Brain dysconnectivity refers broadly to the abnormal integration of brain processes (Stephan et al. Reference Stephan, Friston and Frith2009). Although disrupted brain connectivity has long been considered a core deficit of psychosis on clinical grounds, recent support for the dysconnectivity hypothesis, enabled by technical advances in the acquisition and analysis of non-invasive in vivo neuroimaging data, emphasises impaired integration as a core feature in psychosis pathophysiology (Van den Heuvel & Fornito, Reference Van den Heuvel and Fornito2014). Functional connectivity, referring to synchronised physiological activity between two or more spatially separated brain regions, has been reported to be abnormal in individuals with schizophrenia – for example reduced in fronto-temporal regions during working memory tasks (Stephan et al. Reference Stephan, Friston and Frith2009). Findings from such neuroimaging investigations demonstrate that schizophrenia is unlikely to arise from disruption to one brain region alone, and provide biological models as a basis for the pathophysiology of positive psychotic symptoms, as well as negative and cognitive symptoms (Stephan et al. Reference Stephan, Friston and Frith2009; Van den Heuvel & Fornito, Reference Van den Heuvel and Fornito2014). Given that functional connectivity between anatomically separated regions indicates the existence of structural connections, and there is also a considerable interest in probing anatomical connectivity using structural neuroimaging techniques.

Structural magnetic resonance imaging (sMRI) investigations of schizophrenia have identified regional abnormalities, predominantly deficits in frontotemporal and subcortical grey matter structures. Diffusion-weighted imaging is a neuroimaging technique that enables investigation of microstructural alterations in the organisation and orientation of white matter tracts, wherein diffusion of water molecules is constrained by the anatomy of myelinated axons. Diffusion imaging findings of schizophrenia and psychotic bipolar disorder report that white matter microstructural alterations are present within callosal and fronto-temporal regions in patients relative to healthy controls (Ellison-Wright & Bullmore, Reference Ellison-Wright and Bullmore2009).

Although structural and diffusion imaging have been used to examine focal abnormalities within grey and white matter regions, a novel approach using graph theory can utilise these modalities to assess neuroanatomical connectivity. Graph theory employs parcellations of structural MRI measures of grey matter to model cortical structures (‘nodes’), along with diffusion measures of white matter to reconstruct the set of white matter connections (‘edges’). One advantage of this approach is that structural and diffusion MR images can be captured in a relatively short timeframe, allowing then for a complete reconstruction of the brain as a network at the macro-scale. Once the brain is represented as a graph with all the series of nodes and edges mapped, topological properties can be investigated to determine patterns of brain communication and efficiency (Sporns, Reference Sporns2011; Van den Heuvel & Fornito, Reference Van den Heuvel and Fornito2014). Such networks are commonly observed across many real world patterns. For example, one can like the anatomical wiring of the brains' connections to other networks such as airline patterns and the internet (Sporns, Reference Sporns2011). Characteristically such networks have ‘hub’ regions that are more centrally located with many connections passing through them, e.g. an international connecting airport. Mapping the connectivity structure of these systems provides information on how intact the network would remain if a ‘hub’ was damaged. Deriving graph theory metrics from neuroimaging data in this way can be applied to identify neuroanatomically based abnormalities of connectivity that may be present in psychotic illness.

Examples of metrics employed in studies to date include characteristic path length, global efficiency and clustering coefficient (Sporns, Reference Sporns2011). These are graphically displayed in Fig. 1. Specifically, characteristic path length measures the average shortest path of information flow between any pair of brain regions, i.e. the minimum number of edges that must be traversed to go from one node to another, between all pairs of brain regions (Fig. 1a ). Clustering coefficient measures the frequency with which a node's neighbours are also neighbours of each other – complex networks tending to have high clustering (Fig. 1b ). Global efficiency is presented mathematically as the inverse of path length, providing a reciprocal relationship whereby a shorter path length reflects increased efficiency in the system (Fig. 1a ).

Fig. 1. Graphical representation of some key graph theory metrics. This brain map expresses the series of connections as a network, with white matter connections (edges) linking parcellated cortical regions (nodes). (a) Characteristic path length: a measure of the graphs average shortest distance between node A and node B; global efficiency: measured as the inverse of path length; (b) clustering coefficient: the number of connections that exist between the nearest neighbours of a node as a proportion of the maximum number of possible connections; (c) rich club coefficient: highlights nodes that are more densely interconnected among themselves than with the rest of the nodes in the network.

A number of studies to date have reported abnormal connectivity metrics in cohorts of patients with psychotic illnesses compared with controls. For example, patients with schizophrenia are reported to display longer path length than controls in frontal and temporal regions (Van den Heuvel et al. Reference Van den Heuvel, Mandl, Stam, Kahn and Hulshoff Pol2010) and impairment of connectivity in a network connecting medial frontal to parietal and occipital regions (Zalesky et al. Reference Zalesky, Fornito, Seal, Cocchi, Westin, Bullmore, Egan and Pantelis2011). Patients with euthymic bipolar disorder display longer path length, lower global efficiency and lower clustering coefficient than controls, with particular deficits in interhemispheric integration (Leow et al. Reference Leow, Ajilore, Zhan, Arienzo, GadElkarim, Zhang, Moody, van Horn, Feusner, Kumar, Thompson and ALtshuler2013). A summary of studies is provided in Table 1.

