Analysis and Function of Large-Scale Brain Networks

Organized by Olaf Sporns, PhD

Short Course IIIAnalysis and Function of Large-Scale Brain Networks

Olaf Sporns, PhD

Please cite articles using the model:[AUTHOR’S LAST NAME, AUTHOR’S FIRST & MIDDLE INITIALS] (2010)

[CHAPTER TITLE] In: Analysis and Function of Large-Scale Brain Networks. (Sporns O, ed) pp. [xx-xx]. Washington, DC: Society for Neuroscience.

All articles and their graphics are under the copyright of their respective authors.

Cover graphics and design © 2010 Society for Neuroscience.

Table of Contents

Introduction

Networks of the Brain: Quantitative Analysis and ModelingOlaf Sporns, PhD . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

Moving Between Functional and Effective ConnectivityAnthony R. McIntosh, PhD . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15

Relating Functional Measures to Network Descriptions in the Study of Brain SystemsSteven E. Petersen, PhD, Steven M. Nelson, PhD, Kelly Anne Barnes, PhD, and Bradley L. Schlaggar, MD, PhD . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25

Relating Variations in Network Connectivity to Cognitive FunctionMichelle Hampson, PhD . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35

Large-Scale Brain Networks in Cognition: Emerging PrinciplesVinod Menon, PhD . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43

Clinical Applications of Complex Network AnalysisDanielle S. Bassett, PhD . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55

Introduction

Neurons form complex networks whose anatomical architecture and integrated physiological activity are essential for brain function. Modern recording and imaging technology, combined with quantitative approaches to network analysis, are beginning to reveal characteristic structural and functional patterns in brain networks. At the large scale of brain regions and interregional pathways, recent studies have begun to demonstrate how structural features of brain networks shape their functional dynamics, and how different classes of functional networks become engaged in spontaneous and task-evoked neural activity. Emerging evidence indicates a relationship between network organization and individual cognitive performance, as well as an important role for network disturbances in nervous system dysfunction.

The architecture of large-scale brain networks thus offers new insights into how brain function emerges from the activity of distributed brain systems. Which aspects of network architecture are critical for efficient and coordinated neural processing? Which features of networks are most strongly associated with disruptions of behavior and cognition?

This short course will provide neuroscientists with an overview of current concepts, methods, and analysis tools in this emerging field. Special emphasis will be placed on how the organization of large-scale networks may inform our understanding of behavior and cognition in the healthy and the diseased brain.

Course organizer: Olaf Sporns, PhD, Department of Psychological and Brain Sciences, Indiana University. Faculty: Danielle S. Bassett, PhD, Department of Physics, University of California, Santa Barbara; Michelle Hampson, PhD, Department of Diagnostic Radiology, Yale University; Anthony R. McIntosh, PhD, Rotman Research Institute, Baycrest Centre for Geriatric Care, University of Toronto; Vinod Menon, PhD, Department of Psychiatry and Behavioral Sciences, Department of Neurology and Neurological Sciences, Program in Neuroscience, Stanford University Medical School; and Steven E. Petersen, PhD, Department of Neurology, Washington University in St. Louis School of Medicine.

© 2010 Sporns

Department of Psychological and Brain Sciences Indiana University

Bloomington, Indiana

Networks of the Brain: Quantitative Analysis and Modeling

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From Graph Theory to Modern Network ScienceOver the past decade, the study of networks has rapidly expanded across a number of scientific disciplines, from social sciences to economics, systems biology, and, most recently, neuroscience. The principal reason for this expansion is the realization that a wide range of complex interconnected and dynamic systems can be described and analyzed using a set of mathematical and statistical techniques originally developed in graph theory. Graph theory is a branch of mathematics that originated with Leonhard Euler’s famous 1736 treatment of the Königsberg bridge problem. Today, its applications are extremely broad, ranging from urban planning and traffic control to epidemiology, financial planning, internet search engines, and the analysis of complex biological systems from ecological to molecular scales (Barabási and Oltvai, 2004). Numerous surveys (Strogatz, 2001; Watts, 2004; Boccaletti et al., 2006; Barabási, 2009) have documented different classes of network architectures, dynamics, and growth processes. While much of classical graph theory has dealt with the analysis of random graphs, modern network science, with its renewed focus on real-world systems, has revealed that most, if not all, such systems have a distinctly nonrandom organization. This organization reflects the fundamental processes underlying their growth and functionality.

Understanding the organization of a complex network like the brain is a necessary first step to understanding its functions as an integrated system (Sporns, 2010). The arrival of modern brain mapping and recording techniques, together with renewed and concerted efforts to collect comprehensive brain connectiv-ity data sets (for example, the human connectome) (Sporns et al., 2005), necessitates the development of novel quantitative analysis and modeling tools to reveal features of brain network organization. Col-lectively, the chapters compiled for this short course provide an overview of how network approaches can be brought to bear on the anatomy and function of large-scale brain networks, particularly those of the human brain. The present chapter will briefly outline some of the relevant theoretical and methodological foundations that motivate and enable the analysis of brain networks. More detailed and formal treatments can be found elsewhere (Reijneveld et al., 2007; Bull-more and Sporns, 2009; Rubinov and Sporns, 2010).

Brain Networks and Relevant Network MetricsGiven the variety of methods for observing the brain’s anatomy and physiology, it is not surprising that

there are also a number of different ways to define and record brain connectivity (Horwitz, 2003; Jirsa and McIntosh, 2007). There are three main types of brain connectivity, describing structural, functional, and effective modes of interaction, respectively:• Structural connectivity refers to a set of physical

connections linking neuronal elements, such as synaptic links or fiber pathways;

• Functional connectivity describes patterns of dynamic interactions, usually computed from neural time series data (e.g., cross-correlation, mutual information, or coherence); and

• Effective connectivity captures a network of causal effects between neural elements, often inferred on the basis of temporal precedence cues in time series or on the basis of experimental perturbations.

While structural connectivity (at least on time scales of seconds to minutes) remains fairly stable, functional and effective connectivity can undergo rapid reconfigurations on the order of hundreds of milliseconds in the course of spontaneous or task-evoked neural activity. Common to all modes of brain connectivity is that they can be represented and analyzed as a network or graph.

Graphs are mathematical descriptions of a system that is composed of interconnected elements, comprising a set of nodes and edges. The nodes are the fundamental functional units of the system; in the brain, nodes may correspond to individual neurons, neuronal populations, or brain regions. The edges are connections or links that relate the nodes to each other; in the brain, edges can be synapses, fiber pathways, or statistical or causal relationships that describe functional association or similarity. The complete set of nodes and edges can be represented in a connection matrix, also called the “adjacency matrix” because it records which pairs of nodes are “adjacent” (i.e., directly connected by an edge).

Another fundamental concept is that of neural paths: sequences of edges that indirectly connect nodes to one another. The length of the shortest path between two nodes is also called the distance, defined as the minimal number of edges that lead from one node to the other. Note that, in graphs, distance refers to a topological separation of two nodes, not to their separation in a metric space. Most graph measures described in this brief survey derive either from the adjacency or the distance matrix, i.e., the direct connections (edges) or indirect connections (paths) between neural nodes.

Brain networks can be extracted in a number of different ways, depending on the recording method or

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experimental system employed in a given empirical study. A few basic steps are common to most approaches (Fig. 1). First, network nodes and edges must be defined. This is an extremely important step in any graph-based analysis of a brain network because all statistical analyses depend on the way the biological system is partitioned into a set of nodes and edges. At the level of large-scale brain systems, node definition involves partitioning the brain into coherent regions on the basis of histological or imaging data. Objective, data-driven parcellation methods are an active area of investigation and still face a number of serious challenges. Significant progress has been made by using clustering techniques that assess the similarity profile of structural (Johansen-Berg et al., 2004) or functional (Cohen et al., 2008) connections to derive boundaries between coherent brain regions.

Once nodes are defined, the definition of edges typically involves estimating pairwise associations between nodes. Structural networks are constructed on the basis of measured fiber tracts or pathways, whereas functional and effective edges are often based on statistical associations estimated from time series data. A wealth of possible measures is available for representing functional coupling. While most studies of functional connectivity still utilize simple measures such as correlation or coherence, more complex strategies involving partial correlations or estimates of directed (“causal”) interactions are beginning to gain ground.

Once a brain network has been constructed, it can be analyzed with quantitative tools from graph theory. Many such tools and measures are available, and at the time of writing only a small subset has been adapted and applied in the context of neuroscience. Before graph-theoretical approaches become more widely used, several important methodological issues need to be addressed. For example, recent studies have focused on the impact parcellation schemes and spatial scales make on the robustness of graph metrics (Zalesky et al., 2009) and on their test-retest reproducibility (Deuker et al., 2009). So far, these

methodological studies suggest that graph metrics report key features of network organization with high reliability and robustness.

In the remainder of the chapter, we will distinguish three broad classes of graph metrics that capture distinct aspects of brain network organization:• The existence of specialized communities or

modules (“functional segregation”); • The pattern of global interactions between

communities (“functional integration”); and• The functional impact of individual network

elements (“functional influence”).

Functional Segregation: Clustering and ModularityOf particular importance for a neural node’s processing characteristics and functional contribution are its interactions with its immediate neighbors. These are defined as the collection of nodes to which it is directly connected. Numerous studies of large-scale brain networks have shown that neural regions are arranged in clusters or “communities,” with individual nodes communicating in densely and mutually interconnected “neighborhoods.”

Figure 1. Recording structural and functional brain networks. The diagram illustrates four major steps: definition of network nodes (step 1), estimation of a suitable associa-tion measure (step 2), generation of an association matrix (step 3), and graph theoretical analysis of the resulting network (step 4). Modified with permission from Bullmore and Sporns (2009), their Figure 1.

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The clustering coefficient (Watts and Strogatz, 1998) is one of the most elementary measures for capturing the degree to which nodes in a network form local communities. Clustering of a node is high if the node’s neighbors are also neighbors of each other. In neural terms, a region has a high clustering coefficient if the regions to which it is connected are also connected to each other. Averaged over the entire network, the clustering coefficient reports the degree to which the network as a whole consists of nodes that share local connectivity. Because clustering varies greatly depending on the size and density of any given network, it is important to conduct statistical comparisons within populations of appropriately constructed random networks.

In many (but not all) cases, high clustering indicates the existence of multiple segregated communities of nodes. Such communities or modules can be identified by using algorithms that search for partitioning schemes. These schemes optimally subdivide the network, given a modularity measure: for example, one that is based on the relative density of within-module to between-module connections (Newman, 2006). Numerous studies of structural and functional brain networks have identified modules in large-scale brain networks whose placement and boundaries often coincide with either known cognitive networks (Dosenbach et al., 2008) or functional subdivisions of the human brain. By extending analytic approaches to modularity, investigators have recently demonstrated that modules in brain networks are arranged hierarchically (Meunier et al., 2009). This architectural feature promotes economical physical embedding (Bassett et al., 2010) and may have significant implications for brain dynamics (Kaiser et al., 2007).

Functional Integration: Path Length and EfficiencyWhile clustering and modularity provide information about the network’s local community structure, a complementary set of measures captures the network’s capacity to engage in more global interactions that bind together and integrate its dynamic activity. Several of these measures are based on paths: specifically, the lengths of the shortest paths linking pairs of nodes. Generally, shorter paths are thought to be more effective in passing information. Thus, the average path length for a network can provide an indication of its capacity for global information exchange. A related measure (essentially an inverse of the average path length but less disrupted by the presence of disconnected nodes) is the global efficiency (Latora and Marchiori, 2001). As is the

case for clustering, path length should be quantified in relation to a null population of random graphs, controlling for the size and density of the network.

Because of the importance of communication and information flow in large-scale brain networks, these measures of functional integration have fairly straightforward neurobiological implications. In a network with high efficiency, short communication paths can be identified between most or all pairs of nodes. Since clustering and path length are capturing complementary aspects of a network’s functional organization, they are often measured in conjunction. Also, these measures can be combined to assess the degree to which the network balances the existence of local and segregated communities with global, systemwide integration. High clustering and a short path length are the defining characteristics of a universal class of network architectures found in social, technological, and biological systems, including the brain (Sporns and Zwi, 2004). These are referred to as small-world networks (Watts and Strogatz, 1998). The modular small-world networks encountered in the brain not only allow for efficient information processing but are economical with respect to their wiring and metabolic cost (Bassett and Bullmore, 2006).

Functional Influence: Centrality and HubsReal-world networks deviate from randomness; in many cases, this entails specialization among nodes. Different classes of network elements can be distinguished by the way they participate in the network, i.e., by the way they are connected to the rest of the system. An important distinction can be made based on their “influence”: that is, their potential impact on the system as a whole and their capacity to transfer or process information. Highly influential nodes are often referred to as “hubs,” and identifying such hubs in brain networks can help one to map regions of the brain that are critical for coordinating functional interactions and for generating coherent system states. Hubs can be identified either on the basis of the number of interactions they engage in or by the degree to which they participate in short paths across the network. The latter measure, called “betweenness centrality” (Freeman, 1977), is particularly salient for structural networks, and it can be computed for edges as well.

Once an optimal modularity partition has been identified (Fig. 2A), the diversity of a node’s connections with respect to individual modules can be assessed in the form of a participation coefficient

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(Guimerà et al., 2007) (Fig. 2B). Of particular interest are highly connected nodes with a high participation coefficient: the so-called “connector hubs.” These maintain a diverse set of between-module connections and thus facilitate global intermodule communication. On the other hand, high-degree nodes with few or less diverse between-module connections have a low participation index. Consequently, these so-called “provincial hubs” participate mostly in interactions within their own module.

