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Voxel-based analysis of diffusion MRI data is increasingly popular. However, most white matter voxels contain contributions from multiple fibre populations (often referred to as crossing fibres), and therefore voxel-averaged quantitative measures (e.g. fractional anisotropy) are not fibre-specific and have poor interpretability. Using higher-order diffusion models, parameters related to fibre density can be extracted for individual fibre populations within each voxel (‘fixels’), and recent advances in statistics enable the multi-subject analysis of such data. However, investigating within-voxel microscopic fibre density alone does not account for macroscopic differences in the white matter morphology (e.g. the calibre of a fibre bundle). In this work, we introduce a novel method to investigate the latter, which we call fixel-based morphometry (FBM). To obtain a more complete measure related to the total number of white matter axons, information from both within-voxel microscopic fibre density and macroscopic morphology must be combined. We therefore present the FBM method as an integral piece within a comprehensive fixel-based analysis framework to investigate measures of fibre density, fibre-bundle morphology (cross-section), and a combined measure of fibre density and cross-section. We performed simulations to demonstrate the proposed measures using various transformations of a numerical fibre bundle phantom. Finally, we provide an example of such an analysis by comparing a clinical patient group to a healthy control group, which demonstrates that all three measures provide distinct and complementary information. By capturing information from both sources, the combined fibre density and cross-section measure is likely to be more sensitive to certain pathologies and more directly interpretable. [Display omitted] •A fixel is defined as a specific fibre population within a voxel.•We describe a comprehensive approach to fixel-based analysis (FBA) of white matter.•A novel method to investigate fibre bundle morphology (cross-section) is presented.•We compare fibre density, cross-section and a combined measure in a clinical cohort.•The three different analyses give unique yet complementary information.

In brain regions containing crossing fibre bundles, voxel-average diffusion MRI measures such as fractional anisotropy (FA) are difficult to interpret, and lack within-voxel single fibre population specificity. Recent work has focused on the development of more interpretable quantitative measures that can be associated with a specific fibre population within a voxel containing crossing fibres (herein we use fixel to refer to a specific fibre population within a single voxel). Unfortunately, traditional 3D methods for smoothing and cluster-based statistical inference cannot be used for voxel-based analysis of these measures, since the local neighbourhood for smoothing and cluster formation can be ambiguous when adjacent voxels may have different numbers of fixels, or ill-defined when they belong to different tracts. Here we introduce a novel statistical method to perform whole-brain fixel-based analysis called connectivity-based fixel enhancement (CFE). CFE uses probabilistic tractography to identify structurally connected fixels that are likely to share underlying anatomy and pathology. Probabilistic connectivity information is then used for tract-specific smoothing (prior to the statistical analysis) and enhancement of the statistical map (using a threshold-free cluster enhancement-like approach). To investigate the characteristics of the CFE method, we assessed sensitivity and specificity using a large number of combinations of CFE enhancement parameters and smoothing extents, using simulated pathology generated with a range of test-statistic signal-to-noise ratios in five different white matter regions (chosen to cover a broad range of fibre bundle features). The results suggest that CFE input parameters are relatively insensitive to the characteristics of the simulated pathology. We therefore recommend a single set of CFE parameters that should give near optimal results in future studies where the group effect is unknown. We then demonstrate the proposed method by comparing apparent fibre density between motor neurone disease (MND) patients with control subjects. The MND results illustrate the benefit of fixel-specific statistical inference in white matter regions that contain crossing fibres. [Display omitted] •We introduce the fixel—a specific fibre population within a voxel.•A novel method for whole-brain fixel-based analysis of diffusion MRI is presented.•Structural connectivity between fixels is derived from template-based tractography.•Connectivity information is used for tract-specific smoothing and enhancement.•Quantitative assessment and an in vivo demonstration is performed.

•The fixel-based analysis framework was proposed for fibre-specific statistical analysis of diffusion MRI data.•A “fixel” represents an individual fibre population in a voxel, allowing for increased specificity over voxel-wise measures.•A state-of-the-art fixel-based analysis pipeline consists of several bespoke steps, but is conceptually similar to a voxel-based analysis.•Fixel-based analysis has seen increased adoption recently, with 75 published studies to date.•The framework has unique benefits and future opportunities, but specific challenges and limitations exist as well. Diffusion MRI has provided the neuroimaging community with a powerful tool to acquire in-vivo data sensitive to microstructural features of white matter, up to 3 orders of magnitude smaller than typical voxel sizes. The key to extracting such valuable information lies in complex modelling techniques, which form the link between the rich diffusion MRI data and various metrics related to the microstructural organization. Over time, increasingly advanced techniques have been developed, up to the point where some diffusion MRI models can now provide access to properties specific to individual fibre populations in each voxel in the presence of multiple “crossing” fibre pathways. While highly valuable, such fibre-specific information poses unique challenges for typical image processing pipelines and statistical analysis. In this work, we review the “Fixel-Based Analysis” (FBA) framework, which implements bespoke solutions to this end. It has recently seen a stark increase in adoption for studies of both typical (healthy) populations as well as a wide range of clinical populations. We describe the main concepts related to Fixel-Based Analyses, as well as the methods and specific steps involved in a state-of-the-art FBA pipeline, with a focus on providing researchers with practical advice on how to interpret results. We also include an overview of the scope of all current FBA studies, categorized across a broad range of neuro-scientific domains, listing key design choices and summarizing their main results and conclusions. Finally, we critically discuss several aspects and challenges involved with the FBA framework, and outline some directions and future opportunities. [Display omitted]

