaging observations are supported by a new theoretical result, directly relating compartment eccentricity to FA of individual pores. Copyright © 2013 John Wiley & Sons, Ltd.NMR in Biomedicine 08/2013; · 3.45 Impact Factor
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ABSTRACT: Today, structure elucidation of complex organic molecules relies heavily on the application of proton-detected heteronuclear NMR techniques. Among these techniques, the HMBC experiment is one of the most useful 2D NMR methods. Carbon–proton HMBC experiments allow the assignment of structural frag- ments through correlations between protons and carbons separated by more than one bond, usually two or three bonds via small 1H–13C couplings, usually 2JCH and 3JCH, but also over longer bond chains, n > 3JCH, especially in conjugated systems. In the decade preceding this review, several significant extensions to the basic HMBC experiment have been made. The main directions of develop- ments were widening the range of accessible long-range J-coupling constants, improving sensitivity, refining resolution, suppressing one-bond correlations and accurately determining long-range coupling constants. In addition, increasing the efficiency of multi-dimensional NMR techniques, an important contempo- rary trend in NMR, has also had its impact on HMBC, with multiplex approaches and parallel acquisition techniques emerging. Structure elucidation and signal assignment of proton-deficient molecules like condensed aromatics has bene- fited most substantially from the new possibilities for a detailed analysis of long- range correlations. In this review, we summarize the basic variants of HMBC and discuss recent developments related to the technique, focusing on develop- ments of new pulse sequences and processing protocols.Annual Reports on NMR Spectroscopy 01/2010; 70:1-60. · 1.42 Impact Factor