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Linear least squares estimators are widely used in diffusion MRI for the estimation of diffusion parameters. Although adding proper weights is necessary to increase the precision of these linear estimators, there is no consensus on how to practically define them. In this study, the impact of the commonly used weighting strategies on the accuracy and precision of linear diffusion parameter estimators is evaluated and compared with the nonlinear least squares estimation approach. Simulation and real data experiments were done to study the performance of the weighted linear least squares estimators with weights defined by (a) the squares of the respective noisy diffusion-weighted signals; and (b) the squares of the predicted signals, which are reconstructed from a previous estimate of the diffusion model parameters. The negative effect of weighting strategy (a) on the accuracy of the estimator was surprisingly high. Multi-step weighting strategies yield better performance and, in some cases, even outperformed the nonlinear least squares estimator. If proper weighting strategies are applied, the weighted linear least squares approach shows high performance characteristics in terms of accuracy/precision and may even be preferred over nonlinear estimation methods. •Linear least squares estimators are widely used in diffusion MRI.•Weighting of the linear least squares estimator is needed to improve the precision.•Different weighting strategies are routinely used.•The actual accuracy of linear estimators strongly depends on the weight definition.•The squares of the noisy diffusion-weighted signals should not be used as weights.

Having gained a tremendous amount of popularity since its introduction in 2006, tract-based spatial statistics (TBSS) can now be considered as the standard approach for voxel-based analysis (VBA) of diffusion tensor imaging (DTI) data. Aiming to improve the sensitivity, objectivity, and interpretability of multi-subject DTI studies, TBSS includes a skeletonization step that alleviates residual image misalignment and obviates the need for data smoothing. Although TBSS represents an elegant and user-friendly framework that tackles numerous concerns existing in conventional VBA methods, it has limitations of its own, some of which have already been detailed in recent literature. In this work, we present general methodological considerations on TBSS and report on pitfalls that have not been described previously. In particular, we have identified specific assumptions of TBSS that may not be satisfied under typical conditions. Moreover, we demonstrate that the existence of such violations can severely affect the reliability of TBSS results. With TBSS being used increasingly, it is of paramount importance to acquaint TBSS users with these concerns, such that a well-informed decision can be made as to whether and how to pursue a TBSS analysis. Finally, in addition to raising awareness by providing our new insights, we provide constructive suggestions that could improve the validity and increase the impact of TBSS drastically. •We investigate tract-based spatial statistics (TBSS) considering potential pitfalls.•TBSS is not tract-specific and we show how this may falsify results.•User defined parameters strongly influence the final TBSS-derived results.•We provide suggestions that improve the validity and increase the impact of TBSS.

•We introduce a novel framework to perform spherical deconvolution with multiple anisotropic response functions (mFOD).•We show that the proposed framework can be used to improve the FOD estimation in the cortical gray matter.•Fiber tractography performed with mFOD reaches the cortical GM with more coverage and contiguity than with previous methods.•The proposed framework is a first step towards GM to GM fiber tractography. In diffusion MRI, spherical deconvolution approaches can estimate local white matter (WM) fiber orientation distributions (FOD) which can be used to produce fiber tractography reconstructions. The applicability of spherical deconvolution to gray matter (GM), however, is still limited, despite its critical role as start/endpoint of WM fiber pathways. The advent of multi-shell diffusion MRI data offers additional contrast to model the GM signal but, to date, only isotropic models have been applied to GM. Evidence from both histology and high-resolution diffusion MRI studies suggests a marked anisotropic character of the diffusion process in GM, which could be exploited to improve the description of the cortical organization. In this study, we investigated whether performing spherical deconvolution with tissue specific models of both WM and GM can improve the characterization of the latter while retaining state-of-the-art performances in WM. To this end, we developed a framework able to simultaneously accommodate multiple anisotropic response functions to estimate multiple, tissue-specific, fiber orientation distributions (mFODs). As proof of principle, we used the diffusion kurtosis imaging model to represent the WM signal, and the neurite orientation dispersion and density imaging (NODDI) model to represent the GM signal. The feasibility of the proposed approach is shown with numerical simulations and with data from the Human Connectome Project (HCP). The performance of our method is compared to the current state of the art, multi-shell constrained spherical deconvolution (MSCSD). The simulations show that with our new method we can accurately estimate a mixture of two FODs at SNR≥50. With HCP data, the proposed method was able to reconstruct both tangentially and radially oriented FODs in GM, and performed comparably well to MSCSD in computing FODs in WM. When performing fiber tractography, the trajectories reconstructed with mFODs reached the cortex with more spatial continuity and for a longer distance as compared to MSCSD and allowed to reconstruct short trajectories tangential to the cortical folding. In conclusion, we demonstrated that our proposed method allows to perform spherical deconvolution of multiple anisotropic response functions, specifically improving the performances of spherical deconvolution in GM tissue.

