Fixel-based Analysis of Diffusion MRI: Methods, Applications, Challenges and Opportunities.

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.

In vivo microstructural heterogeneity of white matter lesions in healthy elderly and Alzheimer's disease participants using tissue compositional analysis of diffusion MRI data.

White matter hyperintensities (WMH) are regions of high signal intensity typically identified on fluid attenuated inversion recovery (FLAIR). Although commonly observed in elderly individuals, they are more prevalent in Alzheimer's disease (AD) patients. Given that WMH appear relatively homogeneous on FLAIR, they are commonly partitioned into location- or distance-based classes when investigating their relevance to disease. Since pathology indicates that such lesions are often heterogeneous, probing their microstructure in vivo may provide greater insight than relying on such arbitrary classification schemes. In this study, we investigated WMH in vivo using an advanced diffusion MRI method known as single-shell 3-tissue constrained spherical deconvolution (SS3T-CSD), which models white matter microstructure while accounting for grey matter and CSF compartments. Diffusion MRI data and FLAIR images were obtained from AD (n = 48) and healthy elderly control (n = 94) subjects. WMH were automatically segmented, and classified: (1) as either periventricular or deep; or (2) into three distance-based contours from the ventricles. The 3-tissue profile of WMH enabled their characterisation in terms of white matter-, grey matter-, and fluid-like characteristics of the diffusion signal. Our SS3T-CSD findings revealed substantial heterogeneity in the 3-tissue profile of WMH, both within lesions and across the various classes. Moreover, this heterogeneity information indicated that the use of different commonly used WMH classification schemes can result in different disease-based conclusions. We conclude that future studies of WMH in AD would benefit from inclusion of microstructural information when characterising lesions, which we demonstrate can be performed in vivo using SS3T-CSD.

MRtrix3: A fast, flexible and open software framework for medical image processing and visualisation.

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.

Fibre-specific white matter changes in multiple sclerosis patients with optic neuritis.

Long term irreversible disability in multiple sclerosis (MS) is thought to be primarily driven by axonal degeneration. Axonal degeneration leads to degenerative atrophy, therefore early markers of axonal degeneration are required to predict clinical disability and treatment efficacy. Given that additional pathologies such as inflammation, demyelination and oedema are also present in MS, it is essential to develop axonal markers that are not confounded by these processes. The present study investigated a novel method for measuring axonal degeneration in MS based on high angular resolution diffusion magnetic resonance imaging. Unlike standard methods, this novel method involved advanced acquisition and modelling for improved axonal sensitivity and specificity. Recent work has developed analytical methods, two novel axonal markers, fibre density and cross-section, that can be estimated for each fibre direction in each voxel (termed a "fixel"). This technique, termed fixel-based analysis, thus simultaneously estimates axonal density and white matter atrophy from specific white matter tracts. Diffusion-weighted imaging datasets were acquired for 17 patients with a history of acute unilateral optic neuritis (35.3 ± 10.2 years, 11 females) and 14 healthy controls (32.7 ± 4.8 years, 8 females) on a 3 T scanner. Fibre density values were compared to standard diffusion tensor imaging parameters (fractional anisotropy and mean diffusivity) in lesions and normal appearing white matter. Group comparisons were performed for each fixel to assess putative differences in fibre density and fibre cross-section. Fibre density was observed to have a comparable sensitivity to fractional anisotropy for detecting white matter pathology in MS, but was not affected by crossing axonal fibres. Whole brain fixel-based analysis revealed significant reductions in fibre density and fibre cross-section in the inferior fronto-occipital fasciculus (including the optic radiations) of patients compared to controls. We interpret this result to indicate that this fixel-based approach is able to detect early loss of fibre density and cross-section in the optic radiations in MS patients with a history of optic neuritis. Fibre-specific markers of axonal degeneration should be investigated further for use in early stage therapeutic trials, or to monitor axonal injury in early stage MS.

Fibre-specific white matter reductions in Alzheimer's disease and mild cognitive impairment.

