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Journal ArticleDOI

Determination of the appropriate b value and number of gradient directions for high-angular-resolution diffusion-weighted imaging.

TL;DR: This study estimates the minimum number of DW directions and optimal b values required for HARDI by focusing on the angular frequency content of the DW signal itself, and estimates that SH terms above l = 8 are negligible in practice for b values up to 5000 s/mm2, implying that a minimum of 45 DW directions is sufficient to fully characterise theDW signal.
Abstract: High-angular-resolution diffusion-weighted imaging (HARDI) is one of the most common MRI acquisition schemes for use with higher order models of diffusion. However, the optimal b value and number of diffusion-weighted (DW) directions for HARDI are still undetermined, primarily as a result of the large number of available reconstruction methods and corresponding parameters, making it impossible to identify a single criterion by which to assess performance. In this study, we estimate the minimum number of DW directions and optimal b values required for HARDI by focusing on the angular frequency content of the DW signal itself. The spherical harmonic (SH) series provides the spherical analogue of the Fourier series, and can hence be used to examine the angular frequency content of the DW signal. Using high-quality data acquired along 500 directions over a range of b values, we estimate that SH terms above l = 8 are negligible in practice for b values up to 5000 s/mm(2), implying that a minimum of 45 DW directions is sufficient to fully characterise the DW signal. l > 0 SH terms were found to increase as a function of b value, levelling off at b = 3000 s/mm(2), suggesting that this value already provides the highest achievable angular resolution. In practice, it is recommended to acquire more than the minimum of 45 DW directions to avoid issues with imperfections in the uniformity of the DW gradient directions and to meet signal-to-noise requirements of the intended reconstruction method.
Citations
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Journal ArticleDOI
TL;DR: A high-level overview of the features of the MRtrix3 framework and general-purpose image processing applications provided with the software is provided.

1,228 citations

Journal ArticleDOI
TL;DR: The aim of this study is to incorporate support for multi-shell data into the CSD approach as well as to exploit the unique b-value dependencies of the different tissue types to estimate a multi-tissue ODF.

1,015 citations


Cites methods from "Determination of the appropriate b ..."

  • ...DWdata set 1was acquired on a Siemens TimTrio 3TMRI system equipped with a 32-channel receiver head coil and using a multi-shell acquisition scheme based on the recommendations in Tournier et al. (2013)....

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  • ...Maximum likelihood estimation based on the Rice distribution was used to avoid a Rician bias in the true response functions (Tournier et al., 2013)....

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Posted ContentDOI
15 Feb 2019-bioRxiv
TL;DR: A high-level overview of the features of the MRtrix3 framework and general-purpose image processing applications provided with the software is provided.
Abstract: MRtrix3 is an open-source, cross-platform software package for medical image processing, analysis and visualization, with a particular emphasis on the investigation of the brain using diffusion MRI. It is implemented using a fast, modular and flexible general-purpose code framework for image data access and manipulation, enabling efficient development of new applications, whilst retaining high computational performance and a consistent command-line interface between applications. In this article, we provide a high-level overview of the features of the MRtrix3 framework and general-purpose image processing applications provided with the software.

728 citations


Cites methods from "Determination of the appropriate b ..."

  • ...…(CSD) for single-shell fibre ODF estimation (Tournier et al., 2007, 2004) and multi-shell multi-tissue CSD for multi-shell data (Jeurissen et al., 2014), supported by several response function estimation algorithms (Dhollander et al., 2016; Tax et al., 2014; Tournier et al., 2013) (Figure 3)....

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Journal ArticleDOI
TL;DR: An overview of the key concepts of tractography, the technical considerations at play, and the different types of tractographic algorithm, as well as the common misconceptions and mistakes that surround them are provided.
Abstract: The ability of fiber tractography to delineate non-invasively the white matter fiber pathways of the brain raises possibilities for clinical applications and offers enormous potential for neuroscience In the last decade, fiber tracking has become the method of choice to investigate quantitative MRI parameters in specific bundles of white matter For neurosurgeons, it is quickly becoming an invaluable tool for the planning of surgery, allowing for visualization and localization of important white matter pathways before and even during surgery Fiber tracking has also claimed a central role in the field of “connectomics,” a technique that builds and studies comprehensive maps of the complex network of connections within the brain, and to which significant resources have been allocated worldwide Despite its unique abilities and exciting applications, fiber tracking is not without controversy, in particular when it comes to its interpretation As neuroscientists are eager to study the brain's connectivity, the quantification of tractography-derived “connection strengths” between distant brain regions is becoming increasingly popular However, this practice is often frowned upon by fiber-tracking experts In light of this controversy, this paper provides an overview of the key concepts of tractography, the technical considerations at play, and the different types of tractography algorithm, as well as the common misconceptions and mistakes that surround them We also highlight the ongoing challenges related to fiber tracking While recent methodological developments have vastly increased the biological accuracy of fiber tractograms, one should be aware that, even with state-of-the-art techniques, many issues that severely bias the resulting structural “connectomes” remain unresolved

339 citations


Cites background from "Determination of the appropriate b ..."

