Multi-tissue constrained spherical deconvolution for improved analysis of multi-shell diffusion MRI data

Diffusion-weighted (DW) magnetic resonance imaging (MRI) is a non-invasive imaging method, which can be used to investigate neural tracts in the white matter (WM) of the brain. Significant partial volume effects (PVEs) are present in the DW signal due to relatively large voxel sizes. These PVEs can be caused by both non-WM tissue, such as gray matter (GM) and cerebrospinal fluid (CSF), and by multiple non-parallel WM fiber populations. High angular resolution diffusion imaging (HARDI) methods have been developed to correctly characterize complex WM fiber configurations, but to date, many of the HARDI methods do not account for non-WM PVEs. In this work, we investigated the isotropic PVEs caused by non-WM tissue in WM voxels on fiber orientations extracted with constrained spherical deconvolution (CSD). Experiments were performed on simulated and real DW-MRI data. In particular, simulations were performed to demonstrate the effects of varying the diffusion weightings, signal-to-noise ratios (SNRs), fiber configurations, and tissue fractions. Our results show that the presence of non-WM tissue signal causes a decrease in the precision of the detected fiber orientations and an increase in the detection of false peaks in CSD. We estimated 35–50% of WM voxels to be affected by non-WM PVEs. For HARDI sequences, which typically have a relatively high degree of diffusion weighting, these adverse effects are most pronounced in voxels with GM PVEs. The non-WM PVEs become severe with 50% GM volume for maximum spherical harmonics orders of 8 and below, and already with 25% GM volume for higher orders. In addition, a low diffusion weighting or SNR increases the effects. The non-WM PVEs may cause problems in connectomics, where reliable fiber tracking at the WM–GM interface is especially important. We suggest acquiring data with high diffusion-weighting 2500–3000 s/mm2, reasonable SNR (~30) and using lower SH orders in GM contaminated regions to minimize the non-WM PVEs in CSD.

Constrained spherical deconvolution (CSD) of diffusion‐weighted MRI (DW‐MRI) is a popular analysis method that extracts the full white matter (WM) fiber orientation density function (fODF) in the living human brain, noninvasively. It assumes that the DW‐MRI signal on the sphere can be represented as the spherical convolution of a single‐fiber response function (RF) and the fODF, and recovers the fODF through the inverse operation. CSD approaches typically require that the DW‐MRI data is sampled shell‐wise, and estimate the RF in a purely spherical manner using spherical basis functions, such as spherical harmonics (SH), disregarding any radial dependencies. This precludes analysis of data acquired with nonspherical sampling schemes, for example, Cartesian sampling. Additionally, nonspherical sampling can also arise due to technical issues, for example, gradient nonlinearities, resulting in a spatially dependent bias of the apparent tissue densities and connectivity information. Here, we adopt a compact model for the RFs that also describes their radial dependency. We demonstrate that the proposed model can accurately predict the tissue response for a wide range of b‐values. On shell‐wise data, our approach provides fODFs and tissue densities indistinguishable from those estimated using SH. On Cartesian data, fODF estimates and apparent tissue densities are on par with those obtained from shell‐wise data, significantly broadening the range of data sets that can be analyzed using CSD. In addition, gradient nonlinearities can be accounted for using the proposed model, resulting in much more accurate apparent tissue densities and connectivity metrics.

Constrained spherical deconvolution (CSD) is a new reconstruction technique that extracts white matter fiber orientations from diffusion weighted MRI data of the brain. However, since these orientations are estimated from noisy data, they are subject to errors, which propagate during fiber tractography. Therefore, it is important to estimate the uncertainty associated with the fiber orientations. In this work, we investigate the performance of a statistical method called the bootstrap, when estimating confidence intervals for CSD fiber orientations. The bootstrap is a nonparametric statistical technique based on data resampling. We used Monte Carlo simulations to measure both its accuracy and precision when applied to CSD. Also, we evaluated an alternative method called the bootknife, which aims to increase the precision of the bootstrap.

Differentiation of absolute metabolite concentrations between gray and white matter in the occipital region of normal human brain was performed by in vivo localized single-voxel 1H magnetic resonance spectroscopy at 1.5 Tesla with long echo time (136 ms). With the combination of image segmentation between white and gray matter and cerebrospinal fluid, signal compensation of T1 and T2 effects, tissue water signal as the internal concentration reference, as well as compensation by different water contents in gray and white matters, it was determined that the levels of N-acetylaspartate (NAA), creatine and/or phosphocreatine (Cr), and choline-containing compounds (Cho) in gray matter were significantly higher than in white matter. The averaged NAA, Cr, and Cho concentrations in gray matter were 11.0, 9.7, and 1.9 mM/liter, respectively, in comparison with 7.5, 5.2, and 1.6 mM/liter in white matter. These results suggest that precise composition of white and gray matter and cerebrospinal fluid is necessary to avoid partial voluming effect in a single voxel and to accurately quantify the metabolite concentrations.

