Spherical Deconvolution Methods Research Articles

Changes in diffusion MRI and clinical motor function after physical/occupational therapies in toddler-aged children with spastic unilateral cerebral palsy

Diffusion-weighted magnetic resonance imaging (DMRI) is a potential tool to assess changes in brain connectivity and microstructure resulting from physical and occupational therapy in young children with cerebral palsy. This works was carried out to assess whether DMRI can detect changes after 36 weeks of physical and occupational therapy in the microstructure and connectivity of the brains of children with cerebral palsy and determine whether imaging findings correlate with changes in clinical measures of motor function. Five children underwent anatomical MRI and DMRI and evaluations of motor function skills at baseline and after 36 weeks of intensive or once-weekly physical and occupational Perception-Action Approach therapies. Diffusion tensor imaging and constrained spherical deconvolution methods were used to calculate fractional anisotropy (FA) and fiber orientation distribution functions (fODFs), respectively. The fODFs were used to generate tractograms of the cerebrospinal tract (CST). After 36 weeks of physical and occupational therapy, all children showed increases in motor function. No changes were observed in anatomical MRI before and after therapy but CST tractography did show small differences indicating possible altered microstructure and connectivity in the brain. FA values along the CSTs, however, showed no significant changes. Reliable longitudinal DMRI can be employed in toddler-aged children with CP and DMRI has the potential to monitor neuroplastic changes in white matter microstructure. However, there is a high variability between subjects and clinical improvements were not always correlated with measures of FA along the CST.

Unveiling the Exquisite Microstructural Details in Zebrafish Brain Non-Invasively Using Magnetic Resonance Imaging at 28.2 T

Zebrafish (Danio rerio) is an important animal model for a wide range of neurodegenerative diseases. However, obtaining the cellular resolution that is essential for studying the zebrafish brain remains challenging as it requires high spatial resolution and signal-to-noise ratios (SNR). In the current study, we present the first MRI results of the zebrafish brain at the state-of-the-art magnetic field strength of 28.2 T. The performance of MRI at 28.2 T was compared to 17.6 T. A 20% improvement in SNR was observed at 28.2 T as compared to 17.6 T. Excellent contrast, resolution, and SNR allowed the identification of several brain structures. The normative T1 and T2 relaxation values were established over different zebrafish brain structures at 28.2 T. To zoom into the white matter structures, we applied diffusion tensor imaging (DTI) and obtained axial, radial, and mean diffusivity, as well as fractional anisotropy, at a very high spatial resolution. Visualisation of white matter structures was achieved by short-track track-density imaging by applying the constrained spherical deconvolution method (stTDI CSD). For the first time, an algorithm for stTDI with multi-shell multi-tissue (msmt) CSD was tested on zebrafish brain data. A significant reduction in false-positive tracks from grey matter signals was observed compared to stTDI with single-shell single-tissue (ssst) CSD. This allowed the non-invasive identification of white matter structures at high resolution and contrast. Our results show that ultra-high field DTI and tractography provide reproducible and quantitative maps of fibre organisation from tiny zebrafish brains, which can be implemented in the future for a mechanistic understanding of disease-related microstructural changes in zebrafish models of various brain diseases.

An intracellular isotropic diffusion signal is positively associated with pubertal development in white matter

Puberty is a key event in adolescent development that involves significant, hormone-driven changes to many aspects of physiology including the brain. Understanding how the brain responds during this time period is important for evaluating neuronal developments that affect mental health throughout adolescence and the adult lifespan. This study examines diffusion MRI scans from the cross-sectional ABCD Study baseline cohort, a large multi-site study containing thousands of participants, to describe the relationship between pubertal development and brain microstructure. Using advanced, 3-tissue constrained spherical deconvolution methods, this study is able to describe multiple tissue compartments beyond only white matter (WM) axonal qualities. After controlling for age, sex, brain volume, subject handedness, scanning site, and sibling relationships, we observe a positive relationship between an isotropic, intracellular diffusion signal fraction and pubertal development across a majority of regions of interest (ROIs) in the WM skeleton. We also observe regional effects from an intracellular anisotropic signal fraction compartment and extracellular isotropic free water-like compartment in several ROIs. This cross-sectional work suggests that changes in pubertal status are associated with a complex response from brain tissue that cannot be completely described by traditional methods focusing only on WM axonal properties.