Hubs are of special interest in large-scale brain networks. Their high degree of centrality and, in the case of connectors, high level of participation in multiple functional communities predict that they will play a crucial role in integrative processes and information flow. The association of at least some hubs in the human brain with regions that engage in a high rate of metabolism (Hagmann et al., 2008), as well as with neuropathological changes in degenerative brain disease (Buckner et al., 2009), suggests intriguing hypotheses that may link brain network topology to function. Furthermore, the assessment of centrality or influence is a crucial component for predicting functional disturbances that will occur upon node or edge deletion. In a neurobiological context, the loss of more highly central nodes or edges owing to trauma or disease

should result in more widespread disruptions of information flow and dynamics in the remaining brain (Alstott et al., 2009).

Future ApplicationsGraph methods and their application to large-scale networks have begun to provide significant insights into the organization and function of the human brain. The remaining contributions to this short course illuminate various approaches, ranging from anatomical networks to functional connectivity in the resting brain, task-evoked activity, individual differences, and clinical populations. As the applications of graph theory continue to expand, important methodological and interpretational questions will need to be addressed. For example, objective methods for comparing networks within individual subjects or across subject populations will be needed to facilitate longitudinal studies of brain development and disease progression.Many aspects of brain networks await future investigation. Network approaches have already revealed significant between-subject variability in structural and functional connectivity, so the role of variations in networks for variable cognition and behavior will likely be an intense area of future research. Other promising avenues will lead to the areas of translational neuroscience and in discovering relations between genetic and brain networks.

Figure 2. Modularity and classification of hubs. The schematic diagram A shows three modules (gray circles) linked by provincial (green) and connector hubs (red). Provincial hubs link nodes within a single module, while connector hubs link modules to each other. The diagram B shows a visualization of the community structure of the functional connectivity estimated from simulated blood oxygenation level–dependent (BOLD) responses of 47 regions of the macaque cortex (Honey et al., 2007). Two modules consisting mostly of visual and somatomotor regions are linked by multiple connector hubs located predominantly in parietal and frontal cortex.

A B

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Sporns O (2009) Modeling the impact of lesions in the human brain. PLoS Comput Biol 5:e1000408.

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Reijneveld JC, Ponten SC, Berendse HW, Stam CJ (2007) The application of graph theoretical analysis to complex networks in the brain. Clin Neurophysiol 118:2317-2331.

Rubinov M, Sporns O (2010) Complex network measures of brain connectivity: uses and interpretations. Neuroimage 52:1059-1069.

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Rotman Research Institute Baycrest Centre for Geriatric Care

University of Toronto Ontario, Canada

Moving Between Functional and Effective Connectivity

Anthony R. McIntosh, PhD

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IntroductionOne of the current challenges in neuroscience is to understand how brain operations give rise to mental phenomena ranging from sensation and perception to memory and attention. We are getting to know a great deal about how the brain functions in basic sensory and motor systems. For higher mental functions, however, a long scientific battle has been raging as to whether such functions are localizable. A dominant assumption in neuroscience is that certain parts of the brain play unique roles in mental function. This idea of one region/one function comes from early studies that showed some remarkable cognitive deficits due to lesions in specific parts of the brain. Up until the last 15 to 20 years, the tools available to neuroscientists have allowed them to examine only small parts of the brain at a time; their findings, although limited, have reinforced the notion of discrete functions in specific brain regions.

Modern neuroimaging tools allow us to measure how the entire brain reacts as people perform different mental operations. We are finding that many more brain areas “light up” when someone pays attention, thinks, and remembers than we would have expected based on the results from brain lesion studies. However, many researchers in the field, who continue to focus on one or two critical brain regions, overlook this new information.

The brain is made up of individual elements: from cells to neural ensembles. These elements are connected, so their individual actions can be combined through their interactions. The combined responses of small groups of cells give interacting brain areas a rich response repertoire, ranging from simple sensation to consciousness and reason. When neuroimaging data are examined in terms of brain interactions, it is observed that many regions cooperate in our thought processes. Emerging neurobiological theories emphasize the combined actions of interacting brain elements (cells to ensembles to regions) as the link between the brain and human mental function (McIntosh, 2000a,b).

From a network perspective, anything that affects the integrity of a specific brain region will necessarily influence the operation of the entire network or networks in which this region participates. Behavioral deficits following damage, or arising from disease processes, could thus reflect either the abnormal operation of a damaged network, or the formation of a completely different network with a new behavioral repertoire. Thus, much could be learned about brain dysfunction (as well as normal function) by examining network operations in

subjects where mental functions are compromised by damage or disease.

If normal brain function and dysfunction result from the action of distributed networks, then analytic approaches tuned to such dynamics would best capture these actions. What follows reviews some of the basic methods that have used for network analysis and presents the underlying theory for applying and developing a new perspective that serves to unite the understanding of brain function and dysfunction within one framework.

Theoretical Basis and Tools for Network AnalysisNetwork analysis, as applied to neuroimaging, can be considered a collection of analytic methods: e.g., interregional correlations/covariances or the corresponding measure in the frequency domain, such as coherence. These methods attempt to measure the interdependency among brain areas during different cognitive states. The driving assumption behind the use of these approaches is that the correlations/covariances of activity measure neural interactions. Neural interactions refer, in a general sense, to influences that different elements in the nervous system have on each other via synaptic communication; the term “elements” refers to any constituent of the nervous system, either a single neuron or collections thereof.

Traditional approaches to understanding neural interactions have focused on studying systematic variation in activity with some manipulated parameter. However, activity changes in one neural element usually result from a change in the influence of other connected elements; thus, focusing on activity in one area will cause one to miss the change in afferent influence. Furthermore, it is logically possible for the influences on an element to change without an appreciable change in measured activity. The simplest example is where an afferent influence switches from one source to another, without a change in the strength of the influence. For example, in the feed-forward network depicted in Figure 1, region C may show similar activity patterns when influence from either A or B is strong. Therefore, monitoring regional activity alone would not be able to differentiate the source of the effects, but measures of the relation of activity between elements (e.g., path v versus w) would be able to.

The measurement of neural interactions in neuroimaging has developed under two general approaches. The first emphasizes pairwise

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interactions, often in terms of correlations or covariances. The second incorporates additional information, such as anatomical connections, and considers a simultaneous interaction of several neural elements to explicitly quantify the effect one element has on another. These two approaches are known as “functional connectivity” and “effective connectivity,” respectively. Both terms were introduced in the context of electrophysiological recordings from multiple cells (Aertsen et al., 1987) and have been used with reference to neuroimaging data (Friston et al., 1993; Friston, 1994; Horwitz, 2003).

Although the majority of studies of network interactions have focused on the young healthy brain, tremendous gains could be had in studying these operations in other age-groups and across patient populations. From a developmental perspective, the fact that brain structure changes across the entire life span has obvious implications for network operations. Even where overt behavior does not show an age-related change, there may be quite different sets of regional activity and interactivity between age-groups (Grady, et al., 2003).

In clinical populations, the network reorganiza-tion may be even more dramatic, depending on the source of pathology. In cases of brain damage, observed network reorganization will likely be two-

fold: primary response to damage (de-generation, diaschisis); and secondary responses, as the networks reconfigure in an attempt to adapt to the insult (compensatory mechanisms). An in-teresting implication is that some of the behavioral deficits may reflect the secondary response. In degenerative disorders, a similar reorganization likely occurs, although over a more protracted time scale. Finally, mental disorders (e.g., schizophrenia, major depression) also will affect the integrity of net-work operations (Jennings et al., 1998; Welchew et al., 2002; Seminowicz et al., 2004).

It should be pointed out that the term “functional connectivity” has been applied to both task-dependent changes in functional connections and those that persist in the absence of any overt task: the so-called resting state functional connectivity (Biswal et al., 1995). The term functional connectivity is equally valid in both applications, but the emphasis is quite different:

Task-dependent functional connectivity focuses on whether there is a change in the functional connections between regions as task demands change, while resting state functional connectivity emphasizes the overall pattern of functional connections and its relation to the underlying anatomy. The latter assumes that a functional connection must be mediated at some level by an anatomical connection. It is, however, worth remembering that a non-zero functional connection does not guarantee a direct anatomical connection.

Recent modeling work suggests that the patterns of resting state connectivity directly result from the anatomical and functional architecture of the brain (Honey et al., 2007). In a simulated network, as the architecture and dynamics more closely approximate real neural systems, distributed patterns of functionally connected networks emerge. Remarkably, the spatial patterns of these networks resemble those reported in functional magnetic resonance imaging (fMRI) experiments. If the anatomical structure is perturbed or the dynamics changed, then the patterns break down. Such findings suggest that resting state connectivity may indeed index the integrity of a given brain. This premise has been substantiated by empirical observations of resting state correlations in normal aging, showing a reduction in overall functional connectivity,

Figure 1. Hypothetical anatomical network linking four cortical regions. The labels on the connections, u, v, w, x, y, z, correspond to the estimated path coefficients, which represent the effective connections between regions. Region C may show similar activity between two conditions despite have dif-ferent patterns of effective connections. For instance, the activity in C would be the same if the effect through path v is high and y is zero, or if the effect in v was zero and y was high. Such a change in effective connection is acces-sible only through analysis covariances of activity between regions.

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particularly among frontal and parietal regions. The reduced functional connectivity correlates with a decline in behavioral measures of executive function and overall processing speed (Damoiseaux et al., 2008). Degenerative disorders such as Alzheimer’s disease also show reduced functional connectivity related to disease severity (Stam et al., 2006). Taken together, these empirical and modeling findings suggest that resting state correlations may act as a useful “fingerprint” for the integrity of functional networks.

Functional and effective connectivity can also show task-dependent changes. Horwitz et al. (1992), using positron emission tomography (PET), showed functional connectivity patterns that mapped on to the use of “what” versus “where” cortical visual pathways. Effective connectivity analyses of these data (McIntosh et al., 1994) showed task-dependent switches in prefrontal feedback and strong suppressive interactions between “what” and “where” pathways.

Importantly, effective connectivity can differentiate between top-down versus bottom-up effects. Category-specific responses have been observed frequently in the ventral occipitotemporal lobe (e.g., fusiform gyrus for faces, parahippocampal gyrus for places), which is typically considered a top-down effect. Using dynamic causal modeling (DCM) (Friston et al., 2003) to estimate effective connectivity, Mechelli and colleagues (2003) found that early sensory areas changed their effects on category-specific areas in relation to the stimuli, but higher-order association regions did not show such changes in effects. Thus, category specificity in these data was a bottom-up effect. It is likely that the real story of the neural instantiation of category specificity is an outcome of reciprocal interactions among neural sites. The results from the effective-connectivity analyses have enriched models of cognitive function by moving them beyond strict hierarchical representations and emphasizing the dynamic and interactive nature of neural instantiations.

Major Steps in Network AnalysisThe progression from data collection to the final stage of a network analysis will depend, largely, on the question one asks of the data. Assuming a comprehensive analysis is planned, the steps can be outlined as follows:1. Perform activation analysis. This is the usual

first step in any image analysis. It is reasonable to assume that regions showing similar activity changes between tasks may also be part of the same functional network, though this is not a certainty

(Stephan, 2004). While the typical mode of activation analysis uses a univariate approach, multivariate approaches may be preferable when one is attempting to identify cohesive networks. The primary reason is that, where there are dependencies among measured (dependent) variables, multivariate approaches will have greater sensitivity because they explicitly make use of these correlations (Lukic et al., 2002).

2. Relate brain activity to behavioral measures. Although activation analysis is the most common approach in neuroimaging, a growing number of investigators are relating activity patterns to either performance measured during the experiment or to demographic measures. In the former instance, the brain-behavior analysis may be considered as completing a “causal chain”; that is, the activation analysis would be most sensitive to the input side of the chain, and behavior analysis to the output. Combining brain-behavior analysis with activation analysis can be seen as getting the most comprehensive coverage of most, if not all, regions that are part of the functional network for a given task. Finally, relating the patterns of functional or effective connectivity provides an anchor for interpretation and confirms that the patterns of interactivity actually “make a difference” in performance.

3. Analyze functional connectivity. Once the candidate nodes are collected, the pattern of interactions can be used to examine functional connectivity. Probably the simplest approach to this analysis is calculating pairwise correlations/covariances. Functional connectivity estimates can be compared across tasks or groups to define dependencies on this dimension.

4. Analyze effective connectivity. Functional connectivity can be easily assessed across any number of regions of interest, but effective connectivity requires a more focused approach wherein a subsection of regions identified from the previous steps are considered for more detailed models.

Some neuroscientists are concerned about which source of variance, across tasks or across subjects, is best for estimating neural interactions (Friston, 1995; Strother et al., 1995a,b). The issue of which source of variability is “correct” is not unique to neuroscience (Mandler, 1959), and there is no necessity for making a logical connection between covariances computed across tasks within-subjects, and those computed across subjects within-task. However, there is also no justification for preferring one source of variability to another, particularly in cases where both can be examined, as in fMRI or event-related potential

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(ERP) studies. Within-subjects analysis assesses the direct relation between regions, while across-subjects analysis indicates the stability of that relation. These are complementary, not contradictory, pieces of information.

For illustration, say we chose ten people of varying heights and weight and asked them to pull on a potentiometer by flexing their arm (an arm curl). If you measured muscle activity in the arm of each subject, say through blood flow, and correlated them, you would probably find a strong correlation with the biceps and brachialis muscles. Although each person would differ in the amount of blood flow to the muscles, from the correlation based on this variance, you would conclude that the muscles on the ventral surface of the arm have something to do with flexion. If, instead, you measured muscle activity in a single subject with a progressive increase in the resistance to arm flexion, you would find a correlation between muscle activity in the ventral part of the arm. Replicating the measurement by running different subjects would lead you to the same conclusion you had reached by using the between-subjects covariance. The point here is that computing covariances between or within subjects can lead to complementary conclusions, so long as there are adequate experimental controls and the statistical analysis ensures the answers are reliable.

