Pulsed‐field gradient nuclear magnetic resonance as a tool for studying translational diffusion: Part 1. Basic theory

Price, William S.

doi:10.1002/(sici)1099-0534(1997)9:5<299::aid-cmr2>3.3.co;2-2

Cited by 336 publications

(476 citation statements)

References 84 publications

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“…A complete discussion of the assumptions used in formulating the Bloch-Torrey equation can be found the books by Brown et al, 4 by Jones, 6 and by Callaghan,7 as well as in the papers by Price. 12,13 In this paper, we will not pursue advanced techniques nor will we consider the effects of changing gradient direction (for studying anisotropic materials) or changing the shape of the gradient waveforms (or oscillating gradients).…”

Section: Signal Modelsmentioning

confidence: 99%

Models of diffusion signal decay in magnetic resonance imaging: Capturing complexity

Magin

2016

Concepts Magnetic Resonance

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Diffusion‐weighted MRI is a key diagnostic component of clinical medicine. Radiologists use models of the effects of diffusion weighting to connect the decay of the signal intensity in tissues with macroscopic (diffusion tensor imaging) and microscopic (q‐space imaging) structures. This multi‐scale problem has stimulated the creation of many diffusion models spanning phenomenon in cells, in tissues, and in organs. Such models can be heuristic or based on simulations, stochastic processes, histological structure or physical and physiological constraints. The goal of this paper is to provide an overview of these approaches by considering several different classes of mathematical models (linear, nonlinear, integer, and fractional orders) that can, and have in some cases, been used to fit diffusion attenuation in complex biological tissues, such as brain white and gray matter. The focus here is not on solving the Bloch‐Torrey equation or on fitting curves to data, but on the choices (Gaussian, anomalous, isotropic, anisotropic) one often has to make when beginning the analysis of diffusion data. It is hoped that this presentation, while oversimplified, will be of use to students and to new investigators who seek an introduction to diffusion attenuation model selection and characterization. Examples are given that illustrate the relationship between the functional form of the diffusion decay rate and, in the case of a Stejskal‐Tanner gradient pulse sequence, the expected signal decay. Model limitations are noted and connections to more advanced treatments of diffusion modeling methods are provided.

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Section: Signal Modelsmentioning

confidence: 99%

Models of diffusion signal decay in magnetic resonance imaging: Capturing complexity

Magin

2016

Concepts Magnetic Resonance

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“…Pulsed-field gradient (PFG) nuclear magnetic resonance (NMR; (1,2)) is a powerful means of characterizing diffusion and flow, monodisperse and polydisperse samples, multi-component systems, chemical exchange and reaction kinetics (3)(4)(5)(6)(7)(8). In the case of translational self-diffusion and a single diffusion coefficient D it was shown by Stejskal and Tanner (1) that if the two gradient pulses used in the sequence are perfectly rectangular, i.e.…”

Section: Introductionmentioning

confidence: 99%

Stejskal‐tanner equation for three asymmetrical gradient pulse shapes used in diffusion NMR

Röding

Nydén

2015

Concepts Magnetic Resonance

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When using pulsed‐field gradient nuclear magnetic resonance (NMR) for measurements of translational self‐diffusion, the Stejskal‐Tanner equation is used to relate the signal attenuation to the experimental parameters and to estimate the diffusion coefficient. However, the conventional form of the equation is valid only if the gradient pulse shapes are perfectly rectangular, which is never the case in practice. In light of three asymmetric gradient pulse shapes having reached the NMR mainstream and been implemented into proprietary software, we present explicit expressions for the corresponding Stejskal‐Tanner equations and computer code for easy implementation. We also study the bias introduced by using the common rectangular gradient pulse approximation. © 2015 Wiley Periodicals, Inc. Concepts Magn Reson Part A 44A: 133–137, 2015.

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“…Generally, rotational diffusion is sensitive to motions that occur at the nanometer length scale and at the picosecond-tonanosecond time scale, 8,9 whereas in translational diffusion measurements, motion is measured over the millisecond-tosecond time scale and over distances from tens of nanometers up to hundreds of microns. [10][11][12] In this context, NMR techniques have the advantage of simultaneously and non-invasively measuring the translational and rotational diffusion of molecules. Pulsed field gradient nuclear magnetic resonance diffusometry (PFG-NMR) measures translational diffusion, 11 whereas NMR relaxometry is sensitive to rotational diffusion.…”

Section: Introductionmentioning

confidence: 99%

“…[10][11][12] In this context, NMR techniques have the advantage of simultaneously and non-invasively measuring the translational and rotational diffusion of molecules. Pulsed field gradient nuclear magnetic resonance diffusometry (PFG-NMR) measures translational diffusion, 11 whereas NMR relaxometry is sensitive to rotational diffusion.…”

Section: Introductionmentioning

confidence: 99%

Translational and rotational diffusion of flexible PEG and rigid dendrimer probes in sodium caseinate dispersions and acid gels

et al. 2014

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The dynamics of rigid dendrimer and flexible PEG probes in sodium caseinate dispersions and acid gels, including both translational diffusion and rotational diffusion, were studied by NMR. Above the onset of the close-packing limit (C ∼ 10 g/100 g H2 O), translational diffusion of the probe depended on its flexibility and on the fluctuations of the matrix chains. The PEG probe diffused more rapidly than the spherical dendrimer probe of corresponding hydrodynamic radius. The greater conformational flexibility of PEG facilitated its motion through the crowded casein matrix. Rotational diffusion was, however, substantially less hindered than the translational diffusion and depended on the local protein-probe friction which became high when the casein concentration increased. The coagulation of the matrix led to the formation of large voids, which resulted in an increase in the translational diffusion of the probes, whereas the rotational diffusion of the probes was retarded in the gel, which could be attributed to the immobilized environment surrounding the probe. Quantitative information from PFG-NMR and SEM micrographs have been combined for characterizing microstructural details in SC acid gels.

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Pulsed‐field gradient nuclear magnetic resonance as a tool for studying translational diffusion: Part 1. Basic theory

Cited by 336 publications

References 84 publications

Models of diffusion signal decay in magnetic resonance imaging: Capturing complexity

Models of diffusion signal decay in magnetic resonance imaging: Capturing complexity

Stejskal‐tanner equation for three asymmetrical gradient pulse shapes used in diffusion NMR

Translational and rotational diffusion of flexible PEG and rigid dendrimer probes in sodium caseinate dispersions and acid gels

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