Lester Melie-García

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.

Surface area and cortical thickness descriptors reveal different attributes of the structural human brain networks.

Recently, a related morphometry-based connection concept has been introduced using local mean cortical thickness and volume to study the underlying complex architecture of the brain networks. In this article, the surface area is employed as a morphometric descriptor to study the concurrent changes between brain structures and to build binarized connectivity graphs. The statistical similarity in surface area between pair of regions was measured by computing the partial correlation coefficient across 186 normal subjects of the Cuban Human Brain Mapping Project. We demonstrated that connectivity matrices obtained follow a small-world behavior for two different parcellations of the brain gray matter. The properties of the connectivity matrices were compared to the matrices obtained using the mean cortical thickness for the same cortical parcellations. The topology of the cortical thickness and surface area networks were statistically different, demonstrating that both capture distinct properties of the interaction or different aspects of the same interaction (mechanical, anatomical, chemical, etc.) between brain structures. This finding could be explained by the fact that each descriptor is driven by distinct cellular mechanisms as result of a distinct genetic origin. To our knowledge, this is the first time that surface area is used to study the morphological connectivity of brain networks.

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.

A Method to Determine the Presence of Averaged Event-Related Fields Using Randomization Tests

We present a simple and effective method to test whether an event consistently activates a set of brain electric sources across repeated measurements of event-related scalp field data. These repeated measurements can be single trials, single subject ERPs, or ERPs from different studies. The method considers all sensors simultaneously, but can be applied separately to each time frame or frequency band of the data. This allows limiting the analysis to time periods and frequency bands where there is positive evidence of a consistent relation between the event and some brain electric sources. The test may therefore avoid false conclusions about the data resulting from an inadequate selection of the analysis window and bandpass filter, and permit the exploration of alternate hypotheses when group/condition differences are observed in evoked field data. The test will be called topographic consistency test (TCT). The statistical inference is based on simple randomization techniques. Apart form the methodological introduction, the paper contains a series of simulations testing the statistical power of the method as function of number of sensors and observations, a sample analysis of EEG potentials related to self-initiated finger movements, and Matlab source code to facilitate the implementation. Furthermore a series of measures to control for multiple testing are introduced and applied to the sample data.

Ragu: a free tool for the analysis of EEG and MEG event-related scalp field data using global randomization statistics

We present a program (Ragu; Randomization Graphical User interface) for statistical analyses of multichannel event-related EEG and MEG experiments. Based on measures of scalp field differences including all sensors, and using powerful, assumption-free randomization statistics, the program yields robust, physiologically meaningful conclusions based on the entire, untransformed, and unbiased set of measurements. Ragu accommodates up to two within-subject factors and one between-subject factor with multiple levels each. Significance is computed as function of time and can be controlled for type II errors with overall analyses. Results are displayed in an intuitive visual interface that allows further exploration of the findings. A sample analysis of an ERP experiment illustrates the different possibilities offered by Ragu. The aim of Ragu is to maximize statistical power while minimizing the need for a-priori choices of models and parameters (like inverse models or sensors of interest) that interact with and bias statistics.

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.

Glucose Metabolism during Resting State Reveals Abnormal Brain Networks Organization in the Alzheimer’s Disease and Mild Cognitive Impairment

This paper aims to study the abnormal patterns of brain glucose metabolism co-variations in Alzheimer disease (AD) and Mild Cognitive Impairment (MCI) patients compared to Normal healthy controls (NC) using the Alzheimer Disease Neuroimaging Initiative (ADNI) database. The local cerebral metabolic rate for glucose (CMRgl) in a set of 90 structures belonging to the AAL atlas was obtained from Fluro-Deoxyglucose Positron Emission Tomography data in resting state. It is assumed that brain regions whose CMRgl values are significantly correlated are functionally associated; therefore, when metabolism is altered in a single region, the alteration will affect the metabolism of other brain areas with which it interrelates. The glucose metabolism network (represented by the matrix of the CMRgl co-variations among all pairs of structures) was studied using the graph theory framework. The highest concurrent fluctuations in CMRgl were basically identified between homologous cortical regions in all groups. Significant differences in CMRgl co-variations in AD and MCI groups as compared to NC were found. The AD and MCI patients showed aberrant patterns in comparison to NC subjects, as detected by global and local network properties (global and local efficiency, clustering index, and others). MCI network’s attributes showed an intermediate position between NC and AD, corroborating it as a transitional stage from normal aging to Alzheimer disease. Our study is an attempt at exploring the complex association between glucose metabolism, CMRgl covariations and the attributes of the brain network organization in AD and MCI.

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.