Using mesoscopic tract-tracing data to guide the estimation of fiber orientation distributions in the mouse brain from diffusion MRI

Diffusion MRI (dMRI) tractography is the only tool for non-invasive mapping of macroscopic structural connectivity over the entire brain. Although it has been successfully used to reconstruct large white matter tracts in the human and animal brains, the sensitivity and specificity of dMRI tractography remained limited. In particular, the fiber orientation distributions (FODs) estimated from dMRI signals, key to tractography, may deviate from histologically measured fiber orientation in crossing fibers and gray matter regions. In this study, we demonstrated that a deep learning network, trained using mesoscopic tract-tracing data from the Allen Mouse Brain Connectivity Atlas, was able to improve the estimation of FODs from mouse brain dMRI data. Tractography results based on the network generated FODs showed improved specificity while maintaining sensitivity comparable to results based on FOD estimated using a conventional spherical deconvolution method. Our result is a proof-of-concept of how mesoscale tract-tracing data can guide dMRI tractography and enhance our ability to characterize brain connectivity.

Fiber direction estimation using constrained spherical deconvolution based on multi-model response function

Constrained spherical deconvolution can quantify white matter fiber orientation distribution information from diffusion magnetic resonance imaging data. But this method is only applicable to single shell diffusion magnetic resonance imaging data and will provide wrong fiber orientation information in white matter tissue which contains isotropic diffusion signals. To solve these problems, this paper proposes a constrained spherical deconvolution method based on multi-model response function. Multi-shell data can improve the stability of fiber orientation, and multi-model response function can attenuate isotropic diffusion signals in white matter, providing more accurate fiber orientation information. Synthetic data and real brain data from public database were used to verify the effectiveness of this algorithm. The results demonstrate that the proposed algorithm can attenuate isotropic diffusion signals in white matter and overcome the influence of partial volume effect on fiber direction estimation, thus estimate fiber direction more accurately. The reconstructed fiber direction distribution is stable, the false peaks are less, and the recognition ability of cross fiber is stronger, which lays a foundation for the further research of fiber bundle tracking technology.

Connectome analysis of male world-class gymnasts using probabilistic multishell, multitissue constrained spherical deconvolution tracking.

In athletes, long‐term intensive training has been shown to increase unparalleled athletic ability and might induce brain plasticity. We evaluated the structural connectome of world‐class gymnasts (WCGs), as mapped by diffusion‐weighted magnetic resonance imaging probabilistic tractography and a multishell, multitissue constrained spherical deconvolution method to increase the precision of tractography at the tissue interfaces. The connectome was mapped in 10 Japanese male WCGs and in 10 age‐matched male controls. Network‐based statistic identified subnetworks with increased connectivity density in WCGs, involving the sensorimotor, default mode, attentional, visual, and limbic areas. It also revealed a significant association between the structural connectivity of some brain structures with functions closely related to the gymnastic skills and the D‐score, which is used as an index of the gymnasts' specific physical abilities for each apparatus. Furthermore, graph theory analysis demonstrated the characteristics of brain anatomical topology in the WCGs. They displayed significantly increased global connectivity strength with decreased characteristic path length at the global level and higher nodal strength and degree in the sensorimotor, default mode, attention, and limbic/subcortical areas at the local level as compared with controls. Together, these findings extend the current understanding of neural mechanisms that distinguish WCGs from controls and suggest brain anatomical network plasticity in WCGs resulting from long‐term intensive training. Future studies should assess the contribution of genetic or early‐life environmental factors in the brain network organization of WCGs. Furthermore, the indices of brain topology (i.e., connection density and graph theory indices) could become markers for the objective evaluation of gymnastic performance.

Test-retest reliability and long-term stability of three-tissue constrained spherical deconvolution methods for analyzing diffusion MRI data.

Several recent studies have used a three-tissue constrained spherical deconvolution pipeline to obtain quantitative metrics of brain tissue microstructure from diffusion-weighted MRI data. The three tissue compartments, consisting of white matter, gray matter, and CSF-like (free water) signals, are potentially useful in the evaluation of brain microstructure in a range of pathologies. However, the reliability and long-term stability of these metrics have not yet been evaluated. This study examined estimates of whole-brain microstructure for the three tissue compartments, in three separate test-retest cohorts. Each cohort had different lengths of time between baseline and retest, ranging from within the same scanning session in the shortest interval to 3 months in the longest interval. Each cohort was also collected with different acquisition parameters. The CSF-like compartment displayed the greatest reliability across all cohorts, with intraclass correlation coefficient (ICC) values being above 0.95 in each cohort. White matter-like and gray matter-like compartments both demonstrated very high reliability in the immediate cohort (both ICC > 0.90); however, this declined in the 3-month interval cohort to both compartments having ICC > 0.80. Regional CSF-like signal fraction was examined in bilateral hippocampus and had an ICC > 0.80 in each cohort. The three-tissue constrained spherical deconvolution techniques provide reliable and stable estimates of tissue-microstructure composition, up to 3 months longitudinally in a control population. This forms an important basis for further investigations using three-tissue constrained spherical deconvolution techniques to track changes in microstructure across a variety of brain pathologies.

