AND ITS DISRUPTIONS IN SCHIZOPHRENIA
June, 2012 Sofie Valk, 0569100 Supervisor: Boris Bernhardt, PhDMax Planck Institute of Human Cognitive and Brain Sciences Co-‐assessor:
Mike Cohen, PhD, University of Amsterdam Word count:
15.266 No. of References:
199
Master Brain and Cognitive Sciences, University of Amsterdam Track: Cognitive Sciences
University of Amsterdam
1.0 INTRODUCTION ... 4
2.0 DEFINING AND CONSTRUCTING BRAIN NETWORKS ... 5
2.1 WHAT ARE NETWORKS? ... 5
2.2 ANIMAL CONNECTIVITY MAPPING. ... 5
2.3 HUMAN IN VIVO CONNECTIVITY MAPPING THROUGH MRI ... 7
Structural networks ... 7
Functional networks ... 9
3.0 NETWORK ANALYSIS ... 10
3.1 RELEVANT PARAMETERS ... 11
3.2 FINDINGS IN HEALTHY SUBJECTS ... 13
Graph theoretical characteristics of structural brain networks ... 13
Graph theoretical analysis of functional resting state MRI data ... 14
Interpretation of findings ... 15
3.3 HOW GRAPH THEORY SYNTHESIZES DATA ... 16
4.0 NETWORK DISRUPTIONS IN SCHIZOPHRENIA ... 17
4.1 HISTORY OF SCHIZOPHRENIA; A CLASSIC EXAMPLE OF DYSCONNECTIVITY DISORDER ... 17
4.2 NETWORK STUDIES ON SCHIZOPHRENIA PATIENTS ... 19
Low-‐level connectional differences ... 19
Topological connectional differences ... 22
5.0 CHALLENGES OF CURRENT NETWORK APPROACHES ... 24
6.0 SUMMARY AND CONCLUSION ... 26
7.0 LITERATURE ... 27
1.0 Introduction
One of the reasons why modern neuroscience attracts such a wide interest stems from the inherent and challenging complexity of the human brain. Currently, it is believed that when the structural architecture and the functional dynamics of brain networks are better understood, open questions related to both normal and abnormal mental processes can be answered. With the use of graph theory, the mathematical branch that is used to describe the topology of complex networks, different organizational characteristics of the brain network can be formalized and investigated to probe novel hypotheses about human brain structure and function.
Already in the 19th century, several neurological disorders such as schizophrenia and aphasia were referred to as disconnection syndromes, indicating that an impoverished connectivity between different brain regions leads to dysfunction (Dejerine, 1891; Liepmann, 1977; Wernicke, 1874). However, these theories were largely forgotten during the first half of the 20th century. In the 1960s, Norman Geschwindt reintroduced disconnection as a theme in neuroscience (Geschwindt, 1965). This time, his reformulations triggered explorations of cortico-‐cortical connectivity in both animals and later, with the advent of in vivo imaging, in humans (Catani & Ffytche, 2005)
The conceptual framework of connectivity and its disruptions were used to explain psychiatric diseases, in particular schizophrenia. The idea that schizophrenia is linked to disintegration of the psyche is as old as its name (Bleuler, 1913). On the other hand, approaches attempting to localize psychopathology to individual cortical areas have so far not provided a sufficient explanation for cardinal symptoms of schizophrenia such as hallucinations and delusions (Tandon, Nasrallah, & Keshavan, 2009). Indeed, it has been suggested that these symptoms relate to the abnormal connections between and within brain regions (Bullmore et al., 1998).
This review addresses the concepts and techniques that are currently applied to unravel general principles of functional and structural connectivity in the human brain, and their disruptions in schizophrenia. The first part focuses on general methodological principles of network analysis in neuroscience. We will explain how a brain network can be formalized and how network properties are quantified across several levels of analysis. Contrasting network properties that have been found in healthy human brains to those in patients with schizophrenia, we will outline clinical applications of graph theoretical network analysis to this classical dysconnectivity disorder. We will conclude by summarizing current and future challenges of network analysis in neuroscience.
2.0 Defining and constructing brain networks
2.1 What are networks?
The brain is a paramount example of a complex network. Complex networks are networks that are neither completely organized nor completely unpredictable. In the brain, these characteristics of connectivity found between elements exist at multiple scales. The microscopic scale is based on individual neurons and synapses. A more macroscopic scale focuses on anatomically distinct regions, such as the white matter tracts and interregional projections, and in between, the mesoscale, which consists of neuronal populations and assemblies (Sporns, 2011).
