Estimation of the Effective Self-Diffusion Tensor from the NMR Spin Echo

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

doi:10.1006/jmrb.1994.1037

Cited by 3,351 publications

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“…The estimated diffusion coefficients for the ventricular system filled with cerebrospinal fluid approaches the bulk diffusivity of free water. Lastly,

λ_{∥}

and

λ_{⊥}

are distinct from the axial and radial diffusion parameters provided by the classical tensor model 32, which are influenced by fiber dispersion and crossing.…”

Section: Resultsmentioning

confidence: 98%

“…Figure 6 maps the fractional anisotropy and mean diffusivity for individual axons (top) and the entire fiber population, comparing the proposed technique with the classical tensor model 32. The per‐axon fractional anisotropy, which has factored out the intravoxel fiber orientation distribution, exhibits rather high values close to one in white matter tissue, showing a strong directional preference

λ_{∥} ≫ λ_{⊥}

of the local water diffusion.…”

Section: Resultsmentioning

confidence: 99%

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Quantitative mapping of the per‐axon diffusion coefficients in brain white matter

Kaden

Kruggel

Alexander

2015

Magnetic Resonance in Med

212

296

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PurposeThis article presents a simple method for estimating the effective diffusion coefficients parallel and perpendicular to the axons unconfounded by the intravoxel fiber orientation distribution. We also call these parameters the per‐axon or microscopic diffusion coefficients.Theory and MethodsDiffusion MR imaging is used to probe the underlying tissue material. The key observation is that for a fixed b‐value the spherical mean of the diffusion signal over the gradient directions does not depend on the axon orientation distribution. By exploiting this invariance property, we propose a simple, fast, and robust estimator of the per‐axon diffusion coefficients, which we refer to as the spherical mean technique.ResultsWe demonstrate quantitative maps of the axon‐scale diffusion process, which has factored out the effects due to fiber dispersion and crossing, in human brain white matter. These microscopic diffusion coefficients are estimated in vivo using a widely available off‐the‐shelf pulse sequence featuring multiple b‐shells and high‐angular gradient resolution.ConclusionThe estimation of the per‐axon diffusion coefficients is essential for the accurate recovery of the fiber orientation distribution. In addition, the spherical mean technique enables us to discriminate microscopic tissue features from fiber dispersion, which potentially improves the sensitivity and/or specificity to various neurological conditions. Magn Reson Med, 2015. Magn Reson Med 75:1752–1763, 2016. © 2015 The Authors. Magnetic Resonance in Medicine published by Wiley Periodicals, Inc.

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“…The estimated diffusion coefficients for the ventricular system filled with cerebrospinal fluid approaches the bulk diffusivity of free water. Lastly,

λ_{∥}

and

λ_{⊥}

are distinct from the axial and radial diffusion parameters provided by the classical tensor model 32, which are influenced by fiber dispersion and crossing.…”

Section: Resultsmentioning

confidence: 98%

λ_{∥} ≫ λ_{⊥}

of the local water diffusion.…”

Section: Resultsmentioning

confidence: 99%

Quantitative mapping of the per‐axon diffusion coefficients in brain white matter

Kaden

Kruggel

Alexander

2015

Magnetic Resonance in Med

212

296

View full text Add to dashboard Cite

show abstract

“…Indeed, connecting the observed anisotropy for isotropic media to errors in calibration, misalignment, and cross-talk between the imaging and diffusion gradients has to be assessed. [212202122232425262728]…”

Section: Methodsmentioning

confidence: 99%

Diffusion tensor magnetic resonance imaging strategies for color mapping of human brain anatomy

Boujraf

2018

J Med Signals Sens

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Background:A color mapping of fiber tract orientation using diffusion tensor imaging (DTI) can be prominent in clinical practice. The goal of this paper is to perform a comparative study of visualized diffusion anisotropy in the human brain anatomical entities using three different color-mapping techniques based on diffusion-weighted imaging (DWI) and DTI.Methods:The first technique is based on calculating a color map from DWIs measured in three perpendicular directions. The second technique is based on eigenvalues derived from the diffusion tensor. The last technique is based on three eigenvectors corresponding to sorted eigenvalues derived from the diffusion tensor. All magnetic resonance imaging measurements were achieved using a 1.5 Tesla Siemens Vision whole body imaging system. A single-shot DW echoplanar imaging sequence used a Stejskal–Tanner approach. Trapezoidal diffusion gradients are used. The slice orientation was transverse. The basic measurement yielded a set of 13 images. Each series consists of a single image without diffusion weighting, besides two DWIs for each of the next six noncollinear magnetic field gradient directions.Results:The three types of color maps were calculated consequently using the DWI obtained and the DTI. Indeed, we established an excellent similarity between the image data in the color maps and the fiber directions of known anatomical structures (e.g., corpus callosum and gray matter).Conclusions:In the meantime, rotationally invariant quantities such as the eigenvectors of the diffusion tensor reflected better, the real orientation found in the studied tissue.

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“…Tractography algorithms are able to reveal global fiber structures by estimating continuous streamline connections based on the local diffusion information throughout the brain (Basser, Mattiello, & LeBihan, 1994a,b). The performance of tracking algorithms has significantly improved by considering the information contained in orientation distribution functions (ODF) or fiber orientation distribution (FOD), especially in regions with complex fiber configurations (Behrens, Berg, Jbabdi, Rushworth, & Woolrich, 2007; Fillard et al., 2011; Tournier, Mori, & Leemans, 2011).…”

Section: Introductionmentioning

confidence: 99%

Fiber up‐sampling and quality assessment of tractograms – towards quantitative brain connectivity

et al. 2016

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Background and PurposeDiffusion MRI tractography enables to investigate white matter pathways noninvasively by reconstructing estimated fiber pathways. However, such tractograms remain biased and nonquantitative. Several techniques have been proposed to reestablish the link between tractography and tissue microstructure by modeling the diffusion signal or fiber orientation distribution (FOD) with the given tractogram and optimizing each fiber or compartment contribution according to the diffusion signal or FOD. Nevertheless, deriving a reliable quantification of connectivity strength between different brain areas is still a challenge. Moreover, evaluating the quality of a tractogram and measuring the possible error sources contained in a specific reconstructed fiber bundle also remains difficult. Lastly, all of these optimization techniques fail if specific fiber populations within a tractogram are underrepresented, for example, due to algorithmic constraints, anatomical properties, fiber geometry or seeding patterns.MethodsIn this work, we propose an approach which enables the inspection of the quality of a tractogram optimization by evaluating the residual error signal and its FOD representation. The automated fiber quantification (AFQ) is applied, whereby the framework is extended to reflect not only scalar diffusion metrics along a fiber bundle, but also directionally dependent FOD amplitudes along and perpendicular to the fiber direction. Furthermore, we also present an up‐sampling procedure to increase the number of streamlines of a given fiber population. The introduced error metrics and fiber up‐sampling method are tested and evaluated on single‐shell diffusion data sets of 16 healthy volunteers.Results and ConclusionAnalyzing the introduced error measures on specific fiber bundles shows a considerable improvement in applying the up‐sampling method. Additionally, the error metrics provide a useful tool to spot and identify potential error sources in tractograms.

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Estimation of the Effective Self-Diffusion Tensor from the NMR Spin Echo

Cited by 3,351 publications

References 0 publications

Quantitative mapping of the per‐axon diffusion coefficients in brain white matter

Quantitative mapping of the per‐axon diffusion coefficients in brain white matter

Diffusion tensor magnetic resonance imaging strategies for color mapping of human brain anatomy

Fiber up‐sampling and quality assessment of tractograms – towards quantitative brain connectivity

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