  • ...Experimental evidence suggests that the angular frequency content of the dMRI signal in the brain white matter levels off at a b‐value of approximately b = 3000 s/mm(2), suggesting that this b‐value achieves the highest practically available angular resolution.(122) Given this b‐value, the minimal number of unique diffusion encoding gradient orientations to fully characterize the angular frequency...

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Journal ArticleDOI
TL;DR: This review focuses on studies of normative brain development from birth to early adulthood (˜25 years), and places particular emphasis on longitudinal studies and newer techniques that are being used to study microstructural white matter development.

308 citations


Cites background from "Determination of the appropriate b ..."

  • ...Acquisition techniques such as high angular resolution diffusion imaging (HARDI)(Tuch et al., 2002) and diffusion spectrum imaging (DSI)(Wedeen et al., 2005) collect more directions than DTI and use higher b-values (Tournier et al., 2013)....

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  • ..., 2005) collect more directions than DTI and use higher b-values (Tournier et al., 2013)....

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References
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Journal ArticleDOI
Claude E. Shannon1
01 Jan 1949
TL;DR: A method is developed for representing any communication system geometrically and a number of results in communication theory are deduced concerning expansion and compression of bandwidth and the threshold effect.
Abstract: A method is developed for representing any communication system geometrically Messages and the corresponding signals are points in two "function spaces," and the modulation process is a mapping of one space into the other Using this representation, a number of results in communication theory are deduced concerning expansion and compression of bandwidth and the threshold effect Formulas are found for the maximum rate of transmission of binary digits over a system when the signal is perturbed by various types of noise Some of the properties of "ideal" systems which transmit at this maximum rate are discussed The equivalent number of binary digits per second for certain information sources is calculated

6,712 citations


"Determination of the appropriate b ..." refers methods in this paper

  • ...Our proposed approach is best expressed using the spherical equivalent of Cartesian Nyquist–Shannon sampling theory (41,42)....

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Journal ArticleDOI
TL;DR: Once Deff is estimated from a series of NMR pulsed-gradient, spin-echo experiments, a tissue's three orthotropic axes can be determined and the effective diffusivities along these orthotropic directions are the eigenvalues of Deff.

5,641 citations


"Determination of the appropriate b ..." refers methods in this paper

  • ...It is now widely acknowledged that the most commonly used algorithm to infer white matter fibre orientations, the diffusion tensor model (9), is not appropriate in regions that contain multiple fibre orientations (10–13)....

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Journal ArticleDOI
TL;DR: The purpose of this review is to characterize the relationship of nuclear magnetic resonance measurements of water diffusion and its anisotropy (i.e. directional dependence) with the underlying microstructure of neural fibres.
Abstract: Anisotropic water diffusion in neural fibres such as nerve, white matter in spinal cord, or white matter in brain forms the basis for the utilization of diffusion tensor imaging (DTI) to track fibre pathways. The fact that water diffusion is sensitive to the underlying tissue microstructure provides a unique method of assessing the orientation and integrity of these neural fibres, which may be useful in assessing a number of neurological disorders. The purpose of this review is to characterize the relationship of nuclear magnetic resonance measurements of water diffusion and its anisotropy (i.e. directional dependence) with the underlying microstructure of neural fibres. The emphasis of the review will be on model neurological systems both in vitro and in vivo. A systematic discussion of the possible sources of anisotropy and their evaluation will be presented followed by an overview of various studies of restricted diffusion and compartmentation as they relate to anisotropy. Pertinent pathological models, developmental studies and theoretical analyses provide further insight into the basis of anisotropic diffusion and its potential utility in the nervous system.

4,216 citations

Journal ArticleDOI
Behrens Tej.1, H J Berg1, Saad Jbabdi1, Rushworth Mfs.1, Mark W. Woolrich1 
TL;DR: It is shown that multi-fibre tractography offers significant advantages in sensitivity when tracking non-dominant fibre populations, but does not dramatically change tractography results for the dominant pathways.

3,315 citations

Journal ArticleDOI
TL;DR: The image intensity in magnetic resonance magnitude images in the presence of noise is shown to be governed by a Rician distribution and low signal intensities (SNR < 2) are therefore biased due to the noise.
Abstract: The image intensity in magnetic resonance magnitude images in the presence of noise is shown to be governed by a Rician distribution. Low signal intensities (SNR < 2) are therefore biased due to the noise. It is shown how the underlying noise can be estimated from the images and a simple correction scheme is provided to reduce the bias. The noise characteristics in phase images are also studied and shown to be very different from those of the magnitude images. Common to both, however, is that the noise distributions are nearly Gaussian for SNR larger than two.

2,425 citations