While animal research has provided a wealth of information about the wiring of individual neurons, recent in vivo studies have rather focused on brain regions and large-‐scale network (Sporns, Tononi, & Kötter, 2005). Alongside steep advancements in acquisition and processing technology of cellular neuroscience and human neuroimaging, there was a rise of modern network theory in the late 1990s. The conjoint advancements in these domains stimulated the systematic investigation and description of the brain as a network. Accordingly, brain networks are formalized as a complex graph, which is a collection of nodes (i.e., regions or neurons) and edges (i.e., connections). Such graphs are formally equivalent to connectivity matrices, in which the network’s nodes are represented as row and column indices, with the scalar value in an individual cell quantifying the edge strength between a given pair of nodes. The connectivity matrix is analyzed using mathematical methods derived from graph theory (Bassett & Bullmore, 2009; Bullmore & Sporns, 2009; Sporns, Tononi, & Kötter, 2005).
2.2 Animal connectivity mapping.
A landmark study in both applied neuroscience and theoretical network science was the work of Duncan Watts and Steven Strogatz (1998). They classified the topology of different complex networks on the basis of two global parameters; average clustering coefficient and path length. In a graph, the clustering coefficient defines the strength of connections between nodes in a typical neighborhood are connected among each other. It thus represents a measure of local network efficiency and robustness (Latora & Marchiori, 2001). Path length, on the other hand, relates to the global efficiency of the network, and quantifies the average separation between any two nodes (Bullmore & Sporns, 2012; Guye, Bettus, Bartolomei, & Cozzone, 2010). Given these two parameters, Watts and Strogatz defined random networks as those with random connections between nodes and a low average path length, and regular networks as those with only connections to nearest neighbors. These networks are highly clustered.
They also categorized a third, intermediary class: small-‐world networks. Indeed, these networks have both a high clustering coefficient and a low average path length. The low average path length is guaranteed by the presence of short cut edges that connect clusters of nodes that would otherwise be much farther apart. Both characteristics of small-‐world networks signify a high local and global efficiency of information transfer. These short cuts contribute to a higher interconnectivity of different strongly inter-‐connected sub-‐networks, the so-‐called small worlds. Small-‐world topology is generally associated with global and local parallel information processing, sparse connectivity between nodes, and low wiring costs (Bassett & Bullmore, 2006). To illustrate their ideas about the topology of small-‐world networks, Watts and Strogatz chose to analyze the neuronal network of the nematode worm, C. Elegans. At the time of their study, this was the sole example of a completely mapped neuronal network in an organism.
C. Elegans has a relatively simple network topology. It consists of 959 cells, 302 of which are neurons
that are connected by 6393 synapses and 890 electrical junctions. They represented neurons as nodes and neural connections as edges. For their analysis, Watts and Strogatz considered a sub-‐graph consisting of 282 neurons. They observed that a single neuron was, on average, connected to 14 other neurons. Importantly, comparing the neural network of C. Elegans to an equivalent random network, they observed a five-‐fold increase in clustering coefficient but virtually no increase in overall path length. Their findings thus indicated, for the first time, that the brain network of an organism adheres to a small-‐world topology.
Anatomical connection matrices of larger animals, such as the cat and the macaque monkey, were constructed with the use of tract-‐tracing methods (Hilgetag, O’Neill, & Young, 2000; Sporns & Kötter, 2004). This invasive method is used to trace axonal projections and is considered the gold standard for defining neuronal network anatomy. However, these methods generally only allow the tracing of fairly large cell populations and single axonal pathways. Connections can be visualized in an anterograde fashion, by injecting tracer in the soma, or cell body, and visualizing their transport along the axonal projections to the synapses. To trace projections from a specific regional cell, a genetic construct, virus or protein can be locally injected, after which it is allowed to be transported anterogradely (Kuypers & Ugolini, 1990). Other tracers consist of protein products that can be taken up by the cell and transported across the synapse into the next cell. An example is the wheat-‐germ agglutinin and Phaseolus vulgaris leucoagglutinin (Smith, Hazrati, & Parent, 1990). Conversely, retrograde tracing maps neural connections from their synapses to the soma. Retrograde tracing includes the use of viral strains as markers of a cell’s connectivity to the injection site. Another technique is injecting “beads” into the brain nuclei of anesthetized animals. After a few days the animals are euthanized and the cells in the origin of
injection are visualized through a fluorescence microscope (Luo & Aston-‐Jones, 2009; O’Donnell, Lavin, Enquist, Grace, & Card, 1997). Several seminal studies have mapped the connections of macaque visual cortex (Felleman & Van Essen, 1991) and the feline thalamo-‐cortical system (Scannell, Burns, Hilgetag, O’Neil, & Young, 1999). In macaque monkeys, tract-‐tracing studies have provided a basic map of anatomical links between major cortical areas (Stephan, 2001) and provided valuable data on rostro-‐ caudal and dorsal-‐ventral connectivity gradients between major prefrontal and parietal cortices (Petrides & Pandya, 2009). Furthermore, a broad range of characteristics related to the topology of complex networks have been identified in both the macaque and cat, including the existence of clustering (Hilgetag et al., 2000), segregation (Young, 1992), together with small-‐world organization as well as other important topological attributes (Sporns, Tononi, & Edelman, 2000; Sporns & Zwi, 2004; Young, 1992; Sporns & Kötter, 2004; Sporns et al., 2000; Sporns & Kötter, 2004; Kötter & Stephan, 2003; Hilgetag, O’Neill, & Young, 1996; Hilgetag et al., 2000)
2.3 Human in vivo connectivity mapping through MRI
Tracer-‐based connectivity mapping cannot be applied to the living human brain due to the invasive nature of this method. In humans, noninvasive, in vivo, network mapping can nevertheless be performed in both structural and functional domains. Structural networks can be inferred on the basis of diffusion-‐weighted MRI tractography or through analysis of inter-‐regional covariance patterns of structural measures across subjects. Functional networks can be defined on the basis of electrophysiological and metabolic signal correlations, with recent work being mostly based on time-‐ series correlations of task-‐free, resting-‐state, functional MRI signals. In the following paragraphs, these MRI-‐based methods are explained in more detail, as well as compared with each other, in order to illustrate the benefits and problems associated with each of them.