It should not be taken as a suggestion that all the network analysis steps listed above must be carried across to every data set. Obviously, the choice of analysis (functional connectivity or effective connectivity) depends on the particular question one has to ask of the data. Functional connectivity analyses are likely satisfactory when the goal is in the exploratory/explanatory mode. For example, if a peculiar activation pattern were noted in one group, assessing the functional connectivity of that region with the rest of the brain could help explain the peculiarity in terms of a difference in the pattern of interactions in that group, relative to controls. On the other hand, if the question were phrased in terms of directed influences, then analysis of effective connectivity would be needed. For example, if the question was whether top-down influences from prefrontal to temporal cortices vary between groups, an analysis of effective connectivity must be performed to distinguish top-down from bottom-up effects.

Taxonomy of TechniquesOne has only to casually flip through an issue of NeuroImage or Human Brain Mapping to realize that methodological developments in the estimation of

functional and effective connectivity are exploding. The sections below briefly characterize the major methods used for estimating connectivity and list their advantages and disadvantages. This is by no means an exhaustive list.

Functional connectivityRegional correlationThis is perhaps the simplest and most often used method. Pairwise correlations of regions of interest, or voxels, provide a snapshot of functional connectivity patterns (Horwitz et al., 1984, 1991). This method has the advantage of simplicity and uses a minimal number of assumptions beyond linearity. Where the technique becomes problematic is when the number of correlations grows and one must correct for multiple statistical tests (the same problem as with other univariate measures). Moreover, as the number of correlations grows, easily summarizing the patterns becomes difficult. It is at this point that multivariate methods may be helpful (see below).

Psychophysiological interactionsLinear regression methods sometimes appear to lie in a gray area between functional and effective connectivity. For example, the method to estimate psychophysiological interactions (PPIs) (Friston et al., 1997) in the statistical parametric mapping (SPM) package is used to assess task-dependent changes in the degree that one region (Y) predicts or explains the activity of another (X) (McIntosh and Gonzalez-Lima, 1994). However, the PPI approach provides the same statistical result as would be obtained if the roles of X and Y were reversed. Thus, the PPI method is most similar to an estimate of functional connectivity.

Principal component analysisA tried-and-true method, principal component analysis (PCA) has been applied to a number of neuroimaging data sets to summarize complex patterns of interregional correlations. It is a helpful means to follow from the calculation of pairwise correlations. The PCA solutions are always unique for a given data set (compared with those of independent component analysis [ICA]), and the calculation of the principal components is relatively fast. The main drawbacks include:• Orthogonality of components, which may impose

artifactual groupings within a component. This effect can be alleviated somewhat by orthogonal or oblique rotation; and

• The decomposition depends on the rank of matrix. If there are more regions and observations, the matrix will be rank-deficient, which can obscure the “true” grouping of regions.

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Independent component analysisICA is a newer method than PCA and has been applied extensively to fMRI and EEG data. It was originally a denoising method but has since been shown to be quite powerful for extracting resting state networks in fMRI data (using a variation of the usual ICA: tensor ICA) (Beckmann and Smith, 2005). ICA has the advantage over PCA of not assuming orthogonality but rather maximal independence. In this case, it has the capacity to separate artifactual components from those of interest. This capacity depends, however, on the flavor of ICA used and the nature of the artifact. The drawbacks of ICA include:• Nonunique solutions without additional constraints;

and• Computationally expensive for large data sets.

Partial least squaresThe partial least squares (PLS) method has been used in neuroimaging for more than a decade and has been applied to PET, fMRI, and EEG (McIntosh et al., 1996a; McIntosh and Lobaugh, 2004). It is related to canonical correlation analysis in that it relates the neuroimaging data to the experimental design (e.g., design contrasts); performance measures; or, for functional connectivity, one or more voxels. In the latter case, it can be considered to be a multivariate extension of PPI. PLS has the flexibility to work on combinations of design, behavior, and voxels and has been extended to merge multiple imaging data sets (Martinez-Montes et al., 2004). It has the advantage of creating a flexible framework for direct testing of statistical dependency in neuroimaging data. Its main drawbacks are as follows:• Orthogonal extraction of components like PCA

may obscure the true dependencies. To offset this effect, the extraction can be done with ICA (Lin et al., 2003);

• Interpretation can be complicated in complex designs; and

• Statistical assessment through resampling is computationally expensive.

effective connectivityStructural equation modelingStructural equation modeling (SEM) is a multivariate linear regression tool and has been used primarily for PET and fMRI data (McIntosh and Gonzalez-Lima, 1994; Buchel and Friston, 1997), although its use has been extended to EEG data (Astolfi et al., 2004, 2005). Its primary use has been to identify changes in effective connectivity between tasks or groups within a defined anatomical network (Protzner and McIntosh, 2006). It has also been used to identify likely patterns of effective connectivity in a given

data set (Bullmore et al., 2000). It has the advantage of allowing fast and robust computations and can be used for rather complicated models (McIntosh et al., 1996b); more recently, it was validated for use with neuroimaging data based on large-scale simulations (Kim and Horwitz, 2009; Marrelec et al., 2009). It has a long history and, thus, several software packages and numerous algorithmic variations are available. For its application to neuroimaging, the main drawbacks are as follows:• Absolute assessment of model fit is very dependent

on sample size;• It needs to prespecify connection directions; and• It cannot deal with fully reciprocal models.

Granger causalityGranger causality (GC) is a general methodological approach for analyzing dependencies in time series. Its most common implementation comes in the form of autoregressive modeling (Goebel et al., 2003). There are also variations that operate in the spectral domain (Kaminski et al., 2001), although they have not been used in fMRI. Methods that generally fall under this label have the advantage of working directly with the time series, allowing inferences on directionality without needing to prespecify the direction (cf. SEM and DCM). Its main drawbacks are as follows:• Most implementations are pairwise. Multivariate

extensions are possible (Deshpande et al., 2009), but with many regions, the solutions may become unstable;

• For fMRI, GC requires relatively short repetition time (TR) to get a robust time series; and

• There has been a recent observation that GC may provide spurious estimates of directional effects in fMRI data (David et al., 2008). However, a series of papers that will appear in the journal NeuroImage will address this observation (Roebroeck, et al., in press).

Dynamic causal modelingUnlike SEM and GC, DCM was designed specifically for neuroimaging data and has been applied to fMRI and EEG (Friston et al., 2003; Kiebel et al., 2009). Like SEM, DCM has also received some validation through large-scale simulations (Lee et al., 2006). DCM uses a generative model of the measured signal to infer its neural sources. The effective connectivity estimation then proceeds based on the neural source activity rather than the measured signal (e.g., blood oxygen level–dependent [BOLD] or EEG). The model first estimates the intrinsic connections between sources and then the changes in the connections that come about through external perturbation (usually the experimental design). This can be thought of

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in the general linear model (GLM) framework as estimating the grand mean, and the deviations from the mean, from the experimental manipulation. A Bayesian estimation procedure is used to estimate the effective connections and their change, as well as providing evidence for the “best” model.

The advantages of DCM are the tight coupling to biophysical models, which enables an interpretation of the effective connections in terms of neurophysiology. There is a potential for investigating several models for mediation of effective connections using model evidence. Its main drawbacks are as follows:• It is computationally expensive, and in its present

form, cannot handle more than about six regions;• It cannot easily model intrinsic activity such as

resting state networks; and• Some researchers question the robustness of

parameter estimation, given the extensive constraints on the generative model.

Final ThoughtsFunctional or effective connectivity estimation has benefits for developing theories of brain operation. Brain imaging researchers will often discuss the results from regional activation analysis in terms of “functional networks” without specifically referring to how these networks are formed. By requiring that the networks be expressed through either functional or effective connectivity estimation, the researcher’s assumptions about the network organization are more obvious.

It is also critical to acknowledge, particularly with effective connectivity, that the results are a model. There are decisions that have to be made in the course of estimation, such as the selection of regions to include in the model and how their interactions are mediated (through specification of anatomical connections). Because it is a model, however, it is an approximation of reality and, by definition, false. To paraphrase the statement from statistician George Box that all models are wrong but some are useful, the utility of any model comes from its capacity to explain neural dynamics and cognitive function and to suggest further avenues of research to test and develop the model.

Finally, one of the greatest sins in analyzing neuroimaging data is to assume that there is a single correct method. While one can certainly make mistakes in the application of a method, there is little to be gained from “analytic chauvinism.” The complexity of the data that are extracted from neuroimaging methods dictates that a single analytic approach is insufficient. I strongly concur with

the position advocated by others: that a pluralistic approach will provide a much better appreciation of how the brain brings about human mental function (Lange et al., 1999).

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Deshpande G, LaConte S, James GA, Peltier S, Hu X (2009) Multivariate Granger causality analysis of fMRI data. Hum Brain Mapp 30:1361-1373.

Friston K (1994) Functional and effective connectivity: a synthesis. Hum Brain Mapp 2:56-78.

Friston KJ (1995) Statistical parametric mapping: ontology and current issues. J Cereb Blood Flow Metab 15:361-370.

Friston K, Frith C, Fracowiak R (1993) Time-dependent changes in effective connectivity measured with PET. Hum Brain Mapp 1:69-79.

Friston KJ, Buechel C, Fink GR, Morris J, Rolls E, Dolan RJ (1997) Psychophysiological and modulatory interactions in neuroimaging. Neuroimage 6:218-229.

Friston KJ, Harrison L, Penny W (2003) Dynamic causal modelling. Neuroimage 19:1273-1302.

Goebel R, Roebroeck A, Kim DS, Formisano E (2003) Investigating directed cortical interactions in time-resolved fMRI data using vector autoregressive modeling and Granger causality mapping. Magn Reson Imaging 21:1251-1261.

Grady CL, McIntosh AR, Craik FI (2003) Age-related differences in the functional connectivity of the hippocampus during memory encoding. Hippocampus 13:572-586.

Honey CJ, Kotter R, Breakspear M, Sporns O (2007) Network structure of cerebral cortex shapes functional connectivity on multiple time scales. Proc Natl Acad Sci USA 104:10240-10245.

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Horwitz B, Duara R, Rapoport SI (1984) Intercorrelations of glucose metabolic rates between brain regions: application to healthy males in a state of reduced sensory input. J Cereb Blood Flow Metab 4:484-499.

Horwitz B, Grady C, Haxby J, Schapiro M, Carson R, Herscovitch P, Ungerleider L, Mishkin M, Rapoport SI (1991) Object and spatial visual processing: Intercorrelations of regional cerebral blood flow among posterior brain regions. J Cereb Blood Flow Metab 11:S380.

Horwitz B, Grady CL, Haxby JV, Schapiro MB, Rapoport SI, Ungerleider LG, Mishkin M (1992) Functional associations among human posterior extrastriate brain regions during object and spatial vision. J Cogn Neurosci 4:311-322.

Jennings JM, McIntosh AR, Kapur S, Zipursky RB, Houle S (1998) Functional network differences in schizophrenia: a rCBF study of semantic processing. Neuroreport 9:1697-1700.

Kaminski M, Ding M, Truccolo WA, Bressler SL (2001) Evaluating causal relations in neural systems: Granger causality, directed transfer function and statistical assessment of significance. Biol Cybern 85:145-157.

Kiebel SJ, Garrido MI, Moran R, Chen CC, Friston KJ (2009) Dynamic causal modeling for EEG and MEG. Hum Brain Mapp 30:1866-1876.

Kim J, Horwitz B (2009) How well does structural equation modeling reveal abnormal brain anatomical connections? An fMRI simulation study. Neuroimage 45:1190-1198.

Lange N, Strother SC, Anderson JR, Nielsen FA, Holmes AP, Kolenda T, Savoy R, Hansen LK (1999) Plurality and resemblance in fMRI data analysis. Neuroimage 10:282-303.

Lee L, Friston K, Horwitz B (2006) Large-scale neural models and dynamic causal modelling. Neuroimage 30:1243-1254.

Lin FH, McIntosh AR, Agnew JA, Eden GF, Zeffiro TA, Belliveau JW (2003) Multivariate analysis of neuronal interactions in the generalized partial least squares framework: simulations and empirical studies. Neuroimage 20:625-642.

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Martinez-Montes E, Valdes-Sosa PA, Miwakeichi F, Goldman RI, Cohen MS (2004) Concurrent EEG/fMRI analysis by multiway Partial Least Squares. Neuroimage 22:1023-1034.

McIntosh AR (2000a) From location to integration: how neural interactions form the basis for human cognition. In: Memory, consciousness, and the brain: The Tallinn Conference (Tulving E, ed). pp 346-362. Philadelphia: Psychology Press.

McIntosh AR (2000b) Towards a network theory of cognition. Neural Netw 13:861-876.

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McIntosh AR, Gonzalez-Lima F (1994) Structural equation modeling and its application to network analysis in functional brain imaging. Hum Brain Mapp 2:2-22.

McIntosh AR, Grady CL, Ungerleider LG, Haxby JV, Rapoport SI, Horwitz B (1994) Network analysis of cortical visual pathways mapped with PET. J Neurosci 14:655-666.

McIntosh AR, Bookstein FL, Haxby JV, Grady CL (1996a) Spatial pattern analysis of functional brain images using Partial Least Squares. Neuroimage 3:143-157.

McIntosh AR, Grady CL, Haxby JV, Ungerleider LG, Horwitz B (1996b) Changes in limbic and prefrontal functional interactions in a working memory task for faces. Cereb Cortex 6:571-584.

McIntosh AR, Lobaugh NJ (2004) Partial least squares analysis of neuroimaging data: applications and advances. Neuroimage 23:S250-S263.

Mechelli A, Price CJ, Noppeney U, Friston KJ (2003) A dynamic causal modeling study on category effects: bottom-up or top-down mediation? J Cogn Neurosci 15:925-934.

