NMR signal for particles diffusing under potentials: From path integrals and numerical methods to a model of diffusion anisotropy

Yolcu, Cem; Memic, M.; Şimşek, Kadir; Westin, Carl‐Fredrik; Özarslan, Evren

doi:10.1103/physreve.93.052602

Cited by 25 publications

(52 citation statements)

References 48 publications

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“…Here we demonstrate that, under certain experimental conditions, the influence of restricted diffusion is essentially the same as that for the Hookean potential model, which was studied in-depth recently [13]. After the theoretical grounds for the effective theory are established, we proceed with presenting simulation results that provide additional justification.…”

Section: Effective Potential For Restricted Diffusionsupporting

confidence: 55%

“…Hence we consider the case of diffusing particles subject to a (dimensionless) parabolic confining potential U ( x ) = (1/2) x ⊤ Cx , where C is the confinement tensor [13]. Under this potential, the magnetization density evolves according to the Bloch-Torrey-Smoluchowski equation [17, 18, 13].…”

Section: Effective Potential For Restricted Diffusionmentioning

confidence: 99%

{\tilde{p}}_{cm} false(bold-italicq, δ false) = e^{- \frac{1}{2} q^{⊤} V_{q}},

with the variance matrix

bold-italicV = 2 {false(D δ false)}^{- 2} C^{- 3} false(D bold-italicC δ + e^{- D bold-italicC δ} - 1 false),

which is just a straightforward generalization of an expression in [7] to higher dimensions.…”

Section: Effective Potential For Restricted Diffusionmentioning

confidence: 99%

“…In this Perspective, we argue that the theory of diffusion under a Hookean restoring force [9, 10, 11, 12, 7, 13] can be regarded as the effective theory of restricted diffusion for a wide class of highly relevant NMR signal acquisition scenarios. This is evident at the macroscopic scale when one considers the dependence of the signal on experimental parameters for sequences featuring long gradient pulses or plots the average effective force experienced by the particles against their mean position (center of mass of their trajectories) during the application of a long pulse.…”

Section: Introductionmentioning

confidence: 99%

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Effective Potential for Magnetic Resonance Measurements of Restricted Diffusion

et al. 2017

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The signature of diffusive motion on the NMR signal has been exploited to characterize the mesoscopic structure of specimens in numerous applications. For compartmentalized specimens comprising isolated subdomains, a representation of individual pores is necessary for describing restricted diffusion within them. When gradient waveforms with long pulse durations are employed, a quadratic potential profile is identified as an effective energy landscape for restricted diffusion. The dependence of the stochastic effective force on the center-of-mass position is indeed found to be approximately linear (Hookean) for restricted diffusion even when the walls are sticky. We outline the theoretical basis and practical advantages of our picture involving effective potentials.

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Section: Effective Potential For Restricted Diffusionsupporting

confidence: 55%

Section: Effective Potential For Restricted Diffusionmentioning

confidence: 99%

{\tilde{p}}_{cm} false(bold-italicq, δ false) = e^{- \frac{1}{2} q^{⊤} V_{q}},

with the variance matrix

bold-italicV = 2 {false(D δ false)}^{- 2} C^{- 3} false(D bold-italicC δ + e^{- D bold-italicC δ} - 1 false),

which is just a straightforward generalization of an expression in [7] to higher dimensions.…”

Section: Effective Potential For Restricted Diffusionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Effective Potential for Magnetic Resonance Measurements of Restricted Diffusion

et al. 2017

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“…This means that Ē ( q ) decays faster than any polynomial 6 . This observation implies that for truly Gaussian compartments [73] or long pulse acquisitions [43] (regime C), the asymptotic decay of Ē ( q ) should be faster than any polynomial, which is indeed true for the expression in Eq. (2).…”

Section: Regime a And Bold-italicdboldδ≪rc2mentioning

confidence: 98%

Influence of the Size and Curvedness of Neural Projections on the Orientationally Averaged Diffusion MR Signal

et al. 2018

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Neuronal and glial projections can be envisioned to be tubes of infinitesimal diameter as far as diffusion magnetic resonance (MR) measurements via clinical scanners are concerned. Recent experimental studies indicate that the decay of the orientationally-averaged signal in white-matter may be characterized by the power-law, Ē(q) ∝ q−1, where q is the wavenumber determined by the parameters of the pulsed field gradient measurements. One particular study by McKinnon et al. [1] reports a distinctively faster decay in gray-matter. Here, we assess the role of the size and curvature of the neurites and glial arborizations in these experimental findings. To this end, we studied the signal decay for diffusion along general curves at all three temporal regimes of the traditional pulsed field gradient measurements. We show that for curvy projections, employment of longer pulse durations leads to a disappearance of the q−1 decay, while such decay is robust when narrow gradient pulses are used. Thus, in clinical acquisitions, the lack of such a decay for a fibrous specimen can be seen as indicative of fibers that are curved. We note that the above discussion is valid for an intermediate range of q-values as the true asymptotic behavior of the signal decay is Ē(q) ∝ q−4 for narrow pulses (through Debye-Porod law) or steeper for longer pulses. This study is expected to provide insights for interpreting the diffusion-weighted images of the central nervous system and aid in the design of acquisition strategies.

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Multimodal integration of diffusion MRI for better characterization of tissue biology

Özarslan

2018

NMR in Biomedicine

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The contrast in diffusion-weighted MR images is due to variations of diffusion properties within the examined specimen. Certain microstructural information on the underlying tissues can be inferred through quantitative analyses of the diffusion-sensitized MR signals. In the first part of the paper, we review two types of approach for characterizing diffusion MRI signals: Bloch's equations with diffusion terms, and statistical descriptions. Specifically, we discuss expansions in terms of cumulants and orthogonal basis functions, the confinement tensor formalism and tensor distribution models. Further insights into the tissue properties may be obtained by integrating diffusion MRI with other techniques, which is the subject of the second part of the paper. We review examples involving magnetic susceptibility, structural tensors, internal field gradients, transverse relaxation and functional MRI. Integrating information provided by other imaging modalities (MR based or otherwise) could be a key to improve our understanding of how diffusion MRI relates to physiology and biology.

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NMR signal for particles diffusing under potentials: From path integrals and numerical methods to a model of diffusion anisotropy

Cited by 25 publications

References 48 publications

Effective Potential for Magnetic Resonance Measurements of Restricted Diffusion

Effective Potential for Magnetic Resonance Measurements of Restricted Diffusion

Influence of the Size and Curvedness of Neural Projections on the Orientationally Averaged Diffusion MR Signal

Multimodal integration of diffusion MRI for better characterization of tissue biology

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