Structural networks
Diffusion-‐weighted MRI relies on special pulse sequences, which elicit signals that scale with the orientation and magnitude of diffusion processes in soft tissue, specifically water molecules (Le Bihan, 2003; Basser, Mattiello, & Le Bihan, 1994; Basser & Pierpaoli, 1996). In the human brain, the Brownian motion of water molecules is strongly constrained by myelinated fiber tracts, which hinder any motion across them. The signals recorded therefore indicate two main features: the deviation from randomness of diffusion within each measured voxel, which is expressed by the fractional anisotropy, indicating white matter integrity, and the three-‐dimensional orientation of the diffusion tensor of the corresponding probability functions. High anisotropy can also be observed in un-‐myelinated nerves,
indicating that anisotropy is mainly defined by the axon, and myelination is not required to detect anisotropy (Beaulieu & Allen, 1994). By analyzing paths of diffusion direction throughout adjacent voxels, one can estimate the course of different fiber tracts by means of tractography algorithms (Behrens et al., 2003; Mori, Crain, Chacko, & van Zijl, 1999). In various psychiatric populations such as autism, (Catani et al., 2008; Cheng et al., 2010; Cheung et al., 2009; Thakkar et al., 2008) and schizophrenia (van den Heuvel et al., 2010; Fornito, Zalesky, Pantelis, & Bullmore, 2012; Zalesky, Fornito, et al., 2010) diffusion MRI tractography has been assessed to localize and quantify white matter disturbances. Despite generating visually impressive results and closely approximating the course of fiber tracts in deep white matter regions, such as the corpus callosum, diffusion tractography remains an indirect measure of structural connectivity. Indeed, the reconstruction of the fibers relies mostly on the parameters used for the reconstruction algorithm. There are several additional limitations, such as finding the exact termination of connections, detecting collaterals, tracking the very dense network of horizontal intra-‐cortical connections, discriminating between afferents and efferents and the fact that the uncertainty of the location of a tract increases when the tract spans a larger distance (Jbabdi & Johansen-‐Berg, 2011). Furthermore, seeding from grey matter regions remains challenging for conventional diffusion-‐based tractography given the high uncertainty in fiber directions within and around grey matter (Jbabdi & Johansen-‐Berg, 2011).
An alternative approach to diffusion MRI tractography in the structural domain infers networks based on inter-‐regional covariance patterns in morphological measures. Covariance mapping (Bullmore & Sporns, 2009; Lerch et al., 2006), commonly based on T1-‐weighted MRI, takes advantage of a high anatomical resolution that is, unlike standard echo-‐planar images used for diffusion imaging, only minimally affected by imaging artifacts in anteroventral brain regions. In addition, correlations of structural markers such as cortical thickness directly seed from grey matter regions, complementing diffusion tractography. Lastly, cortical measurements have undergone surface-‐based registration that aligns cortical folding patterns of each individual and thus improves between-‐subject correspondence. While high structural correlations between two regions do not necessarily signify a physical link, structural coupling has been suggested to reflect common genetic and developmental influences, a shared vulnerability to pathology, and the presence of persistent functional-‐trophic interactions (Bernhardt et al., 2008; Bernhardt, Chen, He, Evans, & Bernasconi, 2011; Bullmore & Sporns, 2009; Lerch et al., 2006; Raznahan et al., 2010). Indeed, previous work has demonstrated a high correspondence between structural covariance networks and those obtained from resting-‐state functional connectivity (Seeley, Crawford, Zhou, Miller, & Greicius, 2009; Segall, Allen, et al., 2012).
