Widespread intra-axonal signal fraction abnormalities in bipolar disorder from multicompartment diffusion MRI: Sensitivity to diagnosis, association with clinical features and pharmacologic treatment.

Despite diffusion tensor imaging (DTI) evidence for widespread fractional anisotropy (FA) reductions in the brain white matter of patients with bipolar disorder, questions remain regarding the specificity and sensitivity of FA abnormalities as opposed to other diffusion metrics in the disorder. We conducted a whole-brain voxel-based multicompartment diffusion MRI study on 316 participants (i.e., 158 patients and 158 matched healthy controls) employing four diffusion metrics: the mean diffusivity (MD) and FA estimated from DTI, and the intra-axonal signal fraction (IASF) and microscopic axonal parallel diffusivity (Dpar) derived from the spherical mean technique. Our findings provide novel evidence about widespread abnormalities in other diffusion metrics in BD. An extensive overlap between the FA and IASF results suggests that the lower FA in patients may be caused by a reduced intra-axonal volume fraction or a higher macromolecular content in the intra-axonal water. We also found a diffuse alteration in MD involving white and grey matter tissue and more localised changes in Dpar. A Machine Learning analysis revealed that FA, followed by IASF, were the most helpful metric for the automatic diagnosis of BD patients, reaching an accuracy of 72%. Number of mood episodes, age of onset/duration of illness, psychotic symptoms, and current treatment with lithium, antipsychotics, antidepressants, and antiepileptics were all significantly associated with microstructure abnormalities. Lithium treatment was associated with less microstructure abnormality.

Text as signal. A tutorial with case studies focusing on social media (Twitter).

Sentiment analysis is the automated coding of emotions expressed in text. Sentiment analysis and other types of analyses focusing on the automatic coding of textual documents are increasingly popular in psychology and computer science. However, the potential of treating automatically coded text collected with regular sampling intervals as a signal is currently overlooked. We use the phrase "text as signal" to refer to the application of signal processing techniques to coded textual documents sampled with regularity. In order to illustrate the potential of treating text as signal, we introduce the reader to a variety of such techniques in a tutorial with two case studies in the realm of social media analysis. First, we apply finite response impulse filtering to emotion-coded tweets posted during the US Election Week of 2020 and discuss the visualization of the resulting variation in the filtered signal. We use changepoint detection to highlight the important changes in the emotional signals. Then we examine data interpolation, analysis of periodicity via the fast Fourier transform (FFT), and FFT filtering to personal value-coded tweets from November 2019 to October 2020 and link the variation in the filtered signal to some of the epoch-defining events occurring during this period. Finally, we use block bootstrapping to estimate the variability/uncertainty in the resulting filtered signals. After working through the tutorial, the readers will understand the basics of signal processing to analyze regularly sampled coded text.

Data-driven myelin water imaging based on T1 and T2 relaxometry.

Long acquisition times preclude the application of multiecho spin echo (MESE) sequences for myelin water fraction (MWF) mapping in daily clinical practice. In search of alternative methods, previous studies of interest explored the biophysical modeling of MWF from measurements of different tissue properties that can be obtained in scan times shorter than those required for the MESE. In this work, a novel data-driven estimation of MWF maps from fast relaxometry measurements is proposed and investigated. T1 and T2 relaxometry maps were acquired in a cohort of 20 healthy subjects along with a conventional MESE sequence. Whole-brain quantitative mapping was achieved with a fast protocol in 6 min 24 s. Reference MWF maps were derived from the MESE sequence (TA = 11 min 17 s) and their data-driven estimation from relaxometry measurements was investigated using three different modeling strategies: two general linear models (GLMs) with linear and quadratic regressors, respectively; a random forest regression model; and two deep neural network architectures, a U-Net and a conditional generative adversarial network (cGAN). Models were validated using a 10-fold crossvalidation. The resulting maps were visually and quantitatively compared by computing the root mean squared error (RMSE) between the estimated and reference MWF maps, the intraclass correlation coefficients (ICCs) between corresponding MWF values in different brain regions, and by performing Bland-Altman analysis. Qualitatively, the estimated maps appear to generally provide a similar, yet more blurred MWF contrast in comparison with the reference, with the cGAN model best capturing MWF variabilities in small structures. By estimating the average adjusted coefficient of determination of the GLM with quadratic regressors, we showed that 87% of the variability in the MWF values can be explained by relaxation times alone. Further quantitative analysis showed an average RMSE smaller than 0.1% for all methods. The ICC was greater than 0.81 for all methods, and the bias smaller than 2.19%. It was concluded that this work confirms the notion that relaxometry parameters contain a large part of the information on myelin water and that MWF maps can be generated from T1 /T2 data with minimal error. Among the investigated modeling approaches, the cGAN provided maps with the best trade-off between accuracy and blurriness. Fast relaxometry, like the 6 min 24 s whole-brain protocol used in this work in conjunction with machine learning, may thus have the potential to replace time-consuming MESE acquisitions.

