Article Figures & Data
Figures
- Figure 1.
Criteria for excluding recordings from analysis. Number of segments selected in a recording versus number of non-zero elements in the average adjacency matrix estimated from all the segments in the recording. Each dot represents a single recording. Recordings represented by the encircled dots were excluded from the analysis. A, Matrices estimated using CABS; B, matrices estimated using CMAX; C, matrices estimated using CMIN. Each method produced average adjacency matrices with similar number of non-zero elements.
- Figure 2.
Analysis of background functional connectivity reveals changes over the time course of epileptogenesis. A, E, I, Individual connectivity matrices represented as dots in the first two principal dimensions of the multidimensional scaling of Frobenius distances between the individual connectivity matrices. Each dot represents a single matrix (green, Day 0; yellow, Day 7; red, Day 28; gray, Sham control; empty symbols: circle, diamond, and square represent the median of the connectivity matrices). The first three principal multidimensional scaling dimensions represent ∼70% of the relations encoded in the raw Frobenius distances (R2ABS=0.66, R2MAX=0.72, R2MIN=0.7; R is Pearson’s correlation coefficient between the Frobenius distances in the matrix space and the Euclidian distances in the reconstructed space); for clarity only the first two coordinates are plotted. B–D, F–H, J–L, Median functional connectivity matrices (indicated with empty symbols in A, E, I) resulting from the three different measures at different days with color-coded connection weights (Day 0 over 11 matrices, Day 7 over 6 matrices, Day 28 over 8 matrices; different numbers of matrices for individual days because of quality of recordings; see Materials and Methods).
- Figure 3.
Illustration of changes of network properties over the time course of epileptogenesis. A–C, E–G, I–K, Median degree imbalance at individual nodes; blue indicates indegree>outdegree, red indicates indegree<outdegree. Value of the degree imbalance is color and size coded; larger and darker dots indicate higher degree imbalance. Dots filled in black have a median that is significantly different from the median on Day 0 (FDR < 0.1, two-sided Wilcoxon Mann–Whitney test with Benjamini–Hochberg correction for 30 nodes, effect size AUROC < 0.2 for blue nodes or >0.8 for red nodes; exact p values and effect sizes are presented in Extended data Figure 3-1). Gray arrows show topology of functional connectivity networks on different days illustrated using the strongest 5% of connections of the median connectivity matrices shown in Figure 2. D, H, L, Boxplots showing the degree of assymetry of the individual connectivity matrices.
- Figure 4.
Illustration of changes in spatial distribution of node ictogenicity. A–I, Mean values of NI. Gray arrows are the strongest 5% of connections of the median networks. Value of the NI is color and size coded; larger and darker dots indicate higher NI. Dots filled in black have significantly higher median NI than the median on Day 0 (FDR < 0.1 one-sided Wilcoxon Mann–Whitney test with Benjamini–Hochberg FDR correction for 30 nodes, effect size AUROC > 0.8; exact p values and effect sizes are presented in Extended data Figure 4-1). Shaded regions in H and I show nodes affected by the TTX silencing; identified from Sheybani et al. (2018), their Figure 12B.
Tables
Results Data structure Statistical test Power or confidence intervals Fig. 3A–C, E–G, I–K No assumptions about the distributions of the degree imbalance on each of the 3 days. Two-sided Wilcoxon Mann–Whitney test with Benjamini–Hochberg multiple comparison/FDR correction for 30 nodes.Separate comparison for: Day 0 vs Day 7 and Day 0 and Day 28.We use two-sided test because we expect to see increase and decrease of degree imbalance. Panel B:FDR ≤ 0.08,AUROC<0.2 or AUROC>0.8;Panel C:FDR ≤ 0.08,AUROC<0.2 or AUROC>0.8;Panel D:FDR ≤ 0.1,AUROC<0.2 or AUROC>0.8;Panel E:FDR ≤ 0.07,AUROC<0.2 or AUROC>0.8;Panel G:FDR ≤ 0.07,AUROC<0.2 or AUROC>0.9;Panel H:FDR ≤ 0.07,AUROC<0.2. or AUROC>0.9;See Extended data Figure 3-1 for values. Fig. 3D, H, L; Table 2 No assumptions about the distributions of the network measures. The Kruskal–Wallis test (nonparametric ANOVA) with Benjamini–Hochberg multiple comparison/FDR correction for 20 analyzed measures. FDR and AUROC values are reported in Table 2. Fig. 4 No assumptions about the distributions of the node ictogenicity on each of the 3 days. One-sided Wilcoxon Mann–Whitney test with Benjamini–Hochberg multiple comparison/FDR correction for 30 nodes.Separate comparison for: Day 0 vs Day 7 and Day 0 and Day 28.We use one-sided test because only test increase of node icotgenicity. Panel B: FDR ≤ 0.1, AUROC>0.8;Panel C: FDR ≤ 0.09, AUROC>0.8;Panel E: FDR ≤ 0.08, AUROC>0.8;Panel G: FDR ≤ 0.02, AUROC=1;Panel H: FDR ≤ 0.01, AUROC<0.9.See Extended data Figure 4-1 for values. Columns are part of the results section, the structure of the data, statistical test, and description of the significance levels.