Functional networks
Structural connectivity is neither a sufficient nor a complete description of brain networks (Friston, 2011). In fact, synaptic connections in the brain are in a state of constant flux showing flexible and context-‐sensitive modulations, together with time-‐ and activity-‐dependent effects (Friston, 2011; Saneyoshi, Fortin, & Soderling, 2010). Functional connectivity research addresses inter-‐regional signal associations, which have been quantified using a wide range of measures, including simple correlations and coherence, partial measures, as well as higher-‐order and non-‐linear measures of association (Friston, 2011). These analyses are performed within the context of task free, resting-‐state functional MRI acquisitions, experimental tasks, or biophysical simulations (Smith, 2012). The analysis of resting-‐ state functional MRI generally focuses on low-‐frequency (e.g., 0.01 to 0.1 Hz), spontaneous oscillations in the blood-‐oxygen-‐level-‐dependent (BOLD) responses (Biswal, Zerrin Yetkin, Haughton, & Hydes, 1995). These patterns of BOLD activity have been suggested to reflect intrinsic functional connectivity (Greicius et al., 2009; Pawela et al., 2008). One of the most reproducible networks identified in resting state functional connectivity analysis is the default mode network, a collection of regions such as the medial prefrontal cortex and posterior midline regions, together with lateral parietal cortices, which show extensive deactivation during externally focused cognitive tasks (Greicius, Krasnow, Reiss, & Menon, 2003; Raichle et al., 2001). Other studies have identified intrinsic networks encompassing brains involved in visual, motor, language, and auditory processing that are consistent across subjects (Cordes et al., 2000; Damoiseaux et al., 2006; De Luca, Beckmann, De Stefano, & Smith, 2006; Fox et al., 2005; Greicius et al., 2003; Hampson, Olson, Leung, Skudlarski, & Gore, 2004; Hampson, Peterson, Skudlarski, Gatenby, & Gore, 2002; Lowe, Mock, & Sorenson, 1998). In a seminal study, Smith and colleagues (2009) compared spatial patterns of task activation networks based on meta-‐analyses of nearly 30,000 subjects to the major networks in the resting brain of 36 subjects. Observing close correspondences between task-‐free and task-‐related network components, Smith and colleagues concluded that the full repertoire of functional networks used by the brain in action is continuously and dynamically active even when at rest.
As mentioned earlier, structural and functional network data in humans is commonly inferred from indirect methods. Imaging-‐based findings from animals, where gold-‐standard tracing techniques are available, can thus be used to cross-‐validate different network metrics (Kötter, 2007). In the macaque monkey, diffusion MRI tractography has been shown to produce networks that generally overlap with traditional anatomical tract-‐tracing findings (Schmahmann, Pandya, Wang, Dai, & D’Arceuil, 2007). Extending these results, Hagmann and colleagues found significant overlap between macaque
connectivity data derived from diffusion data and from tract tracing in the same monkeys (Hagmann et al., 2008). However, tract tracing studies in animals and imaging studies in humans are made difficult by the uncertainty of cross species homologies between functionally defined brain regions and brain structure in general (Bressler & Menon, 2010; Orban, Van Essen, & VanDuffel, 2004).
3.0 Network analysis
Despite variations in defining an inter-‐regional link, all imaging techniques mentioned above allow the generation of connectivity matrices. These matrices are equivalent to brain graphs; collections of nodes interconnected by edges, which can be readily analyzed by graph theory, the mathematical analysis of complex, interconnected networks.
In a brain graph, nodes represent distinct, homogeneous elements based on a given structural, functional, or otherwise objective criterion. A variety of techniques have been used to generate anatomical parcellations of the brain, which can then be used to define nodes structurally. In post
mortem data, quantitative cyto-‐architectonic features (Schleicher, Morosan, Amunts, & Zilles, 2009), as
well as neurotransmitter profiles (Zilles & Amunts, 2009), have been used towards this end. Using human imaging analysis, parcellations have been proposed that are based on macroscopic landmarks (Tzourio-‐Mazoyer, Landeau, Papathanassiou, Crivello, & Etard, 2002), gyral folding patterns (Desikan et al., 2006), and more recently, myelin density profiles (Glasser & van Essen, 2011). The choice of nodal parcellation has important consequences for the determination of network connectivity, and diverse tradeoffs between exactness and descriptive power have to be made (Zalesky, Fornito, et al., 2010; Van Dijk et al., 2010). In addition to the aforementioned structural criteria, parcellations have also been performed purely in the functional domain. Examples are task activation (i.e., localizer-‐based) parcellations. Specifically, Eguiluz and colleagues (2005) used a finger-‐tapping task to reconstruct correlation matrices. Moreover, nodes derived from consistently activated regions in meta-‐analyses can be used to define nodes (Fox et al., 2005). Decompositions have also been provided using data driven approaches, such as independent component analysis and hierarchical clustering (Beckmann, DeLuca, Devlin, & Smith, 2005; Damoiseaux et al., 2006; Salvador et al., 2005).
In both structural and functional domains, one can also apply random parcellations (Hagmann et al. 2007; 2008), as well as voxel-‐wise parcellations, which offer a tremendous boost in resolution but also significantly increase computation time (Friston, 2011; Smith, 2012; Lohmann et al., 2010; Tomasi &
Volkow, 2010). Altogether, the choice of definition of a node has a strong influence on the network properties found, and wrongly placed nodes can influence the connections found between nodes.