Revisiting the T2 spectrum imaging inverse problem: Bayesian regularized non-negative least squares.

Multi-echo T2 magnetic resonance images contain information about the distribution of T2 relaxation times of compartmentalized water, from which we can estimate relevant brain tissue properties such as the myelin water fraction (MWF). Regularized non-negative least squares (NNLS) is the tool of choice for estimating non-parametric T2 spectra. However, the estimation is ill-conditioned, sensitive to noise, and highly affected by the employed regularization weight. The purpose of this study is threefold: first, we want to underline that the apparently innocuous use of two alternative parameterizations for solving the inverse problem, which we called the standard and alternative regularization forms, leads to different solutions; second, to assess the performance of both parameterizations; and third, to propose a new Bayesian regularized NNLS method (BayesReg). The performance of BayesReg was compared with that of two conventional approaches (L-curve and Chi-square (X2) fitting) using both regularization forms. We generated a large dataset of synthetic data, acquired in vivo human brain data in healthy participants for conducting a scan-rescan analysis, and correlated the myelin content derived from histology with the MWF estimated from ex vivo data. Results from synthetic data indicate that BayesReg provides accurate MWF estimates, comparable to those from L-curve and X2, and with better overall stability across a wider signal-to-noise range. Notably, we obtained superior results by using the alternative regularization form. The correlations reported in this study are higher than those reported in previous studies employing the same ex vivo and histological data. In human brain data, the estimated maps from L-curve and BayesReg were more reproducible. However, the T2 spectra produced by BayesReg were less affected by over-smoothing than those from L-curve. These findings suggest that BayesReg is a good alternative for estimating T2 distributions and MWF maps.

Fast and high-resolution myelin water imaging: Accelerating multi-echo GRASE with CAIPIRINHA.

PURPOSE: Although several MRI methods have been explored to achieve in vivo myelin quantification, imaging the whole brain in clinically acceptable times and sufficiently high resolution remains challenging. To address this problem, this work investigates the acceleration of multi-echo T2 acquisitions based on the multi-echo gradient and spin echo (GRASE) sequence using CAIPIRINHA undersampling and adapted k-space reordering patterns. METHODS: A prototype multi-echo GRASE sequence supporting CAIPIRINHA parallel imaging was implemented. Multi-echo T2 data were acquired from 12 volunteers using the implemented sequence (1.6 × 1.6 × 1.6 mm3 , 84 slices, acquisition time [TA] = 10:30 min) and a multi-echo spin echo (MESE) sequence as reference (1.6 × 1.6 × 3.2 mm3 , single-slice, TA = 5:41 min). Myelin water fraction (MWF) maps derived from both acquisitions were compared via correlation and Bland-Altman analyses. In addition, scan-rescan datasets were acquired to evaluate the repeatability of the derived maps. RESULTS: Resulting maps from the MESE and multi-echo GRASE sequences were found to be correlated (r = 0.83). The Bland-Altman analysis revealed a mean bias of -0.2% (P = .24) with the limits of agreement ranging from -3.7% to 3.3%. The Pearson's correlation coefficient among MWF values obtained from the scan-rescan datasets was found to be 0.95 and the mean bias equal to 0.11% (P = .32), indicating good repeatability of the retrieved maps. CONCLUSION: By combining a 3D multi-echo GRASE sequence with CAIPIRINHA sampling, whole-brain MWF maps were obtained in 10:30 min with 1.6 mm isotropic resolution. The good correlation with conventional MESE-based maps demonstrates that the implemented sequence may be a promising alternative to time-consuming MESE acquisitions.

