There is much current interest in identifying the anatomical and functional circuits that are the basis of the brain's 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.

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.

Studies of the neural basis of intelligence have focused on comparing brain imaging variables with global scales instead of the cognitive domains integrating these scales or quotients. Here, the relation between mean tract-based fractional anisotropy (mTBFA) and intelligence indices was explored. Deterministic tractography was performed using a regions of interest approach for 10 white-matter fascicles along which the mTBFA was calculated. The study sample included 83 healthy individuals from the second wave of the Cuban Human Brain Mapping Project, whose WAIS-III intelligence quotients and indices were obtained. Inspired by the "Watershed model" of intelligence, we employed a regularized hierarchical Multiple Indicator, Multiple Causes model (MIMIC), to assess the association of mTBFA with intelligence scores, as mediated by latent variables summarizing the indices. Regularized MIMIC, used due to the limited sample size, selected relevant mTBFA by means of an elastic net penalty and achieved good fits to the data. Two latent variables were necessary to describe the indices: Fluid intelligence (Perceptual Organization and Processing Speed indices) and Crystallized Intelligence (Verbal Comprehension and Working Memory indices). Regularized MIMIC revealed effects of the forceps minor tract on crystallized intelligence and of the superior longitudinal fasciculus on fluid intelligence. The model also detected the significant effect of age on both latent variables. K E Y W O R D S crystallized intelligence, fluid intelligence, fractional anisotropy, MIMIC model, white-matter tracts

The estimation of EEG generating sources constitutes an Inverse Problem (IP) in Neuroscience. This is an ill-posed problem due to the non-uniqueness of the solution and regularization or prior information is needed to undertake Electrophysiology Source Imaging. Structured Sparsity priors can be attained through combinations of (L1 norm-based) and (L2 norm-based) constraints such as the Elastic Net (ENET) and Elitist Lasso (ELASSO) models. The former model is used to find solutions with a small number of smooth nonzero patches, while the latter imposes different degrees of sparsity simultaneously along different dimensions of the spatio-temporal matrix solutions. Both models have been addressed within the penalized regression approach, where the regularization parameters are selected heuristically, leading usually to non-optimal and computationally expensive solutions. The existing Bayesian formulation of ENET allows hyperparameter learning, but using the computationally intensive Monte Carlo/Expectation Maximization methods, which makes impractical its application to the EEG IP. While the ELASSO have not been considered before into the Bayesian context. In this work, we attempt to solve the EEG IP using a Bayesian framework for ENET and ELASSO models. We propose a Structured Sparse Bayesian Learning algorithm based on combining the Empirical Bayes and the iterative coordinate descent procedures to estimate both the parameters and hyperparameters. Using realistic simulations and avoiding the inverse crime we illustrate that our methods are able to recover complicated source setups more accurately and with a more robust estimation of the hyperparameters and behavior under different sparsity scenarios than classical LORETA, ENET and LASSO Fusion solutions. We also solve the EEG IP using data from a visual attention experiment, finding more interpretable neurophysiological patterns with our methods. The Matlab codes used in this work, including Simulations, Methods, Quality Measures and Visualization Routines are freely available in a public website.

No abstract