Connections based on structural imaging data are often described as undirected, that is, equivalently strong in both directions. In the framework of structural MRI covariance analysis, connectivity is assumed to be reflected by the cross-‐subject correlation between regional morphometric parameters, such as grey matter volume or cortical thickness (Bullmore & Sporns, 2009; Lerch et al., 2006; Bernhardt et al., 2011; Seeley et al., 2009). Using diffusion-‐weighted MRI, connectivity is typically inferred from a tractographic estimate of fiber tracts between regional pairs. Connectivity strength may be quantified using the proportion of seed fibers terminating on a target region, some index of fiber integrity averaged over the reconstructed tract, or a composite measurement (Jbabdi & Johansen-‐Berg, 2011; Le Bihan, 2003). In functional MRI studies, edge strength is commonly inferred from the correlation of the activity time courses ( Bassett & Bullmore, 2009). The more similar the time courses are between any given pair of nodes, the likelier it is that there is a functional connection between those nodes. Functional connectivity, thus, reflects statistical associations of regions, and does not signify any causal link. Effective connectivity, on the other hand, refers explicitly to the influence that one neural system exerts over another, either at the synaptic or population level (Friston, 2011). Methods that are used to infer effective connectivity in functional networks include structural equation modeling (Bullmore et al., 2003; McIntosh & Gonzalez-‐Lima, 1994), dynamic causal modeling (Friston, 2003) or Granger causality (Brovelli et al., 2004). However, in practice most studies have been based on undirected functional connectivity (Bullmore & Sporns, 2009; Smith, 2012). In the future, it is aimed to unite functional connectivity and effective connectivity (Friston, 2011).
3.1 Relevant parameters
Once nodes and edges of a brain network are defined, graph-‐theoretical parameters can be calculated that characterize various topological aspects of the network. Despite methodological challenges put forward by the sheer complexity of human and animal brains, these parameters allow the identification of general patterns that cogently summarize organizational network principles. Analyzing those characteristics in the unified framework of graph theory may help us to better understand the relationship between different structural configurations, functional brain dynamics, and behavior. Ultimately, this approach promises to shed light on normal variations, developmental alterations, and pathological disruptions in brain networks. Network properties can be calculated on a global level that characterizes the organization and efficiency of the whole network (Bullmore & Sporns, 2012; Guye,
Bettus, Bartolomei, & Cozzone, 2010). However, a network can also be described on a local and
intermediate level.
On a local level, one can use centrality-‐based metrics that quantify the integration of a node into the whole network, such as degree centrality, betweenness centrality, and eigenvector centrality. Degree centrality is the total number of the connections a node has. The betweenness centrality is defined by the factor of shortest paths from one point to another passed through a node, and thus quantifies the location of a node on efficient pathways of information transfer. These two measures give complementary notions of the relevance of a node for the whole network. The additional metric eigenvector centrality uses a recursive formalization, where nodes have high centrality if they are connected to nodes that are central themselves (Lohmann et al., 2010). Although local, these centrality based metrics may also be used to quantify the resilience of a network with respect to targeted network attacks, by which one removes central nodes from the network and assesses the impact on global topological parameters (Achard & Bullmore, 2007; Honey & Sporns, 2008; Kaiser, Martin, Andra, & Young, 2007). Moreover, it has been found that the degree distribution of the brain follows a power law, with many nodes having a low degree centrality and a few nodes having a high degree centrality (Bullmore & Sporns, 2009). Such highly central nodes are called hubs, and it has been suggested that such central nodes are crucial for network dynamics (Freeman, 1977).
An intermediate level of network analysis operates on the scale of modules, which are aggregates of nodes. The human brain small-‐world network is typically characterized by a high number of clusters of local interconnected nodes, called modules (Newman & Girvan, 2004), and a relatively low number of extra-‐modular connections. The modularity of a network is often based on hierarchical clustering (Girvan & Newman, 2002). A modular parcellation allows further characterization of different nodes. For example, nodes that have a high centrality within a module are called provincial hubs; conversely, nodes that have a high centrality between modules are called connector hubs. Modular organization provides the brain with the capacity to modify and adapt one module, without affecting the function of others. Furthermore, a modular structure allows functional segregation within modules as well as functional integration between modules (Sporns, 2000). The close association of areas within clusters makes efficient recurrent processing possible (Sporns, 2011). Finally, the modular structure might support synchronous processing (Kaiser & Hilgetag, 2004) and efficient information exchange (Latora & Marchiori, 2001). Therefore, modularity can be seen as a highly suitable characteristic for brain
networks that must adapt very rapidly across different time scales (Bullmore & Sporns, 2012; Guye et al., 2010).
3.2 Findings in healthy subjects
The parameters described above have been used to characterize structural as well as functional networks in healthy individuals.
