Recurring Functional Interactions Predict Network Architecture of Interictal and Ictal States in Neocortical Epilepsy

Clustering subgraphs based on topological similarity. A, For the set of original subgraphs learned from an epoch of data (left), we generated an equally sized set of surrogate subgraphs (right) by computing a weighted linear combination of the subgraphs with weights drawn from a uniform random distribution on the interval [0, 1]. The surrogate subgraphs have rewired network topology but maintain their functionality as a mathematical basis of the original network. B, For each patient, we constructed a subgraph ensemble matrix, representing the functional connections for each subgraph from all interictal and ictal epochs. The ensemble matrix aggregates functional subgraphs expressed over ∼100 h of intracranial recording. We also constructed a patient-specific surrogate ensemble matrix by aggregating surrogate subgraphs across all epochs. C, We quantified the topological similarity between all subgraphs in the ensemble matrix by applying a consensus NMF algorithm that tracks the number of times every pair of subgraphs is assigned to the same cluster over 100 runs of NMF. This procedure resulted in a coclustering probability matrix representing the frequency with which subgraphs from ictal and interictal epochs are clustered together, a measure of similarity between the connectivity profiles of subgraph pairs. In the example, the coclustering probability matrix of real subgraphs demonstrates less ambiguous similarity (matrix entries are near 0 or 1) and greater clustering than surrogate subgraphs (matrix entries closer to 0.5).

Ictal subgraphs are recapitulated during interictal epochs. A, Example two-dimensional projection of a patient’s subgraph coclustering probability matrix. Each marker represents a subgraph from a single epoch and the distance between a subgraph pair indicates their topological similarity (i.e., closer subgraphs are more similar); circles represent interictal subgraphs and bolded stars represent ictal subgraphs; colors represent cluster assignment based on consensus clustering of the subgraph ensemble. The projections of real subgraphs (left) of the same cluster (color) tend to be closer to one another than to subgraphs of other clusters. In contrast, the projections of surrogate subgraphs from the same cluster tend to be as close to one another as surrogate subgraphs from other clusters. B, Normalized, projected distance of a subgraph to its assigned cluster’s centroid, the mean geographical location of subgraphs in a cluster, relative to its neighboring cluster’s centroid (most proximal, nonassigned cluster centroid), averaged over all subgraphs of each patient (N = 22). Real subgraphs were significantly closer to their cluster centroid compared with surrogate subgraphs (paired $t$-test; t₂₁ = 12.09, p < 7 × 10⁻¹¹), suggesting the same set of brain regions functionally interact repeatedly over several hours. C, Normalized, projected distance of ictal and interictal subgraphs to their cluster centroid, averaged over all ictal or interictal subgraphs of each patient with complex partial (CP) seizures (N = 8) and with secondarily generalized complex partial (CP + GTC) seizures (N = 10). Both groups of patients expressed ictal subgraphs that were significantly further away from their cluster centroid than interictal subgraphs (paired $t$-test; CP: t₇ = −3.29, p = 0.013; CP + GTC: t₉ = −4.26, p = 0.002), suggesting ictal subgraphs may represent functional connections that lie at the transition between interictal subgraphs. (*p < 0.05, **p < 0.01, ***p < 0.001; Bonferroni corrected for multiple comparisons).

Interictal subgraphs are selectively sensitive to the SOZ. A, Distribution of average SOZ sensitivity of subgraphs in each cluster, ranked in decreasing order, from each patient (N = 22). SOZ sensitivity of true SOZ labels in blue and of permuted SOZ labels in gray. We observed a significant effect of SOZ sensitivity for real SOZ labels compared with permuted SOZ labels for clusters 1, 2, 3, and 6 (*p < 0.05, **p < 0.01, ***p < 0.001; Bonferroni corrected for multiple comparisons). These results demonstrate that functional interactions between brain regions are heterogeneously sensitive to dysfunction in the SOZ, depending on cluster-specific subgraph stereotypes. B, Importantly, we observed that subgraphs of cluster 1 were significantly sensitive to connections within the SOZ, while subgraphs of cluster 6 were significantly sensitive to connections outside the SOZ. An example of subgraphs from cluster 1 (left) and cluster 6 (right) are shown here. Connections between SOZ nodes are shown in the top-left box, and connections between non-SOZ nodes are shown in the bottom-right box.

Expression energy and transience differentiate ictal and interictal epochs. A, We computed (i) subgraph expression energy--the overall activity of a subgraph--and (ii) subgraph expression skew--the temporal transience or persistence of a subgraph’s activity. Shown here are four examples of subgraph expression from a single patient, chosen by identifying subgraphs whose expression energy and expression skew were in the bottom and top third of all epochs. These examples demonstrate high energy and transience (red), high energy and persistence (blue), low energy and persistence (yellow), and low energy and transience (green). B, Distribution of subgraph expression energy, averaged across interictal epochs of each cluster (ranked by SOZ sensitivity) for each patient (N = 22). For each cluster, we compared the distribution of expression energy for subgraphs of that cluster to expression energy for subgraphs of all other clusters and found significantly lower expression energy of subgraphs within cluster 1, most sensitive to nodes in the SOZ, than outside cluster 1 (paired $t$-test; t₂₁ = −3.21, p = 0.004; Bonferroni corrected for multiple comparisons). C, Distribution of subgraph expression skew, averaged across interictal epochs of clusters 1 and 6 for each patient (N = 22). We observed subgraphs of cluster 1, which were most sensitive to nodes in the SOZ, exhibited significantly greater skew, and therefore greater temporal transience, than subgraphs of cluster 6, which were most sensitive to nodes outside the SOZ (paired t test; t₂₁ = 2.12, p = 0.04). These findings suggest that subgraphs with strongly connected SOZ nodes exhibit more transient, burst-like, dynamics than subgraphs with strongly connected non-SOZ nodes. D, PSD distribution of ictal and interictal subgraph expression, averaged over patients (N = 22). We observed a significant difference between ictal and interictal subgraph expression, ictal subgraphs modulate their expression at lower frequencies and interictal subgraphs modulate their expression at higher frequencies (FDA; ). These findings suggest that subgraph expression is more gradual and coordinated during ictal epochs than interictal epochs.