Nonlinearities of gradient magnetic fields in diffusion MRI (dMRI) can introduce systematic errors in estimates of diffusion measures. While there are correction methods that can compensate for these errors, as presented in the Human Connectome Project, such nonlinear effects are often assumed to be negligible for typical applications, and as a result, gradient nonlinearities are mostly left uncorrected. In this work, we perform a systematic analysis to investigate the effect of gradient nonlinearities on dMRI studies, from voxel-wise estimates to group study outcomes. We present a novel framework to quantify and visualize these effects by decomposing them into their magnitude and angle components. Mean magnitude deviation and fractional gradient anisotropy are introduced to quantify the distortions in the size and shape of gradient vector distributions. By means of Monte-Carlo simulations and real data from the Human Connectome Project, the errors on dMRI measures derived from the diffusion tensor imaging and diffusional kurtosis imaging are highlighted. We perform a group study to showcase the alteration in the significance and effect size due to ignoring gradient nonlinearity correction. Our results indicate that the effect of gradient field nonlinearities on dMRI studies can be significant and may complicate the interpretation of the results and conclusions. [Display omitted] •We propose a new framework to quantify gradient nonlinearity artifacts in dMRI.•We analyze the effect of ignoring gradient nonlinearity correction (GNC) in dMRI.•With simulations and real data, we study model sensitivity with respect to GNC.•We showcase the importance of GNC in the context of a dMRI group study.

Diffusion-weighted (DW) magnetic resonance imaging (MRI) is a unique method to investigate microstructural tissue properties noninvasively and is one of the most popular methods for studying the brain white matter in vivo. To obtain reliable statistical inferences with diffusion MRI, however, there are still many challenges, such as acquiring high-quality DW-MRI data (e.g., high SNR and high resolution), careful data preprocessing (e.g., correcting for subject motion and eddy current induced geometric distortions), choosing the appropriate diffusion approach (e.g., diffusion tensor imaging (DTI), diffusion kurtosis imaging (DKI), or diffusion spectrum MRI), and applying a robust analysis strategy (e.g., tractography based or voxel based analysis). Notwithstanding the numerous efforts to optimize many steps in this complex and lengthy diffusion analysis pipeline, to date, a well-known artifact in MRI – i.e., Gibbs ringing (GR) – has largely gone unnoticed or deemed insignificant as a potential confound in quantitative DW-MRI analysis. Considering the recent explosion of diffusion MRI applications in biomedical and clinical applications, a systematic and comprehensive investigation is necessary to understand the influence of GR on the estimation of diffusion measures. In this work, we demonstrate with simulations and experimental DW-MRI data that diffusion estimates are significantly affected by GR artifacts and we show that an off-the-shelf GR correction procedure based on total variation already can alleviate this issue substantially. [Display omitted] •We propose a method to identify Gibbs Ringing (GR) artifacts in diffusion MRI data.•We quantify the error introduced by GR artifacts in diffusion estimates.•We optimize a standard GR correction procedure to deal with GR artifacts in real data.

In diffusion tensor magnetic resonance imaging (DT-MRI), limitations concerning complex fiber architecture (when an image voxel contains fiber populations with more than one dominant orientation) are well-known. Fractional anisotropy (FA) values are lower in such areas because of a lower directionality of diffusion on the voxel-scale, which makes the interpretation of FA less straightforward. Moreover, the interpretation of the axial and radial diffusivities is far from trivial when there is more than one dominant fiber orientation within a voxel. In this work, using (i) theoretical considerations, (ii) simulations, and (iii) experimental data, it is demonstrated that the mean diffusivity (or the trace of the diffusion tensor) is lower in complex white matter configurations, compared with tissue where there is a single dominant fiber orientation within the voxel. We show that the magnitude of this reduction depends on various factors, including configurational and microstructural properties (e.g., the relative contributions of different fiber populations) and acquisition settings (e.g., the b-value). These results increase our understanding of the quantitative metrics obtained from DT-MRI and, in particular, the effect of the microstructural architecture on the mean diffusivity. More importantly, they reinforce the growing awareness that differences in DT-MRI metrics need to be interpreted cautiously. ► The mean diffusivity (MD) in diffusion tensor MRI is affected by crossing fibers. ► MD values are lower in complex fiber architecture than in single fiber voxels. ► This is shown using theoretical considerations, simulations and in vivo experiments. ► In vivo, mean diffusivity values decrease when fibers cross at larger angles.