Protzner AB, McIntosh AR (2006) Testing effective connectivity changes with structural equation modeling: what does a bad model tell us? Hum Brain Mapp 27:935-947.

Roebroeck A, Formisano E, Goebel R. Reply to Friston and David: After comments on: The identification of interacting networks in the brain using fMRI: Model selection, causality and deconvolution. Neuroimage, in press.

Seminowicz DA, Mayberg HS, McIntosh AR, Goldapple K, Kennedy S, Segal Z, Rafi-Tari S (2004) Limbic-frontal circuitry in major depression: a path modeling metanalysis. Neuroimage 22:409-418.

Stam CJ, Jones BF, Manshanden I, van Cappellen van Walsum AM, Montez T, Verbunt JP, de Munck JC, van Dijk BW, Berendse HW, Scheltens P (2006) Magnetoencephalographic evaluation of resting-state functional connectivity in Alzheimer’s disease. Neuroimage 32:1335-1344.

Stephan KE (2004) On the role of general system theory for functional neuroimaging. J Anat 205:443-470.

Strother SC, Anderson JR, Schaper KA, Sidtis JJ, Liow J-S, Woods RP, Rottenberg DA (1995a) Principal components analysis and the scaled subprofile model compared to intersubject averaged and statistical parametric mapping: I. “Functional connectivity” of the human motor system studied with [15O]water PET. J Cereb Blood Flow Metab 15:738-753.

Strother SC, Kanno I, Rottenberg DA (1995b) Principal components analysis, variance partitioning, and “functional connectivity”. J Cereb Blood Flow Metab 15:353-360.

Welchew DE, Honey GD, Sharma T, Robbins TW, Bullmore ET (2002) Multidimensional scaling of integrated neurocognitive function and schizophrenia as a disconnexion disorder. Neuroimage 17:1227-1239.

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Department of Neurology Washington University in St. Louis School of Medicine

St. Louis, Missouri

Relating Functional Measures to Network Descriptions in the Study of Brain Systems

Steven e. Petersen, PhD, Steven M. Nelson, PhD, Kelly Anne Barnes, PhD, and Bradley L. Schlaggar, MD, PhD

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IntroductionUnlike in other networks, such as those seen in social systems, the components of brain networks, i.e., their nodes and edges, are not easily defined. As mentioned in the chapter by Sporns, node and edge definition is critical to understanding functional networks in the brain. The teaching points of this chapter relate to an integration of evoked functional responses, as determined from task-related functional magnetic resonance imaging (fMRI), and resting correlations between brain regions, as defined with resting state “functional connectivity” MRI (rs-fcMRI). By integrating the two kinds of data across a number of analyses, we make the following arguments:• That candidate node definitions are aided greatly

by an integrated approach; and• That the outcome of the more calibrated node

definition can provide deeper insights into functional differentiation and interpretation.

To this end, a set of analyses focused on the left lateral parietal cortex (LLPC) will be presented. These studies will include several analyses of task-evoked fMRI activation studies and rs-fcMRI studies. This combined approach results in a sixfold parcellation of LLPC based on several factors: the presence (or absence) of memory retrieval–related activity, dissociations in the profile of task-evoked time courses, and membership in large-scale resting brain networks. This parcellation strategy should serve as a roadmap for future investigations aimed at understanding LLPC function. In addition, this analysis strategy can be applied to other extents of the cerebral cortex.

Why the LLPC?In humans, parietal cortex has traditionally been linked to processing mechanisms involving attention (Corbetta et al., 1998; Rushworth et al., 2001; Corbetta and Shulman, 2002; Yantis et al., 2002; Dosenbach et al., 2006, 2007). Other accounts of parietal cortex function, particularly focused on the left hemisphere, have examined its role in reading (Turkeltaub et al., 2002), as well as numerosity judgments and arithmetic (Göbel and Rushworth, 2004; Hubbard et al., 2005).

More recently, a surge in research has been devoted to understanding the contributions LLPC makes to memory retrieval (Wagner et al., 2005). In particular, a great deal of research has been aimed at understanding how humans distinguish between previously experienced information (“old”) and that which is novel (“new”), a phenomenon known as the “retrieval success effect” (Henson et al., 2000;

Konishi et al., 2000; McDermott et al., 2000; Wheeler and Buckner, 2003). The most common regions showing retrieval success effects are found in the lateral parietal cortex (Simons, 2008), and although this differential activation is typically bilateral, the most robust effects include a large expanse of LLPC (McDermott et al., 2009). A secondary finding across these studies is the presence of a dorsal–ventral distinction in LLPC. This distinction appears to dissociate dorsal regions near intraparietal sulcus (IPS) involved in familiarity judgments from more ventral regions near the angular gyrus (AG) that are involved in recollection (Henson et al., 1999; Wheeler and Buckner, 2004).

Studies across domains have yielded a multitude of processing descriptions, suggesting that distinct regions in parietal cortex might subserve unique functional contributions. The analyses presented here attempt to provide a parcellation scheme based on convergence across multiple data types. In doing so, we highlight the utility of a large-scale network perspective.

Preliminary Parsing of LLPC Region Using rs-fcMRI Boundary MappingThe first step in parsing the LLPC region is to use the recently developed technique of rs-fcMRI boundary mapping to identify “correlationally” distinct regions in LLPC. rs-fcMRI boundary mapping is based on the observation that rs-fcMRI can dissociate regions within the cortex using edge-detection algorithms (Cohen et al., 2008). The technique developed in Cohen et al. (2008) compares whole-brain correlation maps of adjacent cortical seeds and searches for these abrupt changes in maps that depict boundaries between cortical regions.

For the purposes of this experiment, a 27 × 27 grid of small spherical foci (6 mm diameter) was generated over the extent of LLPC (Fig. 1A) using Caret software (Van Essen Laboratory, Saint Louis, MO) (Van Essen et al., 2001; http://brainmap.wustl.edu/caret). The grid extended outside the traditional bounds of parietal cortex to decrease the chance that any functional borders near the anatomical boundaries of LLPC would go undetected.

The resulting rs-fcMRI boundary map depicts the likely boundary at any given focus in the patch (Fig. 1B). “Hot” and “cool” colors indicate high and low probabilities, respectively, of the existence of a boundary. The apparent centers of the bounded regions in LLPC were obtained by inverting the map

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so that hot colors indicate rs-fcMRI map consistency between nearby seeds (Fig. 1C,D). Regions of interest (ROIs) were defined as 10 mm diameter spheres (gray) at peak locations of consistency using two-dimensional peak-finding algorithms. This resulted in 25 ROIs across the grid. Ten of the defined ROIs were outside of the parietal cortex and were excluded from further analyses, leaving 15 LLPC mapping ROIs to become targets of additional investigation.

Preliminary Examination of the Functional Responses of Each ROIWe next applied the 15 mapping ROIs to a number of task-related fMRI studies that contained a contrast of “old” versus “new” items and performed a meta-analysis. Preliminary examination of the functional responses of each ROI showed a geographic distinction between retrieval-related and -unrelated regions. Only the seven more posterior

Figure 1. rs-fcMRI data were used to generate probabilistic boundary maps in order to define regions in LLPC. A, A square patch of 729 spherical foci (6 mm diameter, 27 × 27 grid, spaced 6 mm apart) was created using Caret software (Van Essen et al., 2001) and is shown here on an inflated cortical surface rendering. The surface is rotated to allow better visualization of LLPC. A (anterior), P (posterior), L (lateral), M (medial). B, rs-fcMRI boundary map generated using Canny method indicates the likelihood of a border at each seed. “Cooler” colors represent stable rs-fcMRI patterns, whereas “hotter” colors represent high border likeli-hood, i.e., rapidly changing rs-fcMRI patterns. C, Inverted rs-fcMRI boundary map demonstrates peaks of stability from the previous map. Centers are shown as dark gray spheres (10 mm diameter) on the inflated surface. The blue circle indicates ROIs located within LLPC. D, Unprojected data from previous panel C al-lowing better visualization of borders. Gray dots represent ROIs, and those circled in blue indicate regions located within LLPC. For orientation purposes, the grid contains anatomical labels that roughly correspond to these locations on the cortical surface. aIPS, anterior intraparietal sulcus; SMG, supramarginal gyrus; SPL, superior parietal lobule; vIPS, ventral intraparietal sulcus.

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rs-fcMRI Relationships Between Boundary Mapping ROIs and Other Brain RegionsThe boundary mapping definition of the LLPC regions was driven by differences in whole-brain rs-fcMRI relationships, which were overlapping yet distinct. One avenue to address this ambiguity is to interrogate these relationships among the specific regions of LLPC. In other words, which regions outside of LLPC are most strongly functionally connected to each of the LLPC regions (the region’s “neighborhood”)? And do regions in different neighborhoods show distinct functional time courses? If an LLPC region, such as the posterior inferior parietal lobule (pIPL), possesses a task-evoked time

course reflecting some functional process, do other regions in its neighborhood share similar functional time courses? The following sections aim to answer these questions by exploring the relationships of LLPC regions to regions elsewhere in the brain.

The next step in our analysis was to define sets of regions that are related to LLPC regions using rs-fcMRI data. Although rs-fcMRI boundary mapping and subsequent peak-finding algorithms can separate adjacent cortex into distinct regions based on underlying differences in rs-fcMRI correlation maps, they do not reveal what underlying differences are actually driving the spatial distinctions.

To explore these differences, we generated rs-fcMRI “neighborhoods,” defined as the sets of regions most highly correlated with each of the 15 LLPC ROIs. Neighbors that appeared in more than one seed map were consolidated to eliminate overlap, resulting in 87 final neighbors that spanned the cortex and cerebellum. The 87 neighbors and 15 LLPC ROIs formed a collection of 102 ROIs, which could then

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Figure 2. Regions showing retrieval success effects are located in posterior parietal cortex. A, ROIs circled in green indicate those that showed retrieval success effects across the eight studies that comprised the meta-analysis, while ROIs circled in red did not. The thick black line indicates this distinction. ROIs are displayed on inflated cortical surface renderings of the human brain using Caret software. B, C, D, Time courses from regions showing retrieval success effects. Posterior middle IPS (pmIPS), pIPL, and AG time courses correspond to B, C, and D, as labeled in A. P values indicate level of significance for hit > correct rejection (CR).

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be viewed as a network of 102 nodes related to each other by rs-fcMRI correlations.

The next set of analyses aimed at understanding this network, and in particular, whether distinct groupings or “modules” existed within it that might provide further distinctions between the LLPC ROIs. Community-detection analyses can subdivide networks into functionally related subsets of nodes called “communities” or “modules.” For example, a person’s social network might include a module of coworkers, a module of relatives, and a module

of teammates, each of which is richly connected internally but possesses few connections to other modules.

To assess the underlying grouping of our LLPC ROIs and their neighbors, we performed a two-step community detection analysis using modularity optimization (Newman, 2006) on the matrix of pairwise rs-fcMRI correlations between the 102 ROIs. This resulted in a set of six communities, or submodules, that were related to six separate sets of beginning LLPC ROIs. Among other relationships,

Figure 3. Modularity optimization performed separately on modules not showing retrieval success effects (supramarginal gyrus [SMG] and superior parietal lobule [SPL]) and retrieval success modules (AG and IPS). A, The SPL and SMG modules did not split into separate submodules, although regions within the supple-mentary motor area (SMA) and dorsal anterior cingulate cortex (dACC) separate from the two (SMA/dACC, dark green). The SPL module is now labeled SPL/”frontal eye fields” (FEFs), and the SMG module is now labeled SMG/Insula to more appropriately describe the distributed regions contained therein. B, The AG and IPS modules each split into multiple separate submodules, four of which (AG/mPFC [red], pIPL/sFG [light yellow], LIPS/dlPFC [light blue], and aIPL/aPFC [light green] contained regions within LLPC showing retrieval success effects. Regions in the right IPS (RIPS) and right dlPFC (dlPFC, purple), cerebellum (light brown), and superior occipital cortex (SOC, teal) were also found to be distinct from the other regions. Parameters dictating the placement of nodes in network space are the same as in A. C, Modularity optimization assign-ments shown in LLPC. Lines drawn in LLPC delineate submodule assignments. Colors are as in A and B. D, Modularity optimization shown on lateral and medial views of the cortex using Caret software. Cerebellum (light brown in B) not shown. Colors are as in A and B.

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each set of LLPC ROIs had separate relationships to a different set of frontal regions (Fig. 3A–D, each color representing a different submodule).

The rs-fcMRI–Defined Submodules Are Reflected in Functional Time Course DistinctionsThe final analysis seeks, in part, to further corroborate whether the previously described intermediate time course in pIPL (Fig. 2C) is functionally distinct by examining the time courses in regions within its submodule. If they show a pattern similar to the region in pIPL, and are distinct from the AG/medial prefrontal cortex (mPFC) and left IPS (LIPS)/dorsolateral prefrontal cortex (dlPFC) submodules, this would indicate that the pIPL time course is indeed not an artifact of spatial blurring in LLPC. More generally, this analysis is meant to find out to what degree the distinctions found using rs-fcMRI are reflected in task-evoked signals, both within LLPC and in related regions outside LLPC.

The characterization of submodules that consist of regions outside of, but closely related to, each of the LLPC ROIs now lets us assess task-evoked signals at the submodule level. We extracted time courses for hits and correct rejections (CRs) from the regions comprising each of the four submodules. These submodules contained an LLPC ROI exhibiting retrieval success effects across the eight tasks we had defined in an initial meta-analysis. It is important to note that the following analyses were performed on submodule ROIs in which the original time courses from LLPC ROIs were excluded. As such, any observed effects are necessarily independent of the initial fMRI analysis, which examined only LLPC ROIs.