MRtrix3 is an open-source, cross-platform software package for medical image processing, analysis and visualisation, 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. [Display omitted] •Software package for medical image processing, analysis and visualisation.•Consistent and logical user interface.•Provides a fast, modular and flexible general-purpose code framework.•Focus on diffusion MRI, but software API is general-purpose.

Registration of diffusion-weighted images is an important step in comparing white matter fibre bundles across subjects, or in the same subject at different time points. Using diffusion-weighted imaging, Spherical Deconvolution enables multiple fibre populations within a voxel to be resolved by computing the fibre orientation distribution (FOD). In this paper, we present a novel method that employs FODs for the registration of diffusion-weighted images. Registration was performed by optimising a symmetric diffeomorphic non-linear transformation model, using image metrics based on the mean squared difference, and cross-correlation of the FOD spherical harmonic coefficients. The proposed method was validated by recovering known displacement fields using FODs represented with maximum harmonic degrees (lmax) of 2, 4 and 6. Results demonstrate a benefit in using FODs at lmax=4 compared to lmax=2. However, a decrease in registration accuracy was observed when lmax=6 was used; this was likely caused by noise in higher harmonic degrees. We compared our proposed method to fractional anisotropy driven registration using an identical code base and parameters. FOD registration was observed to perform significantly better than FA in all experiments. The cross-correlation metric performed significantly better than the mean squared difference. Finally, we demonstrated the utility of this method by computing an unbiased group average FOD template that was used for probabilistic fibre tractography. This work suggests that using crossing fibre information aids in the alignment of white matter and could therefore benefit several methods for investigating population differences in white matter, including voxel based analysis, tensor based morphometry, atlas based segmentation and labelling, and group average fibre tractography. ► A new method for registration of fibre orientation distributions (FOD) is presented. ► Quantitative validation is performed using two FOD image metrics on human brain data. ► The cross-correlation metric outperforms the mean squared difference metric. ► Higher-order information in FODs improves white matter alignment. ► The method is applied to a potential application: group average FOD tractography.

This article proposes a new measure called Apparent Fibre Density (AFD) for the analysis of high angular resolution diffusion-weighted images using higher-order information provided by fibre orientation distributions (FODs) computed using spherical deconvolution. AFD has the potential to provide specific information regarding differences between populations by identifying not only the location, but also the orientations along which differences exist. In this work, analytical and numerical Monte-Carlo simulations are used to support the use of the FOD amplitude as a quantitative measure (i.e. AFD) for population and longitudinal analysis. To perform robust voxel-based analysis of AFD, we present and evaluate a novel method to modulate the FOD to account for changes in fibre bundle cross-sectional area that occur during spatial normalisation. We then describe a novel approach for statistical analysis of AFD that uses cluster-based inference of differences extended throughout space and orientation. Finally, we demonstrate the capability of the proposed method by performing voxel-based AFD comparisons between a group of Motor Neurone Disease patients and healthy control subjects. A significant decrease in AFD was detected along voxels and orientations corresponding to both the corticospinal tract and corpus callosal fibres that connect the primary motor cortices. In addition to corroborating previous findings in MND, this study demonstrates the clear advantage of using this type of analysis by identifying differences along single fibre bundles in regions containing multiple fibre populations.

The rate of progress in human neurosciences is limited by the inability to easily apply a wide range of analysis methods to the plethora of different datasets acquired in labs around the world. In this work, we introduce a framework for creating, testing, versioning and archiving portable applications for analyzing neuroimaging data organized and described in compliance with the Brain Imaging Data Structure (BIDS). The portability of these applications (BIDS Apps) is achieved by using container technologies that encapsulate all binary and other dependencies in one convenient package. BIDS Apps run on all three major operating systems with no need for complex setup and configuration and thanks to the comprehensiveness of the BIDS standard they require little manual user input. Previous containerized data processing solutions were limited to single user environments and not compatible with most multi-tenant High Performance Computing systems. BIDS Apps overcome this limitation by taking advantage of the Singularity container technology. As a proof of concept, this work is accompanied by 22 ready to use BIDS Apps, packaging a diverse set of commonly used neuroimaging algorithms.