Spherical deconvolution is a widely used approach to quantify the fiber orientation distribution (FOD) from diffusion MRI data of the brain. The damped Richardson-Lucy (dRL) is an algorithm developed to perform robust spherical deconvolution on single-shell diffusion MRI data while suppressing spurious FOD peaks due to noise or partial volume effects. Due to recent progress in acquisition hardware and scanning protocols, it is becoming increasingly common to acquire multi-shell diffusion MRI data, which allows for the modelling of multiple tissue types beyond white matter. While the dRL algorithm could, in theory, be directly applied to multi-shell data, it is not optimised to exploit its information content to model the signal from multiple tissue types. In this work, we introduce a new framework based on dRL – dubbed generalized Richardson-Lucy (GRL) – that uses multi-shell data in combination with user-chosen tissue models to disentangle partial volume effects and increase the accuracy in FOD estimation. Further, GRL estimates signal fraction maps associated to each user-selected model, which can be used during fiber tractography to dissect and terminate the tracking without need for additional structural data. The optimal weighting of multi-shell data in the fit and the robustness to noise and to partial volume effects of GRL was studied with synthetic data. Subsequently, we investigated the performance of GRL in comparison to dRL and to multi-shell constrained spherical deconvolution (MSCSD) on a high-resolution diffusion MRI dataset from the Human Connectome Project and on an MRI dataset acquired at 3T on a clinical scanner. In line with previous studies, we described the signal of the cerebrospinal-fluid and of the grey matter with isotropic diffusion models, whereas four diffusion models were considered to describe the white matter. With a third dataset including small diffusion weightings, we studied the feasibility of including intra-voxel incoherent motion effects due to blood pseudo-diffusion in the modelling. Further, the reliability of GRL was demonstrated with a test-retest scan of a subject acquired at 3T. Results of simulations show that GRL can robustly disentangle different tissue types at SNR above 20 with respect to the non-weighted image, and that it improves the angular accuracy of the FOD estimation as compared to dRL. On real data, GRL provides signal fraction maps that are physiologically plausible and consistent with those obtained with MSCSD, with correlation coefficients between the two methods up to 0.96. When considering IVIM effects, a high blood pseudo-diffusion fraction is observed in the medial temporal lobe and in the sagittal sinus. In comparison to dRL and MSCSD, GRL provided sharper FODs and less spurious peaks in presence of partial volume effects, but the FOD reconstructions are also highly dependent on the chosen modelling of white matter. When performing fiber tractography, GRL allows to terminate fiber tractography using the signal fraction maps, which results in a better tract termination at the grey-white matter interface or at the outer cortical surface. In terms of inter-scan reliability, GRL performed similarly to or better than compared methods. In conclusion, GRL offers a new modular and flexible framework to perform spherical deconvolution of multi-shell data. •A generalized Richardson-Lucy (GRL) method to leverage multi-shell diffusion MRI data.•GRL improves the quality of the WM FOD estimation.•GRL can fit diffusion signals with models of choice – including DTI, DKI and NODDI.•GRL disentangle partial volume effects of WM with GM, CSF and others like IVIM.•GRL uses the signal fraction estimates to terminate the fiber tractography.

Repetitive transcranial magnetic stimulation (rTMS) is an established treatment for major depressive disorder (MDD), but its clinical efficacy remains rather modest. One reason for this could be that the propagation of rTMS effects via structural connections from the stimulated area to deeper brain structures (such as the cingulate cortices) is suboptimal. We investigated whether structural connectivity — derived from diffusion MRI data — could serve as a biomarker to predict treatment response. We hypothesized that stronger structural connections between the patient-specific stimulation position in the left dorsolateral prefrontal cortex (dlPFC) and the cingulate cortices would predict better clinical outcomes. We applied accelerated intermittent theta burst stimulation (aiTBS) to the left dlPFC in 40 patients with MDD. We correlated baseline structural connectivity, quantified using various metrics (fractional anisotropy, mean diffusivity, tract density, tract volume and number of tracts), with changes in depression severity scores after aiTBS. Exploratory results (p < 0.05) showed that structural connectivity between the patient-specific stimulation site and the caudal and posterior parts of the cingulate cortex had predictive potential for clinical response to aiTBS. We used the diffusion tensor to perform tractography. A main limitation was that multiple fibre directions within voxels could not be resolved, which might have led to missing connections in some patients. Stronger structural frontocingular connections may be of essence to optimally benefit from left dlPFC rTMS treatment in MDD. Even though the results are promising, further investigation with larger numbers of patients, more advanced tractography algorithms and classic daily rTMS treatment paradigms is warranted. http://clinicaltrials.gov/show/NCT01832805

