Disrupted topological organization of structural brain networks in childhood absence epilepsy

Childhood absence epilepsy (CAE) is the most common paediatric epilepsy syndrome and is characterized by frequent and transient impairment of consciousness. In this study, we explored structural brain network alterations in CAE and their association with clinical characteristics. A whole-brain structural network was constructed for each participant based on diffusion-weighted MRI and probabilistic tractography. The topological metrics were then evaluated. For the first time, we uncovered modular topology in CAE patients that was similar to healthy controls. However, the strength, efficiency and small-world properties of the structural network in CAE were seriously damaged. At the whole brain level, decreased strength, global efficiency, local efficiency, clustering coefficient, normalized clustering coefficient and small-worldness values of the network were detected in CAE, while the values of characteristic path length and normalized characteristic path length were abnormally increased. At the regional level, especially the prominent regions of the bilateral precuneus showed reduced nodal efficiency, and the reduction of efficiency was significantly correlated with disease duration. The current results demonstrate significant alterations of structural networks in CAE patients, and the impairments tend to grow worse over time. Our findings may provide a new way to understand the pathophysiological mechanism of CAE.

Where N is the number of nodes in graph (network) G and Si is the sum of the edge weights wij connecting to node i. Efficiency Efficiency of network, including global and local efficiency, is a measure of how efficiently it exchanges information in the network 2 . The global efficiency (Eglob) represents the capability of information flow over the entire network. In this work, we defined the global efficiency using Dijkstra's algorithm 3,4 .
(G) = 1 ( − 1) ∑ 1 ≠ ∈ Where Lij is the shortest path length between node i and node j in G.
The local efficiency (Eloc) indicates how well the information is communicated within the neighbors of a given node. Dijkstra's algorithm was also employed to calculate the local efficiency 3,4 .
(G) = 1 ∑ ( ) ∈ Where Eglob(Gi) is the global efficiency of Gi, the subgraph of the neighbors of node i.

Small-worldness
Small-world measures, including clustering coefficient (CP), characteristic path length (LP), normalized clustering coefficient (γ), normalized characteristic path length (λ), and small-worldness (σ), are most frequently used properties in brain network study 5 . Highly interconnected neighbors around a given node form a cluster, while sparsely interconnected neighbors do not. Clustering coefficient of node i (Ci) reflects the number of connections among the neighbors of node i.

= 2 ( − 1)
Where ki is the degree of node i and ti is the number of triangles around node i. Moreover, the clustering coefficient of a network (CP) is quantified as the average of the clustering coefficient over all nodes, which characterizes network segregation.
(G) = 1 ∑ ∈ Characteristic path length (LP) is defined as the average of shortest path length between all nodal pairs, which characterizes the integration or information transfer capacity across remote cortical regions.
Where Lij is the shortest path length from node i to node j. Moreover, the normalized clustering coefficient (γ) and the normalized characteristic path length (λ) were obtained from comparing CP and LP of brain network with that of 100 random networks with the same number of nodes and degree distribution.

γ = , =
Where and are the mean of CP and LP of 100 matched random networks. The brain network would be considered as small-world if γ ≫ 1 and λ ≈ 1 . Furthermore, these two properties can be summarized into a simple quantitative metric, small-worldness ( ): = which is higher than 1 for the small-world network 6 . Hubs Important brain regions, known as hubs, often communicates more efficiently with the rest of the brain 7,8 . To determine the hubs distribution, we computed the nodal efficiency, Enodal(i), and define node i as a network hub if Enodal(i) follows the criterion: Nodal efficiency measures the average shortest path length between a given node and all of the other nodes in the network.
Where Lij is defined as the length of shortest path between node i and node j.

Modularity
Modular structure is consist of densely interconnected nodes that have only sparse interconnections with others. The modularity index Q is used to estimate the degree how the network may be divided into such subgroups 10 .
Where l is the sum of all weights in the network, wij is the edge weight between node i and node j and ki is the degree of node i. Note that mi is the module containing node i, and δmi,mj =1 if mi =mj and 0 otherwise.

Supplementary Figure S1
Nodal efficiency (Enodal) of 90 regions in CAE and healthy controls (CON). The Enodal of each region is calculated from the average network of each group. Areas are ranked in descending order. The solid line marks the mean Enodal and dashed line marks the mean plus one standard deviation. Hub regions are highlighted in red based on the criterion of ( ) > + for both group, while others are labeled in gray. For abbreviations of the regions, please see Supplementary Table S1.

Supplementary Figure S2
Scatter plots between seizure frequency and integrated Enodal of the left and right precuneus, respectively.

Supplementary Table S1
Regions of interest (45 in each cerebral hemisphere) defined in this study using AAL atlas.

Index
Regions Abbreviation For the statistics based on thresholded graphs, comparisons were conducted over the range from 0.01 to 0.03 for each subject. All of the structural brain networks of CAE patients and healthy controls were significantly more modular than null models. CAE = childhood absence epilepsy, CON = healthy controls.

Supplementary Table S3. The distribution of network parameters
The p-values of the null hypothesis('the data are normally distributed') in patients.