Sparse wars: A survey and comparative study of spherical deconvolution algorithms for diffusion MRI

Spherical deconvolution methods are widely used to estimate the brain's white-matter fiber orientations from diffusion MRI data. In this study, eight spherical deconvolution algorithms were implemented and evaluated. These included two model selection techniques based on the extended Bayesian information criterion (i.e., best subset selection and the least absolute shrinkage and selection operator), iteratively reweighted l2- and l1-norm approaches to approximate the l0-norm, sparse Bayesian learning, Cauchy deconvolution, and two accelerated Richardson-Lucy algorithms. Results from our exhaustive evaluation show that there is no single optimal method for all different fiber configurations, suggesting that further studies should be conducted to find the optimal way of combining solutions from different methods. We found l0-norm regularization algorithms to resolve more accurately fiber crossings with small inter-fiber angles. However, in voxels with very dominant fibers, algorithms promoting more sparsity are less accurate in detecting smaller fibers. In most cases, the best algorithm to reconstruct fiber crossings with two fibers did not perform optimally in voxels with one or three fibers. Therefore, simplified validation systems as employed in a number of previous studies, where only two fibers with similar volume fractions were tested, should be avoided as they provide incomplete information. Future studies proposing new reconstruction methods based on high angular resolution diffusion imaging data should validate their results by considering, at least, voxels with one, two, and three fibers, as well as voxels with dominant fibers and different diffusion anisotropies.

A localized Richardson-Lucy algorithm for fiber orientation estimation in high angular resolution diffusion imaging.

Diffusion tensor imaging is widely used for studying neural fiber trajectories in white matter and for quantifying changes in tissue using diffusion properties at each voxel in the brain. To better model the nature of crossing fibers within complex architectures, rather than using a simplified tensor model that assumes only a single fiber direction at each image voxel, a model mixing multiple diffusion tensors is used to profile diffusion signals from high angular resolution diffusion imaging (HARDI) data. Based on the HARDI signal and a multiple tensors model, spherical deconvolution methods have been developed to overcome the limitations of the diffusion tensor model when resolving crossing fibers. The Richardson-Lucy algorithm is a popular spherical deconvolution method used in previous work. However, it is based on a Gaussian distribution, while HARDI data are always very noisy, and the distribution of HARDI data follows a Rician distribution. This current work aims to present a novel solution to address these issues. By simultaneously considering both the Rician bias and neighbor correlation in HARDI data, the authors propose a localized Richardson-Lucy (LRL) algorithm to estimate fiber orientations for HARDI data. The proposed method can simultaneously reduce noise and correct the Rician bias. Mean angular error (MAE) between the estimated Fiber orientation distribution (FOD) field and the reference FOD field was computed to examine whether the proposed LRL algorithm offered any advantage over the conventional RL algorithm at various levels of noise. Normalized mean squared error (NMSE) was also computed to measure the similarity between the true FOD field and the estimated FOD filed. For MAE comparisons, the proposed LRL approach obtained the best results in most of the cases at different levels of SNR and b-values. For NMSE comparisons, the proposed LRL approach obtained the best results in most of the cases at b-value = 3000 s/mm(2), which is the recommended schema for HARDI data acquisition. In addition, the FOD fields estimated by the proposed LRL approach in regions of fiber crossing regions using real data sets also showed similar fiber structures which agreed with common acknowledge in these regions. The novel spherical deconvolution method for improved accuracy in investigating crossing fibers can simultaneously reduce noise and correct Rician bias. With the noise smoothed and bias corrected, this algorithm is especially suitable for estimation of fiber orientations in HARDI data. Experimental results using both synthetic and real imaging data demonstrated the success and effectiveness of the proposed LRL algorithm.

ADHD severity is associated with white matter microstructure in the subgenual cingulum.

