A tensor model and measures of microscopic anisotropy for double-wave-vector diffusion-weighting experiments with long mixing times

Department of Systems Neuroscience, University Medical Center Hamburg-Eppendorf, Hamburg, Germany.
Journal of Magnetic Resonance (Impact Factor: 2.51). 10/2009; 202(1):43-56. DOI: 10.1016/j.jmr.2009.09.015
Source: PubMed


Experiments with two diffusion-weighting periods applied successively in a single experiment, so-called double-wave-vector (DWV) diffusion-weighting experiments, are a promising tool for the investigation of material or tissue structure on a microscopic level, e.g. to determine cell or compartment sizes or to detect pore or cell anisotropy. However, the theoretical descriptions presented so far for experiments that aim to investigate the microscopic anisotropy with a long mixing time between the two diffusion weightings, are limited to certain wave vector orientations, specific pore shapes, and macroscopically isotropic samples. Here, the signal equations for fully restricted diffusion are re-investigated in more detail. A general description of the signal behavior for arbitrary wave vector directions, pore or cell shapes, and orientation distributions of the pores or cells is obtained that involves a fourth-order tensor approach. From these equations, a rotationally invariant measure of the microscopic anisotropy, termed MA, is derived that yields information complementary to that of the (macroscopic) anisotropy measures of standard diffusion-tensor acquisitions. Furthermore, the detailed angular modulation for arbitrary cell shapes with an isotropic orientation distribution is derived. Numerical simulations of the MR signal with a Monte-Carlo algorithms confirm the theoretical considerations. The extended theoretical description and the introduction of a reliable measure of the microscopic anisotropy may help to improve the applicability and reliability of corresponding experiments.

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Available from: Marco Lawrenz, Apr 15, 2015
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    • "Several methods have been proposed for the quantification of microscopic anisotropy from such data. To this end, Lawrenz and Finsterbusch (2013) used a fourth-order tensor parameterization suggested by Lawrenz et al. (2010) to map the microscopic diffusion anisotropy in human white matter in vivo. Jespersen et al. (2013) developed a rotationally invariant dPFG encoding scheme and mapped the microscopic anisotropy in an excised monkey brain in terms of the fractional eccentricity. "
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    ABSTRACT: Abstract The anisotropy of water diffusion in brain tissue is affected by both disease and development. This change can be detected using diffusion MRI and is often quantified by the fractional anisotropy (FA) derived from diffusion tensor imaging (DTI). Although FA is sensitive to anisotropic cell structures, such as axons, it is also sensitive to their orientation dispersion. This is a major limitation to the use of FA as a biomarker for “tissue integrity”, especially in regions of complex microarchitecture. In this work, we seek to circumvent this limitation by disentangling the effects of microscopic diffusion anisotropy from the orientation dispersion. The microscopic fractional anisotropy (μFA) and the order parameter (OP) were calculated from the contrast between signal prepared with directional and isotropic diffusion encoding, where the latter was achieved by magic angle spinning of the q-vector (qMAS). These parameters were quantified in healthy volunteers and in two patients; one patient with meningioma and one with glioblastoma. Finally, we used simulations to elucidate the relation between FA and μFA in various micro-architectures. Generally, μFA was high in the white matter and low in the gray matter. In the white matter, the largest differences between μFA and FA were found in crossing white matter and in interfaces between large white matter tracts, where μFA was high while FA was low. Both tumor types exhibited a low FA, in contrast to the μFA which was high in the meningioma and low in the glioblastoma, indicating that the meningioma contained disordered anisotropic structures, while the glioblastoma did not. This interpretation was confirmed by histological examination. We conclude that FA from DTI reflects both the amount of diffusion anisotropy and orientation dispersion. We suggest that the μFA and OP may complement FA by independently quantifying the microscopic anisotropy and the level of orientation coherence.
    Full-text · Article · Oct 2014 · NeuroImage
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    • "A similar parameter of microscopic anisotropy, termed fractional eccentricity (FE), but relying on double pulsed field gradient (dPFG) diffusion experiments was introduced by us recently in (Jespersen, Lundell et al. 2013). In it we extended previous work on indices of microscopic anisotropy in the long diffusion time limit proposed by Lawrenz and Finsterbusch (Lawrenz, Koch et al. 2010). The FE terminology was motivated by the existing nomenclature in the dPFG field. "

    Full-text · Article · May 2014 · Frontiers in Physics
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    • "0. This equation conveniently describes the desired generalized signal for any wave vector direction and cell shape. For a mixture of different pore ensembles, the equation remains valid if the weighted sums of the individual ensembles are used as described previously [16]. "
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    ABSTRACT: MR sequences where two diffusion-weighting periods are applied successively in a single acquisition seem to be a promising tool for the investigation of tissue structure on a microscopic level such as the characterization of the compartment size or eccentricity measures of pores. However, the application of such double-wave-vector (DWV) experiments on whole-body MR systems is hampered by the long gradient pulses required that have been shown to reduce the signal modulation. In this work, it is demonstrated that involving multiple concatenations of the two diffusion-weighting periods can ameliorate this problem in experiments with long mixing times between the two wave vectors. The recently presented tensor equation is extended to multiple concatenations. As confirmed by Monte-Carlo simulations, this model shows a good approximation of the signals observed for typical whole-body gradient pulse durations and the derived anisotropy measures are obtained with good accuracy. Most importantly, the signal modulation is increased with multiple concatenations because shorter gradient pulses can be used to achieve the desired diffusion-weighting. Thus, the multiple concatenation approach may help to improve the applicability and reliability of DWV measurements with long mixing times on standard whole-body MR systems.
    Full-text · Article · Sep 2010 · Journal of Magnetic Resonance
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