Erick Jorge Canales-Rodríguez

Studying the human brain anatomical network via diffusion-weighted MRI and Graph Theory.

Our goal is to study the human brain anatomical network. For this, the anatomical connection probabilities (ACP) between 90 cortical and subcortical brain gray matter areas are estimated from diffusion-weighted Magnetic Resonance Imaging (DW-MRI) techniques. The ACP between any two areas gives the probability that those areas are connected at least by a single nervous fiber. Then, the brain is modeled as a non-directed weighted graph with continuous arc weights given by the ACP matrix. Based on this approach, complex networks properties such as small-world attributes, efficiency, degree distribution, vulnerability, betweenness centrality and motifs composition are studied. The analysis was carried out for 20 right-handed healthy subjects (mean age: 31.10, S.D.: 7.43). According to the results, all networks have small-world and broad-scale characteristics. Additionally, human brain anatomical networks present bigger local efficiency and smaller global efficiency than the corresponding random networks. In a vulnerability and betweenness centrality analysis, the most indispensable and critical anatomical areas were identified: putamens, precuneus, insulas, superior parietals and superior frontals. Interestingly, some areas have a negative vulnerability (e.g. superior temporal poles, pallidums, supramarginals and hechls), which suggest that even at the cost of losing in global anatomical efficiency, these structures were maintained through the evolutionary processes due to their important functions. Finally, symmetrical characteristic building blocks (motifs) of size 3 and 4 were calculated, obtaining that motifs of size 4 are the expanded version of motif of size 3. These results are in agreement with previous anatomical studies in the cat and macaque cerebral cortex.

Characterizing brain anatomical connections using diffusion weighted MRI and graph theory

A new methodology based on Diffusion Weighted Magnetic Resonance Imaging (DW-MRI) and Graph Theory is presented for characterizing the anatomical connections between brain gray matter areas. In a first step, brain voxels are modeled as nodes of a non-directed graph in which the weight of an arc linking two neighbor nodes is assumed to be proportional to the probability of being connected by nervous fibers. This probability is estimated by means of probabilistic tissue segmentation and intravoxel white matter orientational distribution function, obtained from anatomical MRI and DW-MRI, respectively. A new tractography algorithm for finding white matter routes is also introduced. This algorithm solves the most probable path problem between any two nodes, leading to the assessment of probabilistic brain anatomical connection maps. In a second step, for assessing anatomical connectivity between K gray matter structures, the previous graph is redefined as a K+1 partite graph by partitioning the initial nodes set in K non-overlapped gray matter subsets and one subset clustering the remaining nodes. Three different measures are proposed for quantifying anatomical connections between any pair of gray matter subsets: Anatomical Connection Strength (ACS), Anatomical Connection Density (ACD) and Anatomical Connection Probability (ACP). This methodology was applied to both artificial and actual human data. Results show that nervous fiber pathways between some regions of interest were reconstructed correctly. Additionally, mean connectivity maps of ACS, ACD and ACP between 71 gray matter structures for five healthy subjects are presented.

Estimating brain functional connectivity with sparse multivariate autoregression

There is much current interest in identifying the anatomical and functional circuits that are the basis of the brains computations, with hope that functional neuroimaging techniques will allow the in vivo study of these neural processes through the statistical analysis of the time-series they produce. Ideally, the use of techniques such as multivariate autoregressive (MAR) modelling should allow the identification of effective connectivity by combining graphical modelling methods with the concept of Granger causality. Unfortunately, current time-series methods perform well only for the case that the length of the time-series Nt is much larger than p, the number of brain sites studied, which is exactly the reverse of the situation in neuroimaging for which relatively short time-series are measured over thousands of voxels. Methods are introduced for dealing with this situation by using sparse MAR models. These can be estimated in a two-stage process involving (i) penalized regression and (ii) pruning of unlikely connections by means of the local false discovery rate developed by Efron. Extensive simulations were performed with idealized cortical networks having small world topologies and stable dynamics. These show that the detection efficiency of connections of the proposed procedure is quite high. Application of the method to real data was illustrated by the identification of neural circuitry related to emotional processing as measured by BOLD.

Brain Hemispheric Structural Efficiency and Interconnectivity Rightward Asymmetry in Human and Nonhuman Primates

Evidence for interregional structural asymmetries has been previously reported for brain anatomic regions supporting well-described functional lateralization. Here, we aimed to investigate whether the two brain hemispheres demonstrate dissimilar general structural attributes implying different principles on information flow management. Common left hemisphere/right hemisphere structural network properties are estimated and compared for right-handed healthy human subjects and a nonhuman primate, by means of 3 different diffusion-weighted magnetic resonance imaging fiber tractography algorithms and a graph theory framework. In both the human and the nonhuman primate, the data support the conclusion that, in terms of the graph framework, the right hemisphere is significantly more efficient and interconnected than the left hemisphere, whereas the left hemisphere presents more central or indispensable regions for the whole-brain structural network than the right hemisphere. From our point of view, in terms of functional principles, this pattern could be related with the fact that the left hemisphere has a leading role for highly demanding specific process, such as language and motor actions, which may require dedicated specialized networks, whereas the right hemisphere has a leading role for more general process, such as integration tasks, which may require a more general level of interconnection.

