, 2009 and Seeley
et al., 2009). At the same time, these correlations are of fundamental interest to neuroscientists because they offer the first opportunity to comprehensively and noninvasively explore the functional network structure of the human brain (Bullmore and Sporns, 2009). Although a variety of methods may be used to study rs-fcMRI data, one of the most powerful and flexible approaches is the graph theoretic approach (Bullmore and Sporns, 2009 and Rubinov and Sporns, 2010). Within this framework, a complex system is formalized as a mathematical object consisting of a set of items and a set of pairwise relationships between the items. Items are called nodes, relationships are called ties, and collections of these nodes with their ties are called graphs or networks. A short and incomplete list of established
topics in graph theory includes quantifying hierarchy and substructure within a graph, identifying BMS-777607 in vitro hubs and critical nodes, determining how easily traffic flows in different portions and at different scales of a network, and estimating the controllability of a system (Liu et al., 2011 and Newman, 2010). Because graph theoretic analyses DAPT molecular weight can model properties at the level of the entire graph, subgraphs, or individual nodes, and because the brain itself is a complex network, graph theoretic approaches are a natural and attractive choice for rs-fcMRI analysis. A current obstacle to the graph-based study of
functional brain organization is that it very difficult to define the individual nodes that make up a brain network. On first principles, treating a graph as a model of a real system, Rolziracetam if the nodes of the graph do not accurately represent real items in the system, the graph itself is a distorted model and graph theoretic properties will diverge from the true properties of the system (Butts, 2009, Smith et al., 2011 and Wig et al., 2011). The brain is a complex network with macroscopic organization at the level of functional areas and subcortical nuclei, but the number and locations of these entities in humans is largely unknown. Standard approaches to forming whole-brain rs-fcMRI graphs often ignore this issue and define nodes as voxels (Buckner et al., 2009, Cole et al., 2010, Fransson et al., 2011, Tomasi and Volkow, 2011 and van den Heuvel et al., 2008), large parcels from anatomically based brain atlases (Hartman et al., 2011, He et al., 2009, Meunier et al., 2009a, Spoormaker et al., 2010 and Tian et al., 2011), or random interpolations between voxels and parcels (Hayasaka and Laurienti, 2010 and Meunier et al., 2009b). These approaches are not meant to correspond to macroscopic “units” of brain organization, and thus there is no direct reason to believe that these approaches result in well-formed nodes (Wig et al., 2011). An overarching goal of this report is to, at least partially, overcome this obstacle.