Analytical Expressions for the b Matrix in NMR Diffusion Imaging and Spectroscopy

Mattiello, James; Basser, Peter J.; LeBihan, D.

doi:10.1006/jmra.1994.1103

Cited by 207 publications

(200 citation statements)

References 10 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%

“…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. In DT-MRI, we first define an effective diffusion tensor (by analogy to Tanner's definition of an apparent diffusion coefficient 27 ), from which a formula relating the effective diffusion tensor to the measured echo can be derived: 22 The b-matrix summarizes the attenuating effect of all gradient waveforms applied in all three directions, x, y and z.…”

Section: Characterizing Diffusion In Biological Systemsmentioning

confidence: 99%

“…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. In DT-MRI, we first define an effective diffusion tensor (by analogy to Tanner's definition of an apparent diffusion coefficient 27 ), from which a formula relating the effective diffusion tensor to the measured echo can be derived: 22 The b-matrix summarizes the attenuating effect of all gradient waveforms applied in all three directions, x, y and z. 22,24,25 We then use each DWI and its corresponding b-matrix to estimate D using multivariate linear regression* of eqn (1) as in Basser et al 20 There are two important distinctions between DI and DT-MRI.…”

Section: Characterizing Diffusion In Biological Systemsmentioning

confidence: 99%

“…20 Second, the b-matrix formalism forces us to expand the notion of 'cross-terms' between imaging and diffusion gradients, to account for possible interactions between imaging and diffusion gradients that are applied in orthogonal directions, and even between imaging gradients that are applied in orthogonal directions. 22,24,25 In isotropic media, gradients applied in orthogonal directions do not result in cross-terms; in anisotropic media, however, they can. …”

Section: Characterizing Diffusion In Biological Systemsmentioning

confidence: 99%

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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%

Section: Characterizing Diffusion In Biological Systemsmentioning

confidence: 99%

Section: Characterizing Diffusion In Biological Systemsmentioning

confidence: 99%

Section: Characterizing Diffusion In Biological Systemsmentioning

confidence: 99%

See 2 more Smart Citations

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

2002

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“…The scalar b q in eqn (1) assumes no background gradients. 39,51 The six unique real elements D ij of the symmetric 3 Â 3 matrix D are calculated from a set of I q intensities by linearizing eqn (1) and performing a w 2 minimization. 39 The eigenvalues and eigenvectors of D are obtained by applying the Jacobi method (pp.…”

Section: Creation Of the Diffusion Tensor And Images Of Its Derived Pmentioning

confidence: 99%

Diffusion tensor fiber tracking of human brain connectivity: aquisition methods, reliability analysis and biological results

et al. 2002

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We present a description, biological results and a reliability analysis for the method of diffusion tensor tracking (DTT) of white matter fiber pathways. In DTT, diffusion-tensor MRI (DT-MRI) data are collected and processed to visualize the line trajectories of fiber bundles within white matter (WM) pathways of living humans. A detailed description of the data acquisition is given. Technical aspects and experimental results are illustrated for the geniculo-calcarine tract with broad projections to visual cortex, occipital and parietal U-fibers, and the temporocalcarine ventral pathway. To better understand sources of error and to optimize the method, accuracy and precision were analyzed by computer simulations. In the simulations, noisy DT-MRI data were computed that would be obtained for a WM pathway having a helical trajectory passing through gray matter. The error vector between the real and ideal track was computed, and random errors accumulated with the square root of track length consistent with a random-walk process. Random error was most dependent on signal-to-noise ratio, followed by number of averages, pathway anisotropy and voxel size, in decreasing order. Systematic error only occurred for a few conditions, and was most dependent on the stepping algorithm, anisotropy of the surrounding tissue, and non-equal voxel dimensions. Both random and systematic errors were typically below the voxel dimension. Other effects such as track rebound and track recovery also depended on experimental conditions. The methods, biological results and error analysis herein may improve the understanding and optimization of DTT for use in various applications in neuroscience and medicine.

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Pulsed‐field gradient nuclear magnetic resonance as a tool for studying translational diffusion: Part 1. Basic theory

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1997

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Analytical Expressions for the b Matrix in NMR Diffusion Imaging and Spectroscopy

Cited by 207 publications

References 10 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

Diffusion tensor fiber tracking of human brain connectivity: aquisition methods, reliability analysis and biological results

Pulsed‐field gradient nuclear magnetic resonance as a tool for studying translational diffusion: Part 1. Basic theory

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