Review TRENDS in Cognitive Sciences Vol.8 No.9 September 2004 hat gith high Box 2.Brain co nectivity:structural.functional and effective functional properties general the connectiona y is the set or phy ctural (synaptic of a cortic I area can serve as an indicator of On the neural circuits linking small sets of connected brain areas the can dynam approach of mo higher frequency in real networks than in randomized en d work same s1ze29,30,31 Biological an e or eds of mil s)and tha motifs such loopsand bi-parallel path alysi a sml ex ve c nother 21. the set o and R.Kotter,in common mode tion proc sing ectivity quires th Large urbations tem raph the oretica ana connectio can also be used 52 reral of which are sha and specie see Box large-scale setsof brain reg ns and path with sh in the s ENGTHS and high CLUSTERING COEFFICIENTS 32-35 (Figure 1a). These es are also tou on the kind of fy istic conetion rues,taking intoaccount metri 361. its fu uggetsth pa multiple of cortical organization The ical substrate ither dir y thre structural conn atterns es,through theng graph ural and the unt of fur ti ver diverg give egion which the area is part of a local collective of tunctionally related regions. The path betw proximity'.If no path exists.no functional interaction participation es (261)can to char acterize can take pla and its transmission'coefficient,defined as the relative numbe nelp of multivariate analysis techniques,such as multi affe ent hubs nng or ster an 25 initial functional characterization of areas as eithe identified that are s zated functionally i371 as well as mainly sen outputs an mutual interconnec the ave t/afferent ratio is clos to 1 with a h out for sigaling pathwavs across cortical n 391. of ngag coope The 'matching in ndexcaptures the paiwis similarity of m te stering co ort etwor of the scienc that the fune tion methoc ified by their in ated as ll numbe of distincti uste and outputs. rsin globa agreeme cept,on e.Bapproaches, or multivariate methods to extract statistical structure by clustering or scaling techniques [25]. Structural contributions of individual areas and motifs At the local level, simple statistical measures (‘network participation indices’, [26]) can be used to characterize inputs and outputs of individual areas. These measures include an area’s IN-DEGREE and OUT-DEGREE, and its ‘transmission’ coefficient, defined as the relative number of efferents to afferents. Such measures allow identifi- cation of highly connected nodes (hubs) and provide an initial functional characterization of areas as either (mainly sending) ‘broadcasters’ or (mainly receiving) ‘integrators’ of signals. For macaque visual cortex [23], the average efferent/afferent ratio is close to 1, with a standard error of 0.4 [25], indicating that brain regions tend to engage in cooperative (‘give-and-take’) infor￾mation-processing. The ‘matching index’ captures the pairwise similarity of areas in terms of their specific afferents and efferents from other parts of the network [25,27]. One of the central assumptions of systems neuroscience is that the func￾tional roles of brain regions are specified by their inputs and outputs. In agreement with this concept, one finds that pairs of areas with high matching index also share functional properties [25]. In general, the ‘connectional fingerprint’ of a cortical area can serve as an indicator of its functional contribution to the overall system [28]. On the next higher level of organization – neural circuits linking small sets of connected brain areas – the approach of motif analysis can be used to identify patterns of local interconnections that occur with a significantly higher frequency in real networks than in randomized networks of the same size [29,30,31]. Biological and technological networks contain several characteristic motifs, such as ‘feedforward loops’ and ‘bi-parallel path￾ways’. A systematic analysis of motifs in brain networks revealed a small number of characteristic motifs shared among several examples of cortical networks (O. Sporns and R. Kotter, in preparation), potentially indicating common modes of information processing. Large-scale connection patterns Graph theoretical analysis of large-scale connection patterns of cat and monkey has revealed characteristic properties, several of which are shared across neural systems and species (see also Box 1). All large-scale cortical connection patterns (ADJACENCY MATRICES) exam￾ined so far exhibit small-world attributes with short PATH LENGTHS and high CLUSTERING COEFFICIENTS [32–35] (Figure 1a). These properties are also found in inter￾mediate-scale connection patterns generated by probabil￾istic connection rules, taking into account metric distance between neuronal units [35,36]. This suggests that high clustering and short path lengths can be found across multiple spatial scales of cortical organization. The quantitative analysis of structural connection patterns using graph theory tools provides several insights into the functioning of neural architectures. In-degree and out-degree specify the amount of functional conver￾gence and divergence of a given region (see above), whereas the clustering coefficient measures the degree to which the area is part of a local collective of functionally related regions. The path length between two brain regions captures their potential ‘functional proximity’. If no path exists, no functional interaction can take place. Various global connectivity features of cortical net￾works have been described and characterized with the help of multivariate analysis techniques, such as multi￾dimensional scaling or hierarchical cluster analyses [25]. For example, streams of visual cortical areas have been identified that are segregated functionally [37] as well as in terms of their inputs, outputs and mutual interconnec￾tions [38]. Topological sequences of areas might provide the layout for signaling pathways across cortical networks [39]. Alternatively, hierarchies of cortices can be con￾structed, based on the laminar origin and termination patterns of interconnections [23,40]. To identify the clusters which are indicated by the high clustering coefficients of cortical networks, a compu￾tational approach based on evolutionary optimization was proposed [32]. This stochastic optimization method delineated a small number of distinctive clusters in global cortical networks of cat and macaque [32] (e.g. Figure 1b) Box 2. Brain connectivity: structural, functional and effective Anatomical connectivity is the set of physical or structural (synaptic) connections linking neuronal units at a given time. Anatomical connectivity data can range over multiple spatial scales, from local circuits to large-scale networks of inter-regional pathways. Anatom￾ical connection patterns are relatively static at shorter time scales (seconds to minutes), but can be dynamic at longer time scales (hours to days); for example, during learning or development. Functional connectivity [72] captures patterns of deviations from statistical independence between distributed and often spatially remote neuronal units, measuring their correlation/covariance, spectral coherence or phase-locking. Functional connectivity is time-dependent (hundreds of milliseconds) and ‘model-free’, that is, it measures statistical interdependence (mutual information) without explicit reference to causal effects. Different methodologies for measuring brain activity will generally result in different statistical estimates of functional connectivity [73]. Effective connectivity describes the set of causal effects of one neural system over another [72]. Thus, unlike functional connec￾tivity, effective connectivity is not ‘model-free’, but requires the specification of a causal model including structural parameters. Experimentally, effective connectivity can be inferred through perturbations, or through the observation of the temporal ordering of neural events. Other measures, estimating causal interactions can also be used (e.g. [52]). Functional and effective connectivity are time-dependent. Statisti￾cal interactions between brain regions change rapidly reflecting the participation of varying subsets of brain regions and pathways in different cognitive tasks [12–15], behavioral or attentional states [65], awareness [14], and changes within the structural substrate related to learning [74]. Importantly, structural, functional and effective connectivity are mutually interrelated. Clearly, structural connec￾tivity is a major constraint on the kinds of patterns of functional or effective connectivity that can be generated in a network. Structural inputs and outputs of a given cortical region, its connectional fingerprint [28], are major determinants of its functional properties. Conversely, functional interactions can contribute to the shaping of the underlying anatomical substrate, either directly through activity (covariance)-dependent synaptic modification, or, over longer time scales, through affecting an organism’s perceptual, cognitive or behavioral capabilities, and thus its adaptation and survival. 420 Review TRENDS in Cognitive Sciences Vol.8 No.9 September 2004 www.sciencedirect.com