Permeability Coefficients from NMR q-Space Data: Models with Unevenly Spaced Semi-permeable Parallel Membranes

Kuchel, Philip W.; Durrant, C. J.

doi:10.1006/jmre.1999.1766

Cited by 36 publications

(18 citation statements)

References 29 publications

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“…The q-space approach, originally used to study porous materials [6,8,[11][12][13][14][15], was shown to be a useful tool for studying, inter alia, the dimensions of yeast cells [9], the structural changes induced after cerebral ischemia [16,17], and the size and shape of red blood cells [18][19][20][21][22][23][24]. In fact, red blood cells are the only biological tissues in which clear meaningful diffraction patterns that could be related to their structural characteristics were observed [18][19][20][21][22][23][24].…”

Section: Introductionmentioning

confidence: 98%

The effect of the diffusion time and pulse gradient duration ratio on the diffraction pattern and the structural information estimated from q-space diffusion MR: Experiments and simulations

Bar‐Shir

Avram

Özarslan

et al. 2008

Journal of Magnetic Resonance

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q-Space diffusion MRI (QSI) provides a means of obtaining microstructural information about porous materials and neuronal tissues from diffusion data. However, the accuracy of this structural information depends on experimental parameters used to collect the MR data. q-Space diffusion MR performed on clinical scanners is generally collected with relatively long diffusion gradient pulses, in which the gradient pulse duration, delta, is comparable to the diffusion time, Delta. In this study, we used phantoms, consisting of ensembles of microtubes, and mathematical models to assess the effect of the ratio of the diffusion time and the duration of the diffusion pulse gradient, i.e., Delta/delta, on the MR signal attenuation vs. q, and on the measured structural information extracted therefrom. We found that for Delta/delta approximately 1, the diffraction pattern obtained from q-space MR data are shallower than when the short gradient pulse (SGP) approximation is satisfied. For long delta the estimated compartment size is, as expected, smaller than the real size. Interestingly, for Delta/delta approximately 1 the diffraction peaks are shifted to even higher q-values, even when delta is kept constant, giving the impression that the restricted compartments are even smaller than they are. When phantoms composed of microtubes of different diameters are used, it is more difficult to estimate the diameter distribution in this regime. Excellent agreement is found between the experimental results and simulations that explicitly account for the use of long duration gradient pulses. Using such experimental data and this mathematical framework, one can estimate the true compartment dimensions when long and finite gradient pulses are used even when Delta/delta approximately 1.

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Section: Introductionmentioning

confidence: 98%

The effect of the diffusion time and pulse gradient duration ratio on the diffraction pattern and the structural information estimated from q-space diffusion MR: Experiments and simulations

Bar‐Shir

Avram

Özarslan

et al. 2008

Journal of Magnetic Resonance

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show abstract

“…3). [50][51][52] Using intra-and extracellular (choline and phosphatidyl choline, respectively) markers, it was possible to assign the maxima and minima of the diffraction peaks to restricted diffusion in the cells and to pore hopping in the extracellular space. 52 These experiments showed that even in biological systems that are known to be heterogeneous, structural information can be extracted, although the diffraction peaks were not as sharp as in porous materials, probably due to the effects of exchange and cell size variability.…”

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confidence: 99%

High b‐value q‐space analyzed diffusion‐weighted MRS and MRI in neuronal tissues – a technical review

2002

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This review deals with high b-value q-space diffusion-weighted MRI (DW-MRI) of neuronal tissues. It is well documented that at sufficiently high b-values (and high q-values) neuronal water signal decay in diffusion experiments is not mono-exponential. This implies the existence of more than one apparent diffusing component or evidence for restriction. The assignment of the different apparent diffusing components to real physical entities is not straightforward. However, the apparent slow diffusing component that was found to be restricted to a compartment of a few microns, if originating mainly from a specific pool and if assigned correctly, may potentially be used to obtain more specific MR images with regard to specific pathologies of the CNS. This review examines the utility of analyzing high b-value diffusion MRS and MRI data using the q-space approach introduced by Callaghan and by Cory and Garroway. This approach provides displacement probability maps that emphasize, at long diffusion times, the characteristics of the apparent slow diffusing component. Examples from excised spinal cord, where the experimental conditions for which the q-space analysis of MR diffusion data was developed can be met or approached will be presented. Then examples from human MS patients, where q-space requirement for the short gradient pulse is clearly violated, are presented. In the excised spinal cord studies, this approach was used to study spinal cord maturation and trauma, and was found to be more sensitive than other conventional methods in following spinal cord degeneration in an experimental model of vascular dementia (VaD). High b-value q-space DWI was also recently used to study healthy and MS diseased human brains. This approach was found to be very sensitive to the disease load in MS, compared with other conventional MRI methods, especially in the normal appearing white matter (NAWM) of MS brains. Finally, the potential diagnostic capacity embedded in high b-value q-space analyzed diffusion MR images is discussed. The potentials and caveats of this approach are outlined and experimental data are presented that show the effect of violating the short gradient pulse (SGP) approximation on the extracted parameters from the q-space analysis.

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“…They showed how their method could be modified to analyze spin-echo measurements using NMR in situations in which the lengths of all the cells are not equal. Kuchel and Durrant (1999) also considered a generalization of Tanner's problem with uneven cell lengths that can be applied to NMR data. They considered the 'inverse problem' in which one must estimate the permeability of the membrane given the spin-echo attenuation measurements.…”

Section: Introductionmentioning

confidence: 98%

Restricted Diffusion in Cellular Media: (1+1)-Dimensional Model

2010

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We consider the diffusion of molecules in a one-dimensional medium consisting of a large number of cells separated from the extra-cellular space by permeable membranes. The extra-cellular space is completely connected and allows unrestricted diffusion of the molecules. Furthermore, the molecules can diffuse within a given cell, i.e., the intra-cellular space; however, direct diffusion from one cell to another cell cannot occur. There is a movement of molecules across the permeable membranes between the intra- and extra-cellular spaces. Molecules from one cell can cross the permeable membrane into the extra-cellular space, then diffuse through the extra-cellular space, and eventually enter the intra-cellular space of a second cell. Here, we develop a simple set of model equations to describe this phenomenon and obtain the solutions using an eigenfunction expansion. We show that the solutions obtained using this method are particularly convenient for interpreting data from experiments that use techniques from nuclear magnetic resonance imaging.

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Permeability Coefficients from NMR q-Space Data: Models with Unevenly Spaced Semi-permeable Parallel Membranes

Cited by 36 publications

References 29 publications

The effect of the diffusion time and pulse gradient duration ratio on the diffraction pattern and the structural information estimated from q-space diffusion MR: Experiments and simulations

The effect of the diffusion time and pulse gradient duration ratio on the diffraction pattern and the structural information estimated from q-space diffusion MR: Experiments and simulations

High b‐value q‐space analyzed diffusion‐weighted MRS and MRI in neuronal tissues – a technical review

Restricted Diffusion in Cellular Media: (1+1)-Dimensional Model

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