The time course profiles between the submodules AG/mPFC, pIPL/superior frontal gyrus (sFG) and LIPS/dlPFC are distinct from one another (Fig. 4E–H), mirroring both the apparent time course distinctions of Figure 2 and the modularity analysis that defined submodules (Fig. 3B). Additionally,

Relating Functional Measures to Network Descriptions in the Study of Brain Systems

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Figure 4. Four rs-fcMRI–derived submodules show different task-evoked fMRI time course dynamics and retain retrieval success effects independent of the LLPC ROIs. A, A region in AG is shown on a lateral view of the left hemisphere using Caret software. Time courses (below) were extracted for hits and correct rejections across the eight studies that comprised the meta-analysis. P values represent the significance of the difference between hits and CRs, determined by a response time X repeated across mea-sures, ANOVA with two levels of response and seven levels of time. B, C, D, Same as in A but for pIPL (B), LIPS (C), and aIPL (D). E, All ROIs in the AG/mPFC submodule (excluding AG) are shown on lateral and medial views of the cortex using Caret software. Time course data were extracted as in A, but were averaged across all ROIs shown here. P values are the same as in A. F, G, H, Same as in E but for pIPL/sFG (F), LIPS/dlPFC (G), and aIPL/aPFC (H).

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regions in the pIPL/sFG and anterior IPL (aIPL)/anterior prefrontal cortex (aPFC) submodules were dissociable throughout all levels of the rs-fcMRI analyses. The overall take-home concept from this section is that differences found in defined network substructures, based on rs-fcMRI, are reflected in specific aspects of the functional signals found during task.

Similar Mapping Regions Are Defined in Children, but With Different Network RelationshipsA common observation is that there are developmental differences in the overall rs-fcMRI network structure (Fair et al., 2009; Supekar et al., 2009). It is unknown whether this difference would extend to areal parcellation, as in Cohen’s work (2008), given that animal models suggest that cortical area parcellation is completed early in development.

To address this question, we applied boundary mapping methods for parcellating the LLPC using rs-fcMRI data (Cohen et al., 2008; Nelson et al., 2010) to 7- to 10-year-old children and 23- to 28-year-old adults. The topography of the LLPC areal parcellation maps was qualitatively similar across children and adults (see Fig. 5A,B), which suggested that the locations of LLPC areas would be similar across groups. We identified LLPC areas in each group using peak finding algorithms applied to the areal parcellation maps. We then applied a modified approach using the Hungarian assignment algorithm to objectively “match” LLPC areas across groups based on their distance in stereotactic space. The assignment algorithm revealed 10 LLPC areas that were separated by less than 9 mm in stereotactic space (average distance between labeled pairs <5 mm).

We then examined whether the similar parcellation maps resulted from similar patterns of functional connectivity over age. We queried the matched LLPC areas and discovered that children showed stronger functional connectivity with anatomically proximal regions (i.e., other regions in parietal cortex), whereas adults showed stronger functional connectivity with anatomically distant regions (i.e., regions outside parietal cortex). Thus, although anatomically similar LLPC “areas” can be identified in 7- to 10-year-old children as well as in adults, the patterns of functional connectivity for LLPC areas continue to change during development. Our findings converge with previous rs-fcMRI work that revealed that functional connectivity networks change from a “local” to a “distributed” organization during the course of childhood and adolescence (Fair et al., 2007, 2009). However, our findings suggest that the locations of cortical areal boundaries are established in school-aged children.

ConclusionsWe believe that this series of studies/analyses has several important implications:• Adopting a large-scale network perspective

is profoundly useful, even for making local distinctions between neighboring regions of cortex;

• Patterns of resting correlation are closely related to patterns of task-evoked activity, consistent with a hypothesis that resting correlation results from a strong statistical history of task-evoked coactivation; and

• rs-fcMRI and a network perspective can be used to elucidate both stable (e.g., the location of putative area boundaries) and changeable (e.g., the patterns of connectivity for cortical areas) properties of the developing brain, making it a powerful method for studying human development.

ReferencesCohen AL, Fair DA, Dosenbach NU, Miezin FM,

Dierker D, Van Essen DC, Schlaggar BL, Petersen SE (2008) Defining functional areas in individual human brains using resting functional connectivity MRI. Neuroimage 41:45-57.

Corbetta M, Shulman G (2002) Control of goal-directed and stimulus-driven attention in the brain. Nat Rev Neurosci 3:201-215.

Corbetta M, Akbudak E, Conturo TE, Snyder AZ, Ollinger JM, Drury HA, Linenweber MR, Petersen SE, Raichle ME, Van Essen DC, Shulman GL (1998) A common network of functional areas for attention and eye movements. Neuron 21:761-773.

Figure 5. LLPC boundary mapping has a similar topography in children aged 7 to 10 years (A) and adults aged 23 to 28 years (B).

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Dosenbach NUF, Visscher KM, Palmer ED, Miezin FM, Wenger KK, Kang HC, Burgund ED, Grimes AL, Schlaggar BL, Petersen SE (2006) A core system for the implementation of task sets. Neuron 50:799-812.

Dosenbach NUF, Fair DA, Miezin FM, Cohen AL, Wenger KK, Dosenbach RAT, Fox MD, Snyder AZ, Vincent JL, Raichle ME, Schlaggar BL, Petersen SE (2007) Distinct brain networks for adaptive and stable task control in humans. Proc Natl Acad. Sci. USA 104:11073-11078.

Fair DA, Dosenbach NUF, Church JA, Cohen AL, Brahmbhatt S, Miezin FM, Barch DM, Raichle ME, Petersen SE, Schlaggar BL (2007) Development of distinct control networks through segregation and integration. Proc Natl Acad Sci USA 104:13507-13512.

Fair DA, Cohen AL, Power JD, Dosenbach NUF, Church JA, Miezin FM, Schlaggar BL, Petersen SE (2009) Functional brain networks develop from a “local to distributed” organization. PLoS Comput Biol 5:e1000381.

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Henson RN, Rugg MD, Shallice T, Josephs O, Dolan RJ (1999) Recollection and familiarity in recognition memory: an event-related functional magnetic resonance imaging study. J Neurosci 19:3962-3972.

Henson RN, Rugg MD, Shallice T, Dolan RJ (2000) Confidence in recognition memory for words: dissociating right prefrontal roles in episodic retrieval. J Cogn Neurosci 12:913-923.

Hubbard EM, Piazza M, Pinel P, Dehaene S (2005) Interactions between number and space in parietal cortex. Nat Rev Neurosci 6:435-448.

Konishi S, Wheeler ME, Donaldson DI, Buckner RL (2000) Neural correlates of episodic retrieval success. Neuroimage 12:276-286.

McDermott KB, Jones TC, Petersen SE, Lageman SK, Roediger III HL (2000) Retrieval success is accompanied by enhanced activation in anterior prefrontal cortex during recognition memory: an event-related fMRI study. J Cogn Neurosci 12:965-976.

McDermott KB, Szpunar KK, Christ SE (2009) Laboratory-based and autobiographical retrieval tasks differ substantially in their neural substrates. Neuropsychologia 47:2290-2298.

Nelson SM, Cohen AL, Power JD, Wig GS, Miezin FM, Wheeler ME, Velanova K, Donaldson DI, Phillips JS, Schlaggar BL, Petersen SE (2010) A parcellation scheme for human left lateral parietal cortex. Neuron 67:156-170.

Newman ME (2006) Modularity and community structure in networks. Proc Natl Acad Sci USA 103:8577-8582.

Rushworth MFS, Paus T, Sipila PK (2001) Attention systems and the organization of the human parietal cortex. J Neurosci 21:5262-5271.

Simons JS, Peers PV, Hwang DY, Ally BA, Fletcher PC, Budson AE (2008) Is the parietal lobe necessary for recollection in humans? Neuropsychologia 46:1185-1191.

Supekar K, Musen M, Menon V (2009) Development of large-scale functional brain networks in children. PLoS Biol 7:e1000157.

Turkeltaub PE, Eden GF, Jones KM, Zeffiro TA (2002) Meta-analysis of the functional neuroanatomy of single-word reading: method and validation. Neuroimage 16:765-780.

Van Essen DC, Dickson J, Harwell J, Hanlon D, Anderson CH, Drury HA (2001) An integrated software suite for surface-based analyses of cerebral cortex. J Am Med Inform Assoc 41:1359-1378. See also http://brainmap.wustl.edu/caret.

Wagner AD, Shannon BJ, Kahn I, Buckner RL (2005) Parietal lobe contributions to episodic memory retrieval. Trends Cogn Sci 9:445-453.

Wheeler ME, Buckner RL (2003) Functional dissociation among components of remembering: control, perceived oldness, and content. J Neurosci 23:3869-3880.

Wheeler ME, Buckner RL (2004) Functional-anatomic correlates of remembering and knowing. Neuroimage 21:1337-1349.

Yantis S, Schwarzbach J, Serences JT, Carlson RL, Steinmetz MA, Pekar JJ, Courtney SM (2002) Transient neural activity in human parietal cortex during spatial attention shifts. Nat Neurosci 5:995-1002.

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Department of Diagnostic Radiology Yale University

New Haven, Connecticut

Relating Variations in Network Connectivity to Cognitive Function

Michelle Hampson, PhD

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IntroductionCognitive science is evolving from a focus on discrete brain areas towards an emphasis on distributed models of brain function. In the latter, cognition emerges from the complex interaction of widespread brain areas. To examine interregional interactions, early neuroimaging studies used positron emission tomography (PET) to correlate activity patterns in different brain areas across subjects (Clark et al., 1984; Horwitz et al., 1984; Metter et al., 1984). By contrasting one group of subjects with another, group differences in brain function could then be related to interactions between brain areas (Horwitz et al., 1998). However, the study of individual differences in connectivity patterns with PET was typically not feasible because limited temporal resolution prevented the assessment of connectivity in each subject (although an exception can be found in the work of Glaubus et al., 2003).

The ability to assess network connectivity patterns for each individual subject was one of the exciting advances made possible by the improved temporal resolution of functional magnetic resonance imaging (fMRI). This capability has enabled researchers to examine relationships between individuals’ cognitive function and their network connectivity, which has proven to be a powerful approach for studying the neural basis of individual differences. For example, an early study we conducted revealed robust correlations in a relatively limited sample size between reading skills and connectivity between brain areas in the reading circuitry (Hampson et al., 2006a). More recently, studies relating cognitive variables to network connectivity have become popular in cognitive neuroscience. This research has tended to highlight the role of two specific networks in human cognition: the cognitive control network and the default mode network, which are discussed in more detail below.

Cognitive Control or “Task-Positive” NetworkNeuroimaging studies have identified a set of frontal and parietal brain regions that appear to be important in human intelligence (Jung and Haier, 2007). In particular, activation-based functional imaging studies have reported increased activity in many brain regions: dorsolateral and ventrolateral prefrontal cortices, premotor areas, dorsomedial prefrontal cortex, anterior insula, the intraparietal sulcus, and portions of the inferior parietal lobule. This activity is seen during a range of working memory and attention/executive function tasks (Cabeza and Nyberg, 2000; Corbetta and Shulman,

2002; Owen et al., 2005). These cognitive control areas have been shown to fluctuate together in the resting state (Fox et al., 2005; Seeley et al., 2007), suggesting that they form an intrinsic brain network. Adopting the terminology of Fox et al. (2005), we refer to these cognitive control regions as “task-positive” areas.

The strength of functional connectivity between task-positive brain areas in the resting state has proven relevant to cognitive function. For example, Seeley and colleagues identified this network via independent components analysis. They reported that the strength of the intraparietal sulcus within the extracted component was correlated with performance on the Trail Making Test, a measure of executive function (Seeley et al., 2007). Another study, by Song et al., identified many functional connections between the dorsolateral prefrontal cortex and other task-positive brain areas that were correlated with intelligence scores on the Wexler Adult Intelligence Scale (Song et al., 2008). Thus, functional connectivity within the task-positive network appears to play a role in individual differences in cognitive ability.

Default Mode or “Task-Negative” NetworkAnother set of regions that appear to be relevant to cognitive function are the default-mode regions. This set of brain areas includes the ventromedial prefrontal cortex, a region of the posterior cingulate cortex extending into the precuneus, and lateral parietal regions, all of which have been found in meta-analyses to have decreased blood flow during a variety of tasks (Shulman et al., 1997; Mazoyer et al., 2001). These regions were also shown to fluctuate together at rest, supporting the view that they form a well-integrated network (Greicius et al., 2003). This network has been hypothesized to perform the default mental processes subjects engage in when their attention is not focused on a specific task—hence the term “default mode” network (Raichle et al., 2001).

According to the default mode theory, task engagement suspends default mode processing, resulting in decreased activity in these regions. However, it is important to note that a decrease in blood flow can be associated with an increase in information processing and engagement and does not necessarily imply suspension of processing. For example, a region that shifts from random baseline firing to phase-locking with other regions at a lower firing rate may decrease its net activity level (resulting

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in decreased local blood flow) when it becomes more engaged in information processing. Because of the implications inherent in the term “default mode,” we prefer the term “task-negative,” introduced by Fox et al. (2005). This term accounts for the fact that these brain areas decrease their signal during task performance in neuroimaging studies but does not imply that they are engaged in critical information processing only during the resting (or default) mental state.

To investigate how engagement of the task-negative network relates to cognitive function, we examined functional connectivity between two key regions in this network (the medial prefrontal and posterior cingulate regions), both at rest and during performance of a demanding cognitive task (Hampson et al., 2006b). Furthermore, we correlated the strength of this connection with task performance. We found that these two task-negative regions significantly correlated with each other, both at rest and during task performance, and did not find a significant change in the strength of that connection across conditions (note, however, that this null finding across conditions may have been the result of limited power) (Fransson, 2006). Significantly, the strength of connectivity between the medial prefrontal and posterior cingulate regions in the task-negative network, whether assessed at rest or during task performance, positively related to task performance. In contrast to the default mode theory, our data suggest that these regions work together to facilitate cognitive processing rather than being suspended during cognitive tasks.

