Restricted Self‐Diffusion of Protons in Colloidal Systems by the Pulsed‐Gradient, Spin‐Echo Method
15 Aug 1968-Journal of Chemical Physics (American Institute of Physics)-Vol. 49, Iss: 4, pp 1768-1777
TL;DR: The pulsed gradient, spin-echo technique has been used to study self-diffusion of protons in several colloidal systems in order to examine the usefulness of that technique in determining the extent to which the free movement of molecules in these systems is restricted by the colloidal structures present as discussed by the authors.
Abstract: The pulsed‐gradient, spin‐echo technique has been used to study self‐diffusion of protons in several colloidal systems in order to examine the usefulness of that technique in determining the extent to which the free movement of molecules in these systems is restricted by the colloidal structures present. The pulsed‐gradient experiment is preferred to the steady‐gradient experiment because it affords better definition and control over the time during which diffusion is observed. Diffusion times between 1 sec and 10−3 sec have been used. One artificial system of thin liquid layers, three different kinds of plant cells, and one emulsion have been studied. Clear indications of restricted diffusion are found in all the systems. When fitted to theoretical expressions derived for such behavior, the data yielded a description of each system, as seen by the diffusing molecules, adequately in agreement with the known structure and properties. Critiera for recognizing and analyzing restricted diffusion are discussed. Necessary conditions for the successful study of restricted diffusion are also discussed.
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TL;DR: A magnetic resonance (MR) method to image intravoxel incoherent motions (IVIMs) by using appropriate gradient pulses and nonuniform slow flow of cerebrospinal fluid appeared as a useful feature on IVIM images.
Abstract: Molecular diffusion and microcirculation in the capillary network result in a distribution of phases in a single voxel in the presence of magnetic field gradients. This distribution produces a spin-echo attenuation. The authors have developed a magnetic resonance (MR) method to image such intravoxel incoherent motions (IVIMs) by using appropriate gradient pulses. Images were generated at 0.5 T in a high-resolution, multisection mode. Diffusion coefficients measured on images of water and acetone phantoms were consistent with published values. Images obtained in the neurologic area from healthy subjects and patients were analyzed in terms of an apparent diffusion coefficient (ADC) incorporating the effect of all IVIMs. Differences were found between various normal and pathologic tissues. The ADC of in vivo water differed from the diffusion coefficient of pure water. Results were assessed in relation to water compartmentation in biologic tissues (restricted diffusion) and tissue perfusion. Nonuniform slow flow of cerebrospinal fluid appeared as a useful feature on IVIM images. Observation of these motions may significantly extend the diagnostic capabilities of MR imaging.
3,679 citations
TL;DR: In this paper, the stimulated echo attenuation due to self-diffusion was derived for the general case of a time-dependent field gradient, and the result was found experimentally to be correct for the special case of field gradient applied in two equal, square pulses.
Abstract: The stimulated echo in a three‐rf‐pulse experiment is shown to be useful in extending the range of measurement of diffusion coefficients to more viscous substances or the measurement of barrier separations to wider spacings in systems where the diffusing substance has T1 > T2. The spin‐echo attenuation due to self‐diffusion is derived for the general case of a time‐dependent field gradient, and the result is found experimentally to be correct for the special case of a field gradient applied in two equal, square pulses.
1,549 citations
1,250 citations
TL;DR: It is argued that the diffusional kurtosis is sensitive to diffusional heterogeneity and suggested that DKI may be useful for investigating ischemic stroke and neuropathologies, such as Alzheimer's disease and schizophrenia.
Abstract: Quantification of non-Gaussianity for water diffusion in brain by means of diffusional kurtosis imaging (DKI) is reviewed. Diffusional non-Gaussianity is a consequence of tissue structure that creates diffusion barriers and compartments. The degree of non-Gaussianity is conveniently quantified by the diffusional kurtosis and derivative metrics, such as the mean, axial, and radial kurtoses. DKI is a diffusion-weighted MRI technique that allows the diffusional kurtosis to be estimated with clinical scanners using standard diffusion-weighted pulse sequences and relatively modest acquisition times. DKI is an extension of the widely used diffusion tensor imaging method, but requires the use of at least 3 b-values and 15 diffusion directions. This review discusses the underlying theory of DKI as well as practical considerations related to data acquisition and post-processing. It is argued that the diffusional kurtosis is sensitive to diffusional heterogeneity and suggested that DKI may be useful for investigating ischemic stroke and neuropathologies, such as Alzheimer’s disease and schizophrenia.
1,056 citations
Cites background from "Restricted Self‐Diffusion of Proton..."
...For the diffusion-weighted signal, we shall have in mind that obtained for water with the canonical Stejskal-Tanner sequence (1,30), although the essential considerations can be readily extended for many of the other related sequences....
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..., a glass of water), this displacement probability distribution function (PDF) is Gaussian (1), and the diffusion is referred to as Gaussian diffusion....