- Table 2.
Statistical analysis of network properties for the three kinds of connectivity matrices
Name of the network property C ABS C MAX C MIN Mean weighted outdegree 0.69 0.83 0.5 Variance of weighted outdegree 0.055 (0.23; 0.13) 0.035 (0.17; 0.13) 0.12 Spectral norm 0.0099 (0; 0.091) 0.0083 (0.061; 0.046) 0.026 (0.11; 0.13) Frobenius norm 0.42 0.47 0.27 Mean neighbor weighted outdegree 0.21 0.24 0.4 Variance of neighbor weighted outdegree 0.0099 (0.03; 0.079) 0.0131 (0.076; 0.1) 0.0233 (0.71; 0.89) Mean betweenness 0.20 0.75 0.66 Variance of betweenness 0.098 (0.12; 0.48) 0.44 0.3 Mean page-rank 0.4 0.96 0.58 Variance of page-rank 0.17 0.47 0.27 Mean length of the shortest path between two nodes 0.29 0.47 0.4 Variance of length of the shortest paths 0.17 0.8 0.4 Mean harmonic closeness centrality 0.29 0.47 0.4 Variance of harmonic closeness centrality 0.068 (0.91; 0.62) 0.2 0.5 Assortative mixing (Pearson’s total weighted degree correlation) 0.17 0.66 0.058 S-metric, sum of the product of nodal degrees across edges 0.81 0.5 0.78 Degree of asymmetry, largest eigenvalue of the skew-symmetric part of the Laplacian of a directed graph (Li and Zhang, 2012). 0.026 (0.14; 0.1) 0.011 (0.21; 0) 0.026 (0.26; 0.045) Mean spectrum, mean of eigenvalues of symmetric part of the Laplacian matrix of the directed graph (Li and Zhang, 2012). 0.74 0.8 0.14 Variance of spectrum, variance of eigenvalues of symmetric part of the Laplacian matrix of the directed graph (Li and Zhang, 2012). 0.4 0.25 0.88 Maximum of spectrum, largest eigenvalue of symmetric part of the Laplacian matrix of the directed graph (Li and Zhang, 2012). 0.17 0.25 0.76 Table contains values of the Benjamini–Hochberg FDR for the Kruskal–Wallis test for comparison of medians of measures on Days 0, 7, and 28. In brackets post hoc effect sizes quantified with AUROC: (Day 0 vs Day 7; Day 0 vs Day 28). Bold values show FDR < 0.1 and AUROC < 0.2 or AUROC > 0.8.
Figure 3-1
Detailed illustration of changes in spatial distribution of degree imbalance (DI). A–C, Boxplots of distributions of DI values on each node on Day 0 (green), Day 7 (yellow) and Day 28 (Red). Shaded yellow bar indicates significant difference between Day 0 and Day 7. Shaded red bar indicates significant difference between Day 0 and Day 28. Text labels are as follows: first row FDR, second row (AUROC) for comparison of Day 0 and Day 28; third row FDR and fourth row (AUROC) for comparison of Day 0 and Day 7. Two-sided Wilcoxon Mann–Whitney test with Benjamini–Hochberg FDR correction for 30 nodes; effect size measured as AUROC. Download Figure 3-1, EPS file.
Figure 4-1
Detailed illustration of changes in spatial distribution of NI. A–C, Boxplots of distributions of NI values on each node on Day 0 (green), Day 7 (yellow), and Day 28 (red). Shaded yellow bar indicates significant difference between Day 0 and Day 7. Shaded red bar indicates significant difference between Day 0 and Day 28. Text labels are as follows: first row FDR, second row (AUROC) for comparison of Day 0 and Day 28; third row FDR and fourth row (AUROC) for comparison of Day 0 and Day 7. One-sided Wilcoxon Mann–Whitney test with Benjamini–Hochberg FDR correction for 30 nodes; effect size measured as AUROC. Download Figure 4-1, EPS file.
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