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.

Validity of modulation and optimal settings for advanced voxel-based morphometry.

Voxel-based morphometry (VBM) is a widely-used structural neuroimaging technique for comparing meso- and macroscopic regional brain volumes between patients and controls in vivo, but some of its steps, particularly the modulation, lack an experimental validation. The aims of this study were two-fold: a) to assess the effects of modulation to detect mesoscopic (i.e. between microscopic and macroscopic) abnormalities on published, classic VBM; and b) to suggest a set of potentially optimal settings for detecting mesoscopic abnormalities with new, advanced, high-resolution diffeomorphic VBM normalization algorithms. Sensitivity and false positive rate after modulating or not in classic VBM using different software packages and spatial statistics, and after setting a range of different parameters in advanced VBM (ANTS-SyN), were calculated in 10 VBM comparisons of 32 altered vs. 32 unaltered gray matter images from different healthy controls. Simulated brain abnormalities comprised mesoscopic volume differences mainly due to cortical thinning. In classic VBM, modulation was associated with a substantial decrease of the sensitivity to detect mesoscopic abnormalities (p<0.001). Optimal settings for advanced VBM included the omission of modulation, the use of large smoothing kernels, and the application of voxel-based or threshold-free cluster enhancement (TFCE) spatial statistics. The modulation-related decrease in sensitivity was due to an increase in variance, and it was more severe in higher-resolution normalization algorithms. Findings from this study suggest the use of unmodulated VBM to detect mesoscopic abnormalities such as cortical thinning.

NRN1 epistasis with BDNF and CACNA1C: mediation effects on symptom severity through neuroanatomical changes in schizophrenia.

The expression of Neuritin-1 (NRN1), a neurotrophic factor crucial for neurodevelopment and synaptic plasticity, is enhanced by the Brain Derived Neurotrophic Factor (BDNF). Although the receptor of NRN1 remains unclear, it is suggested that NRN1's activation of the insulin receptor (IR) pathway promotes the transcription of the calcium voltage-gated channel subunit alpha1 C (CACNA1C). These three genes have been independently associated with schizophrenia (SZ) risk, symptomatology, and brain differences. However, research on how they synergistically modulate these phenotypes is scarce. We aimed to study whether the genetic epistasis between these genes affects the risk and clinical presentation of the disorder via its effect on brain structure. First, we tested the epistatic effect of NRN1 and BDNF or CACNA1C on (i) the risk for SZ, (ii) clinical symptoms severity and functionality (onset, PANSS, CGI and GAF), and (iii) brain cortical structure (thickness, surface area and volume measures estimated using FreeSurfer) in a sample of 86 SZ patients and 89 healthy subjects. Second, we explored whether those brain clusters influenced by epistatic effects mediate the clinical profiles. Although we did not find a direct epistatic impact on the risk, our data unveiled significant effects on the disorder's clinical presentation. Specifically, the NRN1-rs10484320 x BDNF-rs6265 interplay influenced PANSS general psychopathology, and the NRN1-rs4960155 x CACNA1C-rs1006737 interaction affected GAF scores. Moreover, several interactions between NRN1 SNPs and BDNF-rs6265 significantly influenced the surface area and cortical volume of the frontal, parietal, and temporal brain regions within patients. The NRN1-rs10484320 x BDNF-rs6265 epistasis in the left lateral orbitofrontal cortex fully mediated the effect on PANSS general psychopathology. Our study not only adds clinical significance to the well-described molecular relationship between NRN1 and BDNF but also underscores the utility of deconstructing SZ into biologically validated brain-imaging markers to explore their mediation role in the path from genetics to complex clinical manifestation.