Alzheimer's disease is increasingly considered a large-scale network disconnection syndrome, associated with progressive aggregation of pathological proteins, cortical atrophy, and functional disconnections between brain regions. These pathological changes are posited to arise in a stereotypical spatiotemporal manner, targeting intrinsic networks in the brain, most notably the default mode network. While this network-specific disruption has been thoroughly studied with functional neuroimaging, changes to specific white matter fibre pathways within the brain's structural networks have not been closely investigated, largely due to the challenges of modelling complex white matter structure. Here, we applied a novel technique known as 'fixel-based analysis' to comprehensively investigate fibre tract-specific differences at a within-voxel level (called 'fixels') to assess potential axonal loss in subjects with Alzheimer's disease and mild cognitive impairment. We hypothesized that patients with Alzheimer's disease would exhibit extensive degeneration across key fibre pathways connecting default network nodes, while patients with mild cognitive impairment would exhibit selective degeneration within fibre pathways connecting regions previously identified as functionally implicated early in Alzheimer's disease. Diffusion MRI data from Alzheimer's disease (n = 49), mild cognitive impairment (n = 33), and healthy elderly control subjects (n = 95) were obtained from the Australian Imaging, Biomarkers and Lifestyle study of ageing. We assessed microstructural differences in fibre density, and macrostructural differences in fibre bundle morphology using fixel-based analysis. Whole-brain analysis was performed to compare groups across all white matter fixels. Subsequently, we performed a tract of interest analysis comparing fibre density and cross-section across 11 selected white matter tracts, to investigate potentially subtle degeneration within fibre pathways in mild cognitive impairment, initially by clinical diagnosis alone, and then by including amyloid status (i.e. a positive or negative amyloid PET scan). Our whole-brain analysis revealed significant white matter loss manifesting both microstructurally and macrostructurally in Alzheimer's disease patients, evident in specific fibre pathways associated with default mode network nodes. Reductions in fibre density and cross-section in mild cognitive impairment patients were only exhibited within the posterior cingulum when statistical analyses were limited to tracts of interest. Interestingly, these degenerative changes did not appear to be associated with high amyloid accumulation, given that amyloid-negative, but not positive, mild cognitive impairment subjects exhibited subtle focal left posterior cingulum deficits. The findings of this study demonstrated a stereotypical distribution of white matter degeneration in patients with Alzheimer's disease, which was in line with canonical findings from other imaging modalities, and with a network-based conceptualization of the disease.awx355media15726254535001.

BIDS apps: Improving ease of use, accessibility, and reproducibility of neuroimaging data analysis methods.

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.

Investigating white matter fibre density and morphology using fixel-based analysis.

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.

Tract-specific atrophy in focal epilepsy: Disease, genetics, or seizures?

OBJECTIVE: To investigate whether genetics, underlying pathology, or repeated seizures contribute to atrophy in specific white matter tracts. METHODS: Medically refractory unilateral temporal lobe epilepsy (TLE) with hippocampal sclerosis (HS-TLE, n = 26) was studied as an archetype of focal epilepsy, using fixel-based analysis of diffusion-weighted imaging. A genetic effect was assessed in first-degree relatives of HS-TLE subjects who did not have epilepsy themselves (HS-1°Rel; n = 26). The role of disease process was uncovered by comparing HS-TLE to unilateral TLE with normal clinical magnetic resonance imaging (MRI-neg TLE; n = 26, matched for seizure severity). The effect of focal seizures was inferred from lateralized atrophy common to both HS-TLE and MRI-neg TLE, in comparison to healthy controls (n = 76). RESULTS: HS-1 °Rel had bilaterally small hippocampi, but no focal white matter atrophy was detected, indicating a limited effect of genetics. HS-TLE subjects had lateralized atrophy of most temporal lobe tracts, and hippocampal volumes in HS-TLE correlated with parahippocampal cingulum and anterior commissure atrophy, indicating an effect of the underlying pathology. Ipsilateral atrophy of the tapetum, uncinate, and inferior fronto-occipital fasciculus was found in both HS-TLE and MRI-neg TLE, suggesting a common lateralized effect of focal seizures. Both epilepsy groups had bilateral atrophy of the dorsal cingulum and corpus callosum fibers, which we interpret as a consequence of bilateral insults (potentially generalized seizures and/or medications). INTERPRETATION: Underlying pathology, repeated focal seizures, and global insults each contribute to atrophy in specific tracts. Genetic factors make less of a contribution in this cohort. A multifactorial model of white matter atrophy in focal epilepsy is proposed. Ann Neurol 2017;81:240-250.