Graph theoretical characteristics of structural brain networks
In humans, structural connectivity studies of diffusion networks have revealed highly clustered large-‐ scale cortical networks. These networks have strong connections between areas that are spatially proximal and functionally related, as well as a relatively high local efficiency, but with a similar global efficiency in comparison to random networks (Gong et al., 2009; Iturria-‐Medina et al., 2008; Hagmann et al., 2008; Zalesky, Fornito, et al., 2010). Hagmann and colleagues (2008) identified structural modules interconnected by highly central hub regions, as well as a structural core of highly interconnected brain regions in posterior medial frontal cortex. Regions in the structural core share high degree and betweenness centrality, and they contain connector hubs that connect to all other main structural modules. This structural core also contained brain regions corresponding to the posterior part of the default mode network. These findings indicate that the structural core may be an important basis for shaping large-‐scale brain dynamics (Hagmann et al., 2008). Furthermore, hubs regions such as the precuneus, posterior cingulate gyrus, putamen, insula, superior parietal, and superior frontal cortex have been identified, indicating the importance of these regions within the structural network of the brain (Gong et al., 2009; Iturria-‐Medina and colleagues., 2008).
Using the complementary framework of correlation analysis of cortical thickness measurements, multiple studies (He, Chen, & Evans, 2007; He, Chen, & Evans, 2008; Yao et al., 2010) found robust small-‐ world properties with cohesive neighborhoods in the cortex and they found the brain network had truncated power-‐law distributions. Furthermore, a modularity analysis of the relationships between structural cortical networks identified modules similar to known functional domains, such as sensorimotor, visual, auditory/language, strategic/executive, and mnemonic processing (Chen, He, Rosa-‐ Neto, Germann, & Evans, 2008).
Age, gender and intelligence have also been examined from the perspective of topological patterns of structural brain networks. Using diffusion tractography, it was found that age was negatively correlated with overall connectivity, and a shift of regional efficiency from parietal and occipital regions to frontal
and temporal regions (Gong et al., 2009). Also, a structural covariance study found that an elder group (mean age = 66.6 years) had higher local clustering but lower global efficiency in comparison to a younger group (mean age = 46.7) (Zhu et al., 2012). Gender differences have also been found. In a diffusion tensor imaging study, it was found that females had higher local efficiency than males, and small brains had greater local efficiencies in females but not in males (Yan et al., 2011). Previously another diffusion tensor study had also found females showed greater overall cortical connectivity and a more efficient organization both locally and globally (Gong et al., 2009). The relation between intelligence and graph structure has also been investigated. In a diffusion tensor imaging study, a significantly higher global efficiency and a shorter characteristic path length were found in the networks of the high intelligence groups (Li et al., 2009). The findings of these studies illustrate the relation between the structural network topology in the brain with age, gender and intelligence.
Graph theoretical analysis of functional resting state MRI data
Network-‐level findings in the functional domain generally correspond to those in the structural domain. Salvador and colleagues were the first to demonstrate small-‐world properties in functional MRI resting state data (Salvador et al., 2005). Their study calculated an undirected graph derived by thresholding the healthy group mean based on partial correlation measurements of 90 cortical and subcortical regions. At around the same time, an independent study reported small world properties in a set of activated voxels in fMRI data as well (Eguiluz, Chialvo, Cecchi, Baliki, & Apkarian, 2005). Other studies have explored the (modular) community structure of fMRI networks using hierarchical clustering analysis (Ferrarini et al., 2009; Meunier, Achard, Morcom, & Bullmore, 2008) and have shown that functionally related brain regions are more densely interconnected, with relatively few connections between functional clusters.
Moreover, it has been found that a higher global efficiency of functional networks can be associated with a higher IQ (Langer et al., 2012; Li et al., 2009; van den Heuvel, Mandl, Kahn, & Hulshoff Pol, 2009), suggesting potential benefits of shorter path lengths in the cerebral cortex for higher cognitive functioning. Age-‐related efficiency characteristics of functional networks, closely related to clustering and path length, have also been investigated (Achard, Salvador, Whitcher, Suckling, & Bullmore, 2006). The authors used resting-‐state fMRI data from young and elderly adults and found that brain networks in the younger group were of small-‐world and efficient layout, indicated by high local and global efficiency despite relative low connection cost. In the elderly group, efficiency was reduced disproportionately to the wiring cost of adding a connection (Achard et al., 2006), albeit still showing a small-‐world layout. This study illustrates how normal processes of brain maturation are represented
through quantifiable changes in functional network topology. Gender related differences have also been found in resting state networks, with women showing more symmetric functional organization than men (Liu, Stufflebeam, Sepulcre, Hedden, & Buckner, 2009), as well as a gender-‐by-‐hemisphere interaction (Tian, Wang, Yan, & He, 2011).
