Discussion

In this study, we start by summarising the main findings about the topology of the func- tional connectome of the human brain. Furthermore, to investigate the healthy brain, we also discuss how these topological features can be used as bio-markers to identify changes during Schizophrenia.

By applying a clustering coefficient and local efficiency we showed that the human brain is more segregated than an equivalent random graph, which suggests that brain re- gions are in tight intra-connection with each other. In addition to the segregation measure, we also used path length and its normalised version to investigate the level of integration within the human brain. The results of characteristic path length and global efficiency sug- gest that the functional connectome of the human brain exhibits a level of integration as

high as its corresponding random network. This leads us to conclude that the human brain enjoys a constant balance between segregation and integration. This balance is one of the fundamental evidences for considering the human brain connectome as a complex system. The level of complexity within the human brain is measured by small-worldness which was proven to be a useful tool to summarise the topological features of a network. The global features that we discussed in this study strongly align with previous findings in the network neuroscience literature (Bullmore and Bassett, 2011; Sporns, 2011b;Sporns and Honey,

2006).

Besides the clustering coefficient and local efficiency, one additional important mea- sure of segregation that we discuss in this study is modularity. By applying a modularity detection algorithm, we showed that the functional connectome of the human brain has a modular structure meaning that the human brain is formed by a combination of modules which are tightly intra-connected and sparsely inter-connected with each other. More im- portantly, results of the modularity algorithm on functional data suggest that without any prior knowledge of brain structure, the modules are spatially consistent. Our findings about the modular structure of the human brain and close association between its function and structure are widely similar to other studies in the field (Meunieret al.,2010,2014).

Further examination of the functional connectome in this study reveal that the key to emergence of complexity in the functional connectome is the collection of degree hubs which facilitates the integration among the modules. Throughout this study, we use de- gree centrality and betweenness centrality to detect these ’elite’ nodes. Nodes among the traditional the Default Mode Network such as the majority of regions from the bilateral Precuneus, Cingulate and bilateral Inferior Parietal Lobes. These findings widely overlap with other studies of hubs in the functional connectome (Crossleyet al.,2014;Spornset al.,

2007). In addition to identifying the degree hubs, we also examine the interactions between these influential nodes. We use the Rich Club to measure the level of intra-connection between degree hubs. By investigating the Rich Club organisation across the functional connectome we conclude that the Rich Club organisation plays a vital role in efficiency of the human brain. It is likely that this important role is due to the spatial configuration of the RC nodes. We showed that the RC nodes are geographically spread over the brain. These findings are consistent with other studies which suggest that the RC organisation plays role of a backbone to the human brain (van den Heuvelet al.,2012b;Graysonet al.,2014).

Although we showed how graph theoretical measures can be used to describe macro- scale human functional connectome, it is also essential to explore how these measures can be used as bio-markers for detecting changes during Schizophrenia. Prior to investigating the changes in topological features, we examined how the edge weights of un-thresholded networks change during the disease. Understanding the changes in edge weights can be

helpful to interpret the changes which are later identified in topological features. The re- sults suggest that connections in the Parietal, Insular and Frontal lobes experience a de- crease during schizophrenia. Decrease in the strength of connections in these regions were already reported in studies with different cohorts and pre-processing steps (Zaleskyet al.,

2010,2012b). A decrease in connectivity strength may result in the connection to be able to survive the density thresholding and therefore cause a reduction in the degree of relevant regions.

We continue examining the changes during schizophrenia by comparing the integra- tion levels. Results of integration measures suggest that there are no differences between healthy and schizophrenic brain networks. Further to the integration level, we also in- vestigated the changes in segregation level between healthy and schizophrenic functional connectome. Examining the Clustering coefficient and Local Efficiency suggests a decrease in the level of segregation during schizophrenia. The decrease in the level of segregation aligns with other studies in the field (Liuet al.,2008;Alexander-Blochet al.,2010). How- ever, it is notable that the normalised clustering coefficient,Ω, suggests the opposite. This contradiction may suggest that schizophrenic brain networks are more distant from their random networks which make the schizophrenic brains close to a lattice network. Eventu- ally, we summarise the normalised integration and segregations measures by the measure of small-wordlness. Our findings suggest that the small-worldness is higher in the functional connectome of schizophrenic brains.