Predicting hand function after hemidisconnection.

Hemidisconnections (i.e. hemispherectomies or hemispherotomies) invariably lead to contralateral hemiparesis. Many patients with a pre-existing hemiparesis, however, experience no deterioration in motor functions, and some can still grasp with their paretic hand after hemidisconnection. The scope of our study was to predict this phenomenon. Hypothesizing that preserved contralateral grasping ability after hemidisconnection can only occur in patients controlling their paretic hands via ipsilateral corticospinal projections already in the preoperative situation, we analysed the asymmetries of the brainstem (by manual magnetic resonance imaging volumetry) and of the structural connectivity of the corticospinal tracts within the brainstem (by magnetic resonance imaging diffusion tractography), assuming that marked hypoplasia or Wallerian degeneration on the lesioned side in patients who can grasp with their paretic hands indicate ipsilateral control. One hundred and two patients who underwent hemidisconnections between 0.8 and 36 years of age were included. Before the operation, contralateral hand function was normal in 3/102 patients, 47/102 patients showed hemiparetic grasping ability and 52/102 patients could not grasp with their paretic hands. After hemidisconnection, 20/102 patients showed a preserved grasping ability, and 5/102 patients began to grasp with their paretic hands only after the operation. All these 25 patients suffered from pre- or perinatal brain lesions. Thirty of 102 patients lost their grasping ability. This group included all seven patients with a post-neonatally acquired or progressive brain lesion who could grasp before the operation, and also all three patients with a preoperatively normal hand function. The remaining 52/102 patients were unable to grasp pre- and postoperatively. On magnetic resonance imaging, the patients with preserved grasping showed significantly more asymmetric brainstem volumes than the patients who lost their grasping ability. Similarly, these patients showed striking asymmetries in the structural connectivity of the corticospinal tracts. In summary, normal preoperative hand function and a post-neonatally acquired or progressive lesion predict a loss of grasping ability after hemidisconnection. A postoperatively preserved grasping ability is possible in hemiparetic patients with pre- or perinatal lesions, and this is highly likely when the brainstem is asymmetric and especially when the structural connectivity of the corticospinal tracts within the brainstem is asymmetric.

Structural connectivity of the anterior cingulate in children with unilateral cerebral palsy due to white matter lesions.

In this work we investigate the structural connectivity of the anterior cingulate cortex (ACC) and its link with impaired executive function in children with unilateral cerebral palsy (UCP) due to periventricular white matter lesions. Fifty two children with UCP and 17 children with typical development participated in the study, and underwent diffusion and structural MRI. Five brain regions were identified for their high connectivity with the ACC using diffusion MRI fibre tractography: the superior frontal gyrus, medial orbitofrontal cortex, rostral middle frontal gyrus, precuneus and isthmus cingulate. Structural connectivity was assessed in pathways connecting these regions to the ACC using three diffusion MRI derived measures: fractional anisotropy (FA), mean diffusivity (MD) and apparent fibre density (AFD), and compared between participant groups. Furthermore we investigated correlations of these measures with executive function as assessed by the Flanker task. The ACC-precuneus tract had significantly different MD (p < 0.0001) and AFD (p = 0.0072) between groups, with post-hoc analysis showing significantly increased MD in the right hemisphere of children with left hemiparesis compared with controls. The ACC-superior frontal gyrus tract had significantly different FA (p = 0.0049) and MD (p = 0.0031) between groups. AFD in this tract (contralateral to side of hemiparesis; right hemisphere in controls) showed a significant relationship with Flanker task performance (p = 0.0045, ß = -0.5856), suggesting that reduced connectivity correlates with executive dysfunction. Reduced structural integrity of ACC tracts appears to be important in UCP, in particular the connection to the superior frontal gyrus. Although damage to this area is heterogeneous it may be important in early identification of children with impaired executive function.