Table 1. Studies employing graph theory analyses of structural neuroimaging data in psychotic illness

CC, clustering coefficient; CPL, characteristic path length; Eglobal, global efficiency; PLACE, path length associated community estimation.

Further exploration of brain organisational properties has led to the development of social theory measures in network analysis. The term ‘rich club’ originates from the analogy of being ‘rich’ in connections, and forming a ‘club’ because the set of regions are densely interlinked among themselves (Fig. 1c ). The rich club coefficient metric derived from social theory represents the hierarchy, power distribution and conduction of information flow throughout the brain (Van den Heuvel et al. Reference Van den Heuvel, Sporns, Collin, Scheewe, Mandl, Cahn, Goni, Hulshoff Pol and Kahn2013). An association between global efficiency and rich club organisation suggests rich club organisation is affiliated with global brain communication (Van den Heuvel et al. Reference Van den Heuvel, Sporns, Collin, Scheewe, Mandl, Cahn, Goni, Hulshoff Pol and Kahn2013). The rich club metric identifies crucial circuits for establishing and maintaining efficient global brain communication (Van den Heuvel & Sporns, Reference Van den Heuvel, Sporns, Collin, Scheewe, Mandl, Cahn, Goni, Hulshoff Pol and Kahn2013). Collin et al. (Reference Collin, Khan, de Reus, Cahn and van den Heuvel2014) employed this metric and identified substantially reduced connectivity between rich club hubs in patients with schizophrenia compared with healthy volunteers and additionally intermediate levels of rich club connectivity among unaffected relatives of the patient cohort, suggesting a genetic contribution to impaired rich club connectivity in schizophrenia. These recent investigations implicate rich club dysconnectivity as a core feature of psychosis, in which the rich club coefficient may prove to represent an endophenotype of psychosis (Van den Heuvel et al. Reference Van den Heuvel, Sporns, Collin, Scheewe, Mandl, Cahn, Goni, Hulshoff Pol and Kahn2013; Collin et al. Reference Collin, Khan, de Reus, Cahn and van den Heuvel2014). Crossley et al. (Reference Crossley, Mechelli, Scott, Carletti, Fox, McGuire and Bullmore2014) utilised normative DTI data to identify a series of high degree hub nodes that were efficiently interconnected to form a rich club, and linked these maps to a meta-analysis of voxel based morphometry data across a range of brain disorders including schizophrenia, demonstrating that brain disorders tended to involve deficits in hub node regions and that involved hubs demonstrated disorder specificity, incorporating frontal and temporal regions in schizophrenia.

While investigations of structural dysconnectivity have been increasingly implemented, few studies have applied graph analysis to both diffusion MRI and functional MRI modalities to study the pathophysiology of schizophrenia. However, one has raised the potential for reduced structural connectivity to contribute to increased functional connectivity (Skudlarski et al. Reference Skudlarski, Jagannathan, Anderson, Stevens, Calhoun, Skudlarska and Pearlson2010). Fornito and Bullmore (Reference Fornito and Bullmore2015) discuss the various mechanistic contributions to such de-coupling in connectivity findings in schizophrenia, in which functional hyperconnectivity may represent a neurodevelopmental or compensatory feature. Such decoupling of structural and functional connectivity highlights the need to examine network abnormalities at both anatomical and physiological levels and to incorporate multimodal imaging to develop a deeper understanding of dysconnectivity in psychotic illness.

In summary, cross-sectional studies indicate that graph theory metrics can be applied to MRI data to detect neuroanatomical dysconnectivity in psychotic illnesses, extending neuroanatomical research beyond identifying focal deficits in grey matter regions or white matter tracts, and providing further material evidence from in vivo neuroimaging to support the long held clinical construction of psychosis as a dysconnection syndrome. Abnormal connectivity may underpin the development of positive psychotic symptoms, with initial studies identifying short and long range frontal connectivity deficits in schizophrenia, and also widespread dysconnectivity in bipolar disorder that includes intrahemispheric integration. These novel analytical techniques are of considerable interest for application in epidemiological study designs into the aetiopathogenesis of psychotic illness. They can be potentially analysed on large, representative cohorts of patients with psychotic illness since they can be acquired from clinical MR scanners in a reasonable timeframe and processed using automated methodology. Preliminary studies suggest potential utility as biomarkers present at trait level in well patients (Leow et al. Reference Leow, Ajilore, Zhan, Arienzo, GadElkarim, Zhang, Moody, van Horn, Feusner, Kumar, Thompson and ALtshuler2013) and in genetically susceptible relatives (Collin et al. Reference Collin, Khan, de Reus, Cahn and van den Heuvel2014) of patients with psychotic illness. Investigations are underway to assess their utility as clinically relevant biomarkers in studies employing a longitudinal design tracking these network based metrics through development of and recovery from psychosis.