A variety of more recent studies have also supported the viewpoint that the task-negative network facilitates cognition. An examination of resting state network properties in the task-negative network and their relationship to intelligence scores reported that individuals with high intelligence quotients (IQs) display greater efficiency in this network (Song et al., 2009). Furthermore, several functional connections between task-negative regions, including the connection between medial frontal and posterior cingulate regions, were related to IQ. Another study reported that episodic memory performance is correlated with the strength of resting state functional connectivity between the posterior cingulate cortex and the hippocampus (Wang et al., 2010b). The hippocampus is generally considered a “default mode” or task-negative region (Greicius and Menon, 2004), although it is likely not a central node in the network (Song et al., 2009). Finally, a study examining network properties in the resting brain reported that the global connectivity efficiency

of several task-negative regions is correlated with IQ (van den Heuvel et al., 2009).

Analyses of network properties in the brain, based on both structural connectivity and resting state functional connectivity, have reported that the task-negative regions are hubs, that is, areas of very high global connectivity (Hagmann et al., 2008; Buckner et al., 2009). This centrality may account for their ubiquitous importance across a range of cognitive tasks. It is interesting to note that the same study reporting correlations between the global connectivity efficiency of task-negative regions and IQ also reported that whole-brain efficiency is highly correlated with IQ (van den Heuvel et al., 2009). These data, taken together, suggest that integrity of the task-negative network plays a critical role in the whole-brain dynamics associated with higher level cognition.

Interactions Between Task-Positive and Task-Negative NetworksThe task-positive and task-negative networks have been shown to fluctuate in antiphase in the resting brain (Greicius et al., 2003; Fox et al., 2005; Fransson, 2005); however, their antiphase relationship may be an artifact of a commonly used analysis step known as “global regression” (Murphy et al., 2008). Regardless, the strength of the functional connection between task-positive and task-negative regions at rest appears to be related to cognitive function. In one study using global regression, the strength of the anticorrelation between task-positive and task-negative networks was inversely related to intra-individual variability in response time, a measure inversely related to cognitive function (Kelly et al., 2008). In another study, the connectivity between dorsolateral prefrontal cortex (a key task-positive region) and medial prefrontal cortex (a key task-negative region) negatively correlated with the percentage of correct answers on a working memory task (Hampson et al., 2010) when the data were analyzed both with and without global regression. Thus, in all cases, better cognitive function was associated with smaller or more negative correlations between task-positive and task-negative brain areas.

In summary, connectivity both within and between the task-positive and task-negative networks is associated with individual differences in cognitive ability. According to recent analyses of resting state functional connectivity data, task-positive (as well as task-negative) regions act as network hubs in the brain (Cole et al., 2010). Thus, efficient communication between hub regions of

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the brain may be a critical variable for determining cognitive ability.

Clinical ApplicationsConnectivity within the task-negative network has become a recent focus in aging research. As shown in Figure 1, our finding that cognitive function is related to connectivity between medial areas of the task-negative network was extended to healthy older populations (Andrews-Hanna et al., 2007; Sambataro et al., 2010). In addition, these studies reported that, relative to younger adults, older adults had decreased connectivity in the default mode network. These findings suggest a mechanism for the decrease in cognitive function associated with healthy aging. Other studies have reported altered network connectivity in older adults (Achard and Bullmore, 2007; Gong, 2009; Wang et al., 2010a) but have not correlated these changes with cognitive measures.

Similarly, a variety of studies have reported disrupted network connectivity in Alzheimer’s disease (Greicius et al., 2004; Supekar et al., 2008; Wang et al., 2006, 2007) but have not directly correlated network measures with cognitive variables in this group. Interestingly, a growing literature has implicated the disruption of the default mode network in the pathophysiology of Alzheimer’s disease, as well as in healthy aging. Decreased connectivity within the default mode network has been reported in patients with Alzheimer’s disease (Greicius et al., 2004; Wang et al., 2006), and the default mode regions

have been found to overlap with areas showing amyloid- deposition, a characteristic feature of the disorder (Buckner et al., 2005). Furthermore, two recent studies have reported a relationship between amyloid- deposition and connectivity in the default mode network (Hedden et al., 2009; Sheline et al., 2010). Finally, genetic predisposition to Alzheimer’s disease has been associated with decreased coactivation of default mode regions in healthy young adults (Filippini et al., 2009).

Studies have examined connectivity changes in other clinical populations and related those connectivity changes to cognitive function. For example, aberrant connectivity has been related to disturbed cognitive function in schizophrenics (Camchong et al., 2009; Meda et al., 2009; Whitfield-Gabrieli et al., 2009; Wolf et al., 2009) and in children born preterm (Myers et al., 2010). Such studies have the potential to reveal the dysfunctional network interactions that underlie the cognitive impairments associated with various clinical conditions.

Future DirectionsIn cognitive neuroscience, interest has shifted from regional activation to connectivity patterns, moving the field towards a more network-oriented perspective. However, for the most part, this trend has not progressed beyond the examination of pairwise connectivity measures. More distributed measures of network properties are just beginning to be explored (Buckner et al., 2009; Bullmore and Sporns, 2009; Song et al., 2009; van den Heuvel

Figure 1. Functional connectivity between ventromedial prefrontal cortex and posterior cingulate/precuneus is plotted against measures of cognitive function for adults aged 28-45 in panel a and for older adults aged 60-93 (after adjusting for age) in panel b. The relationships are significant for both populations. Data from panel a were reported in Hampson et al., 2006b; panel b is from Andrews-Hanna et al., 2007, their Figure 8B, reproduced with permission. Units of functional connectivity on the y-axis are not comparable across studies owing to differences in normalization applied.

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et al., 2009). These new measures have great potential to summarize the complex patterns of network connectivity that determine brain function, and as such, to provide promising new tools for cognitive neuroscientists.

As more is learned regarding the network properties underlying individual differences in cognition, a critical challenge will be to modulate these patterns in order to improve cognitive function. Along these lines, a recent study explored the relationship between cardiovascular fitness, functional connectivity, and cognition (Voss et al., 2010). Its findings point to the importance of physical exercise as a potential intervention for improving cognitive networks in older adults and the need for more longitudinal studies. Another study involving a paradigm for visual perceptual learning reported significant changes in functional connectivity associated with the degree of learning (Lewis et al., 2009), illustrating our capacity for modulating network dynamics and thereby improving cognitive function. In our lab, a particularly interesting new form of intervention is biofeedback of real-time fMRI, which has been shown effective in modulating pain perception (deCharms et al., 2005) and in facilitating linguistic processing (Rota et al., 2009). Studies examining the relationship between changes in network properties during such interventions, and coincident changes in cognitive function, are likely to yield new insights into the brain organization underlying cognition and its plasticity.

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Department of Psychiatry and Behavioral Sciences Department of Neurology and Neurological Sciences

Program in Neuroscience Stanford University Medical School

Stanford, California

Large-Scale Brain Networks in Cognition: Emerging Principles

Vinod Menon, PhD

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A Network Perspective on CognitionFunctional brain imaging has focused primarily on localization of function, revealing activation in specific brain regions during the performance of particular cognitive tasks. It is becoming increasingly apparent that cognitive neuroscience needs to go beyond this mapping of complex cognitive and psychological constructs onto individual brain areas (Fuster, 2006). As a result, a network paradigm is becoming increasingly useful for understanding the neural underpinnings of cognition (Bressler and Menon, 2010). Furthermore, a consensus is emerging that the key to understanding the functions of any specific brain region lies in understanding how its connectivity differs from the pattern of connections in other functionally related brain areas (Passingham et al., 2002). In recent years, neuroscientists’ interests have shifted towards developing a deeper understanding of how intrinsic brain architecture influences cognitive and affective information processing (Greicius et al., 2003; Fox and Raichle, 2007; Dosenbach et al., 2008).

In the sections that follow, we briefly review emerging methods for characterizing and identifying major neurocognitive networks in the human brain. We then provide two specific examples of how such networks can provide fundamental new insights into the brain bases of fundamental cognitive processes. The first example focuses on the surprisingly crucial role of the insular cortex in salience, attention, and cognitive control. The second example demonstrates how intrinsic functional and structural connectivity of the parietal cortex can inform and constrain information processing models across multiple cognitive domains.

Identifying Major Cognitive NetworksA formal characterization of core brain networks—anatomically distinct, large-scale brain systems having distinct cognitive functions—was first enunciated by Mesulam (1990). In this view, the human brain contains at least five major core functional networks:1. A spatial attention network anchored in posterior

parietal cortex (PPC) and frontal eye fields;2. A language network anchored in Wernicke’s and

Broca’s areas;3. An explicit memory network anchored in the

hippocampal–entorhinal complex and inferior parietal cortex;

4. A face-object recognition network anchored in midtemporal and temporopolar cortices; and

5. A working memory–executive function network anchored in prefrontal and inferior parietal cortices.

The nodes of these core networks have been inferred from the results of fMRI studies, during tasks that manipulate one or more of these cognitive functions. A full characterization of core functional brain networks, however, will require additional studies to validate the nodes of these networks using other criteria, to measure their edges, and to determine whether other core networks exist.

In recent years, diffusion tensor imaging (DTI) and resting state fMRI have emerged as novel tools for characterizing structural and functional brain networks. They are able to do so independently of cognitive domains, experimental manipulations, and behavior. Recent work in systems neuroscience has characterized several major brain networks that are identifiable in both the resting brain (Damoiseaux et al., 2006; Seeley et al., 2007b) and the active brain (Toro et al., 2008). Importantly, major functional brain networks (and their composite subnetworks) show close correspondence in independent analyses of resting and task-related connectivity patterns (Smith et al., 2009), suggesting that functional networks coupled at rest are also systematically engaged during cognition. The analysis of resting state functional connectivity, using both model-based and model-free approaches, has proved to be a useful technique for investigating functionally coupled networks in the human brain. Although the method relies on analysis of low-frequency signals in fMRI data, electrophysiological studies point to a reliable neurophysiological basis for these signals (He et al., 2008; Nir et al., 2008).

The analysis of resting state fMRI allows us to discover the organization and connectivity of several major brain networks that cannot be easily captured with the help of other techniques. Conceptualizing the brain as comprising multiple distinct, interacting networks provides a systematic framework for understanding fundamental aspects of human brain function.

Independent component analysis (ICA) has turned out to be an important method for identifying intrinsic connectivity networks (ICNs) from resting state fMRI data (Damoiseaux et al., 2006; Seeley et al., 2007a). ICA has been used to identify ICNs involved in executive control, episodic memory, autobiographical memory, self-related processing, and detection of salient events. ICA has also revealed a sensorimotor ICN anchored in bilateral somatosensory and motor cortices; a

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visuospatial attention network anchored in intraparietal sulci and frontal eye fields; a higher-order visual network anchored in lateral occipital and inferior temporal cortices; and a lower-order visual network anchored in the striate and extrastriate cortex (Damoiseaux et al., 2006). This technique has also allowed intrinsic (Fig. 1) as well as task-related (Fig. 2) fMRI activation patterns to be used for the identification of distinct functionally coupled systems. These systems include a central-executive network (CEN) anchored in dorsolateral prefrontal cortex (DLPFC) and PPC, and a salience network (SN) anchored in anterior insula (AI) and anterior cingulate cortex (ACC) (Seeley et al., 2007a; Sridharan et al., 2008).

These prominent networks can be readily identified across a wide range of cognitive tasks, and their responses increase and decrease proportionately with task demands. The CEN and SN typically show increases in activation, whereas the default-mode network (DMN) shows decreases in activation (Raichle et al., 2001; Greicius et al., 2003; Greicius and Menon, 2004). CEN nodes that show strong intrinsic functional coupling also show strong coactivation during cognitively challenging tasks. In particular, the CEN is critical for actively maintaining and manipulating information in working memory, and for judgment and decision-making in the context of goal-directed behavior (Miller and Cohen, 2001; Petrides, 2005; Muller and Knight, 2006; Koechlin and Summerfield, 2007).

The DMN includes the medial temporal lobes and the angular gyrus (AG), in addition to the posterior cingulate cortex (PCC) and the ventromedial prefrontal cortex (VMPFC). These areas perform a variety of functions: The PCC is activated during tasks that involve autobiographical memory and self-referential processes (Buckner and Carroll, 2007); the VMPFC is associated with social cognitive processes related to self and others (Amodio and Frith, 2006); the medial temporal lobe is engaged in episodic and autobiographical memory (Cabeza et al., 2004); and the

Figure 1. Two core neurocognitive networks identified using intrinsic physiological coupling in resting state fMRI data. The SN (shown in red) is important for monitoring the saliency of external inputs and internal brain events, and the CEN (shown in blue) is engaged in higher-order cognitive and attentional control. The SN is anchored in AI and ACC and features extensive connectivity with subcortical and limbic structures involved in reward and motivation. The CEN links the dorsolateral prefrontal and pos-terior parietal cortices, and has subcortical coupling that is distinct from that of the SN. Seeley et al. (2007), their Fig. 2, reprinted with permission. antTHAL, anterior thalamus; dACC, dorsal anterior cingulate cortex; dCN, dorsal caudate nucleus; dmTHAL, dorsomedial thalamus; FI, fronto-insular cortex; HT, hypothalamus; PAG, periaqueductal gray; Put, putamen; SLEA, sublenticular extended amygdala; SN/VTA, substantia nigra/ventral teg-mental area; TP, temporal pole.

Figure 2. Three major functional networks in the human brain. Task-relat-ed activation patterns in the CEN and SN, and deactivation patterns in the DMN, during an auditory event segmentation task. Activation and deacti-vation patterns can be decomposed into distinct subpatterns. A, Analysis with the general linear model (GLM) revealed regional activations (Left) in the right anterior insula (rAI) and ACC (blue circles); DLPFC and PPC (green circles) and deactivations (Right) in the VMPFC and PCC. B, ICA provided converging evidence for spatially distinct networks. From left to right: SN (rAI and ACC), CEN (rDLPFC and rPPC), and DMN (VMPFC and PCC). Srid-haran et al. (2008), their Fig. 1, reprinted with permission.