Previous research using functional MRI identified brain regions associated with sensory processing sensitivity (SPS), a proposed normal phenotype trait. To further validate SPS, to characterize it anatomically, and to test the usefulness in psychology of methodologies that assess axonal properties, the present study correlated SPS proxy questionnaire scores (adjusted for neuroticism) with diffusion tensor imaging (DTI) measures. Participants (n = 408) from the Human Connectome Project were studied. Voxelwise analysis showed that mean- and radial diffusivity correlated positively with SPS scores in the right and left subcallosal and anterior–ventral cingulum bundle, and the right forceps minor of the corpus callosum, all frontal cortex areas generally underlying emotion, motivation, and cognition. Further analyses showed correlations throughout medial frontal cortical regions in the right and left ventromedial prefrontal cortex, including the superior longitudinal fasciculus, inferior fronto-occipital fasciculus, uncinate, and arcuate fasciculus. Fractional anisotropy was negatively correlated with SPS scores in white matter (WM) of the right premotor/motor/somatosensory/supramarginal gyrus regions. Region of interest (ROI) analysis showed small effect sizes (− 0.165 to 0.148) in WM of the precuneus and inferior frontal gyrus. Other ROI effects were found in the dorsal-, ventral visual pathways and primary auditory cortex. The results reveal that in a large group of participants, axonal microarchitectural differences can be identified with SPS traits that are subtle and in the range of typical behavior. The results suggest that the heightened sensory processing in people who show that SPS may be influenced by the microstructure of WM in specific cortical regions. Although previous fMRI studies had identified most of these areas, the DTI results put a new focus on brain areas related to attention and cognitive flexibility, empathy, emotion, and first levels of sensory processing, as in primary auditory cortex. Psychological trait characterization may benefit from DTI methodology by identifying influential brain systems for traits.

Quantification methods based on the acquisition of diffusion magnetic resonance imaging (dMRI) with multiple diffusion weightings (e.g., multi-shell) are becoming increasingly applied to study the in-vivo brain. Compared to single-shell data for diffusion tensor imaging (DTI), multi-shell data allows to apply more complex models such as diffusion kurtosis imaging (DKI), which attempts to capture both diffusion hindrance and restriction effects, or biophysical models such as NODDI, which attempt to increase specificity by separating biophysical components. Because of the strong dependence of the dMRI signal on the measurement hardware, DKI and NODDI metrics show scanner and site differences, much like other dMRI metrics. These effects limit the implementation of multi-shell approaches in multicenter studies, which are needed to collect large sample sizes for robust analyses. Recently, a post-processing technique based on rotation invariant spherical harmonics (RISH) features was introduced to mitigate cross-scanner differences in DTI metrics. Unlike statistical harmonization methods, which require repeated application to every dMRI metric of choice, RISH harmonization is applied once on the raw data, and can be followed by any analysis. RISH features harmonization has been tested on DTI features but not its generalizability to harmonize multi-shell dMRI. In this work, we investigated whether performing the RISH features harmonization of multi-shell dMRI data removes cross-site differences in DKI and NODDI metrics while retaining longitudinal effects. To this end, 46 subjects underwent a longitudinal (up to 3 time points) two-shell dMRI protocol at 3 imaging sites. DKI and NODDI metrics were derived before and after harmonization and compared both at the whole brain level and at the voxel level. Then, the harmonization effects on cross-sectional and on longitudinal group differences were evaluated. RISH features averaged for each of the 3 sites exhibited prominent between-site differences in the frontal and posterior part of the brain. Statistically significant differences in fractional anisotropy, mean diffusivity and mean kurtosis were observed both at the whole brain and voxel level between all the acquisition sites before harmonization, but not after. The RISH method also proved effective to harmonize NODDI metrics, particularly in white matter. The RISH based harmonization maintained the magnitude and variance of longitudinal changes as compared to the non-harmonized data of all considered metrics. In conclusion, the application of RISH feature based harmonization to multi-shell dMRI data can be used to remove cross-site differences in DKI metrics and NODDI analyses, while retaining inherent relations between longitudinal acquisitions.