Constrained spherical deconvolution of nonspherically sampled diffusion MRI data

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

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.

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) 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.

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.

Diffusion weighted magnetic resonance imaging (DW-MRI) captures tissue microarchitecture at millimeter scale. With recent advantages in data sharing, large-scale multi-site DW-MRI datasets are being made available for multi-site studies. However, DW-MRI suffers from measurement variability (e.g., inter- and intra-site variability, hardware performance, and sequence design), which consequently yields inferior performance on multi-site and/or longitudinal diffusion studies. In this study, we propose a novel, deep learning-based method to harmonize DW-MRI signals for a more reproducible and robust estimation of microstructure. Our method introduces a data-driven scanner-invariant regularization scheme to model a more robust fiber orientation distribution function (FODF) estimation. We study the Human Connectome Project (HCP) young adults test-retest group as well as the MASiVar dataset (with inter- and intra-site scan/rescan data). The 8th order spherical harmonics coefficients are employed as data representation. The results show that the proposed harmonization approach maintains higher angular correlation coefficients (ACC) with the ground truth signals (0.954 versus 0.942), while achieves higher consistency of FODF signals for intra-scanner data (0.891 versus 0.826), as compared with the baseline supervised deep learning scheme. Furthermore, the proposed data-driven framework is flexible and potentially applicable to a wider range of data harmonization problems in neuroimaging.

We present a novel neural network-based method for analyzing intra-voxel structures, addressing critical challenges in diffusion-weighted MRI analysis for brain connectivity and development studies. The network architecture, called the Local Neighborhood Neural Network, is designed to use the spatial correlations of neighboring voxels for an enhanced inference while reducing parameter overhead. Our model exploits these relationships to improve the analysis of complex structures and noisy data environments. We adopt a self-supervised approach to address the lack of ground truth data, generating signals of voxel neighborhoods to integrate the training set. This eliminates the need for manual annotations and facilitates training under realistic conditions. Comparative analyses show that our method outperforms the constrained spherical deconvolution (CSD) method in quantitative and qualitative validations. Using phantom images that mimic in vivo data, our approach improves angular error, volume fraction estimation accuracy, and success rate. Furthermore, a qualitative comparison of the results in actual data shows a better spatial consistency of the proposed method in areas of real brain images. This approach demonstrates enhanced intra-voxel structure analysis capabilities and holds promise for broader application in various imaging scenarios.

Structural connectomics derives subject-specific brain connectivity from diffusion-weighted MRI and has potential as a biomarker for clinical Parkinson's disease (PD) detection. In this study, we applied probabilistic tractography (iFOD2) to derive different types of connectomes and analyzed group discriminability between PD patients and healthy controls from the Parkinson's Progression Markers Initiative (PPMI) dataset (n = 233). Particular emphasis was placed on the streamline filtering stage with SIFT2 and the comparison of different connectivity metrics, including streamline count, fractional anisotropy (FA), axial diffusivity (AD), mean diffusivity (MD), and radial diffusivity (RD). We performed a three-level analysis comprising (1) connection-level statistical analysis, (2) graph theory measures at the node and whole-brain levels, and (3) classification using support vector machines (SVM) and graph neural networks. We did not find any statistical difference at any level after correction for multiple comparisons. Also, the classifiers performed poorly with AUC values close to chance levels. However, we found differences between filtered and unfiltered tractograms at the node level. Our findings suggest that structural connectivity analyses for PD are highly sensitive to specific pipeline configurations and fine-tuning.

Abstract. Computerized ionospheric tomography (CIT) is a technique that allows reconstructing the state of the ionosphere in terms of electron content from a set of slant total electron content (STEC) measurements. It is usually denoted as an inverse problem. In this experiment, the measurements are considered coming from the phase of the GPS signal and, therefore, affected by bias. For this reason the STEC cannot be considered in absolute terms but rather in relative terms. Measurements are collected from receivers not evenly distributed in space and together with limitations such as angle and density of the observations, they are the cause of instability in the operation of inversion. Furthermore, the ionosphere is a dynamic medium whose processes are continuously changing in time and space. This can affect CIT by limiting the accuracy in resolving structures and the processes that describe the ionosphere. Some inversion techniques are based on ℓ2 minimization algorithms (i.e. Tikhonov regularization) and a standard approach is implemented here using spherical harmonics as a reference to compare the new method. A new approach is proposed for CIT that aims to permit sparsity in the reconstruction coefficients by using wavelet basis functions. It is based on the ℓ1 minimization technique and wavelet basis functions due to their properties of compact representation. The ℓ1 minimization is selected because it can optimize the result with an uneven distribution of observations by exploiting the localization property of wavelets. Also illustrated is how the inter-frequency biases on the STEC are calibrated within the operation of inversion, and this is used as a way for evaluating the accuracy of the method. The technique is demonstrated using a simulation, showing the advantage of ℓ1 minimization to estimate the coefficients over the ℓ2 minimization. This is in particular true for an uneven observation geometry and especially for multi-resolution CIT.