Anisotropic Kernels for Coordinate-Based Meta-Analyses of Neuroimaging Studies

Peak-based meta-analyses of neuroimaging studies create, for each study, a brain map of effect size or peak likelihood by convolving a kernel with each reported peak. A kernel is a small matrix applied in order that voxels surrounding the peak have a value similar to, but slightly lower than that of the peak. Current kernels are isotropic, i.e., the value of a voxel close to a peak only depends on the Euclidean distance between the voxel and the peak. However, such perfect spheres of effect size or likelihood around the peak are rather implausible: a voxel that correlates with the peak across individuals is more likely to be part of the cluster of significant activation or difference than voxels uncorrelated with the peak. This paper introduces anisotropic kernels, which assign different values to the different neighboring voxels based on the spatial correlation between them. They are specifically developed for effect-size signed differential mapping (ES-SDM), though might be easily implemented in other meta-analysis packages such as activation likelihood estimation (ALE). The paper also describes the creation of the required correlation templates for gray matter/BOLD response, white matter, cerebrospinal fluid, and fractional anisotropy. Finally, the new method is validated by quantifying the accuracy of the recreation of effect size maps from peak information. This empirical validation showed that the optimal degree of anisotropy and full-width at half-maximum (FWHM) might vary largely depending on the specific data meta-analyzed. However, it also showed that the recreation substantially improved and did not depend on the FWHM when full anisotropy was used. Based on these results, we recommend the use of fully anisotropic kernels in ES-SDM and ALE, unless optimal meta-analysis-specific parameters can be estimated based on the recreation of available statistical maps. The new method and templates are freely available at http://www.sdmproject.com/.

Accelerated Microstructure Imaging via Convex Optimization (AMICO) from diffusion MRI data

Microstructure imaging from diffusion magnetic resonance (MR) data represents an invaluable tool to study non-invasively the morphology of tissues and to provide a biological insight into their microstructural organization. In recent years, a variety of biophysical models have been proposed to associate particular patterns observed in the measured signal with specific microstructural properties of the neuronal tissue, such as axon diameter and fiber density. Despite very appealing results showing that the estimated microstructure indices agree very well with histological examinations, existing techniques require computationally very expensive non-linear procedures to fit the models to the data which, in practice, demand the use of powerful computer clusters for large-scale applications. In this work, we present a general framework for Accelerated Microstructure Imaging via Convex Optimization (AMICO) and show how to re-formulate this class of techniques as convenient linear systems which, then, can be efficiently solved using very fast algorithms. We demonstrate this linearization of the fitting problem for two specific models, i.e. ActiveAx and NODDI, providing a very attractive alternative for parameter estimation in those techniques; however, the AMICO framework is general and flexible enough to work also for the wider space of microstructure imaging methods. Results demonstrate that AMICO represents an effective means to accelerate the fit of existing techniques drastically (up to four orders of magnitude faster) while preserving accuracy and precision in the estimated model parameters (correlation above 0.9). We believe that the availability of such ultrafast algorithms will help to accelerate the spread of microstructure imaging to larger cohorts of patients and to study a wider spectrum of neurological disorders.

Quantitative Comparison of Reconstruction Methods for Intra-Voxel Fiber Recovery From Diffusion MRI

Validation is arguably the bottleneck in the diffusion magnetic resonance imaging (MRI) community. This paper evaluates and compares 20 algorithms for recovering the local intra-voxel fiber structure from diffusion MRI data and is based on the results of the “HARDI reconstruction challenge” organized in the context of the “ISBI 2012” conference. Evaluated methods encompass a mixture of classical techniques well known in the literature such as diffusion tensor, Q-Ball and diffusion spectrum imaging, algorithms inspired by the recent theory of compressed sensing and also brand new approaches proposed for the first time at this contest. To quantitatively compare the methods under controlled conditions, two datasets with known ground-truth were synthetically generated and two main criteria were used to evaluate the quality of the reconstructions in every voxel: correct assessment of the number of fiber populations and angular accuracy in their orientation. This comparative study investigates the behavior of every algorithm with varying experimental conditions and highlights strengths and weaknesses of each approach. This information can be useful not only for enhancing current algorithms and develop the next generation of reconstruction methods, but also to assist physicians in the choice of the most adequate technique for their studies.

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.

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. Magn Reson Med, 2009.

Multimodal Voxel-Based Meta-Analysis of White Matter Abnormalities in Obsessive–Compulsive Disorder

White matter (WM) abnormalities have long been suspected in obsessive–compulsive disorder (OCD) but the available evidence has been inconsistent. We conducted the first multimodal meta-analysis of WM volume (WMV) and fractional anisotropy (FA) studies in OCD. All voxel-wise studies comparing WMV or FA between patients with OCD and healthy controls in the PubMed, ScienceDirect, Google Scholar, Web of Knowledge and Scopus databases were retrieved. Manual searches were also conducted and authors were contacted soliciting additional data. Thirty-four data sets were identified, of which 22 met inclusion criteria (five of them unpublished; comprising 537 adult and pediatric patients with OCD and 575 matched healthy controls). Whenever possible, raw statistical parametric maps were also obtained from the authors. Peak and raw WMV and FA data were combined using novel multimodal meta-analytic methods implemented in effect-size signed differential mapping. Patients with OCD showed widespread WM abnormalities, but findings were particularly robust in the anterior midline tracts (crossing between anterior parts of cingulum bundle and body of corpus callosum), which showed both increased WMV and decreased FA, possibly suggesting an increase of fiber crossing in these regions. This finding was also observed when the analysis was limited to adult participants, and especially pronounced in samples with a higher proportion of medicated patients. Therefore, patients with OCD may have widespread WM abnormalities, particularly evident in anterior midline tracts, although these changes might be, at least in part, attributable to the effects of therapeutic drugs.