AimsThis analysis examined hypothesised associations between microstructural attributes in specific white matter (WM) tracts selected a priori and measures of clinical variability in adolescents with a diagnosis of attention deficit hyperactivity disorder (ADHD). Firstly, associations were explored between WM microstructure and ADHD severity in the subgenual cingulum. Secondly, to ensure that tract-specific approaches afforded enhanced rather than differential sensitivity, associations were measured between WM microstructure and autistic traits in the right corticospinal tract based on results of a previously-published voxelwise analysis.Methods40 right-handed males aged 14–18 years (19 with DSM-IV combined type ADHD and 21 healthy controls) underwent a 60 direction diffusion MRI scan. Clinical ADHD and autism variation were assessed by validated questionnaires. Deterministic tractography based on spherical deconvolution methods was used to map the subgenual cingulum and corticospinal tract.ResultsFractional anisotropy was positively correlated and radial diffusivity was negatively correlated with a) ADHD severity in the left subgenual cingulum and b) autistic traits in the inferior segment of the right corticospinal tract. No case–control differences were found.ConclusionsResults shed light on possible anatomical correlates of ADHD severity and autistic symptoms in pathways which may be involved in the ADHD phenotype. They provide further evidence that tract-specific approaches may a) reveal associations between microstructural metrics and indices of phenotypic variability which would not be detected using voxelwise approaches, and b) provide improved rather than differential sensitivity compared to voxelwise approaches.

Non-Negative Spherical Deconvolution (NNSD) for estimation of fiber Orientation Distribution Function in single-/multi-shell diffusion MRI

Spherical Deconvolution (SD) is commonly used for estimating fiber Orientation Distribution Functions (fODFs) from diffusion-weighted signals. Existing SD methods can be classified into two categories: 1) Continuous Representation based SD (CR-SD), where typically Spherical Harmonic (SH) representation is used for convenient analytical solutions, and 2) Discrete Representation based SD (DR-SD), where the signal profile is represented by a discrete set of basis functions uniformly oriented on the unit sphere. A feasible fODF should be non-negative and should integrate to unity throughout the unit sphere S2. However, to our knowledge, most existing SH-based SD methods enforce non-negativity only on discretized points and not the whole continuum of S2. Maximum Entropy SD (MESD) and Cartesian Tensor Fiber Orientation Distributions (CT-FOD) are the only SD methods that ensure non-negativity throughout the unit sphere. They are however computational intensive and are susceptible to errors caused by numerical spherical integration. Existing SD methods are also known to overestimate the number of fiber directions, especially in regions with low anisotropy. DR-SD introduces additional error in peak detection owing to the angular discretization of the unit sphere. This paper proposes a SD framework, called Non-Negative SD (NNSD), to overcome all the limitations above. NNSD is significantly less susceptible to the false-positive peaks, uses SH representation for efficient analytical spherical deconvolution, and allows accurate peak detection throughout the whole unit sphere. We further show that NNSD and most existing SD methods can be extended to work on multi-shell data by introducing a three-dimensional fiber response function. We evaluated NNSD in comparison with Constrained SD (CSD), a quadratic programming variant of CSD, MESD, and an L1-norm regularized non-negative least-squares DR-SD. Experiments on synthetic and real single-/multi-shell data indicate that NNSD improves estimation performance in terms of mean difference of angles, peak detection consistency, and anisotropy contrast between isotropic and anisotropic regions.

Cognitive Deficits In Friedreich Ataxia Correlate with Micro-structural Changes in Dentatorubral Tract

Atrophy of the dentate nucleus is one of the major neuropathological changes in Friedreich ataxia (FRDA). Neuroimaging studies demonstrated white matter (WM) degeneration in FRDA. In this study, we used advanced tractography techniques to quantitatively measure WM changes in the dentato-thalamic and dentato-rubral tracts, and correlated these changes with cognitive profiles of FRDA. We also analysed diffusivity changes of the thalamo-cortical tract to assess whether neurological degeneration of WM extends beyond the primary site of involvement in FRDA. Twelve genetically proven individuals with FRDA and 14 controls were recruited. Sixty directions diffusion tensor images were acquired. The WM bundles from the dentate nucleus were estimated using a constrained spherical deconvolution method and the diffusivity characteristics measured. The Simon task was used to assess cognitive profile of FRDA. The dentato-rubral, dentato-thalamic and thalamo-cortical tracts manifested significantly lower fractional anisotropy, higher mean diffusivity and increased radial diffusivity in FRDA compared with controls. There was no difference in axial diffusivity between the two groups. The mean and radial diffusivity of the dentato-rubral tract was positively correlated with choice reaction time, congruent reaction time, incongruent reaction time and Simon effect reaction time and negatively with the larger GAA repeat. Significant changes in diffusivity characteristics were observed in the dentato-thalamic and thalamo-cortical tracts, suggesting extensive WM degeneration and affected WM structures in FRDA. Correlation of WM changes in the dentato-rubral tract with the cognitive assessment suggested that this tract is an important contributor to cognitive disturbances in FRDA.

