MR diffusion–“diffraction” phenomenon in multi-pulse-field-gradient experiments

Özarslan, Evren; Basser, Peter J.

doi:10.1016/j.jmr.2007.08.002

Cited by 93 publications

(150 citation statements)

References 18 publications

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“…This model is based on solutions of fractionalized Bloch-Torrey differential equation with respect to space (21,22). The theoretical results demonstrate that the fractional order differential operator yields mathematical expressions similar to those developed by Ö zarslan et al (29), Bennett et al (18), and Hall and Barrick (20), without relying on fractals or empiric information.…”

Section: Discussionmentioning

confidence: 58%

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Studies of anomalous diffusion in the human brain using fractional order calculus

et al. 2010

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It is well known that diffusion-induced MR signal loss deviates from monoexponential decay, particularly at high b-values (e.g., >1500 sec/mm 2 for human brain tissues). A number of models have been developed to describe this anomalous diffusion behavior and relate the diffusion measurements to tissue structures. Recently, a new diffusion model was proposed by solving the Bloch-Torrey equation using fractional order calculus with respect to time and space (Magin et al., J Magn Reson 2008;190:255-270; Zhou et al., Proc Int'l Soc Magn Reson Med 2008). Using a spatial Laplacian $ 2b , this model yields a new set of parameters to describe anomalous diffusion: diffusion coefficient D, fractional order derivative in space b, and a spatial parameter m (in units of mm). In this study, we demonstrate that the fractional calculus model can be successfully applied to analyzing diffusion images of healthy human brain tissues in vivo. Five human volunteers were scanned on a commercial 3-T scanner using a customized single-shot echo-planar imaging diffusion sequence with 15 b values ranging from 0 to 4700 sec/mm 2 . The set of images was analyzed using the fractional calculus model, producing spatially resolved maps of D, b, and m. The b and m maps showed notable contrast between white and gray matter. The contrast has been attributed to the varying degree of complexity of the underlying tissue structures and microenvironment. Although the biophysical basis of b and m remains elusive, the potential utility of these parameters to characterize the environment for molecular diffusion, as a complement to apparent diffusion coefficient, may lead to a new way to investigate tissue structural changes in disease progression, intervention, and regression. Magn Reson Med 63:562-569,

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Section: Discussionmentioning

confidence: 58%

“…Unlike b, which can also be derived from fractals (19,20,29), m is unique to the FC diffusion model. Although m was introduced as a parameter to preserve the nominal units of diffusion coefficient, it appears to provide a measure of diffusion environment with a surprisingly high contrast between the white and gray matter (Fig.…”

Section: Discussionmentioning

confidence: 99%

Studies of anomalous diffusion in the human brain using fractional order calculus

et al. 2010

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“…We partially attenuate this uncertainty by combining data from voxels in a same local neighborhood, this assumption being weighted by α r as shown in Eq. (19). We compute the distance between two voxels directly from the SPF coefficients.…”

Section: Regularization Function ϕmentioning

confidence: 99%

“…However this method focuses only on the radial reconstruction of the MR signal and do not recover angular information. Yet, several promising recent studies [18,19] propose new echo sequences optimized for q-space NMR.…”

Section: Introductionmentioning

confidence: 99%

Efficient and robust computation of PDF features from diffusion MR signal

Assemlal

Tschumperlé

Brun

2009

Medical Image Analysis

131

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We present a method for the estimation of various features of the tissue micro-architecture using the diffusion magnetic resonance imaging. The considered features are designed from the displacement probability density function (PDF). The estimation is based on two steps: first the approximation of the signal by a series expansion made of Gaussian-Laguerre and Spherical Harmonics functions; followed by a projection on a finite dimensional space. Besides, we propose to tackle the problem of the robustness to Rician noise corrupting in-vivo acquisitions. Our feature estimation is expressed as a variational minimization process leading to a variational framework which is robust to noise. This approach is very flexible regarding the number of samples and enables the computation of a large set of various features of the local tissues structure. We demonstrate the effectiveness of the method with results on both synthetic phantom and real MR datasets acquired in a clinical time-frame.

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“…The d-PFG experiment is sensitized to the temporal correlations of molecular motion within the two diffusion periods and is sensitive to the direction of the applied gradients. 23 Using this experiment one can obtain the average pore size [24][25][26] and the microscopic anisotropy. 27 As the relative angle can be varied, 3D information regarding the restricting compartment can be obtained, including the CSA.…”

Section: Introductionmentioning

confidence: 99%

Joint radius-length distribution as a measure of anisotropic pore eccentricity: An experimental and analytical framework

Benjamini

Basser

2014

The Journal of Chemical Physics

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In this work, we present an experimental design and analytical framework to measure the nonparametric joint radius-length (R-L) distribution of an ensemble of parallel, finite cylindrical pores, and more generally, the eccentricity distribution of anisotropic pores. Employing a novel 3D double pulsed-field gradient acquisition scheme, we first obtain both the marginal radius and length distributions of a population of cylindrical pores and then use these to constrain and stabilize the estimate of the joint radius-length distribution. Using the marginal distributions as constraints allows the joint R-L distribution to be reconstructed from an underdetermined system (i.e., more variables than equations), which requires a relatively small and feasible number of MR acquisitions. Three simulated representative joint R-L distribution phantoms corrupted by different noise levels were reconstructed to demonstrate the process, using this new framework. As expected, the broader the peaks in the joint distribution, the less stable and more sensitive to noise the estimation of the marginal distributions. Nevertheless, the reconstruction of the joint distribution is remarkably robust to increases in noise level; we attribute this characteristic to the use of the marginal distributions as constraints. Axons are known to exhibit local compartment eccentricity variations upon injury; the extent of the variations depends on the severity of the injury. Nonparametric estimation of the eccentricity distribution of injured axonal tissue is of particular interest since generally one cannot assume a parametric distribution a priori. Reconstructing the eccentricity distribution may provide vital information about changes resulting from injury or that occurred during development.

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MR diffusion–“diffraction” phenomenon in multi-pulse-field-gradient experiments

Cited by 93 publications

References 18 publications

Studies of anomalous diffusion in the human brain using fractional order calculus

Studies of anomalous diffusion in the human brain using fractional order calculus

Efficient and robust computation of PDF features from diffusion MR signal

Joint radius-length distribution as a measure of anisotropic pore eccentricity: An experimental and analytical framework

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