Minimal gradient encoding for robust estimation of diffusion anisotropy☆

Papadakis, N.; Murrills, Chris D; Hall, Laurance D.; Huang, Christopher L.‐H.; Carpenter, T. Adrian

doi:10.1016/s0730-725x(00)00151-x

Cited by 130 publications

(134 citation statements)

References 14 publications

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“…This bias theoretically should influence the anisotropy error, due to the explicit inverse dependence on anisotropy value in Eqs. [23] and [24]. We did observe an increase in error as N decreased (Fig.…”

Section: Discussionmentioning

confidence: 56%

“…[23] and [24], the fluctuation is not sufficient to cause the increase in anisotropy error as observed in Fig. 4 (a 64% increase for RA, 58% for FA, going from b ϭ 500 seconds/mm 2 to b ϭ 2500 seconds/ mm 2 at N ϭ 6).…”

Section: Discussionmentioning

confidence: 92%

“…Consequently, the errors in Eqs. [23] and [24] can be amplified. Our analytic noise formalism did not take the biexponential effect into consideration, but may be expanded to reflect the biexponential behavior for future studies.…”

Section: Discussionmentioning

confidence: 99%

“…To minimize that variation, Jones et al (6) suggested using gradient orientations derived from a model of electrostatic repulsion on the surface of a sphere, whereas Papadakis et al (21), Skare et al (22), and Cao (25) introduced parameters that could be minimized for an optimal diffusion-weighting scheme. Simulations by Papadakis et al (23) suggested that a minimum number of gradient directions (N Ϸ 20) was necessary. However, Hasan (26) found that icosahedral schemes with fewer N were equally effective.…”

Section: Magnetic Resonance (Mr) Diffusion Tensor Imaging (Dti) Is a mentioning

confidence: 99%

“…[21] and [22], and the mean anisotropy error for each index using Eqs. [23] and [24]. The anisotropy and anisotropy error were averaged over the ROI as described previously.…”

Section: Application 1: Comparison Of Dti Acquisition Protocolsmentioning

confidence: 99%

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Analytical error propagation in diffusion anisotropy calculations

Poonawalla

Zhou

2004

Magnetic Resonance Imaging

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Purpose:To develop an analytical formalism describing how noise and selection of diffusion-weighting scheme propagate through the diffusion tensor imaging (DTI) computational chain into variances of the diffusion tensor elements, and errors in the relative anisotropy (RA) and fractional anisotropy (FA) indices. Materials and Methods:Singular-value decomposition (SVD) was used to determine the tensor variances, with diffusion-weighting scheme and measurement noise incorporated into the design matrix. Anisotropy errors were then derived using propagation of error. To illustrate the applications of the model, 12 data sets were acquired from each human subject, over a range of b-values (500 -2500 seconds/mm 2 ) and diffusion-weighting gradient directions (N ϭ 6 -55). The mean RA and FA values and their respective errors were calculated within a region of interest (ROI) in the splenium. The RA and FA errors as a function of b-value and N were evaluated, and a number of diffusion-weighting schemes were assessed based on a new metric, sum of diffusion tensor variances.Results: When the acquisition time was held constant, the sum of the diffusion tensor variances decreased as N increased. The same trend was also observed for several diffusion-weighting schemes with constant condition number when noise in the diffusion-weighted (DW) images was assumed unity. Errors in both FA and RA increased with b-value and decreased with N. The FA error in the splenium was approximately threefold smaller than RA error, irrespective of b-value or N. Conclusion:The condition number may not adequately characterize the noise sensitivity for a given diffusionweighting scheme. Signal averaging may not be as effective as increasing N, especially when N is small (e.g., N Ͻ 13). Due to its smaller error, FA is preferred over RA for quantitative DTI applications.

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Section: Discussionmentioning

confidence: 56%

Section: Discussionmentioning

confidence: 92%

Section: Discussionmentioning

confidence: 99%

Section: Magnetic Resonance (Mr) Diffusion Tensor Imaging (Dti) Is a mentioning

confidence: 99%

“…[21] and [22], and the mean anisotropy error for each index using Eqs. [23] and [24]. The anisotropy and anisotropy error were averaged over the ROI as described previously.…”

Section: Application 1: Comparison Of Dti Acquisition Protocolsmentioning

confidence: 99%

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Analytical error propagation in diffusion anisotropy calculations

Poonawalla

Zhou

2004

Magnetic Resonance Imaging

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Coronary chronic total occlusions

Godino

Latib

Economou

et al. 2012

Cathet Cardio Intervent

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Introduction to diffusion tensor imaging mathematics: Part I. Tensors, rotations, and eigenvectors

Kingsley

2006

Concepts Magnetic Resonance

107

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ABSTRACT:The mathematical aspects of diffusion tensor magnetic resonance imaging (DTMRI, or DTI), the measurement of the diffusion tensor by magnetic resonance imaging (MRI), are discussed in this three-part series. In part I, some general features of diffusion imaging are presented briefly, including the relationship between the diffusion ellipsoid and the diffusion tensor. Rotations of vectors and tensors are explained for both two and three dimensions. Rotationally invariant properties of the diffusion tensor are discussed. Calculation of the eigenvectors and eigenvalues of the diffusion tensor, which correspond to the directions of the diffusion ellipsoid axes and the squares of the hemiaxis lengths, is explained.

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Minimal gradient encoding for robust estimation of diffusion anisotropy☆

Cited by 130 publications

References 14 publications

Analytical error propagation in diffusion anisotropy calculations

Analytical error propagation in diffusion anisotropy calculations

Coronary chronic total occlusions

Introduction to diffusion tensor imaging mathematics: Part I. Tensors, rotations, and eigenvectors

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