Pulsed-gradient spin-echo diffusion studies in nmr imaging. Effects of the imaging gradients on the determination of diffusion coefficients

Neeman, Michal; Freyer, James P.; Sillerud, Laurel O.

doi:10.1016/0022-2364(90)90136-w

Cited by 80 publications

(78 citation statements)

References 15 publications

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“…20 Just as in diffusion imaging (DI) where a scalar b-factor is calculated for each DWI, in DT-MRI a symmetric b-matrix is calculated for each DWI. 22 Whereas the b-value summarizes the attenuating effect on the MR signal of all diffusion and imaging gradients in one direction, 23 the b-matrix summarizes the attenuating effect of all gradient waveforms applied in all three directions, x, y and z. 22,24,25 In DI 26 one uses a set of DWIs and their corresponding scalar b-factors to estimate an ADC along a particular direction using linear regression.…”

Section: Characterizing Diffusion In Biological Systemsmentioning

confidence: 99%

Diffusion‐tensor MRI: theory, experimental design and data analysis – a technical review

2002

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This article treats the theoretical underpinnings of diffusion-tensor magnetic resonance imaging (DT-MRI), as well as experimental design and data analysis issues. We review the mathematical model underlying DT-MRI, discuss the quantitative parameters that are derived from the measured effective diffusion tensor, and describe artifacts thet arise in typical DT-MRI acquisitions. We also discuss difficulties in identifying appropriate models to describe water diffusion in heterogeneous tissues, as well as in interpreting experimental data obtained in such issues. Finally, we describe new statistical methods that have been developed to analyse DT-MRI data, and their potential uses in clinical and multi-site studies.

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Section: Characterizing Diffusion In Biological Systemsmentioning

confidence: 99%

Diffusion‐tensor MRI: theory, experimental design and data analysis – a technical review

2002

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“…The second-order correction is: [21] where n j is the degeneracy (number of dimensions) of level j. The second order shift depends on the matrix elements of the perturbation between the state i and all states with different zero order eigenvalue.…”

Section: Degenerate Casementioning

confidence: 99%

“…Since Eq. [21] covers both degenerate and nondegenerate cases, it can be used to show that the sum of the second-order shifts of all states is zero (see Appendix C):…”

Section: Degenerate Casementioning

confidence: 99%

Theoretical analysis of the effects of noise on diffusion tensor imaging

Anderson

2001

Magnetic Resonance in Med

256

270

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A theoretical framework is presented for understanding the effects of noise on estimates of the eigenvalues and eigenvectors of the diffusion tensor at moderate to high signal-to-noise ratios. Image noise produces a random perturbation of the diffusion tensor. Power series solutions to the eigenvalue equation are used to evaluate the effects of the perturbation to second order. It is shown that in anisotropic systems the expectation value of the largest eigenvalue is overestimated and the lowest eigenvalue is underestimated. Hence, diffusion anisotropy is overestimated in general. This result is independent of eigenvalue sorting bias. Furthermore, averaging eigenvalues over a region of interest produces greater bias than averaging tensors prior to diagonalization. Finally, eigenvector noise is shown to depend on the eigenvalue contrast and imposes a theoretical limit on the accuracy of simple fiber tracking schemes. Key words: diffusion tensor; noise; fiber trackingDiffusion tensor imaging (DTI) is a noninvasive method of characterizing tissue microstructure (1). In simple models of water diffusion in tissues, the directional dependence of diffusion is defined by the diffusion tensor. For example, the directions of highest and lowest diffusion are eigenvectors of the tensor and the diffusion coefficients in these directions are the corresponding eigenvalues. The anisotropy of diffusion in tissues is due primarily to cell membranes (2,3). Hence, the diffusion tensor depends on the cellular structure of tissues. DTI has been used to classify tissues on the basis of diffusion anisotropy (4), characterize changes associated with disease (5-7) and aging (8), and construct three-dimensional models of fiber tracts (9 -11).The diffusion tensor is estimated using a set of diffusion weighted images. Image noise produces errors in the calculated tensor and hence in its eigenvalues (principal diffusivities) and eigenvectors (principal axes). Random variations in these quantities complicate the analysis and interpretation of DTI experiments. For example, a basic step in quantifying diffusion is the calculation of mean eigenvalues of the tensor over repeated measures in a pixel, or across pixels in a homogeneous region of interest (ROI). Typically, this is accomplished by diagonalizing each independent measure of the tensor and averaging the corresponding eigenvalues. However, to perform this calculation some rule must be used to identify the corresponding eigenvalues in the independent measurements. At high signal-to-noise ratio (SNR) this is trivial, but otherwise noise perturbs the eigenvalues, making misclassification more likely. Pierpaoli and Basser (12) used Monte Carlo simulations to show that sorting eigenvalues by magnitude leads to an overestimate of the highest eigenvalue and an underestimate of the lower eigenvalue. This in turn leads to an overestimate of diffusion anisotropy. Hence, the difference between eigenvalues in an isotropic system can appear to be statistically significant. Other studies have used im...

