Analysis of PFG Anomalous Diffusion via Real-Space and Phase-Space Approaches

Lin, Guoxing

doi:10.3390/math6020017

Cited by 4 publications

(5 citation statements)

References 47 publications

(129 reference statements)

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“…The biophysical origin of pseudo-superdiffusion depends on the multi-compartmentalization of water diffusion and on the presence of local magnetic in-homogeneities. The recent development of DW-signal representation of AD [32][33][34][35] should be used in order to investigate the role of the interplay between internal (background) and diffusion gradients, and to consider the effect of finite width of the diffusion gradient pulses. In conclusion, AD MRI is still in its early stages due to the noflexible conventional acquisition modality of the clinical MRI, the lack of validation experiments (for example by using optical imaging) and the difficulties in a reliable signal representation.…”

Section: Resultsmentioning

confidence: 99%

“…To overcome this drawback, Lin [32,33] recently developed general expressions of PFG signal attenuation describing the AD NMR signal. Of particular interest is the general analytical expressions of PFG signal attenuation for AD that include the finite gradient pulse width effect, namely, the DW-signal attenuation during each gradient pulse application period [34,35].…”

Section: Ad By Mri: Mathematical and Physical Effective Approachesmentioning

confidence: 99%

See 1 more Smart Citation

Mini Review on Anomalous Diffusion by MRI: Potential Advantages, Pitfalls, Limitations, Nomenclature, and Correct Interpretation of Literature

Capuani

Palombo

2020

Front. Phys.

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In this mini-review, we addressed the transient-anomalous diffusion by MRI, starting from the assumption that transient-anomalous diffusion is ubiquitously observed in biological tissues, as demonstrated by different single-particle-tracking optical experiments. The purpose of this review is to identify the main pitfalls that can be encountered when venturing into the field of anomalous diffusion quantified by diffusion-MRI methods. Therefore, the theory of anomalous diffusion deriving from its mathematical definition was reported and connected with the consolidated description and the established procedures of conventional diffusion-MRI of tissues. We highlighted the two different modalities for quantifying subdiffusion and superdiffusion parameters of anomalous diffusion. Then we showed that most of the papers concerning anomalous diffusion, actually deal with pseudo-superdiffusion due to the use of a superdiffusion signal representation. Pseudo-superdiffusion depends on water diffusion multi-compartmentalization and local magnetic in-homogeneities that mimic the superdiffusion of spins. In addition to the relatively large production of pseudosuperdiffusion images, anomalous diffusion research is still in its early stages due to the limited flexibility of conventional clinical MRI scanners that currently prevent the acquisition of diffusion-weighted images by varying the diffusion time (the necessary acquisition modality to quantify transient-subdiffusion in human tissues). Moreover, the wide diffusion gradient pulses complicates the definition of a reliable function representative of anomalous diffusion signal behavior to fit data. Nevertheless, it is important and possible to address these limitations, as one of the potentialities of anomalous diffusion imaging is to increase the resolution, sensitivity, and specificity of MRI.

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Section: Resultsmentioning

confidence: 99%

Section: Ad By Mri: Mathematical and Physical Effective Approachesmentioning

confidence: 99%

Mini Review on Anomalous Diffusion by MRI: Potential Advantages, Pitfalls, Limitations, Nomenclature, and Correct Interpretation of Literature

Capuani

Palombo

2020

Front. Phys.

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“…This behavior can be captured by the VDC model, but it is also naturally encoded in the Mittag-Leffler decay, S(b) = S 0 E α [−(bD 0 ) α ], which for low b-values approximates the stretched exponential, and for high b-values decays asymptotically as (bD 0 ) −α . The Kilbas-Saigo generalization of the Mittag-Leffer function is the mother function (model) for all three cases, and has been applied before by Hanyga and Seredynska [34] to diffusion in MRI and by Lin to problems in NMR [40,41]. The behavior of the Kilbas-Saigo modeling approach for the case of varying ∆ (for fixed g and δ) has not yet been fully examined.…”

Section: Discussionmentioning

confidence: 99%

Fractional Order Complexity Model of the Diffusion Signal Decay in MRI

et al. 2019

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Fractional calculus models are steadily being incorporated into descriptions of diffusion in complex, heterogeneous materials. Biological tissues, when viewed using diffusion-weighted, magnetic resonance imaging (MRI), hinder and restrict the diffusion of water at the molecular, sub-cellular, and cellular scales. Thus, tissue features can be encoded in the attenuation of the observed MRI signal through the fractional order of the time- and space-derivatives. Specifically, in solving the Bloch-Torrey equation, fractional order imaging biomarkers are identified that connect the continuous time random walk model of Brownian motion to the structure and composition of cells, cell membranes, proteins, and lipids. In this way, the decay of the induced magnetization is influenced by the micro- and meso-structure of tissues, such as the white and gray matter of the brain or the cortex and medulla of the kidney. Fractional calculus provides new functions (Mittag-Leffler and Kilbas-Saigo) that characterize tissue in a concise way. In this paper, we describe the exponential, stretched exponential, and fractional order models that have been proposed and applied in MRI, examine the connection between the model parameters and the underlying tissue structure, and explore the potential for using diffusion-weighted MRI to extract biomarkers associated with normal growth, aging, and the onset of disease.

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“…In the paper by Guoxing Lin [17]: Analysis of PFG Anomalous Diffusion via Real-Space and Phase-Space Approaches, two significantly different methods are proposed to analyze the pulsed-field gradient (PFG) anomalous diffusion: the effective phase-shift diffusion equation (EPSDE) method and a method based on observing the signal intensity at the origin. The EPSDE method describes the phase evolution in virtual phase space, while the method to observe the signal intensity at the origin describes the magnetization evolution in real space.…”

Section: Applicationsmentioning

confidence: 99%