José M. Sánchez-Bornot

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.

Model driven EEG/fMRI fusion of brain oscillations

This article reviews progress and challenges in model driven EEG/fMRI fusion with a focus on brain oscillations. Fusion is the combination of both imaging modalities based on a cascade of forward models from ensemble of post‐synaptic potentials (ePSP) to net primary current densities (nPCD) to EEG; and from ePSP to vasomotor feed forward signal (VFFSS) to BOLD. In absence of a model, data driven fusion creates maps of correlations between EEG and BOLD or between estimates of nPCD and VFFS. A consistent finding has been that of positive correlations between EEG alpha power and BOLD in both frontal cortices and thalamus and of negative ones for the occipital region. For model driven fusion we formulate a neural mass EEG/fMRI model coupled to a metabolic hemodynamic model. For exploratory simulations we show that the Local Linearization (LL) method for integrating stochastic differential equations is appropriate for highly nonlinear dynamics. It has been successfully applied to small and medium sized networks, reproducing the described EEG/BOLD correlations. A new LL‐algebraic method allows simulations with hundreds of thousands of neural populations, with connectivities and conduction delays estimated from diffusion weighted MRI. For parameter and state estimation, Kalman filtering combined with the LL method estimates the innovations or prediction errors. From these the likelihood of models given data are obtained. The LL‐innovation estimation method has been already applied to small and medium scale models. With improved Bayesian computations the practical estimation of very large scale EEG/fMRI models shall soon be possible. Hum Brain Mapp, 2009.

EEG source imaging with spatio‐temporal tomographic nonnegative independent component analysis

This article describes a spatio‐temporal EEG/MEG source imaging (ESI) that extracts a parsimonious set of “atoms” or components, each the outer product of both a spatial and a temporal signature. The sources estimated are localized as smooth, minimally overlapping patches of cortical activation that are obtained by constraining spatial signatures to be nonnegative (NN), orthogonal, sparse, and smooth‐in effect integrating ESI with NN‐ICA. This constitutes a generalization of work by this group on the use of multiple penalties for ESI. A multiplicative update algorithm is derived being stable, fast and converging within seconds near the optimal solution. This procedure, spatio‐temporal tomographic NN ICA (STTONNICA), is equally able to recover superficial or deep sources without additional weighting constraints as tested with simulations. STTONNICA analysis of ERPs to familiar and unfamiliar faces yields an occipital‐fusiform atom activated by all faces and a more frontal atom that only is active with familiar faces. The temporal signatures are at present unconstrained but can be required to be smooth, complex, or following a multivariate autoregressive model. Hum Brain Mapp, 2009.

Identifying Complex Brain Networks Using Penalized Regression Methods

The recorded electrical activity of complex brain networks through the EEG reflects their intrinsic spatial, temporal and spectral properties. In this work we study the application of new penalized regression methods to i) the spatial characterization of the brain networks associated with the identification of faces and ii) the PARAFAC analysis of resting-state EEG. The use of appropriate constraints through non-convex penalties allowed three types of inverse solutions (Loreta, Lasso Fusion and ENet L) to spatially localize networks in agreement with previous studies with fMRI. Furthermore, we propose a new penalty based in the Information Entropy for the constrained PARAFAC analysis of resting EEG that allowed the identification in time, frequency and space of those brain networks with minimum spectral entropy. This study is an initial attempt to explicitly include complexity descriptors as a constraint in multilinear EEG analysis.

Penalized Regression Methods in the Source Analysis of Face Recognition

Recent developments in the field of variable selection through penalized least squares regression provide means for the analysis of neuroscience data. Particularly, combinations of non-convex penalties allow for sparse solutions and other unexplored properties that are especially attractive in their application to e.g. EEG/MEG inverse problem. Here, we explore the use of these techniques for the source analysis of a cognitive process, namely, the recognition of faces. Found sources are in agreement with previous studies and new methods, based on combination of penalties, provided for more physiologically plausible solutions.

Information Entropy-Based Penalty for PARAFAC Analysis of Resting EEG

PARAFAC analysis of time-varying EEG spectra data provides a parsimonious representation in terms of topographic, temporal and spectral signatures, which allows for the identification of functional neural networks. This networks work in a critical state where short and long range connections coexist. Although PARAFAC is unique through usual least squares estimation, the use of penalized least squares allows to incorporate this kind of knowledge into the decomposition. Here we propose the use of Information Entropy-based penalties for obtaining atoms with minimum spectral entropy. They offer sparse spectral signatures corresponding to networks oscillating in a well-defined (sharp) frequency band.

Hyperacute stroke evolution mapped by individualized tomographic qEEG

Tomographic qEEG (qEEGt) has recently been introduced for the 3D in vivo visualization of the sources of abnormal EEG oscillations, including those induced by cerebral ischemia. The cross-spectrum of the EEG is used to estimate source spectra at each voxel by means of Brain Electrical Tomography (BET), a Bayesian EEG inverse solution based on anatomical constraints and a suitable smoothness prior. In turn the source spectra are log transformed and compared to age regressed population means and standard deviations by calculating the z score for each voxel and frequency. These values are then imaged using thresholded SPM procedures to map either excess or defect of oscillations at each frequency with respect to the normative database. qEEGT has been shown to correctly identify the anatomical locus of hyper-acute, acute and chronic stroke. It was also shown that the use of statistical images in BET is mandatory due to a depth bias that is only compensated for by mapping statistics rather than raw values of source spectra. The studies just described however used the MNI probabilistic atlas as an anatomical constraint instead of the subjects own MRI and were not compared to either perfusion weighted (PWI) or diffusion weighted (DWI) images. The present study was designed to explore the feasibility of using the subjects individual anatomy as a basis for qEEGT methods and compares the resulting electrophysiological image to DWI and PWI MRI.Two cases of Cruveilhier-Baumgarten syndrome not clinically evident and without esophageal varices in patients with liver cirrhosis and portal hypertension are presented. The diagnosis was made by real-time ultrasonography, which showed echographic caput medusae with large afferent umbilical veins and efferent inferior superficial epigastric veins. Doppler flowmetry documented high blood flow rates in these collateral portal-systemic circulations, and this explained the absence of large varices at endoscopy. The role of massive spontaneous portal-systemic shunts in preventing the formation of other shunts and particularly esophageal variceal bleeding is discussed.