A biological parameter that would be valuable to be able to extract from diffusion MRI data is the local white matter axonal density. Track-density imaging (TDI) has been used as if it could provide such a measure; however, this has been the subject of controversy, primarily due to the fact that track-count quantitation is highly sensitive to tracking biases and errors. The spherical-deconvolution informed filtering of tractograms (SIFT) post-processing method was recently introduced to minimise tractography biases, and thus provides a more biologically meaningful measure that could be used in track-count mapping (i.e. TDI following SIFT). The TDI intensity following SIFT ideally corresponds to the orientational average of the fibre orientation distribution (FOD), which corresponds to the total Apparent Fibre Density (AFDtotal) within the AFD framework; in fact, AFDtotal provides a direct measure of local fibre density at native resolution that does not rely on fibre-tracking. In this study, we demonstrate problems associated with quantitative TDI investigations, which can be avoided by using SIFT processing or directly by using AFDtotal maps. We also characterise the intra- and inter-subject reproducibility of TDI maps (with and without SIFT pre-processing) and AFDtotal maps. It is shown that SIFT improves the quantitative characteristics of TDI, but is still vastly inferior to the properties of the AFDtotal parameter itself, because the latter does not require tracking. While standard TDI might be preferable in applications when high anatomical contrast is required, particularly when combined with super-resolution, for voxel-wise quantitation of total tract density (i.e. without tract orientation information) at native resolution, the total AFD maps are preferable to TDI or other related track-count maps. Regardless of the track-count measure, it should be noted that all of these voxel-averaged approaches discard important information that is retained in fibre-specific approaches such as AFD. [Display omitted] •Track-density imaging (TDI) was introduced as super-resolution anatomical method.•TDI and other related maps have been also used as quantitative track-count maps.•We demonstrate problems associated with quantitative TDI investigations.•Total apparent fibre density (AFDtotal) is more appropriate for fibre-density mapping.•TDI after SIFT is also a good alternative, although less reproducible than AFDtotal.

Diffusion MR images are prone to artefacts caused by head movement and cardiac pulsation. Previous techniques for the automated voxel-wise detection of signal intensity outliers have relied on the fit of the diffusion tensor to the data (RESTORE). However, the diffusion tensor cannot appropriately model more than a single fibre population, which may lead to inaccuracies when identifying outlier voxels in crossing fibre regions, particularly when high b-values are used to obtain increased angular contrast. HOMOR (Higher Order Model Outlier Rejection) was developed to overcome this limitation and is introduced in this study. HOMOR is closely related to RESTORE, but employs a higher order model capable of resolving multiple fibre populations within a voxel. Using high b-value (b=3000s/mm2) diffusion data from a population of 90 healthy participants, as well as simulations, HOMOR was found to identify a decreased number of outlier voxels compared to RESTORE primarily within areas of crossing, bending and fanning fibres. At lower b-values, however, RESTORE and HOMOR give similar results, which is demonstrated using diffusion data acquired at b=1000s/mm2 in a mixed cohort. This study demonstrates that, although RESTORE is suitable for low b-value data, HOMOR is better suited for high b-value data. ► Outlier detection using the tensor model at high b identifies voxels incorrectly. ► Higher order model outlier rejection improves outlier detection at high b- values. ► At low b-values both outlier detection techniques show equal performance.

Recently several novel image contrasts derived from whole-brain fibre tracking-data (tractograms) have been introduced. The novel contrasts of these track-weighted imaging (TWI) methods may provide important information for clinical neuroscience studies. However, before they can be used reliably to generate quantitative measures, it is important to characterise their within-subject reproducibility, and between-subject variability. In this work we compute the within-subject reproducibility (intra-scan, intra-session and inter-session), and between-subject variability of TWI for a number of different TWI contrasts across multiple subjects. The results are used in simple voxel-wise power calculations within illustrative regions of interest to provide guidelines for required sample sizes and observable effect sizes for individual subjects and between groups. It was found that the required sample sizes and observable effect sizes varied considerably between different TWI maps and for different ROIs. For some TWI contrast and ROI combinations, the power calculations yielded clinically practical values. These results provide important information concerning the potential usefulness and sensitivity of TWI maps for individual diagnosis, longitudinal studies and group comparisons, as well as for study designs. [Display omitted] •Track weighted imaging (TWI) provides a number of novel image contrasts.•Within-subject reproducibility and between-subject variability of TWI is assessed.•Sample size requirements and observable effect sizes are calculated.•A number of TWI maps are shown to be suitable for quantitative clinical comparisons.