Quantification of voxel-wise total fibre density: Investigating the problems associated with track-count mapping.

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.

Connectivity-based fixel enhancement: Whole-brain statistical analysis of diffusion MRI measures in the presence of crossing fibres.

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.

Quantification of track-weighted imaging (TWI): characterisation of within-subject reproducibility and between-subject variability.

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.

Track-weighted functional connectivity (TW-FC): a tool for characterizing the structural-functional connections in the brain.

MRI provides a powerful tool for studying the functional and structural connections in the brain non-invasively. The technique of functional connectivity (FC) exploits the intrinsic temporal correlations of slow spontaneous signal fluctuations to characterise brain functional networks. In addition, diffusion MRI fibre-tracking can be used to study the white matter structural connections. In recent years, there has been considerable interest in combining these two techniques to provide an overall structural-functional description of the brain. In this work we applied the recently proposed super-resolution track-weighted imaging (TWI) methodology to demonstrate how whole-brain fibre-tracking data can be combined with FC data to generate a track-weighted (TW) FC map of FC networks. The method was applied to data from 8 healthy volunteers, and illustrated with (i) FC networks obtained using a seeded connectivity-based analysis (seeding in the precuneus/posterior cingulate cortex, PCC, known to be part of the default mode network), and (ii) with FC networks generated using independent component analysis (in particular, the default mode, attention, visual, and sensory-motor networks). TW-FC maps showed high intensity in white matter structures connecting the nodes of the FC networks. For example, the cingulum bundles show the strongest TW-FC values in the PCC seeded-based analysis, due to their major role in the connection between medial frontal cortex and precuneus/posterior cingulate cortex; similarly the superior longitudinal fasciculus was well represented in the attention network, the optic radiations in the visual network, and the corticospinal tract and corpus callosum in the sensory-motor network. The TW-FC maps highlight the white matter connections associated with a given FC network, and their intensity in a given voxel reflects the functional connectivity of the part of the nodes of the network linked by the structural connections traversing that voxel. They therefore contain a different (and novel) image contrast from that of the images used to generate them. The results shown in this study illustrate the potential of the TW-FC approach for the fusion of structural and functional data into a single quantitative image. This technique could therefore have important applications in neuroscience and neurology, such as for voxel-based comparison studies.

HOMOR: higher order model outlier rejection for high b-value MR diffusion data.

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=3000 s/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=1000 s/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.

Reorientation of fiber orientation distributions using apodized point spread functions.

Using high angular resolution diffusion-weighted images, spherical deconvolution enables multiple white matter fiber populations to be resolved within a single voxel by computing the fiber orientation distribution (FOD). Higher order information provided by FODs could improve several methods for investigating population differences in white matter, including image registration, voxel-based analysis, atlas-based segmentation and labeling, and group average fiber tractography. All of these methods require spatial normalization of FODs. In this article, a novel method to reorient the FOD is presented, which is an important step required for FOD spatial normalization. The proposed method was assessed using both qualitative and quantitative experiments, with numerical simulations and in vivo human data. Results demonstrate that the proposed method improves FOD reorientation accuracy, removes undesired artefacts, and decreases computation time compared to a previous approach. The utility of the proposed method is illustrated by nonlinear FOD spatial normalization of 10 human subjects. Accurate reorientation and normalization of FODs is a critical step toward investigating white matter tissue in the context of multiple fiber orientations.

Apparent Fibre Density: a novel measure for the analysis of diffusion-weighted magnetic resonance images.

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.

Symmetric diffeomorphic registration of fibre orientation distributions.

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 (l(max)) of 2, 4 and 6. Results demonstrate a benefit in using FODs at l(max)=4 compared to l(max)=2. However, a decrease in registration accuracy was observed when l(max)=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.