Theory of Spin Echo in Restricted Geometries under a Step-wise Gradient Pulse Sequence

Barzykin, A. V.

doi:10.1006/jmre.1999.1778

Cited by 92 publications

(90 citation statements)

References 48 publications

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“…8,9 An alternative approach to understanding the effect of restricted diffusion is to treat a general gradient waveform as a piecewise-constant function. 10,11 Such a sequence is illustrated in Fig. 1͑a͒.…”

Section: Introductionmentioning

confidence: 99%

A general framework to quantify the effect of restricted diffusion on the NMR signal with applications to double pulsed field gradient NMR experiments

Özarslan

Shemesh

Basser

2009

The Journal of Chemical Physics

102

160

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Based on a description introduced by Robertson, Grebenkov recently introduced a powerful formalism to represent the diffusion-attenuated NMR signal for simple pore geometries such as slabs, cylinders, and spheres analytically. In this work, we extend this multiple correlation function formalism by allowing for possible variations in the direction of the magnetic field gradient waveform. This extension is necessary, for example, to incorporate the effects of imaging gradients in diffusion-weighted NMR imaging scans and in characterizing anisotropy at different length scales via double pulsed field gradient ͑PFG͒ experiments. In cylindrical and spherical pores, respectively, two-and three-dimensional vector operators are employed whose form is deduced from Grebenkov's results via elementary operator algebra for the case of cylinders and the Wigner-Eckart theorem for the case of spheres. The theory was validated by comparison with known findings and with experimental double-PFG data obtained from water-filled microcapillaries.

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Section: Introductionmentioning

confidence: 99%

A general framework to quantify the effect of restricted diffusion on the NMR signal with applications to double pulsed field gradient NMR experiments

Özarslan

Shemesh

Basser

2009

The Journal of Chemical Physics

102

160

View full text Add to dashboard Cite

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“…An interesting contribution in the context of developing a theoretical framework was presented in the nineties by Barzykin where the time integrated form of the Bloch-Torrey equation was investigated [3,11]. This approach was an extension of the work by Robertson and showed promise for analyzing the geometrical impact on the signal, since the theory was developed using an arbitrary geometry.…”

Section: Introductionmentioning

confidence: 99%

“…This gave an important generalization, since the diffusion operator then does not need to be fully diagonalized for calculation of the magnetization and hence complex geometries could be investigated using numerically obtained eigenfunctions/eigenvalues [12,15]. The calculation then leads to a resulting matrix exponential that can numerically be solved for most problems on a standard laptop [11,12]. It is however still rather unsatisfactory that the neat analytical structure revealed using this approach is obscured in the numerical machinery of performing a matrix exponential.…”

Section: Introductionmentioning

confidence: 99%

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Commutator expansions in NMR diffusometry

Nordin

2015

Microporous and Mesoporous Materials

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In this paper commutator expansions for solving the Bloch-Torrey's equation are derived. An exact solution for free diffusion in a constant magnetic field gradient is found. Furthermore the moments of the signal in the short gradient pulse limit for spins confined to a restricted geometry are derived. The moments are tested numerically against the known solution of diffusing spins between two perpendicular plates in the short gradient pulse limit.

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“…2. For simple confining domains (such as slab, cylinder, sphere, cylindrical, and spherical shells), the computation of the macroscopic signal by using matrix formalisms is easy, rapid, and very accurate (2,47,50,62,(71)(72)(73)(74)(75)(76). Unknown parameters (such as the compartment size or free diffusion coefficient) can be extracted by fitting experimental data to numerical curves.…”

Section: Can One Go Beyond Adc?mentioning

confidence: 99%

Use, misuse, and abuse of apparent diffusion coefficients

Grebenkov

2010

Concepts Magnetic Resonance

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ABSTRACT:The notion of effective, time-dependent or, equivalently, apparent diffusion coefficient (ADC) and its use for characterization of porous media are revisited. It is argued that the dynamic ADC, quantifying the mean-square displacement of spin-bearing particles, should not be confused with its counterpart measured by a pulsed gradient spin echo technique. The former is an intrinsic characteristic of the medium, independent of the applied magnetic field. In contrast, the spin-echo ADC depends on the experimental setup (e.g., gradient intensity and temporal profile), raising potential ambiguities in the interpretation of diffusion-weighted measurements, which may be strongly misleading when the Gaussian phase approximation (GPA) does not hold. The oversimplified use of a single b-value is criticized. Several fitting models beyond the GPA are discussed.

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Theory of Spin Echo in Restricted Geometries under a Step-wise Gradient Pulse Sequence

Cited by 92 publications

References 48 publications

A general framework to quantify the effect of restricted diffusion on the NMR signal with applications to double pulsed field gradient NMR experiments

A general framework to quantify the effect of restricted diffusion on the NMR signal with applications to double pulsed field gradient NMR experiments

Commutator expansions in NMR diffusometry

Use, misuse, and abuse of apparent diffusion coefficients

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