Can spherical deconvolution provide more information than fiber orientations? Hindrance modulated orientational anisotropy, a true-tract specific index to characterize white matter diffusion

Diffusion tensor imaging (DTI) methods are widely used to reconstruct white matter trajectories and to quantify tissue changes using the average diffusion properties of each brain voxel. Spherical deconvolution (SD) methods have been developed to overcome the limitations of the diffusion tensor model in resolving crossing fibers and to improve tractography reconstructions. However, the use of SD methods to obtain quantitative indices of white matter integrity has not been extensively explored. In this study, we show that the hindrance modulated orientational anisotropy (HMOA) index, defined as the absolute amplitude of each lobe of the fiber orientation distribution, can be used as a compact measure to characterize the diffusion properties along each fiber orientation in white matter regions with complex organization. We demonstrate that the HMOA is highly sensitive to changes in fiber diffusivity (e.g., myelination processes or axonal loss) and to differences in the microstructural organization of white matter like axonal diameter and fiber dispersion. Using simulations to describe diffusivity changes observed in normal brain development and disorders, we observed that the HMOA is able to identify white matter changes that are not detectable with conventional DTI indices. We also show that the HMOA index can be used as an effective threshold for in vivo data to improve tractography reconstructions and to better map white matter complexity inside the brain. In conclusion, the HMOA represents a true tract-specific and sensitive index and provides a compact characterization of white matter diffusion properties with potential for widespread application in normal and clinical populations.

De l’estimation locale par imagerie q-ball à la tractographie des croisements de fibres

Fibre crossing is an important problem for most existing diffusion tensor imaging (DTI) based tractography algorithms. To overcome limitations of DTI, high angular resolution diffusion imaging (HARD1) techniques such as q-ball imaging (QBI) have been introduced. The purpose of this article is to first give an extensive state of the art review of the existing local HARDI reconstruction techniques as well as the existing HARDI-based tractography algorithms. Then, we describe our analytical QBI solution to reconstruct the diffusion orientation distribution function (ODF) of water molecules and we propose a spherical deconvolution method to transform the diffusion ODF into a sharper fibre ODF. Finally, we propose a new deterministic and a new probabilistic algorithm based on this fibre ODF. We show that the diffusion ODF and fibre ODF can recover fibre crossing in simulated data, in a biological phantom and in real datasets. The fibre ODF improves angular resolution of QBI by more than 15° and greatly improves tractography results in regions of complex fibre crossing, fanning and branching.

MRtrix: Diffusion tractography in crossing fiber regions

AbstractIn recent years, diffusion‐weighted magnetic resonance imaging has attracted considerable attention due to its unique potential to delineate the white matter pathways of the brain. However, methodologies currently available and in common use among neuroscientists and clinicians are typically based on the diffusion tensor model, which has comprehensively been shown to be inadequate to characterize diffusion in brain white matter. This is due to the fact that it is only capable of resolving a single fiber orientation per voxel, causing incorrect fiber orientations, and hence pathways, to be estimated through these voxels. Given that the proportion of affected voxels has been recently estimated at 90%, this is a serious limitation. Furthermore, most implementations use simple “deterministic” streamlines tracking algorithms, which have now been superseded by “probabilistic” approaches. In this study, we present a robust set of tools to perform tractography, using fiber orientations estimated using the validated constrained spherical deconvolution method, coupled with a probabilistic streamlines tracking algorithm. This methodology is shown to provide superior delineations of a number of known white matter tracts, in a manner robust to crossing fiber effects. These tools have been compiled into a software package, called MRtrix, which has been made freely available for use by the scientific community. © 2012 Wiley Periodicals, Inc. Int J Imaging Syst Technol, 22, 53–66, 2012

A modified damped Richardson–Lucy algorithm to reduce isotropic background effects in spherical deconvolution

Spherical deconvolution methods have been applied to diffusion MRI to improve diffusion tensor tractography results in brain regions with multiple fibre crossing. Recent developments, such as the introduction of non-negative constraints on the solution, allow a more accurate estimation of fibre orientations by reducing instability effects due to noise robustness. Standard convolution methods do not, however, adequately model the effects of partial volume from isotropic tissue, such as gray matter, or cerebrospinal fluid, which may degrade spherical deconvolution results. Here we use a newly developed spherical deconvolution algorithm based on an adaptive regularization (damped version of the Richardson–Lucy algorithm) to reduce isotropic partial volume effects. Results from both simulated and in vivo datasets show that, compared to a standard non-negative constrained algorithm, the damped Richardson–Lucy algorithm reduces spurious fibre orientations and preserves angular resolution of the main fibre orientations. These findings suggest that, in some brain regions, non-negative constraints alone may not be sufficient to reduce spurious fibre orientations. Considering both the speed of processing and the scan time required, this new method has the potential for better characterizing white matter anatomy and the integrity of pathological tissue.