Dynamic connectivity states estimated from resting fMRI Identify differences among Schizophrenia, bipolar disorder, and healthy control subjects.

Brain connectivity datasets comprise networks of brain regions connected by anatomical tracts or by functional associations. Complex network analysis-a new multidisciplinary approach to the study of complex systems-aims to characterize these brain networks with a small number of neurobiologically meaningful and easily computable measures. In this article, we discuss construction of brain networks from connectivity data and describe the most commonly used network measures of structural and functional connectivity. We describe measures that variously detect functional integration and segregation, quantify centrality of individual brain regions or pathways, characterize patterns of local anatomical circuitry, and test resilience of networks to insult. We discuss the issues surrounding comparison of structural and functional network connectivity, as well as comparison of networks across subjects. Finally, we describe a Matlab toolbox (http://www.brain-connectivity-toolbox.net) accompanying this article and containing a collection of complex network measures and large-scale neuroanatomical connectivity datasets. Copyright (c) 2009 Elsevier Inc. All rights reserved.

We consider the problem of estimating sparse graphs by a lasso penalty applied to the inverse covariance matrix. Using a coordinate descent procedure for the lasso, we develop a simple algorithm--the graphical lasso--that is remarkably fast: It solves a 1000-node problem ( approximately 500,000 parameters) in at most a minute and is 30-4000 times faster than competing methods. It also provides a conceptual link between the exact problem and the approximation suggested by Meinshausen and Bühlmann (2006). We illustrate the method on some cell-signaling data from proteomics.

There is great interest in estimating brain "networks" from FMRI data. This is often attempted by identifying a set of functional "nodes" (e.g., spatial ROIs or ICA maps) and then conducting a connectivity analysis between the nodes, based on the FMRI timeseries associated with the nodes. Analysis methods range from very simple measures that consider just two nodes at a time (e.g., correlation between two nodes' timeseries) to sophisticated approaches that consider all nodes simultaneously and estimate one global network model (e.g., Bayes net models). Many different methods are being used in the literature, but almost none has been carefully validated or compared for use on FMRI timeseries data. In this work we generate rich, realistic simulated FMRI data for a wide range of underlying networks, experimental protocols and problematic confounds in the data, in order to compare different connectivity estimation approaches. Our results show that in general correlation-based approaches can be quite successful, methods based on higher-order statistics are less sensitive, and lag-based approaches perform very poorly. More specifically: there are several methods that can give high sensitivity to network connection detection on good quality FMRI data, in particular, partial correlation, regularised inverse covariance estimation and several Bayes net methods; however, accurate estimation of connection directionality is more difficult to achieve, though Patel's τ can be reasonably successful. With respect to the various confounds added to the data, the most striking result was that the use of functionally inaccurate ROIs (when defining the network nodes and extracting their associated timeseries) is extremely damaging to network estimation; hence, results derived from inappropriate ROI definition (such as via structural atlases) should be regarded with great caution. Copyright © 2010 Elsevier Inc. All rights reserved.