Diffusion weighted magnetic resonance imaging (DW-MRI) is interpreted as a quantitative method that is sensitive to tissue microarchitecture at a millimeter scale. However, the sensitization is dependent on acquisition sequences (e.g., diffusion time, gradient strength, etc.) and susceptible to imaging artifacts. Hence, comparison of quantitative DW-MRI biomarkers across field strengths (including different scanners, hardware performance, and sequence design considerations) is a challenging area of research. We propose a novel method to estimate microstructure using DW-MRI that is robust to scanner difference between 1.5T and 3T imaging. We propose to use a null space deep network (NSDN) architecture to model DW-MRI signal as fiber orientation distributions (FOD) to represent tissue microstructure. The NSDN approach is consistent with histologically observed microstructure (on previously acquired ex vivo squirrel monkey dataset) and scan-rescan data. The contribution of this work is that we incorporate identical dual networks (IDN) to minimize the influence of scanner effects via scan-rescan data. Briefly, our estimator is trained on two datasets. First, a histology dataset was acquired on three squirrel monkeys with corresponding DW-MRI and confocal histology (512 independent voxels). Second, 37 control subjects from the Baltimore Longitudinal Study of Aging (67-95 y/o) were identified who had been scanned at 1.5T and 3T scanners (b-value of 700 s/mm2, voxel resolution at 2.2mm, 30-32 gradient volumes) with an average interval of 4 years (standard deviation 1.3 years). After image registration, we used paired white matter (WM) voxels for 17 subjects and 440 histology voxels for training and 20 subjects and 72 histology voxels for testing. We compare the proposed estimator with super-resolved constrained spherical deconvolution (CSD) and a previously presented regression deep neural network (DNN). NSDN outperformed CSD and DNN in angular correlation coefficient (ACC) 0.81 versus 0.28 and 0.46, mean squared error (MSE) 0.001 versus 0.003 and 0.03, and general fractional anisotropy (GFA) 0.05 versus 0.05 and 0.09. Further validation and evaluation with contemporaneous imaging are necessary, but the NSDN is promising avenue for building understanding of microarchitecture in a consistent and device-independent manner.

Cranial Ultrasonography

The properties of fiber reinforced polymers are strongly related to the length and orientation of the fibers within the polymer matrix, the latter of which can be studied using X-ray computed tomography (XCT). Unfortunately, resolving individual fibers is challenging because they are small compared to the XCT voxel resolution and because of the low attenuation contrast between the fibers and the surrounding resin. To alleviate both problems, anisotropic dark field tomography via grating based interferometry (GBI) has been proposed. Here, the fiber orientations are extracted by applying a Funk-Radon transform (FRT) to the local scatter function. However, the FRT suffers from a low angular resolution, which complicates estimating fiber orientations for small fiber crossing angles. We propose constrained spherical deconvolution (CSD) as an alternative to the FRT to resolve fiber orientations. Instead of GBI, edge illumination phase contrast imaging is used because estimating fiber orientations with this technique has not yet been explored. Dark field images are generated by a Monte Carlo simulation framework. It is shown that the FRT cannot estimate the fiber orientation accurately for crossing angles smaller than 70∘, while CSD performs well down to a crossing angle of 50∘. In general, CSD outperforms the FRT in estimating fiber orientations.

ABSTRACTUnderstanding how the brain develops, matures, ages, and declines is one of the fundamental questions facing neuroscience. This study uses 3‐tissue constrained spherical deconvolution (3T‐CSD) and more recently developed fixel‐based derivatives to examine the relationship between brain diffusion microstructure and chronological age. These metrics are able to quantify signal fraction measurements at the voxel‐wise level from six different tissue microenvironments found in the brain: extracellular free water, intracellular isotropic, intracellular anisotropic, fiber density and cross‐section, the g‐ratio, and aggregate conduction velocity. This study analyzes the Nathanial Kline Institute's Rockland cohort, a large‐scale community sample of brain MRI data across the lifespan (409 subjects, ages 5–85 years). Microstructural measurements were taken in a number of structures throughout the white matter, subcortical gray matter, and lobar cortical regions while additionally evaluating lateral differences in microstructural measurements. The general trajectory of signal fraction measurements was a positive relationship with age and extracellular signal fraction and g‐ratio, a negative relationship between age and intracellular isotropic signal fraction, fiber density and cross‐section, and conduction velocity, and an inverted U‐shaped trajectory for the intracellular anisotropic signal fraction. In individual sub‐areas, these trends tended to still be present, with some notable exceptions. However, there were large differences in microstructure measurements between individual structures, including significant lateral differences between hemispheres for each of the subcortical gray matter structures and for each of the cortical regions. These results demonstrate that 3T‐CSD and fixel‐based metrics are able to describe age‐related change across the brain and lifespan. By using a healthy population cohort this study can be used as a point of comparison for analysis of microstructure changes in the presence of pathology or with behavior. Finally, the detailed analysis of lateralized ROI results can inform diffusion microstructure studies examining cortical and subcortical regions.