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AG is implicated in semantic processing (Binder et al., 2009). The DMN thus collectively comprises an integrated system for autobiographical, self-monitoring, and social cognitive functions, even though a unique task-based function cannot be assigned to each of its nodes (Spreng et al., 2009). Furthermore, the identification and characterization of these distinct networks provide a framework for systematically examining attentional and control processes in the brain.

An Example: Insula — a Network Model of Saliency, Attention, and ControlThe insula is a brain structure implicated in disparate cognitive, affective, and regulatory functions, including interoceptive awareness, emotional responses, and empathic processes. Although classically considered a limbic region, recent evidence from network analysis suggests a critical role for the insula, particularly the anterior division, in high-level cognitive control and attentional processes. The insula’s complex and as yet only partially characterized pattern of structural connectivity highlights the need for a more principled understanding of its functional links. In task-based functional imaging, it has been difficult to isolate insula responses because it is often coactivated with the ACC, the DLPFC and ventrolateral prefrontal cortex (VLPFC), and the PPC. To circumvent this problem, Dosenbach and colleagues used resting state functional connectivity to show that these regions can be grouped into distinct frontoparietal and cingulo-opercular components (Dosenbach et al., 2007). Similarly, Seeley and colleagues used region-of-interest (ROI) and ICA of resting state fMRI data to demonstrate the existence of an ICN comprising the AI, dorsal ACC, and subcortical structures, including the amygdala, substantia nigra/ventral tegmental area, and thalamus (Seeley et al., 2007a).

The crucial insight that network analysis affords is of the AI as an integral hub in mediating dynamic interactions between other large-scale brain networks involved in externally oriented attention and internally oriented, or self-related, cognition (Sridharan et al., 2008), as Figure 3 illustrates. This model postulates that the insula is sensitive to salient events, and that its core functions are to mark such events for additional processing and to initiate appropriate control signals. The AI and the ACC form a “salience network” that functions to segregate the most relevant internal and extrapersonal stimuli in order to guide behavior.

Within the framework of a network model, the disparate functions ascribed to the insula can be conceptualized by a few basic mechanisms:1. Bottom-up detection of salient events;2. Switching between other large-scale networks to

facilitate access to attention and working memory resources when a salient event occurs;

3. Interaction of the anterior and posterior insula to modulate autonomic reactivity to salient stimuli; and

4. Strong functional coupling with the ACC that facilitates rapid access to the motor system.

With the AI as its integral hub, the SN assists target brain regions in the generation of appropriate behavioral responses to salient stimuli. We have proposed that this framework provides a parsimonious account of insula function in neurotypical adults and may provide novel insights into the neural basis of disorders of affective and social cognition (Menon and Uddin, 2010).

Previous studies have suggested that the inferior frontal gyrus and ACC are involved in a variety of monitoring, decision-making, and cognitive control processes (Crottaz-Herbette and Menon, 2006; Cole and Schneider, 2007; Johnston et al., 2007; Posner and Rothbart, 2007; Dosenbach et al., 2008; Eichele et al., 2008). However, the AI has not been a particular focus of most of these studies. Our model posits that the core function of the proposed SN, and

Figure 3. Multinetwork switching initiated by the SN (salience network). The SN is hypothesized to initiate dynamic switch-ing between the CEN (central-executive network) and DMN (default-mode network), and to mediate between attention to endogenous and exogenous events. In this model, sensory and limbic inputs are processed by the AI, which detects sa-lient events and initiates appropriate control signals to regulate behavior via the ACC and homeostatic state via the mid and posterior insular cortex. Key nodes of the SN include the AI and ACC; the DMN includes the VMPFC and PCC; the CEN includes the DLPFC and the PPC. Bressler and Menon (2010), their Fig. 1, reprinted with permission.

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the AI in particular, is to first identify stimuli from the vast and continuous stream that impacts the senses. Once such a stimulus is detected, the AI facilitates task-related information processing by initiating appropriate transient control signals. These signals engage brain areas that mediate attentional, working memory, and higher order cognitive processes while disengaging the DMN via mechanisms that have been described in the previous section.These crucial switching mechanisms help focus attention on external stimuli; as a result, they take on added significance or saliency. The large-scale network switching mechanisms we have described here can be thought of as the culmination of a hierarchy of saliency filters. In these filters, each successive stage helps to differentially amplify a stimulus sufficiently to engage the AI. The precise pathways and filters underlying the transformation of external stimuli, and the manner in which the AI is activated, remain to be investigated. Of critical importance, our model suggests that, once a stimulus activates the AI, it will have preferential access to the brain’s attentional and working memory resources.

Although dynamical systems analysis of fMRI data can help capture aspects of causal interactions between distributed brain areas, a more complete characterization of bottom-up and top-down attentional control requires access to temporal dynamics on the 30-70 ms time scale. Analysis of

combined EEG and fMRI data provides additional insights into how the SN plays an important role in attentional control (Crottaz-Herbette and Menon, 2006). Figure 4 is a schematic model of bottom-up and top-down interactions that underlie attentional control. This model was suggested by the relative timing of responses in the AI and ACC, versus other cortical regions, based on our dynamic source-imaging study and by lesion studies of the P3a complex (Soltani and Knight, 2000). The spatiotemporal dynamics underlying this process have five distinct stages:• Stage 1: ~150 ms poststimulus, primary sensory

areas detect a deviant stimulus, as indexed by the mismatch negativity (MMN) component of the evoked potential;

• Stage 2: This bottom-up MMN signal is transmitted to other brain regions, notably the AI and the ACC;

• Stage 3: ~200-300 ms poststimulus, the AI and ACC generate a top-down control signal, as indexed by the N2b/P3a component of the evoked potential. This signal is simultaneously transmitted to primary sensory areas, as well as other neocortical regions;

• Stage 4: ~300-400 ms poststimulus, neocortical regions, notably the premotor cortex and temporoparietal areas, respond to the attentional shift with a signal that is indexed by the time-averaged P3b evoked potential; and

Figure 4. Schematic model of dynamic bottom-up and top-down interactions underlying at-tentional control. See text for description of stages. Crottaz-Herbette and Menon (2006), their Fig. 6, adapted with permission.

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• Stage 5: The ACC facilitates response selection and motor response via its links to the midcingulate cortex, supplementary motor cortex, and other motor areas (Rudebeck et al., 2008; Vogt, 2009).

Within the framework of the network model described above, we suggest that the AI plays a more prominent role in detecting salient stimuli, whereas the ACC plays a more prominent role in modulating responses in the sensory, motor, and association cortices. A wide range of functional imaging studies and theoretical models has suggested that the ACC plays a prominent role in action selection (Rushworth, 2008). Together, as part of a functionally coupled network, the AI and ACC help to integrate bottom-up attention switching with top-down control and biasing of sensory input. This dynamic process enables an organism to sift through many different incoming sensory stimuli and to adjust gain for task-relevant stimuli—processes central to attention (Yantis, 2008).

An examination of the differential pattern of input–output connectivity of the AI and the ACC yields further insights into the functions of the AI and SN. While the AI receives multimodal sensory input, the ACC and associated dorsomedial prefrontal cortex (DMPFC) receive very little sensory input (Averbeck and Seo, 2008). Conversely, while the ACC and associated DMPFC send strong motor output, there is very little direct motor input to, or output from, the AI. Furthermore, the ACC and DMPFC have direct connections to the spinal cord and subcortical oculomotor areas (Fries, 1984), giving them direct control over action. With these differential anatomical pathways and von Economo neurons, which facilitate rapid signaling between the AI and the ACC, the SN is well positioned to influence not only attention but also motor responses to salient sensory stimuli. In this manner, the AI plays both a direct and an indirect role in attention, cognition, and behavioral control. In the context of our model, this critical input–output pattern suggests that the AI may generate the signals to trigger hierarchical control. Consistent with this view, among patients with frontal lobe damage, those with lesions in the AI were the most impaired in altering their behavior in accordance with the changing rules of an oculomotor-switching task (Hodgson et al., 2007). Our model further suggests that when the ACC is dysfunctional (Fellows and Farah, 2005; Baird et al., 2006), the AI is well positioned to trigger alternative cognitive control signals via other lateral cortical regions such as the VLPFC and the DLPFC (Johnston et al., 2007). Thus, our network model helps to clarify an important controversy regarding

the primacy and uniqueness of control signals in the prefrontal cortex (Fellows and Farah, 2005).

A Second Example: Dissecting Parietal CircuitsThe PPC, and in particular the inferior parietal lobule (IPL), is a brain region that is engaged in a wide variety of cognitive domains ranging from visuospatial attention (Corbetta and Shulman, 2002) to episodic memory (Cabeza et al., 2008) and numerical cognition (Menon et al., 2000). The human IPL consists of three prominent functional and anatomical subdivisions: the AG, the supramaginal gyrus, and the banks of the intraparietal sulcus (IPS). Situated at the junction of the temporal, parietal, and occipital lobes, the AG is a heteromodal region. Previous functional neuroimaging studies have focused mainly on its role in language and semantic processing (Binder et al., 2009; Brownsett and Wise, 2009) and spatial attention and orienting (Chambers et al., 2004), but it has also been implicated in verbally mediated fact retrieval during mathematical cognition tasks (Dehaene et al., 2004). However, resting state fMRI and positron emission tomography (PET) studies have consistently identified the AG as a key parietal node of the DMN (Raichle et al., 2001; Greicius et al., 2003; Uddin et al., 2009). Also, task-related deactivations have been widely reported in the AG (Shulman et al., 1997; Wu et al., 2009).

The IPL’s involvement in multiple cognitive operations suggests that it is highly functionally heterogeneous. Until recently, the subdivisions of the human IPL were not well understood, and their relation to functional and structural connectivity was completely unknown. Autoradiographic tracer studies in the macaque brain had demonstrated a rostrocaudal gradient of connectivity within the IPL, with rostral IPL connected to ventral premotor areas, and caudal IPL connected to Brodmann areas 44 and 45 (Petrides and Pandya, 2009). However, the extent to which the human IPL can be considered strictly homologous to its monkey counterpart is a matter of debate. While Brodmann’s initial characterization of the region led him to conclude that the human IPL consists of novel cortical areas not present in the monkey, others have argued that the IPL is similar across both species (Husain and Nachev, 2007). Thus, it is unclear to what degree monkey anatomical tracer studies can be extrapolated to understanding these pathways in the human brain.By capitalizing on methodological advances for examining the connectivity of putative distinct cortical regions, we can gain new insights into the functional roles of specific regions within the PPC.

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Furthermore, recent cytoarchitectonic analyses of the human IPL have suggested that the AG and IPS can be parcellated into distinct subregions (Choi et al., 2006; Caspers et al., 2008). Using observer-independent definitions of cytoarchitectonic borders, Caspers and colleagues have defined two subdivisions within the AG: one anterior (PGa), and one posterior (PGp) (Caspers et al., 2006). Within the IPS, this research group has demonstrated at least three cytoarchitectonically distinct human intraparietal (hIP) areas, labeled hIP2, hIP1, and hIP3 (Caspers et al., 2008). Resting state functional connectivity analyses showed that PGa was more strongly linked to basal ganglia, ventral premotor areas, and VLPFC, whereas PGp was more strongly connected with VMPFC, PCC, and hippocampus: regions comprising the default mode network. The anterior-most IPS ROIs (hIP2 and hIP1) have been linked with ventral premotor and middle frontal gyrus, whereas the posterior-most IPS ROI (hIP3) showed connectivity with extrastriate visual areas. Tractography using DTI revealed structural connectivity between most of these functionally connected regions (Fig. 5).

These findings provide evidence for functional heterogeneity of cytoarchitectonically defined subdivisions within the IPL. They also offer a novel framework for synthesizing and interpreting the task-related activations and deactivations that involve the IPL during cognition. Our connectivity analyses of networks associated with the IPS suggest a general principle of organization; by means of it, posterior IPS regions that are closely linked to the visual system transform stimuli into motor action via anterior IPS connections to the prefrontal cortex. Specifically, functional and structural connectivity results point to strong connections between hIP1 and insula. Along with the findings noted in the previous section, this observation suggests that such an interconnected system may help to mediate the detection of visually salient stimuli. More broadly, such investigations provide new information about the functional and structural organization of the human parietal cortex. This understanding, in turn, places constraints on information processing models of parietal cortex function, with broad implications across multiple cognitive domains (Uddin et al., 2010).

Figure 5. Differential structural connectivity within the PPC. Structural connectivity of hIP subdivisions. A, DTI tractography and density of fibers between hIP2, hIP1, and hIP3 and target inferior frontal oper-cular ROIs. Both hIP2 and hIP1 showed greater structural connectivity with inferior frontal opercular than did hIP3 (*p < 0.05, **p < 0.01). B, DTI tractography and density of fibers between hIP2, hIP1, and hIP3 and target insula ROIs. hIP1 showed greater structural connectivity than hIP2 and hIP3 with insula (*p < 0.05, **p < 0.01). C, DTI tractography and density of fibers between hIP2, hIP1, and hIP3 and target superior occipital cortex ROIs. hIP3 showed greater structural connectivity with superior occipital cortex than did hIP2 (**p < 0.01). Uddin et al. (2010), their Fig. 5, reprinted with permission.

