Graph Theory Analyses

Nodes of the functional network were defined as one of 360 non-overlapping parcels from the HCP's MMP. We constructed functional connectivity matrices for each subject by taking the average timeseries of each of the 360 cortical regions from the pre-processed fMRI data. We then computed the Pearson's correlation coefficient for each pair of cortical regions before applying a Fisher-z transformation (Figure 1A). We then thresholded all graphs at the same network densities and binarized them to avoid biased graph metric comparisons between patient populations (54–56). Binarization is a very effective method of preserving the most probable functional connections (57, 58). Since there is no universally accepted threshold for functional connectivity strength, we decided to threshold connections within the top 15% by network density for each individual, in steps of 2.5% up to 30% density, to create binary undirected graphs for each density. The graph theory metrics were then averaged across these thresholds for each node (35, 36, 59).

Diagrammatic representation of the data processing pipeline. (A) First, resting-state functional connectivity (rsFC) matrices are computed for each subject. (B) Graph theory features are then extracted from the connectivity matrices. (C) Features were selected using an (i) Elastic Net feature selection method, and (ii) proposed Elastic Net-subset (Elastic Net + optimal subset selection) approach to identify predictive features while reducing feature redundancy. (D) Two SVM models were constructed for each of the feature selection approaches. (E) Each model's performance (accuracy, AUC, sensitivity, specificity, and the total number of features used in the final model) were computed and then compared between both models. A significance test was performed using a permutation test approach. The whole process was repeated for each feature set and their combinations (for example, BC+CC+DC). BC, Betweenness Centrality; CC, Clustering Coefficient; DC, Degree Centrality; LE, Local Efficiency.

We used the Brain Connectivity Toolbox (60) to calculate the following local graph measures for each patient: clustering coefficient, local efficiency, degree centrality, and betweenness centrality (Figure 1B). The clustering coefficient (the fraction of connected triangles in a network) measures the degree to which a node's neighbors are connected to each other (60). The degree centrality (the number of edges for a specific node) assumes that the importance of a node is related to the number of nodes that it is directly connected to Barabási and Albert (61). The betweenness centrality (a centrality measure based on shortest paths) is a measure of how influential a node is as information passes through it to other nodes (62). The local efficiency measures the efficiency of information transfer within the local neighborhood of a node (63). These metrics investigate network properties within the local neighborhood of a node and have been the subject of many studies across various chronic pain conditions (25, 34, 59).