What Are the Conditions for Exponential Time-Cubed Echo Decays?

Pfitsch, D.W.; McDowell, Andrew F.; Conradi, Mark S.

doi:10.1006/jmre.1999.1804

Cited by 11 publications

(6 citation statements)

References 19 publications

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“…Substituting the correlation function (11) in Eq. (3), the external pool signal attenuation functions for the FID and SE signals can be written in the form:…”

Section: Impermeable Spheres (External Pool)mentioning

confidence: 99%

“…In particular, such a t 3 time dependence of the attenuation function can be obtained based on the assumption that at short time, when a spinÕs displacement is small, its diffusion can be considered as unrestricted diffusion in the constant local field gradients, and the attenuation function for the SE signal is (see, e.g. [8][9][10][11]):…”

Section: (Solid Lines) Dashed Lines Inmentioning

confidence: 99%

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Gaussian approximation in the theory of MR signal formation in the presence of structure-specific magnetic field inhomogeneities. Effects of impermeable susceptibility inclusions

Sukstanskiı̆

Yablonskiy

2004

Journal of Magnetic Resonance

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“…Substituting the correlation function (11) in Eq. (3), the external pool signal attenuation functions for the FID and SE signals can be written in the form:…”

Section: Impermeable Spheres (External Pool)mentioning

confidence: 99%

Section: (Solid Lines) Dashed Lines Inmentioning

confidence: 99%

Gaussian approximation in the theory of MR signal formation in the presence of structure-specific magnetic field inhomogeneities. Effects of impermeable susceptibility inclusions

Sukstanskiı̆

Yablonskiy

2004

Journal of Magnetic Resonance

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“…2b (green crosses and triangles). The free diffusion regime exhibits the simplest behavior: since the delays between pulses x, y τ c , the filter function F peaks at frequencies ω 1/τ c [9,11] and decoherence effects are dominated by the tail of the spectral density S(ω) ∝ 1 ω 2 τcπ [31]. The signal decay therefore follows a decay rate proportional to ω −2 = (T E/N ) 2 (dashes and crosses in Fig.…”

mentioning

confidence: 99%

Coherent Dynamical Recoupling of Diffusion-Driven Decoherence in Magnetic Resonance

2013

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During recent years, dynamical decoupling (DD) has gained relevance as a tool for manipulating and interrogating quantum systems. This is particularly relevant for spins involved in nuclear magnetic resonance (NMR), where DD sequences can be used to prolong quantum coherences, or to selectively couple or decouple the effects imposed by random environmental fluctuations. In this Letter, we show that these concepts can be exploited to selectively recouple diffusion processes in restricted spaces. The ensuing method provides a novel tool to measure restriction lengths in confined systems such as capillaries, pores or cells. The principles of this method for selectively recoupling diffusion-driven decoherence, its standing within the context of diffusion NMR, extensions to the characterization of other kinds of quantum fluctuations, and corroborating experiments, are presented.

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“…2). 49,53 To quantify this feature we consider the magnetization decays for the two parts of the SDR sequence in Fig. 1.…”

Section: Selective Dynamical Recoupling Of Background Gradients Amentioning

confidence: 99%

Diffusion-assisted selective dynamical recoupling: A new approach to measure background gradients in magnetic resonance

Álvarez

Shemesh

Frydman

2014

The Journal of Chemical Physics

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Dynamical decoupling, a generalization of the original NMR spin-echo sequence, is becoming increasingly relevant as a tool for reducing decoherence in quantum systems. Such sequences apply non-equidistant refocusing pulses for optimizing the coupling between systems, and environmental fluctuations characterized by a given noise spectrum. One such sequence, dubbed Selective Dynamical Recoupling (SDR) [P. E. S. Smith, G. Bensky, G. A. Álvarez, G. Kurizki, and L. Frydman, Proc. Natl. Acad. Sci. 109, 5958 (2012)], allows one to coherently reintroduce diffusion decoherence effects driven by fluctuations arising from restricted molecular diffusion [G. A. Álvarez, N. Shemesh, and L. Frydman, Phys. Rev. Lett. 111, 080404 (2013)]. The fully-refocused, constant-time, and constant-number-of-pulses nature of SDR also allows one to filter out "intrinsic" T1 and T2 weightings, as well as pulse errors acting as additional sources of decoherence. This article explores such features when the fluctuations are now driven by unrestricted molecular diffusion. In particular, we show that diffusion-driven SDR can be exploited to investigate the decoherence arising from the frequency fluctuations imposed by internal gradients. As a result, SDR presents a unique way of probing and characterizing these internal magnetic fields, given an a priori known free diffusion coefficient. This has important implications in studies of structured systems, including porous media and live tissues, where the internal gradients may serve as fingerprints for the system's composition or structure. The principles of this method, along with full analytical solutions for the unrestricted diffusion-driven modulation of the SDR signal, are presented. The potential of this approach is demonstrated with the generation of a novel source of MRI contrast, based on the background gradients active in an ex vivo mouse brain. Additional features and limitations of this new method are discussed.

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What Are the Conditions for Exponential Time-Cubed Echo Decays?

Cited by 11 publications

References 19 publications

Gaussian approximation in the theory of MR signal formation in the presence of structure-specific magnetic field inhomogeneities. Effects of impermeable susceptibility inclusions

Gaussian approximation in the theory of MR signal formation in the presence of structure-specific magnetic field inhomogeneities. Effects of impermeable susceptibility inclusions

Coherent Dynamical Recoupling of Diffusion-Driven Decoherence in Magnetic Resonance

Diffusion-assisted selective dynamical recoupling: A new approach to measure background gradients in magnetic resonance

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