The displacement correlation tensor: Microstructure, ensemble anisotropy and curving fibers

Jespersen, Sune Nørhøj; Buhl, Niels

doi:10.1016/j.jmr.2010.10.003

Cited by 35 publications

(64 citation statements)

References 36 publications

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“…In the short mixing time regime, interesting diffusion-diffraction phenomena can be produced [32][33][34][35][36], and angular dependencies can provide insight into pore sizes as shown experimentally first by Koch and Finsterbusch [37,38] and then by others [39][40][41]; however, by analyzing the displacement correlation tensor [42], the short τ m angular DDE experiment aiming to measure compartment sizes was found by Jespersen to be equivalent to a time-dependent SDE experiment [43]. By contrast, in the long mixing time regime, the second order term in the displacement correlation tensor, from which sizes are measured, is decoupled from µA, making its measurement much less complicated [25,31].…”

Section: Introductionmentioning

confidence: 99%

Axon Diameters and Myelin Content Modulate Microscopic Fractional Anisotropy at Short Diffusion Times in Fixed Rat Spinal Cord

Shemesh

2018

Front. Phys.

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Mapping tissue microstructure accurately and noninvasively is one of the frontiers of biomedical imaging. Diffusion Magnetic Resonance Imaging (MRI) is at the forefront of such efforts, as it is capable of reporting on microscopic structures orders of magnitude smaller than the voxel size by probing restricted diffusion. Double Diffusion Encoding (DDE) and Double Oscillating Diffusion Encoding (DODE) in particular, are highly promising for their ability to report on microscopic fractional anisotropy (µFA), a measure of the pore anisotropy in its own eigenframe, irrespective of orientation distribution. However, the underlying correlates of µFA have insofar not been studied. Here, we extract µFA from DDE and DODE measurements at ultrahigh magnetic field of 16.4T with the goal of probing fixed rat spinal cord microstructure. We further endeavor to correlate µFA with Myelin Water Fraction (MWF) derived from multiexponential T 2 relaxometry, as well as with literature-based spatially varying axon diameter. In addition, a simple new method is presented for extracting unbiased µFA from three measurements at different b-values. Our findings reveal strong anticorrelations between µFA (derived from DODE) and axon diameter in the distinct spinal cord tracts; a moderate correlation was also observed between µFA derived from DODE and MWF. These findings suggest that axonal membranes strongly modulate µFA, which-owing to its robustness toward orientation dispersion effects-reflects axon diameter much better than its typical FA counterpart. µFA varied when measured via oscillating or blocked gradients, suggesting selective probing of different parallel path lengths and providing insight into how those modulate µFA metrics. Our findings thus shed light into the underlying microstructural correlates of µFA and are promising for future interpretations of this metric in health and disease.

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Section: Introductionmentioning

confidence: 99%

Axon Diameters and Myelin Content Modulate Microscopic Fractional Anisotropy at Short Diffusion Times in Fixed Rat Spinal Cord

Shemesh

2018

Front. Phys.

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“…Conversely, this approximation is implicitly assumed when keeping only terms of second order in g in the Taylor expansion of log S or S . Thus, employing Einstein summation convention and using subscript letters to label Cartesian components of vectors and tensors, Equation can be simplified to yield:

\begin{matrix} left \\ S \approx \exp (- \frac{1}{2} 〈φ^{2}〉) = \exp (- \frac{1}{2} γ^{2} \int_{0}^{T} d t \int_{0}^{T} {dt}^{'} g_{i} (t) g_{j} (t^{'}) 〈r_{i} (t) r_{j} (t^{'})〉) \\ = \exp (\frac{1}{2} γ^{2} \int_{0}^{T} d t \int_{0}^{T} {dt}^{'} D_{italicij} (| t - t^{'} |) | t - t^{'} | g_{i} (t) g_{j} (t^{'})) \end{matrix}

where the definition of the time‐dependent diffusion tensor:

2 D_{italicij} (| t - t^{'} |) | t - t^{'} | = 〈(r_{i} (t) - r_{i} (t^{'})) (r_{j} (t) - r_{j} (t^{'}))〉

is used, and balanced gradients as well as no macroscopic flow are assumed; thus, 〈 r ( t 1 ) − r ( t 2 )〉 = 0 and 〈 r 1 i r 2 j 〉 = 〈 r 2 i r 1 j 〉 . Equation explicitly shows that, for any pulse shape in the low‐diffusion‐weighting regime, signal attenuation is gov...…”

Section: Resultsmentioning

confidence: 99%

Equivalence of double and single wave vector diffusion contrast at low diffusion weighting

Jespersen

2011

NMR in Biomedicine

122

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Multiple pulsed field gradient diffusion sequences have received renewed interest in recent years as a potentially new type of MRI contrast. This attention is largely a result of the ability to measure pore sizes using low-amplitude diffusion gradients, and to distinguish between macroscopically isotropic systems of anisotropic pores and systems of isotropic pores. In this article, it is shown that, under many circumstances, the same type of information can be obtained by combining two or more standard single pulse diffusion-weighted experiments acquired at different diffusion times. Similarly, information from multiple pulsed field gradient diffusion can be reconstructed from several single pulsed diffusion experiments. This possibility is rooted in the information contained in the time dependence of the diffusion tensor, which provides a complete description of the diffusion-weighted MR signal at low gradient amplitudes. The new information arising at the fourth order in the cumulant expansion is discussed. The coupling of the wave vectors at long mixing times is found to be controlled by the variance of the single pore mean displacement tensor. In particular, a discussion is given concerning the way in which the sensitivity of the fourth-order term to the pore shape anisotropy is modulated by pore orientation anisotropy and vanishes in coherently oriented homogeneous ensembles. For macroscopically isotropic systems, a new index of pore shape anisotropy is proposed.

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“…Angular DDE in the zero mixing time limit has been proposed for extracting pore sizes , with exact solutions as well as simulations subsequently developed for this experiment in various regimes. Extensive experimental work has since explored angular DDE's potential to reconstruct pore sizes in myriad systems , and the methodology's application in vivo in humans using clinical scanners has been reported more recently .…”

Section: Unique Microstructural Information Obtainable From Dde and Mmentioning

confidence: 99%

Conventions and nomenclature for double diffusion encoding NMR and MRI

Shemesh

Jespersen

Alexander

et al. 2015

Magnetic Resonance in Med

176

204

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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. V C 2015 Wiley Periodicals, Inc.

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The displacement correlation tensor: Microstructure, ensemble anisotropy and curving fibers

Cited by 35 publications

References 36 publications

Axon Diameters and Myelin Content Modulate Microscopic Fractional Anisotropy at Short Diffusion Times in Fixed Rat Spinal Cord

Axon Diameters and Myelin Content Modulate Microscopic Fractional Anisotropy at Short Diffusion Times in Fixed Rat Spinal Cord

Equivalence of double and single wave vector diffusion contrast at low diffusion weighting

Conventions and nomenclature for double diffusion encoding NMR and MRI

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