Interpretation of findings
There is now strong evidence that the human brain generally has small world properties, with high clustering and global efficiency (Achard & Bullmore, 2007), a modular community structure (Chen et al., 2008; He et al., 2007; Meunier et al., 2008; Meunier, Lambiotte, & Bullmore, 2010), and an increased proportion of central hubs relative to random graphs (Achard et al., 2006; Eguiluz, Chialvo, Cecchi, Baliki, & Apkarian, 2005; Sporns, Honey, & Kötter, 2007). Generally speaking, brain networks are topologically complex and efficiently organized given likely evolutionary constraints on wiring cost. The combination of high clustering, high efficiency, and modular small-‐world architecture can deliver both specialized and distributed processes (Sporns, 2011). Specialized and local processes could possibly benefit from a vast amount of local connections, while the integration of segregated processes could rather benefit from a high global information transfer efficiency that makes rapid communication between several specialized regions possible (Bullmore & Sporns, 2012; Tononi, Spons, & Edelman, 1994; Tononi & Sporns, 2003). For example, it has been found that functionally specialized regions show high clustering with areas having the same functional specialization in the same anatomical neighborhood (Bullmore & Sporns, 2012). Even more so, the brain is characterized by a hierarchical group of modules, with each node often sharing functional specializations with other nodes in the same module (Chen et al, 2008; Chen et al., 2011; He et al., 2009; Meunier et al., 2009). Moreover, topological measures can be used to describe neurodevelopmental processes, which currently have already been assessed in recent studies on aging in healthy adults (Achard, Salvador, Whitcher, Suckling, & Bullmore, 2006; Gong et al., 2009; Yan et al., 2011). For example, it has been found that location of cortical hubs in the (±39 week old) infant brain stands in stark contrast to the situation in adults. In infants, cortical hubs and their associated cortical networks are largely limited to primary sensory and motor brain regions, supporting perception-‐action tasks (Fransson, Aden, Blennow, & Langercrantz, 2011). In contrast, the cortical hubs in adults are located in areas supporting more higher order cognitive processing (Fransson, Aden, Blennow, & Lagercrantz, 2011). A series of resting-‐state functional MRI studies in children of age 7 and older have suggested that large-‐scale cortical networks develop from a “local and segregated” to a “distributed and integrated” organization (Fair et al., 2009; Fair et al., 2008; Fair et al., 2007; Supekar, Musen, & Menon, 2009). These findings suggest that brain organization may have evolved following an adaptive and
dynamic balance of network cost and network efficiency (Bullmore & Sporns, 2012; Latora & Marchiori, 2001).
3.3 How graph theory synthesizes data
Graph theoretical parameters allow a seamless integration of topological information from both structural and functional data across different modalities, and in principle, spatial scales. Moreover, graph theoretical analysis makes it possible to study the characteristics of the brain beyond the strength of low-‐level connections and disconnections between nodes (Bullmore & Sporns, 2012).
Structure-‐function relationships in the brain are still not fully understood. However, recent studies have begun to use network analysis to fill this gap (Hagmann et al., 2008; Honey et al., 2009; Skudlarski et al., 2008; Greicius, Supekar, Menon and Dougherty, 2009; Seeley et al., 2009; van den Heuvel et al., 2009). In their seminal study, Honey et al. compared functional networks based on resting state signal correlations and structural networks based on diffusion tractography in the same individuals and observed a moderately strong correlation (Honey et al., 2009). However, they also found functional connectivity between regions that were not directly linked. Some of the variance in functional connectivity could be explained for by indirect connections and interregional distance, as well as high variability within and across both scanning sessions and model runs. Another study compared resting-‐ state functional MRI data with diffusion tractography specifically in the default mode network (Greicius et al., 2009). They obtained ROIs of the default mode network based on resting state data, and used diffusion tensor fiber tractography to estimate the connections between the regions. Although they found high consistency between resting-‐state-‐based and diffusion-‐based connectivity, they too concluded that there was a dichotomy between functional and structural data, illustrated by an absent structural connection between the medial prefrontal and the medial temporal ROI. Extending this analysis approach to more networks, van den Heuvel and colleagues (2009) found that eight out of nine functionally linked resting-‐state networks were interconnected by white matter tracts.
Intrinsic functional connectivity networks have also been found to be related to structural covariance patterns. Seeley and colleagues (2009) discovered a direct link between intrinsic connectivity and grey matter structure. Across healthy individuals, nodes within each functional network showed closely correlated grey matter volumes. Furthermore, Kelly and colleagues (2012) specifically investigated the functional architecture of the insula. They parcellated the insula on the basis of three distinct neuroimaging modalities (task-‐evoked co-‐activation, intrinsic functional connectivity, and gray matter
structural covariance) and demonstrated convergence among modalities at a finer resolution. The convergence among large-‐scale networks defined in multiple modalities supports the hypothesis of a fundamental brain architecture governing both structure and function.