Comparing the modular structures between group-averaged healthy and schizophrenic brain networks also suggests a larger number of clusters in schizophrenia, however, the in- dividual modularity indexes suggest no differences between the two groups. The majority of nodes which were found to be members of the Occipital and Frontal lobes, module 3 and module 4, are represented in module B and module D, respectively. It is notable that mod- ule B in schizophrenia also accommodates other nodes of Temporal lobes. The majority of nodes in the remaining modules of healthy subjects, module 1 and module 2, share their nodes with every other module in schizophrenia.

Besides investigating the changes in global architectural features of the functional connectome during schizophrenia, we also used disruption plots to examine how the central- ity measures as well as measure of local segregation changes during schizophrenia. Results of the degree centrality suggest that degree hubs lose their prominent role. These regions are mainly parts of the conjunction of the Default Mode Network and Parietal lobe includ- ing the Precuneus and parts of the Cingulate cortex. These results may routes back to the reduction in edge weights that explained earlier. In contrast, regions of the Cerebellum which were considered as peripheral nodes in healthy subjects gained more degrees during schizophrenia. Our findings of abnormalities in the role of the degree hubs is consistent

with other studies across modalities (Rubinov and Bullmore,2013;Collinet al.,2013;Ly- nallet al.,2010). This pattern of changes can also be seen in local segregation measures where the Cuneus and Postcentral lose their local efficiency and the Cereberal Tonsil ex- periences an increase in its Local Efficiency. Finally, the last local measure of centrality, betweenness, suggests that nodes from the Default Mode and Saliency functional networks, such as Insular and Precuneus and Thalamus, are subject to a decrease in their Betweenness centrality, while, The Anterior Cingulate, bilateral Superior Frontal regions experience an increase.

Eventually, we propose a method to conduct multi-subject group inference between the Rich Club organisation and the coefficients of two groups. In terms of the Rich Club coefficients, the nodes that mostly experienced changes during schizophrenia are among nodes of the Parietal lobe, Frontal lobe and Cerebellum. The Rich Club coefficients in the first two lobes, Parietal and Frontal, experienced a significant decrease and the latter cortex, the Cerebellum, experienced a significant increase in its Rich Club coefficients. Similarly, the examining the Rich Club organisation also reveals that the nodes which mainly overlap with the Default Model Network, including the nodes of the Frontal and Parietal lobes, are no longer members of the Rich Club organisation in schizophrenia, instead, member of the Cerebellum cortex joins the Rich Club organisation in schizophrenic brain networks.

As it is essential to investigate the role of the Rich Club nodes in integration and centrality of brain networks, we also found that the Rich Club nodes have higher density in comparison to local and feeder regions of the networks. Betweenness centrality of the Rich Club nodes is also significantly larger across both groups. Notably, local efficiency of the Rich Club nodes in healthy subjects is significantly higher than the corresponding nodes in schizophrenia. These results suggest that the Rich Club organisations in schizophrenia play a relatively lower role in efficiency of the human brain during schizophrenia. It is no- table that similar results regarding alteration of RC organisation, but in regards to structural connectivity, were reported by (van den Heuvelet al.,2013a;Collinet al.,2014a).

3.4.1 Summary

In this chapter, we discussed empirical graph theoretical measures which can be used to describe the macroscale connectome of the human brain in healthy and diseased conditions. • We used total of 25 subjects, 13 healthy subjects and 12 schizophrenic subjects. A range of graph theoretical metrics were applied on the both subject and group-average levels.

• The Parietal lobe were identified as the lobe which experienced the highest level of disruption, in terms of connection strength, during schizophrenia.

• In terms of the global topological features, schizophrenic brains demonstrate a higher level of segregation which results in a higher level of small-worldness (1.43 and 1.6 in healthy and schizophrenic subjects, respectively).

• Results for another measure of segregation, modularity, suggests that the level of modularity remains the same between the two group, however the module arrange- ments changes due to the disorder (For instance, healthy subjects demonstrate four modules, whereas, the schizophrenic group demonstrates six modules.).

• Results for the local measures, in particular degree centrality, suggest that during schizophrenia the degree hubs lose their prominent roles and, instead, local nodes experience a rise in number of their connections (For instance, on subject level, the disruption index is -0.27).

• Two statistical frameworks were proposed to investigate the changes in organisation and coefficient, NRCI and NRCC respectively, during the disorder.

• Using the proposed frameworks, the results show that the regions, mainly related to the Parietal lobe and the DMN, experience a decrease in their RC coefficients, whereas, some regions of the Cerebellum gain some strength in their RC coefficients.