Statistical analysis of brain tissue images in the wavelet domain: wavelet-based morphometry.

Wavelet-based methods have been developed for statistical analysis of functional MRI and PET data, where the wavelet transformation is employed as a tool for efficient signal representation. A number of studies using these approaches have reported better estimation capabilities, in terms of increased sensitivity and specificity, than the standard statistical analyses in the spatial domain. In line with these previous studies, the present report proposes a statistical analysis in the wavelet domain for the estimation of inter-group differences from structural MRI data. The procedure, called wavelet-based morphometry (WBM), was implemented under a voxel-based morphometry (VBM) style analysis. It was evaluated by comparing the gray-matter images of a group of 32 healthy subjects whose images were artificially altered to induce thinning of the cortex, with a different group of 32 healthy subjects whose images were unaltered. In order to quantify the performance of the reconstruction from a practical perspective, the same comparison was also conducted with standard VBM using SPM's Gaussian random fields and FSL's cluster-based statistics, family-wise error corrected, for datasets spatially-normalized via two different registration methods (i.e., SyN and FNIRT). The effect of using different amounts of smoothing, Battle-Lemarié filters and resolution levels in the wavelet transform was also investigated. Results support the proposed approach as a different and promising methodology to assess the structural morphometric differences between different populations of subjects.

Axial and radial axonal diffusivities and radii from single encoding strongly diffusion-weighted MRI.

We enable the estimation of the per-axon axial diffusivity from single encoding, strongly diffusion-weighted, pulsed gradient spin echo data. Additionally, we improve the estimation of the per-axon radial diffusivity compared to estimates based on spherical averaging. The use of strong diffusion weightings in magnetic resonance imaging (MRI) allows to approximate the signal in white matter as the sum of the contributions from only axons. At the same time, spherical averaging leads to a major simplification of the modeling by removing the need to explicitly account for the unknown distribution of axonal orientations. However, the spherically averaged signal acquired at strong diffusion weightings is not sensitive to the axial diffusivity, which cannot therefore be estimated although needed for modeling axons - especially in the context of multi-compartmental modeling. We introduce a new general method for the estimation of both the axial and radial axonal diffusivities at strong diffusion weightings based on kernel zonal modeling. The method could lead to estimates that are free from partial volume bias with gray matter or other isotropic compartments. The method is tested on publicly available data from the MGH Adult Diffusion Human Connectome project. We report reference values of axonal diffusivities based on 34 subjects, and derive estimates of axonal radii from only two shells. The estimation problem is also addressed from the angle of the required data preprocessing, the presence of biases related to modeling assumptions, current limitations, and future possibilities.

Improved estimation of the risk of manic relapse by combining clinical and brain scan data.

INTRODUCTION: Estimating the risk of manic relapse could help the psychiatrist individually adjust the treatment to the risk. Some authors have attempted to estimate this risk from baseline clinical data. Still, no studies have assessed whether the estimation could improve by adding structural magnetic resonance imaging (MRI) data. We aimed to evaluate it. MATERIAL AND METHODS: We followed a cohort of 78 patients with a manic episode without mixed symptoms (bipolar type I or schizoaffective disorder) at 2-4-6-9-12-15-18 months and up to 10 years. Within a cross-validation scheme, we created and evaluated a Cox lasso model to estimate the risk of manic relapse using both clinical and MRI data. RESULTS: The model successfully estimated the risk of manic relapse (Cox regression of the time to relapse as a function of the estimated risk: hazard ratio (HR)=2.35, p=0.027; area under the curve (AUC)=0.65, expected calibration error (ECE)<0.2). The most relevant variables included in the model were the diagnosis of schizoaffective disorder, poor impulse control, unusual thought content, and cerebellum volume decrease. The estimations were poorer when we used clinical or MRI data separately. CONCLUSION: Combining clinical and MRI data may improve the risk of manic relapse estimation after a manic episode. We provide a website that estimates the risk according to the model to facilitate replication by independent groups before translation to clinical settings.

