Disrupted Topology of Frontostriatal Circuits Is Linked to the Severity of Insomnia

Insomnia is one of the most common health complaints, with a high prevalence of 30~50% in the general population. In particular, neuroimaging research has revealed that widespread dysfunctions in brain regions involved in hyperarousal are strongly correlated with insomnia. However, whether the topology of the intrinsic connectivity is aberrant in insomnia remains largely unknown. In this study, resting-state functional magnetic resonance imaging (rsfMRI) in conjunction with graph theoretical analysis, was used to construct functional connectivity matrices and to extract the attribute features of the small-world networks in insomnia. We examined the alterations in global and local small-world network properties of the distributed brain regions that are predominantly implicated in the frontostriatal network between 30 healthy subjects with insomnia symptoms (IS) and 62 healthy subjects without insomnia symptoms (NIS). Correlations between the small-world properties and clinical measurements were also generated to identify the differences between the two groups. Both the IS group and the NIS group exhibited a small-worldness topology. Meanwhile, the global topological properties didn't show significant difference between the two groups. By contrast, participants in the IS group showed decreased regional degree and efficiency in the left inferior frontal gyrus (IFG) compared with subjects in the NIS group. More specifically, significantly decreased nodal efficiency in the IFG was found to be negatively associated with insomnia scores, whereas the abnormal changes in nodal betweenness centrality of the right putamen were positively correlated with insomnia scores. Our findings suggested that the aberrant topology of the salience network and frontostriatal connectivity is linked to insomnia, which can serve as an important biomarker for insomnia.


Small-world network parameters
The functional connectivity network can be evaluated using graph theory analysis in which a network comprised the nodes and edges. For an N × N (N = 90 indicates 90 nodes in the present study) binary undirected graph G, the topological properties were defined on the basis of the following graph construction: If the absolute (the Fisher r-to-z of the partial correlation coefficient between node and node ) exceeds a given threshold T, an undirected edge is said to exist; otherwise it does not exist.
The clustering coefficient of a node is defined as the ratio of the number of existing connections among the node's neighbors to the number of all possible connections in the subgraph (Onnela et al., 2005) and is expressed as: in which and denote the number of edges and nodes respectively in the subgraph . Then the clustering coefficient of a functional connectivity network is the average of the clustering coefficients of all nodes: it measures the local interconnectivity of a network.
The mean shortest path length of a node is defined as: where | | is the absolute shortest path length (i.e. the smallest number of edges traversed between two nodes ) between node and node j. The mean shortest path length of a network is then the average of the shortest path lengths between the nodes: The normalized clustering coefficient = and normalized characteristic path length = were computed, where and indicate the mean clustering coefficient and shortest path length of the functional connectivity network, respectively. and represent the mean clustering coefficient and shortest path length of 100 matched random networks that preserved the same number of nodes, edges, and degree distribution as the real network (Sporns and Zwi, 2004;Ding et al., 2011). Typically, a small-word network meet the conditions of γ > 1 and λ ≈ 1, and therefore, the small-wordness scalar σ = λ ⁄ will be more than 1.

Efficiency of small-world networks
Network efficiency can be measured by global efficiency, , local efficiency, and nodal efficiency, , and described the ability of information transmission of a network at the global and local level, respectively. The global efficiency of a network is the inverse of the harmonic mean of the shortest path length between each pair of nodes (Latora and Marchiori, 2001;Achard and Bullmore, 2007): | | is the absolute shortest path length between node and node j in network G. It indicates the capability of parallel information transfer through the whole network.
The nodal efficiency of a node is calculated as: The local efficiency denoted the mean of all the local efficiencies of the nodes in subgraph which is defined as: where ( ) = ( ). Since the node is not an element of the subgraph , the local efficiency can also be considered as a measure of the fault tolerance of the network, suggesting how well each subgraph exchanges information when the node was eliminated (Achard and Bullmore, 2007).
The integrated area under curve (AUC) of a network metric Y was computed over the sparsity threshold range from 1 to with interval of ∆ , which was expressed as: . Tables   Table S1.

Region name
Introduction of topological properties in the brain functional network.

Global network properties
Clustering coefficient of a network which measures the local interconnectivity of a network. It is the average of the clustering coefficients over all nodes.
Path length of a network which quantified the level of overall routing efficiency of a network. It is the mean minimum number of connections between any two nodes in the network.
Global efficiency of a network which indicates the capability of parallel information transfer through the whole network. It is the inverse of the harmonic mean of the minimum path length between any two nodes in the network.
Local efficiency of a network which captures the fault tolerance of a network.
It is the average of the local efficiency over all nodes.

Local network properties
Nodal degree which evaluates the extent to which the node is connected to the rest of other nodes in a network.
Nodal local efficiency which measures the level of information propagation of a node with all other nodes in the network.
Betweenness which estimates the influence of a node over information flow with the rest of the nodes in a network.