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Clinical Applications of Complex Network Analysis

Danielle S. Bassett, PhD

Department of Physics University of California, Santa Barbara

Santa Barbara, California

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Complex Network ModelsThe contemporary formalism of complex network theory stems from the historical mathematical discipline of graph theory. Complex network theory provides representation rules that can be used to describe any complex system specifically in terms of its subcomponents and their relationships to one another. As such, complex network theory can be widely applied and provides an extremely powerful tool for comparing disparate systems within the same representational scheme. A complex network model is simply one representation of any given system constructed in terms of the complex network formalism. Important parameter choices for these models therefore include the definition of nodes and edges, whereas model results can be analyzed using graph theoretical metrics such as clustering or modularity. Although these choices and metrics have been discussed in detail elsewhere (Bullmore and Sporns, 2009; Rubinov and Sporns, 2009), here we will review complex network applications to clinical neuroscience and suggest relevant open research questions.

Network Organization in Health and DiseaseComplex network theory provides a compelling framework in which to study the human brain, whose intricacies span a broad range of spatial and temporal scales. In particular, network formalism is particularly suited to a system such as the brain, which can be broken down into functional or anatomical subsystems, and in which hard-wired or functional relationships between these subsystems are foundational to the system’s behavior as a whole. Indeed, the brain’s discrete organization into modules has been studied extensively, both anatomically (Brodmann, 1909) and functionally (Hubel and Wiesel, 2005). Complex network theory is particularly appealing when applied to the study of clinical neuroscience, where disease states and other clinical states have been characterized by a range of hypoconnectivity, hyperconnectivity, and dysconnectivity profiles. For example, in schizophrenia, a profound disconnection between frontal and temporal cortices has been suggested to characterize the brain (Friston and Frith, 1995); in contrast, people with autism may display a complex pattern of hyperconnectivity within frontal cortices but hypoconnectivity between the frontal cortex and the rest of the brain (Courchesne and Pierce, 2005).

Biological plausibilityIn order for any proposed modeling endeavor to be useful, it must produce results that are inherently

plausible, i.e., realistic within the bounds of current knowledge. Simple tests have therefore sought to determine whether constructed network organization displays characteristics consistent with known brain architecture. Initial studies have been performed across a wide range of imaging modalities: functional magnetic resonance imaging (fMRI) (Achard et al., 2006); EEG (Micheloyannis et al., 2006a); magnetoencephalography (MEG) (Bassett et al., 2006); MRI (He et al., 2007); and diffusion spectrum imaging (DSI) (Hagmann et al., 2008). Their results have shown that human brain networks are characterized by the nonrandom property of local connection clustering, while the entire system maintains global integration (Sporns et al., 2004). Complementary studies have also highlighted the wiring efficiency of anatomical brain networks, consistent with the existing constraints on energy consumption during both brain development and daily metabolic function (He et al., 2007; Bassett et al., 2008, 2010). Wiring efficiency is further reflected in the organization of both low-frequency and high-frequency functional networks (Achard et al., 2007; Bassett et al., 2009).

Biological relevanceEven though healthy brain networks display a significant nonrandom and apparent energy-efficient structure, it is still necessary to prove that the modeling endeavor is biologically relevant. In particular, a model of the brain should be sensitive to factors that might alter underlying connectivity structure or cognitive function. For example, we might expect disease states to display significantly different network architectures or for behavioral or cognitive variables to correlate with measured network metrics. In a stream of successes, complex brain networks have been shown to be sensitive to numerous factors:• Behavioral variability (Bassett et al., 2009);• Cognitive ability (van den Heuvel et al., 2009; Li

et al., 2009);• Shared genetic factors (Smit et al., 2008);• Genetic information (Schmitt et al., 2008);• Experimental task (Bassett et al., 2006; De Vico

Fallani et al., 2008b);• Age (Meunier et al., 2009; Micheloyannis et

al., 2009);• Gender (Gong et al., 2009);• Drug exposure (the dopamine receptor antagonist

sulpiride) (Achard et al., 2007); and• Disease.

Clinical findingsGiven their biological plausibility and relevance, complex network models of the human brain could

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theoretically provide a sensitive framework in which to compare healthy and clinically abnormal brain states. Indeed, complex network analyses have recently been used to probe several disease states, including schizophrenia and Alzheimer’s disease (AD), as well as other clinical states, such as stroke and spinal cord injury. In each case, complex network models of brain structure and function have corroborated previous findings from alternative analysis paradigms and provided novel insights into both global and local cortical (dys)organization.

Complex Network Models of SchizophreniaSchizophrenia is a neuropsychiatric disease characterized by a complex pattern of structural and functional abnormalities that are evident across a gamut of neuroimaging modalities. In a large-scale study (N = 203 people with schizophrenia, N = 259 controls) of a complex network model of brain structure in schizophrenia, we found broad structural connectivity to be altered in the three classical subnetworks of unimodal cortex (primary areas), multimodal cortex (heteromodal association areas), and transmodal cortex (extended limbic system). Specifically, whereas the connection length in the schizophrenia population was increased over all subnetworks, suggesting an inherent inefficiency of wiring, the multimodal subnetwork, composed of prefrontal and temporal cortices, among others, was characterized by a particularly inverted hierarchical structure (Bassett et al., 2008).

It is intuitively plausible that such structural disconnection signatures could constrain cortical function. Indeed, studies of both fMRI and EEG/MEG data suggest that functional network architecture in schizophrenia is altered in kind. Both Lynall et al. (2010) and Liu et al. (2008) found that the strength of functional connectivity measured during resting-state fMRI experiments was significantly decreased in people with schizophrenia. Collectively, they further reported that network measures derived from these data correlated significantly with both verbal fluency and duration of illness. These findings open up the possibility of using network

architectural signatures as biomarkers for the disease and its severity.

In contrast to these studies, EEG and MEG experiments in both resting and n-back tasks have demonstrated increased functional connectivity in schizophrenia in comparison with controls (Bassett et al., 2009; Rubinov et al., 2009). At rest, proband networks display an increase in intercluster connections and an associated lack of central hubs, consistent with a subtle randomization of network architecture predicted by medication dose (Rubinov et al., 2009). And, although medication dose was not predictive of network alterations during a working memory task condition (Micheloyannis et al., 2006b), randomization of that network architecture was maintained (Micheloyannis et al., 2006b; Bassett et al., 2009). Such randomization could theoretically lead to an increase in point-to-point efficiency, albeit at an increased connection cost. Network cost-efficiency of high frequency (-band, 12-20 Hz) function captured the trade-off between network efficiency and communication cost: It not only significantly decreased in the patient group, but was significantly predictive of individual performance accuracy on the working memory task in both patients and controls (Bassett et al., 2009) (Fig. 1).

Figure 1. Associations between cognitive performance and cost-efficiency of upper and lower band networks. Head surface maps show regions where nodal cost-efficiency in the 1-band (A) and 2-band (B) networks predicted accuracy of task performance across all subjects (top), in healthy controls alone (middle), and in schizophrenics alone (bottom). Red indicates that an association between task accuracy and nodal cost-efficiency was significant (p < 0.05 uncorrected); orange indicates that the association passed false-positive correction (all p < 0.0036); and bright yellow indicates that the association passed false discovery rate (FDR) correction (minimum p < 0.00018). Data are as reported in Bassett et al., 2009.

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Complex Network Models of Alzheimer’s DiseaseIn addition to estimating alterations in underlying structure, network studies in AD have focused predominantly on resting state rather than task-related functional connectivity (He et al., 2009a). Using covariation in cortical thickness as an indirect measurement of anatomical connectivity, He et al. (2008) reported an increase in local connectivity and a corresponding decrease in global connectivity in a sample of 92 elderly AD subjects they compared with 97 elderly controls. Regional differences between the control and patient groups were located in temporal and parietal areas (decreased centrality) and occipital regions (increased centrality).

The regional specificity of AD-related changes in network structure was further underscored by the work of Buckner et al. (2009). They showed that amyloid- deposition, as measured using positron emission tomography (PET) radiotracer Pittsburgh Compound-B (PiB) imaging, was concentrated in functional hub areas defined in healthy human resting state fMRI (Fig. 2). This finding suggests that cortical hubs may be particularly vulnerable in AD because of their relatively high activity, associated metabolism, and consistent recruitment across task states.

The direct characterization of functional brain networks in AD has been undertaken using fMRI, EEG, and MEG imaging modalities. In a resting-state fMRI experiment, Supekar et al. (2008) found that the clustering coefficient was significantly decreased in AD—specifically in bilateral hippocampus—and could be used to distinguish AD participants from controls with a specificity of 78% and a sensitivity of 72%. This finding implies that clustering coefficient might be useful as an imaging biomarker for the disease. In a resting-state MEG study, Stam and colleagues also reported a decreased clustering of functional connectivity in AD (Stam et al., 2009), consistent with Supekar’s low-frequency fMRI measurements. Mini Mental State Examination (MMSE) scores, which provide a measurement of disease severity, positively correlated with clustering across individuals. However, this pattern of results was not retained in a resting-state EEG study in which no difference in clustering was found, and the MMSE scores were instead found to negatively correlate with path length (Stam et al., 2007).

Complex Network Models of Other Diseases and Clinical StatesIn addition to schizophrenia and AD, complex network analyses have been carried out in several other disease and clinical states. These include epilepsy (van Dellen et al., 2009; Horstmann et al.,

2010; Raj et al., 2010), multiple sclerosis (He et al., 2009b), acute depression (Leistedt et al., 2009), absence seizures (Ponten et al., 2009), medial temporal lobe seizures (Ponten et al., 2007), attention deficit hyperactivity disorder (Wang et al., 2009), stroke (De Vico Fallani et al., 2009; Wang et al., 2010), spinal cord injury (De Vico Fallani et al., 2008a), frontotemporal lobar degeneration (de Haan et al., 2009), and early blindness (Shu et al., 2009).

In light of these results, several opportunities exist to pursue complementary modeling efforts. Numerical simulations, in particular, could be undertaken to positive advantage where the relationship between putative generative mechanisms of disease or clinical state and resultant network topology is either categorically unknown or incompletely understood. Honey

Figure 2. Network hubs have increased amyloid- (A) deposition in AD. A, Location of cortical hubs, that is, nodes with a high number of connections or degree centrality in healthy resting-state fMRI networks. B, Location of greatest A deposition in people with AD, as measured in a PET study. Data are reproduced with permission from Buckner et al., 2009.

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and Sporns (2008) and Netoff et al. (2004) provide recent examples of studies conducted in lesions and epilepsy, respectively. Future studies of this kind are likely to be highly instructive because they will enable researchers to directly compare the theoretical network consequences of abnormal growth or neurodegenerative mechanisms with empirically determined network architectures in clinical states.

Open FrontiersReproducibility and specificityAlthough applications of complex network theory to the study of human brain structure and function have proven useful in a broad range of clinical states, several lines of inquiry remain open for further exploration. While the majority of disease states studied display altered topological properties of brain networks, it is as yet unclear to what degree the patterns of alterations are both reproducible and disease-specific. In this context, it is interesting to note that several functional analyses of schizophrenia have reported a decreased path length or increased global efficiency, suggesting a randomization of network architecture (Bassett et al., 2009; Rubinov et al., 2009;), whereas AD networks display a relatively increased path length (Stam et al., 2007, 2009), suggesting a regularization of network architecture. Thus, additional studies are needed to highlight specific network measures, or groups of networks measures, that can successfully distinguish between disease states. In addition to their lack of disease specificity, very few studies have addressed the issue of reproducibility in the context of disease, although a few have reported relatively good reproducibility over either scanning sessions or imaging acquisition parameters in healthy controls (Deuker et al., 2009; Vaessen et al., 2010).

Structure-functionAnother set of comparisons to be made are those spanning diverse imaging modalities. Such studies raise important theoretical questions, such as, “To what extent should we expect agreement between clinically specific network alterations in structure–versus-function? Or across disparate functional modalities such as fMRI and EEG? Or between arguably more similar imaging modalities such as EEG and MEG?” Preliminary evidence from work in AD suggests that the picture may be complicated: While morphometric structural network analyses showed increased clustering in AD (He et al., 2008), functional resting-state analyses in both fMRI and MEG showed decreased clustering (Supekar et al., 2008; Stam et al., 2009). In healthy

populations, by contrast, diffusion-based rather than morphometric-based structural networks display a significant topological overlap with resting-state fMRI connectivity profiles (Honey et al., 2009). Furthermore, combining anatomical and functional connectivity profiles has been shown to provide a more comprehensive description of disease-specific architectural changes in schizophrenia (Camchong et al., 2009; Skudlarski et al., 2010).

Function-functionStructure aside, simpler comparisons between functional imaging modalities are likely to be sensitive to modality-specific noise or artifact and differential signatures of neuro-oscillatory function. For example, resting-state functional connectivity, as measured by fMRI, is decreased in schizophrenia (Liu et al., 2008; Lynall et al., 2010), while connectivity measured by EEG/MEG is reportedly increased (Rubinov et al., 2009). In order to clarify the interaction between disease and measured function in such cases, it is becoming increasingly important to apply a more precise understanding of the inherent relationships between neurophysiological time series, classical measures of functional connectivity (e.g., principal components analysis), and the resultant network structures (Lynall et al., 2010).

MethodsIn addition to providing insight into neurophysiological disease markers, the relationship between functional connectivity and network struc-ture directly impacts the methodological challenge of comparing graphs between subject populations or comparing individual graph metrics with behavior, cognitive variables, or symptom scores. Parsing the effects of functional connectivity differences, net-work fragmentation profile differences, and inher-ent network architectural differences constitutes an important methodological challenge to the current analysis stream. In the flow of analysis, the use of weighted network measures and alternative thresh-olding strategies are likely to add value.

ConclusionComplex network models of human brain structure and function have produced biologically relevant and plausible results. Subsequent applications of this framework to clinically relevant topics have been highly successful, particularly in the study of schizophrenia and AD. Important future directions for research to take include assessing disease specificity and network reproducibility; in addition, researchers will need to characterize similarities and

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differences in network structure as measured over multiple imaging modalities.

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