Traumatic brain injury (TBI) has been assessed with diffusion tensor imaging (DTI), a commonly used magnetic resonance imaging (MRI) marker for white matter integrity. However, given that the DTI model only fits a single fiber orientation, results can become confounded in regions of "crossing" white matter fibers. In contrast, constrained spherical deconvolution estimates a fiber orientation distribution directly from high angular resolution diffusion-weighted images. Consequently, constrained spherical deconvolution-based measures, such as apparent fiber density (AFD) and track-weighted imaging (TWI) metrics (including tract density imaging, average pathlength mapping, and mean curvature), may be more sensitive than DTI metrics to white matter injury post-TBI. As such, this study administered the lateral fluid percussion injury (FPI) model of TBI, assessed for changes in AFD and TWI metrics, and compared these results to the DTI metrics, fractional anisotropy (FA), mean diffusivity (MD), radial diffusivity (RD), and axial diffusivity (AD). Rats received either an FPI (n = 11) or sham injury (n = 9) and after a recovery period of 12 weeks underwent MRI. AFD was calculated as described previously and statistical testing was performed using connectivity-based fixel enhancement. TWI and DTI metrics were assessed using voxel-wise nonparametric permutation testing. We found that rats given an FPI had significantly reduced AFD, tract density, average pathlength, and mean curvature when compared to sham-injured rats and significant changes in DTI metrics, including reduced FA and increased MD, RD, and AD. However, the latter DTI metrics identified fewer voxels affected by TBI. Additionally, analysis of AFD with connectivity-based fixel enhancement was the only method that identified damage within the corticospinal tract of rats given an FPI. These results support the use of constrained spherical deconvolution, in conjunction with DTI metrics, to better assess disease progression and treatment post-TBI.

Validation and interpretation of diffusion magnetic resonance imaging (dMRI) requires detailed understanding of the actual microstructure restricting the diffusion of water molecules. In this study, we used serial block-face scanning electron microscopy (SBEM), a three-dimensional electron microscopy (3D-EM) technique, to image seven white and grey matter volumes in the rat brain. SBEM shows excellent contrast of cellular membranes, which are the major components restricting the diffusion of water in tissue. Additionally, we performed 3D structure tensor (3D-ST) analysis on the SBEM volumes and parameterised the resulting orientation distributions using Watson and angular central Gaussian (ACG) probability distributions as well as spherical harmonic (SH) decomposition. We analysed how these parameterisations described the underlying orientation distributions and compared their orientation and dispersion with corresponding parameters from two dMRI methods, neurite orientation dispersion and density imaging (NODDI) and constrained spherical deconvolution (CSD). Watson and ACG parameterisations and SH decomposition captured well the 3D-ST orientation distributions, but ACG and SH better represented the distributions due to its ability to model asymmetric dispersion. The dMRI parameters corresponded well with the 3D-ST parameters in the white matter volumes, but the correspondence was less evident in the more complex grey matter. SBEM imaging and 3D-ST analysis also revealed that the orientation distributions were often not axially symmetric, a property neatly captured by the ACG distribution. Overall, the ability of SBEM to image diffusion barriers in intricate detail, combined with 3D-ST analysis and parameterisation, provides a step forward toward interpreting and validating the dMRI signals in complex brain tissue microstructure.