Axonal T2 estimation using the spherical variance of the strongly diffusion-weighted MRI signal.

In magnetic resonance imaging, the application of a strong diffusion weighting suppresses the signal contributions from the less diffusion-restricted constituents of the brain's white matter, thus enabling the estimation of the transverse relaxation time T2 that arises from the more diffusion-restricted constituents such as the axons. However, the presence of cell nuclei and vacuoles can confound the estimation of the axonal T2, as diffusion within those structures is also restricted, causing the corresponding signal to survive the strong diffusion weighting. We devise an estimator of the axonal T2 based on the directional spherical variance of the strongly diffusion-weighted signal. The spherical variance T2 estimates are insensitive to the presence of isotropic contributions to the signal like those provided by cell nuclei and vacuoles. We show that with a strong diffusion weighting these estimates differ from those obtained using the directional spherical mean of the signal which contains both axonal and isotropically-restricted contributions. Our findings hint at the presence of an MRI-visible isotropically-restricted contribution to the signal in the white matter ex vivo fixed tissue (monkey) at 7T, and do not allow us to discard such a possibility also for in vivo human data collected with a clinical 3T system.

Model-informed machine learning for multi-component T2 relaxometry.

Recovering the T2 distribution from multi-echo T2 magnetic resonance (MR) signals is challenging but has high potential as it provides biomarkers characterizing the tissue micro-structure, such as the myelin water fraction (MWF). In this work, we propose to combine machine learning and aspects of parametric (fitting from the MRI signal using biophysical models) and non-parametric (model-free fitting of the T2 distribution from the signal) approaches to T2 relaxometry in brain tissue by using a multi-layer perceptron (MLP) for the distribution reconstruction. For training our network, we construct an extensive synthetic dataset derived from biophysical models in order to constrain the outputs with a priori knowledge of in vivo distributions. The proposed approach, called Model-Informed Machine Learning (MIML), takes as input the MR signal and directly outputs the associated T2 distribution. We evaluate MIML in comparison to a Gaussian Mixture Fitting (parametric) and Regularized Non-Negative Least Squares algorithms (non-parametric) on synthetic data, an ex vivo scan, and high-resolution scans of healthy subjects and a subject with Multiple Sclerosis. In synthetic data, MIML provides more accurate and noise-robust distributions. In real data, MWF maps derived from MIML exhibit the greatest conformity to anatomical scans, have the highest correlation to a histological map of myelin volume, and the best unambiguous lesion visualization and localization, with superior contrast between lesions and normal appearing tissue. In whole-brain analysis, MIML is 22 to 4980 times faster than the non-parametric and parametric methods, respectively.

Comparison of non-parametric T2 relaxometry methods for myelin water quantification.

Multi-component T2 relaxometry allows probing tissue microstructure by assessing compartment-specific T2 relaxation times and water fractions, including the myelin water fraction. Non-negative least squares (NNLS) with zero-order Tikhonov regularization is the conventional method for estimating smooth T2 distributions. Despite the improved estimation provided by this method compared to non-regularized NNLS, the solution is still sensitive to the underlying noise and the regularization weight. This is especially relevant for clinically achievable signal-to-noise ratios. In the literature of inverse problems, various well-established approaches to promote smooth solutions, including first-order and second-order Tikhonov regularization, and different criteria for estimating the regularization weight have been proposed, such as L-curve, Generalized Cross-Validation, and Chi-square residual fitting. However, quantitative comparisons between the available reconstruction methods for computing the T2 distribution, and between different approaches for selecting the optimal regularization weight, are lacking. In this study, we implemented and evaluated ten reconstruction algorithms, resulting from the individual combinations of three penalty terms with three criteria to estimate the regularization weight, plus non-regularized NNLS. Their performance was evaluated both in simulated data and real brain MRI data acquired from healthy volunteers through a scan-rescan repeatability analysis. Our findings demonstrate the need for regularization. As a result of this work, we provide a list of recommendations for selecting the optimal reconstruction algorithms based on the acquired data. Moreover, the implemented methods were packaged in a freely distributed toolbox to promote reproducible research, and to facilitate further research and the use of this promising quantitative technique in clinical practice.