To provide an improved correction for gradient nonlinearity (GN) effects in diffusion-weighted imaging (DWI). These effects produce spatially varying apparent diffusion coefficient (ADC), a result that will be significant in large field-of-view imaging, and may be confounded by distortion and concomitant fields related to the DWI acquisition. The effect of more accurate gradient field maps on GN correction (GNC) of ADC was evaluated. A simulation compared GN effects in commonly imaged anatomy. A temperature-controlled phantom was imaged at positions 0 cm and 11 cm from isocenter and in two whole-body MRI systems at 1.5T with different patient bore diameters (55 cm and 60 cm). Varying correction methods were applied to determine the errors from spatial variance and interscanner reproducibility. As compared to conventional fifth-order spherical harmonics, a seventh-order GNC improved ADC accuracy by 1%. The combination of GNC with a dual-spin-echo pulse sequence and a retrospective concomitant field correction reduced ADC error due to spatial variance from 9.5% to 1.8% (55 cm bore) and from 4.2% to 1.8% (60 cm bore). The error in ADC attributed to interscanner reproducibility was reduced from 5.8% to 0.15% (at isocenter) and from 10% to 0.63% (11 cm from isocenter). GNC in DWI improved spatial accuracy and interscanner reproducibility of ADC.

Fatigue and cognitive complaints are the most frequent persistent symptoms in patients after severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) infection. This study aimed to assess fatigue and neuropsychological performance and investigate changes in the thickness and volume of gray matter (GM) and microstructural abnormalities in the white matter (WM) in a group of patients with mild-to-moderate coronavirus disease 2019 (COVID-19). We studied 56 COVID-19 patients and 37 matched controls using magnetic resonance imaging (MRI). Cognition was assessed using Montreal Cognitive Assessment and Cambridge Neuropsychological Test Automated Battery, and fatigue was assessed using Chalder Fatigue Scale (CFQ-11). T1-weighted MRI was used to assess GM thickness and volume. Fiber-specific apparent fiber density (FD), free water index, and diffusion tensor imaging data were extracted using diffusion-weighted MRI (d-MRI). d-MRI data were correlated with clinical and cognitive measures using partial correlations and general linear modeling. COVID-19 patients had mild-to-moderate acute illness (95% non-hospitalized). The average period between real-time quantitative reverse transcription polymerase chain reaction-based diagnosis and clinical/MRI assessments was 93.3 (±26.4) days. The COVID-19 group had higher total CFQ-11 scores than the control group (p < 0.001). There were no differences in neuropsychological performance between groups. The COVID-19 group had lower FD in the association, projection, and commissural tracts, but no change in GM. The corona radiata, corticospinal tract, corpus callosum, arcuate fasciculus, cingulate, fornix, inferior fronto-occipital fasciculus, inferior longitudinal fasciculus, superior longitudinal fasciculus, and uncinate fasciculus were involved. CFQ-11 scores, performance in reaction time, and visual memory tests correlated with microstructural changes in patients with COVID-19. Quantitative d-MRI detected changes in the WM microstructure of patients recovering from COVID-19. This study suggests a possible brain substrate underlying the symptoms caused by SARS-CoV-2 during medium- to long-term recovery.

We analyse a discretisation method for solving (systems of) semilinear parabolic equations on Euclidean spheres. The approximation method is based upon a discretisation in space using spherical basis functions and can hence be of arbitrary order in space, provided that the true solution is sufficiently smooth, which is, at least locally in time, true for semilinear parabolic problems. We rigorously prove stability and convergence of the semi-discrete approximation, if basis functions with a prescribed Sobolev regularity are employed. For discretisation in time, we give two examples and prove the expected convergence orders in space and time for the fully discretised system.

We open this chapter by establishing the basic notation that will be used regularly throughout the book. We then provide some motivation behind what we aim to achieve in this book, namely to develop the theory and explore the applications of spherical basis functions (SBFs).

Characterization and correlation of signal drift in diffusion weighted MRI

High angular resolution diffusion imaging (HARDI) methods have enabled the reconstruction of complex spin diffusion profiles in central nervous system white matter through diffusion-weighted MRI. For recovery of the underlying fiber orientations, conventional spherical deconvolution techniques based on spherical harmonics typically have difficulty producing fiber orientation distributions (FODs) that simultaneously satisfy the physical constraints of being real, symmetric, and non-negative. In this work, we propose a novel approach for HARDI reconstruction that is guaranteed to generate FODs satisfying these constraints. By using a meshed representation of the unit sphere, we formulate the spherical deconvolution as a convex optimization problem and compute the solution using a projected gradient descent algorithm. Flexible regularization is also included in our method to allow for tuning the sharpness of the reconstructed FOD. In our experiments, we present simulated results to examine the effects of varying the regularization parameters, and we illustrate the robustness of our method by applying it to several biological data sets to reconstruct known white matter fiber geometry.