Background: Structural brain damage, especially to white matter, is well documented in chronic alcohol abuse. There is also evidence for brain metabolic abnormalities in this condition. It is unknown, however, to what extent these structural and metabolic changes are present in treated alcohol abusers who achieve long-term abstinence versus treatment-naïve, heavily drinking individuals. Methods: This study compared 12 recovering alcoholics with 8 actively heavily drinking subjects. Participants underwent magnetic resonance (MR) imaging and proton MR spectroscopic imaging of the brain. Semiautomated image segmentation techniques yielded volumes for gray matter, white matter, white matter lesions, and cerebral spinal fluid in multiple brain regions defined by Talairach stereotaxic coordinates. Automated spectral processing methods yielded gray and white matter concentrations of the metabolites N-acetylaspartate, creatine, and choline for the same regions. Results: Recovering alcoholics had greater volumes of frontal white matter, but the opposite was true for white matter in a “remainder” region encompassing the basal frontal and temporal lobes, the cerebellum, and the brainstem. Recovering alcoholics also had smaller volumes of white matter lesions in whole brain, in occipital and mesial parietal regions, and in the remainder region. Recovering alcoholics had greater gray matter volumes in the orbital frontal pole and postcentral gyrus, but smaller gray matter volumes in the anterior cingulate. Whole-brain and regional metabolite concentrations did not differ significantly between the two groups. Conclusions: White and gray matter volumes in different regions of the brain were greater or smaller in recovering, treated alcoholics. The findings suggest region-specific structural recovery from chronic alcohol–induced brain injury, but also region-specific long-term structural damage in abstinent alcoholics. White matter lesions were widespread in active drinkers and may partly resolve during long-term abstinence. Proton MR spectroscopic measures, as applied in this cross-sectional study, were largely ineffective in revealing metabolic effects of abstinence on the alcohol-damaged brain.

Patients with spina bifida (SB) have variable intellectual outcomes. The authors used diffusion tensor (DT) imaging to quantify whole-brain volumes of gray matter, white matter, and cerebrospinal fluid (CSF), and perform regional quantitative microstructural assessments of gray matter nuclei and white matter tracts in relation to intellectual outcomes in patients with SB. Twenty-nine children with myelomeningoceles and 20 age- and sex-matched children with normal neural tube development underwent MR imaging with DT image acquisition and assessments of intelligence. The DT imaging-derived metrics were the fractional anisotropy (FA), axial (parallel), and transverse (perpendicular) diffusivities. These metrics were also used to segment the brain into white matter, gray matter, and CSF. A region-of-interest analysis was conducted of the white and gray matter structures implicated in hydrocephalus. The amount of whole-brain gray matter was decreased in patients with SB, with a corresponding increase in CSF (p < 0.0001). Regional transverse diffusivity in the caudate nucleus was decreased (p < 0.0001), and the corresponding FA was increased (p < 0.0001), suggesting reduced dendritic branching and connectivity. Fractional anisotropy in the posterior limb of the internal capsule increased in the myelomeningocele group (p = 0.02), suggesting elimination of some divergent fascicles; in contrast, the FA in several white matter structures (such as the corpus callosum genu [p < 0.001] and arcuate fasciculus) was reduced, suggesting disruption of myelination. Diffusion tensor imaging-metrics involving gray matter volume and the caudate nucleus, but not other structures, predicted variations in IQ (r = 0.37-0.50; p < 0.05). Diffusion tensor imaging-derived metrics provide noninvasive neuronal surrogate markers of the pathogenesis of SB and predict variations in general intellectual outcomes in children with this condition.