Age- and gender-related differences in brain tissue microstructure revealed by multi-component T2 relaxometry.

In spite of extensive work, inconsistent findings and lack of specificity in most neuroimaging techniques used to examine age- and gender-related patterns in brain tissue microstructure indicate the need for additional research. Here, we performed the largest Multi-component T2 relaxometry cross-sectional study to date in healthy adults (N = 145, 18-60 years). Five quantitative microstructure parameters derived from various segments of the estimated T2 spectra were evaluated, allowing a more specific interpretation of results in terms of tissue microstructure. We found similar age-related myelin water fraction (MWF) patterns in men and women but we also observed differential male related results including increased MWF content in a few white matter tracts, a faster decline with age of the intra- and extra-cellular water fraction and its T2 relaxation time (i.e. steeper age related negative slopes) and a faster increase in the free and quasi-free water fraction, spanning the whole grey matter. Such results point to a sexual dimorphism in brain tissue microstructure and suggest a lesser vulnerability to age-related changes in women.

Deconvolution in diffusion spectrum imaging.

Diffusion spectrum magnetic resonance imaging (DSI) allows the estimation of the displacement probability density function (pdf) of water molecules, which contain valuable information about the microgeometry of the medium where the diffusion process occurs. It provides a more general approach to disentangle complex fiber structures in biological tissues because it does not assume any particular model of diffusion; even so, it has a number of limitations that remain unstudied. For instance, the theoretical model used to compute the displacement pdf is based on a Fourier transformation defined in the whole measurement space; however, in practice, it is computed using discrete signals with a finite support. As a consequence, the displacement pdf obtained from the experiments is the convolution between the true pdf and a point spread function (PSF) that completely depends on the experimental sampling scheme. In this work, a general framework to rectify and decontaminate the displacement pdf reconstructed from DSI is introduced. This framework is based on model-free deconvolution techniques that allow obtaining clearer and sharper DSI estimates. The method was tested in synthetic data as well as in real data measured from a healthy human volunteer. The results demonstrated that the angular resolution of DSI can be increased, potentially revealing new real fiber components and reducing both the artefactual peaks and the uncertainty of the local diffusion orientational distribution. Furthermore, the deconvolution process provides scalar maps of quantities derived from the propagator, such as the zero displacement probability, with higher tissue contrast.

Diffusion orientation transform revisited.

Diffusion orientation transform (DOT) is a powerful imaging technique that allows the reconstruction of the microgeometry of fibrous tissues based on diffusion MRI data. The three main error sources involving this methodology are the finite sampling of the q-space, the practical truncation of the series of spherical harmonics and the use of a mono-exponential model for the attenuation of the measured signal. In this work, a detailed mathematical description that provides an extension to the DOT methodology is presented. In particular, the limitations implied by the use of measurements with a finite support in q-space are investigated and clarified as well as the impact of the harmonic series truncation. Near- and far-field analytical patterns for the diffusion propagator are examined. The near-field pattern makes available the direct computation of the probability of return to the origin. The far-field pattern allows probing the limitations of the mono-exponential model, which suggests the existence of a limit of validity for DOT. In the regimen from moderate to large displacement lengths the isosurfaces of the diffusion propagator reveal aberrations in form of artifactual peaks. Finally, the major contribution of this work is the derivation of analytical equations that facilitate the accurate reconstruction of some orientational distribution functions (ODFs) and skewness ODFs that are relatively immune to these artifacts. The new formalism was tested using synthetic and real data from a phantom of intersecting capillaries. The results support the hypothesis that the revisited DOT methodology could enhance the estimation of the microgeometry of fiber tissues.

