A peer-reviewed, evidence-based journal for clinicians in the field of neuroscience

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63 ICNS INNOVATIONS IN CLINICAL NEUROSCIENCE November-December 2017 • Volume 14 • Number 11–12 O R I G I N A L R E S E A R C H and represent nodes that are connected to many other nodes in the networks. 19 Degree centrality of a node for the weighted network is calculated as follows: where N represents the set of nodes of the network and w i j represents link weight between node i and node j in the network. The closeness centrality represents how much a particular node in the network is accessible to the other nodes in the network. Nodes with high degrees of closeness centrality can quickly access other nodes in the network. For example, in symptom interaction networks, any changes to the symptoms with high closeness centrality can quickly spread out to other reachable nodes in the network. Formally, the closeness centrality for weighted graphs is defined as: 20 where N represents the number of nodes in the network and d i j represents the weighted distance between nodes i and j. We used a Kolmogorov-Smirnov test to examine whether the microscopic measures (closeness centrality and degree centrality) have a significant difference between treatment-resistant and treatment-responsive groups before and after treatment. In this study, macroscopic and mesoscopic variables cannot be analyzed for group differences because these variables provide a single value to describe the overall network structure/ properties and therefore cannot be used to infer statistics for the group difference of treatment resistant and treatment responsive patients. Nevertheless, these variables are essential to understand the overall network structure/ properties of the treatment resistant and responsive patients. All analyses were conducted in Python programming language using the NetworkX package. 23,24 RESULTS Macroscopic analysis. We first analyzed the partial correlation-based network of treatment-resistant and treatment-responsive patients at the macroscopic level before and after treatment. Table 2 shows the macroscopic properties of constructed networks. The results indicate that the networks of the treatment resistant group were denser (i.e., the treatment-resistant group networks displayed higher density and average clustering coefficients as well as lower average shortest path length and modularity) as compared with the treatment-responsive group before and after treatment. However, the within- group comparison of macroscopic properties indicates that density, average shortest path length, and average clustering coefficient of the symptom network were almost the same for the treatment-resistant group before and after treatment. On the other hand, in the treatment-responsive group, the density and average clustering coefficient were increased after treatment, while the average shortest path length and modularity were decreased. Thus, macroscopic level analyses suggest that the networks of treatment-responsive patients become more connected after antipsychotic treatment, whereas antipsychotics have no effect on global connectivity in treatment- resistant patients. Mesoscopic analysis. We analyzed the symptom networks at the mesoscopic level using the Louvain method, which is a greedy optimization method (a step-by-step approach where, at each step, the optimum decision is made based on the information available at that step) to find the optimal community FIGURE 1. Community detection (mesoscopic analysis) results. Clockwise from top-left: treatment-resistant baseline, treatment-resistant 18-month follow-up, 18-month follow-up treatment-responsive, and baseline treatment responsive. The nodes in the network represent the PANSS symptoms; the node colors represent detected communities by the Louvain method; and the edge width represents the strength of absolute value of partial correlation. The number of communities detected in the treatment-resistant group at baseline and at the end of phase 1 were 13 and 11 respectively, whereas the number of communities detected in treatment-responsive groups were 13 and 12 at baseline and the end of phase 1, respectively. Community detection is a problem of finding maximal modularity. Higher modularity of a network is an indication of dense connections within modules and sparse connections between nodes from different modules. Finding the communities in a network can be formulated as an optimization problem. In this study, we used a greedy optimization method known as the Louvain method to find the optimal community structures. 18 pos _ p1 = Delusions; pos _ p2 = Conceptual Organization; pos _ p3 = Hallucinatory Behavior; pos _ p4 = Excitement; pos _ p5 = Grandiosity; pos _ p6 = Suspiciousness/Persecution; pos _ p7 = Hostility; neg _ n1 = Blunted Affect; neg _ n2 = Emotional Withdrawal; neg _ n3 = Poor Rapport; neg _ n4 = Passive/Apathetic Social Withdrawal; neg _ n5 = Difficulty in Abstract Thinking; neg _ n6 = Lack of Spontaneity and Flow of Conversation; neg _ n7 = Stereotyped Thinking; gps _ g1 = Somatic Concern; gps _ g2 = Anxiety; gps _ g3 = Guilt Feelings; gps _ g4 = Tension; gps _ g5 = Mannerisms and Posturing; gps _ g6 = Depression; gps _ g7 = Motor Retardation; gps _ g8 = Uncooperativeness; gps _ g9 = Unusual Thought Content; gps _ g10 = Disorientation; gps _ g11 = Poor Attention; gps _ g12 = Lack of Judgement and Insight; gps _ g13 = Disturbance of Volition; gps _ g14 = Poor Impulse Control; gps _ g15 = Preoccupation; gps _ g16 = Active Social Avoidance.

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