Structural MRI findings of abnormalities in the prefrontal cortex in schizophrenia and affective disorder have been inconsistent likely due to small, heterogeneous samples, the evaluation of prefrontal gray and white matter combined, and the fact that prefrontal cortex is typically not delineated into separate gyri (e.g., Shenton et al., 2001; Strakowski et al., 2002). We previously reported smaller prefrontal gray matter in first-episode schizophrenia relative to first-episode affective psychosis and controls (Hirayasu et al., 2001). One unresolved question in the literature is whether or not further volume reduction will be observed over time, the focus of this report. Prefrontal gray and white matter volumes were measured (see Fig. 1) in patients at the time of first hospitalization for schizophrenia (n=12, 3 females) or affective psychosis (n=10, 1 female, 9 bipolar, 1 unipolar), and psychiatrically well subjects (n=15, 1 female). Subjects were rescanned approximately 1.5 years later. Seven schizophrenia, six affective, and four comparison subjects were previously described solely at first scan (Hirayasu et al., 2001). Samples did not differ in age (28.1±8.4; 22.9±2.8; 25.4±4.5; F(2,34)=2.2, p=0.12) or WAIS Information scores (11.8±3.4; 12.2±3.1, 11.8±2.0; F(2.32)=0.6, p=0.9), nor in parental socioeconomic status (F(2.34)=2.32, p=0.11) or handedness (F(2.33)=1.6, p=0.22). BPRS scores were higher in schizophrenics (41.2±13.2) than affectives (33.8±8.0) (F(1,20)=5.71, p=0.027). Similar neuroleptics were prescribed for the patient groups (schizophrenics: 7 typical, 4 atypical, 1 none; affectives: 6 typical, 3 atypical, 1 none). Fig. 1 Prefrontal ROI definitions and volumes. (a) Coronal slice, (b) axial slice showing prefrontal gray and white matter, and (c) three. Three-dimensional reconstruction of the extent of gray and white matter boundaries. MR images were acquired with a 1.5-T ... Relative volumes [i.e., absolute volumes divided by intracranial contents (ICC)] were used in the analyses. Repeated-measures ANOVA was performed with diagnosis as the between-subjects factor and time and side as the within-subjects factors for gray and white matter separately. Prefrontal gray matter at time 1 was significantly different among groups (F2,30=5.56, p=0.009), with schizophrenics smaller than controls and affectives, who did not differ from each other. There was no interaction for group by time by side for prefrontal gray matter (F2,34=0.65, p=0.53). All groups showed larger gray matter on the left (F2,30=8.72, p=0.006). White matter volumes did not differ among groups (p>0.87), and all groups showed more white matter on the right (F1,30=39.20, p<0.001) and a reduction over time (F1,30=10.902, p=0.002), there was a trend for this effect to be larger on the right (F1,30=3.14, p=0.086) (%change over time for right white matter: schizophrenics 2.8%; affectives 6.5%; controls 2.1%). Neither removing the unipolar depression subject nor removing the females altered the results. There was no significant correlation between ROI volume change and medication dosage at time 1 for either patient group (Time 2 data came from out patients based on self-report and was for this reason not used). These data suggest that prefrontal cortical gray matter is selectively smaller at first hospitalization for schizophrenia relative to affective psychosis and controls, but this volume difference did not change over the relatively short post-first hospitalization time examined. Small gray matter volumes may be due to reduced dendritic arborization or increased neural density in prefrontal cortex in schizophrenia (Benes et al., 1992; Selemon et al., 1998). White matter, which was not different among groups, showed a decline with time in all groups, possibly consistent with normal aging (Good et al., 2001, although Bartzokis et al., 2001). Potential reasons for our not observing selective gray matter reductions point to several limitations of this study including the gender distribution, as females may have greater dorsolateral and orbitofrontal lobe involvement and males greater dorsomedial changes in schizophrenia (Gur et al., 2000); the use of large ROI, as sub-regions within the prefrontal cortex may change in volume at different rates (Gur et al., 1998; DeLisi et al., 1997); and lack of exact medication dosages and compliance histories during the intrascan interval cannot be ruled out as possible confounds. Although the sample size was small, the effect size was also small (Fig. 1) suggesting that even enlarging the sample would not result in a significant change in volume over time for either gray or white matter.

The brain volume of chronic drinkers is known to partially recover with abstinence from alcohol. To investigate the relative contribution of grey and white brain matter to this process, magnetic resonance imaging and brain tissue segmentation was used to study brain tissue in acute alcohol withdrawal and abstinence in seven alcohol-dependent men. The patients were studied on three occasions; within 48 h after the last drink and approximately one month and two and a half months later. Total brain tissue class volumes [grey matter (GM) and white matter (WM) and cerebrospinal fluid (CSF)] were measured. Eleven healthy volunteers were scanned twice to serve as a control group. The alcohol-dependent patients were investigated with regard to drinking variables, neuropsychological performance and blood biochemistry. In the alcohol-dependent patients, intracranial volume and total GM volume did not change between scan occasions, except in a single patient who demonstrated a GM increase of 4.8% (4.2% relative volume) between scans 2 and 3. For all patients, the increase in total WM volume ranged between 1.9 and 22.4% (absolute volumes) and 2.1 and 21.2% (relative volumes). Between scans 2 and 3, the increase in total WM volume ranged between 0.3 and 13.2% (absolute volumes), and between 1.5 and 14.0% (relative volumes). One patient resumed drinking and was investigated a second time during acute withdrawal. In this patient, the measured decrease of 8.1 and 8.5% of absolute and relative WM volumes corresponded to the size of the volume increase between scans 1 and 2. CSF, GM and WM volumes in the healthy subjects were constant over time. The results demonstrate that changes in brain volume during short-term abstinence in chronic alcohol-dependent patients are confined to the WM. The time limit of WM volume restitution is variable and continues longer than 3 weeks after withdrawal.

Longitudinal changes in gray and white matter microstructure during epileptogenesis in pilocarpine-induced epileptic rats