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...Let D1 ≡ D(1) (n), D2 ≡ D(2) (n), and f ≡ f1....
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...The diffusion-weighted signal intensity, S, can be regarded as a function of the “b-value,” which for a Stejskal-Tanner sequence is defined by b ≡ (γδg)2 (Δ − δ/3) where γ is the proton gyromagnetic ratio, g is the amplitude of the diffusion sensitizing magnetic field gradient pulses, δ is the duration of the gradient pulses, and Δ is time interval between the centers of the gradient pulses (1,30)....
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...Eqn (4) is a direct application of the general formula for kurtosis of eqn (1) to molecular diffusion....
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Environmental Molecular Sciences Laboratory1, Yale University2, University of California, Davis3, Los Alamos National Laboratory4, University of Wyoming5, Texas A&M University6, École Polytechnique Fédérale de Lausanne7, Colorado State University8, California Institute of Technology9, Johns Hopkins University10, IBM11
TL;DR: This poster presents a probabilistic procedure to constrain the number of particles in the response of the immune system to the presence of Tau.
Abstract: Reference LPI-ARTICLE-1999-017View record in Web of Science Record created on 2006-02-21, modified on 2017-05-12
966 citations
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31 Dec 1959
TL;DR: In this paper, a classic account describes the known exact solutions of problems of heat flow, with detailed discussion of all the most important boundary value problems, including boundary value maximization.
Abstract: This classic account describes the known exact solutions of problems of heat flow, with detailed discussion of all the most important boundary value problems.
21,807 citations
TL;DR: In this article, a derivation of the effect of a time-dependent magnetic field gradient on the spin-echo experiment, particularly in the presence of spin diffusion, is given.
Abstract: A derivation is given of the effect of a time‐dependent magnetic field gradient on the spin‐echo experiment, particularly in the presence of spin diffusion. There are several reasons for preferring certain kinds of time‐dependent magnetic field gradients to the more usual steady gradient. If the gradient is reduced during the rf pulses, H1 need not be particularly large; if the gradient is small at the time of the echo, the echo will be broad and its amplitude easy to measure. Both of these relaxations of restrictions on the measurement of diffusion coefficients by the spin‐echo technique serve to extend its range of applicability. Furthermore, a pulsed gradient can be recommended when it is critical to define the precise time period over which diffusion is being measured.The theoretical expression derived has been verified experimentally for several choices of time dependent magnetic field gradient. An apparatus is described suitable for the production of pulsed gradients with amplitudes as large as 100 ...
7,781 citations
TL;DR: In this paper, the effect of diffusion on free precession in nuclear resonance has been studied, and a new scheme for measuring the transverse relaxation time is described, which largely circumvents the diffusion effect.
Abstract: Nuclear resonance techniques involving free precession are examined, and, in particular, a convenient variation of Hahn's spin-echo method is described. This variation employs a combination of pulses of different intensity or duration ("90-degree" and "180-degree" pulses). Measurements of the transverse relaxation time ${T}_{2}$ in fluids are often severely compromised by molecular diffusion. Hahn's analysis of the effect of diffusion is reformulated and extended, and a new scheme for measuring ${T}_{2}$ is described which, as predicted by the extended theory, largely circumvents the diffusion effect. On the other hand, the free precession technique, applied in a different way, permits a direct measurement of the molecular self-diffusion constant in suitable fluids. A measurement of the self-diffusion constant of water at 25\ifmmode^\circ\else\textdegree\fi{}C is described which yields $D=2.5(\ifmmode\pm\else\textpm\fi{}0.3)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}5}$ ${\mathrm{cm}}^{2}$/sec, in good agreement with previous determinations. An analysis of the effect of convection on free precession is also given. A null method for measuring the longitudinal relaxation time ${T}_{1}$, based on the unequal-pulse technique, is described.
5,630 citations
1,803 citations
TL;DR: In this article, the Bloch-Torrey equations are modified to include the case of anisotropic, restricted diffusion and flow, and the problem of solving these modified equations for the amplitude of a spin echo in a time-dependent magnetic field gradient subject to restricting boundary conditions is discussed.
Abstract: The Bloch—Torrey equations are modified to include the case of anisotropic, restricted diffusion and flow. The problem of solving these modified equations for the amplitude of a spin echo in a time‐dependent magnetic‐field gradient subject to restricting boundary conditions is discussed. This problem is solved for a number of selected cases. In particular, it is found that a magnetic‐field gradient applied in short, intense pulses is effective in defining the time during which nuclear displacements take place. A simplified equation, suitable for the pulsed‐gradient experiment, is presented and solved for two different examples of systems showing restricted diffusion. A procedure for analyzing the data from pulsed‐gradient measurements is suggested, and its merits are discussed. Suggestions are made of systems which may well be expected to show restricted, anisotropic diffusion or interesting flow properties.
866 citations