Robust Monte-Carlo Simulations in Diffusion-MRI: Effect of the Substrate Complexity and Parameter Choice on the Reproducibility of Results.

Monte-Carlo Diffusion Simulations (MCDS) have been used extensively as a ground truth tool for the validation of microstructure models for Diffusion-Weighted MRI. However, methodological pitfalls in the design of the biomimicking geometrical configurations and the simulation parameters can lead to approximation biases. Such pitfalls affect the reliability of the estimated signal, as well as its validity and reproducibility as ground truth data. In this work, we first present a set of experiments in order to study three critical pitfalls encountered in the design of MCDS in the literature, namely, the number of simulated particles and time steps, simplifications in the intra-axonal substrate representation, and the impact of the substrate's size on the signal stemming from the extra-axonal space. The results obtained show important changes in the simulated signals and the recovered microstructure features when changes in those parameters are introduced. Thereupon, driven by our findings from the first studies, we outline a general framework able to generate complex substrates. We show the framework's capability to overcome the aforementioned simplifications by generating a complex crossing substrate, which preserves the volume in the crossing area and achieves a high packing density. The results presented in this work, along with the simulator developed, pave the way toward more realistic and reproducible Monte-Carlo simulations for Diffusion-Weighted MRI.

Multivariate Brain Functional Connectivity Through Regularized Estimators.

Functional connectivity analyses are typically based on matrices containing bivariate measures of covariability, such as correlations. Although this has been a fruitful approach, it may not be the optimal strategy to fully explore the complex associations underlying brain activity. Here, we propose extending connectivity to multivariate functions relating to the temporal dynamics of a region with the rest of the brain. The main technical challenges of such an approach are multidimensionality and its associated risk of overfitting or even the non-uniqueness of model solutions. To minimize these risks, and as an alternative to the more common dimensionality reduction methods, we propose using two regularized multivariate connectivity models. On the one hand, simple linear functions of all brain nodes were fitted with ridge regression. On the other hand, a more flexible approach to avoid linearity and additivity assumptions was implemented through random forest regression. Similarities and differences between both methods and with simple averages of bivariate correlations (i.e., weighted global brain connectivity) were evaluated on a resting state sample of N = 173 healthy subjects. Results revealed distinct connectivity patterns from the two proposed methods, which were especially relevant in the age-related analyses where both ridge and random forest regressions showed significant patterns of age-related disconnection, almost completely absent from the much less sensitive global brain connectivity maps. On the other hand, the greater flexibility provided by the random forest algorithm allowed detecting sex-specific differences. The generic framework of multivariate connectivity implemented here may be easily extended to other types of regularized models.

Mathematical description of q-space in spherical coordinates: exact q-ball imaging.

Novel methodologies have been recently developed to characterize the microgeometry of neural tissues and porous structures via diffusion MRI data. In line with these previous works, this article provides a detailed mathematical description of q-space in spherical coordinates that helps to highlight the differences and similarities between various related q-space methodologies proposed to date such as q-ball imaging (QBI), diffusion spectrum imaging (DSI), and diffusion orientation transform imaging (DOT). This formulation provides a direct relationship between the orientation distribution function (ODF) and the diffusion data without using any approximation. Under this relationship, the exact ODF can be computed by means of the Radon transform of the radial projection (in q-space) of the diffusion MRI signal. This new methodology, termed exact q-ball imaging (EQBI), was put into practice using an analytical ODF estimation in terms of spherical harmonics that allows obtaining model-free and model-based reconstructions. This work provides a new framework for combining information coming from diffusion data recorded on multiple spherical shells in q-space (hybrid diffusion imaging encoding scheme), which is capable of mapping ODF to a high accuracy. This represents a step toward a more efficient development of diffusion MRI experiments for obtaining better ODF estimates.