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“…Equations [3] and [4] were solved following the same procedure as that used by Neeman et al (7), although in this case the echo attenuation was defined in terms of the q-value rather than the b-value commonly used in DWI. Furthermore, it was possible to use a scalar description since the diffusion and imaging gradients were applied colinearly (7,8); if this were not the case, then Eq.…”

Section: Theorymentioning

confidence: 99%

“…This interaction between the imaging gradients and diffusion gradients is well known in standard diffusionweighted imaging (DWI) (7)(8)(9) and is generally referred to as "cross-term interaction." If those interactions are not accounted for in the experimental analysis, misinterpretation of the data can easily occur, particularly when the q-space experiments are performed using strong imaging gradients.…”

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confidence: 99%

Effects of, and corrections for, cross‐term interactions in q‐space MRI

Brihuega-Moreno

Heese

Tejos

et al. 2004

Magnetic Resonance in Med

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The present study assesses the effects of cross-term interactions between diffusion and imaging gradients in magnetic resonance imaging q-space analysis, and corrects for those effects for both spin echo and stimulated echo diffusionweighted sequences. These corrections are demonstrated experimentally in unrestricted media for water and theoretically by simulating the case of restricted diffusion in a sphere. By correcting for the cross-term interactions, large imaging gradients can be used without compromising the results. Ignoring cross-term interactions could lead to a misunderstanding of the q-space analysis; for instance, the microstructural size of the sample could be overestimated, or isotropic media could be misinterpreted as being anisotropic. In the early 1990s Callaghan (1) and Cory and Garroway (2) demonstrated that structural information too small to be detected by conventional nuclear magnetic resonance (NMR) methods can be inferred from the measurement of water diffusion. Their studies demonstrated that the echo attenuation in a spin echo sequence due to the effect of a pair of finite duration diffusion pulse field gradients, separated by a long diffusion time, could be related to the displacement probability of the observed spins following Fourier transformation (FT) of the echo intensity, E(q), with respect to the so-called "reciprocal spatial vector," q. This technique was termed q-space imaging, and it has since been used almost exclusively in bulk NMR spectroscopy. Recently, however, q-space imaging has been extended both to localized NMR spectroscopy (3) and to MRI (3-5).If additional magnetic field gradients (e.g., imaging gradients) are introduced into the diffusion sequence, however, these may contribute to the diffusion weighting, which in turn may translate into greater echo attenuation than would be expected from the diffusion gradients alone. This interaction between the imaging gradients and diffusion gradients is well known in standard diffusionweighted imaging (DWI) (7-9) and is generally referred to as "cross-term interaction." If those interactions are not accounted for in the experimental analysis, misinterpretation of the data can easily occur, particularly when the q-space experiments are performed using strong imaging gradients.For standard DWI experiments, Neeman et al. (7) and Eis and Hoehn-Berlage (8) solved this problem for unidirectional diffusion measurements, whereas Mattiello et al. (9) have done so for diffusion tensor measurements. However, if the q-space technique is to be implemented successfully in conjunction with imaging gradients, the cross-term interactions must also be evaluated for this sequence. In the present study, expressions for calculation of corrected qvalues, which account for cross-term interactions with imaging gradients, were derived and the practical implications of the imaging gradients in q-space imaging were examined. These corrections were determined for two sequences commonly used in q-space analysis, namely, the spin echo (10) and stimulat...

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Pulsed-gradient spin-echo diffusion studies in nmr imaging. Effects of the imaging gradients on the determination of diffusion coefficients

Cited by 80 publications

References 15 publications

Diffusion‐tensor MRI: theory, experimental design and data analysis – a technical review

Diffusion‐tensor MRI: theory, experimental design and data analysis – a technical review

Theoretical analysis of the effects of noise on diffusion tensor imaging

Effects of, and corrections for, cross‐term interactions in q‐space MRI

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