4.0 Network disruptions in schizophrenia
Recent years have seen graph theoretical applications in clinical settings to neurological and psychiatric disorders. Such approaches promise to provide a phenotypical description of these conditions that complement accounts that rather focus on the localization of pathology. In the next sections, we will outline such clinical applications, using the example of schizophrenia.
4.1 History of schizophrenia; a classic example of dysconnectivity disorder
Schizophrenia has been characterized as a prototypical disorder of brain connectivity. The notion that schizophrenia is not caused by focal brain abnormalities, but results from pathological interaction between brain regions, is an old and influential notion in schizophrenia research (Bleuler, 1913; Wernicke, 1906). Carl Wernicke hypothesized that the origin of psychosis was sejunction, the anatomical disruption of fiber tracks that blocks the regular associative processes and shunts them into an abnormal direction. These factors of sejunction are theoretically localizable. In 1908 Bleuler came up with the term schizophrenia, which is a conjunction of the Greek words schizein (σχίζειν) and phrēn, phren-‐ (φρήν, φρεν-‐), which translates to the “splitting of the mind”, in order to describe the separation of function between personality, thinking, memory, and perception.
There is no agreement regarding the exact nature of the cognitive/neuropsychological impairment in schizophrenia (Rund, 1998; Rund, 2009). To capture the heterogeneous nature of the disorder, schizophrenia has been classified into a number of subtypes, including simple, catatonic, disorganized, paranoid, schizoaffective, undifferentiated, residual and latent schizophrenia (Tandon et al., 2009; American Psychiatric Association, 2000; ICD-‐10, 1993). Furthermore, symptoms of schizophrenia can be grouped as positive, negative, and cognitive symptoms (Broome et al., 2005; Kurtz, 2005). Positive symptoms include delusions, disordered thoughts or speech and hallucinations. Negative symptoms encompass deficits, such as flat affect and emotions, lack of motivation and poverty of speech (Sims, 2002; van Os & Kapur, 2009). Moreover, disease severity and the relative proportions of different symptomatologies can vary across patients and through the course of the illness. Schizophrenia has also been associated with cognitive deficits such as impaired theory of mind (Penn, Sanna, & Roberts, 2008;
Sprong, Schothorst, & Vos, 2007; Vauth, Rusch, Wirtz, & Corrigan, 2004) and anxiety (Bleuler, 1913; Kraepelin, 1919; Rund, 2009). Difficulties in working and long-‐term memory, attention, executive functioning, and speed of processing also occur (van Os & Kapur, 2009). Finally, schizophrenics are likely to have comorbid conditions such as major depression and substance abuse (Buckley, Miller, Lehrer, & Castle, 2009).
On a macroscopic level, imaging studies have shown that schizophrenia is associated with ventricular enlargement (Daniel, Goldberg, Gibbons, & Weinberger, 1991; Lawrie & Abukmeil, 1998; van Horn & McManus, 1992) and decreased cortical volume, mainly in lateral and medial temporal regions (Lawrie & Abukmeil, 1998). Overall, grey matter atrophy appears to be more marked than white matter changes (Lawrie & Abukmeil, 1998; Zipursky, Lambe, Kapur, & Mikulis, 1998). Furthermore, Voets and colleagues (2008) identified folding abnormalities, supporting the hypothesis of abnormal cortical development. Similarly, young adults at high risk of developing schizophrenia by virtue of their family history, also show enlarged ventricles (Cannon et al., 1993) and smaller medial temporal lobes (Lawrie et al., 1999). These findings suggest structural abnormalities prior to the onset of disease (Harrison, 1999) and support a neurodevelopmental model of schizophrenia. Post-‐mortem studies on the cellular level have demonstrated abnormal reduction in presynaptic and dendritic parameters (Harrison, 1999). However, there are many contradictory findings and difficulties in replicating the findings, possibly because studied patient groups often suffer comorbid diseases (Harrison, 1999), which makes it difficult to infer definitive conclusions.
Functional imaging studies have studied brain activation changes related to the positive, negative, and cognitive symptoms. Comparing hallucinations, a cardinal positive symptom, to non-‐hallucinatory states revealed largely increases in brain activity in right temporal regions, such as the right superior temporal cortex (Hoffman, Anderson, Varanko, Gore, & Hampson, 2008; Lennox, Park, Jones, & Morris, 1999; Shergill, Brammer, Williams, Murray, & McGuire, 2000) and frontal regions, including inferior frontal gyri (Shergill et al., 2004, 2000; Simons et al., 2010). Further studies suggest that disordered memory functioning, mediated by mesial temporal regions, may contribute to hallucinations (Seal, Aleman, & McGuire, 2004).
Negative symptoms, on the other hand, have also been related to a frontal lobe abnormalities (Andreasen et al., 1992; Volkow et al., 1987; Wolkin et al., 1992). In studies where patients were to participate in cognitively challenging tasks, especially when performing working memory tasks, abnormalities in frontal activation have indeed been found (Brown et al., 2009; Callicott et al., 2000;
