Brain hothubs and dark functional networks: correlation analysis between amplitude and connectivity for Broca’s aphasia

Source localization and functional brain network modeling are methods of identifying critical regions during cognitive tasks. The first activity estimates the relative differences of the signal amplitudes in regions of interest (ROI) and the second activity measures the statistical dependence among signal fluctuations. We hypothesized that the source amplitude–functional connectivity relationship decouples or reverses in persons having brain impairments. Five Broca’s aphasics with five matched cognitively healthy controls underwent overt picture-naming magnetoencephalography scans. The gamma-band (30–45 Hz) phase-locking values were calculated as connections among the ROIs. We calculated the partial correlation coefficients between the amplitudes and network measures and detected four node types, including hothubs with high amplitude and high connectivity, coldhubs with high connectivity but lower amplitude, non-hub hotspots, and non-hub coldspots. The results indicate that the high-amplitude regions are not necessarily highly connected hubs. Furthermore, the Broca aphasics utilized different hothub sets for the naming task. Both groups had dark functional networks composed of coldhubs. Thus, source amplitude–functional connectivity relationships could help reveal functional reorganizations in patients. The amplitude–connectivity combination provides a new perspective for pathological studies of the brain’s dark functional networks.

240 reported that the weighted definition of transitivity was the local clustering coefficient having 241 constant edge weights between the target and adjacent nodes. The k-coreness of a node was 242 derived from a thresholding method called the "k-core decomposition". This method reduces the 243 graph to a maximal subgraph in which each node has at least a degree, k. A valid k-coreness 244 means that a node belongs to the k-core but not to the (k+1)-core, and the k-coreness measures 245 whether a node involves the highly connected core of the brain graph. The Laplacian centrality 246 is a measure that concerns the possible destructive effects of deactivating or deleting a node from 247 a graph (Qi et al., 2013). The higher the Laplacian centrality of a node, the more indispensable it 248 is. Note that the k-coreness and Laplacian centrality algorithms do not consider the edge weights.
249 Finally, the eigenvector centrality of a node is assigned based on whether the node connects to 250 many other nodes and/or to highly connected nodes. Highly scored nodes are highly connected 251 with highly connected neighbors. That is, they are hubs of the graph (de Nooy et al., 2018).
252 Weighted definitions were applied to the eigenvector centralities obtained in this study.

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To measure the distribution of a node's connections across modules, we also calculated 254 three variables that depend on the network partitions. We used 16 functional modules, as detailed 255 in Supplementary Table S1. The participation coefficient of a node measures the distribution of 257 participation coefficient is zero. If the node is equally connected to all other modules, the 258 participation coefficient is one. The gateway coefficient of a node refers to both its inter-259 modular and within-modular connections (Vargas & Wahl, 2014). If a node links to the hub 260 within its module and occupies most of the outer connections from other modules to its module, 261 this node has a larger gateway coefficient. As described by Vargas and Wahl (2014), this 262 coefficient makes it feasible to identify nodes with unique inter-modular connections. The 263 within-module-degree z-score of a node is its normalized number of edges that connect to other 264 nodes in the same module of the target node.  Manuscript to be reviewed 291 correlations with the effect of subjects removed. Thus, the individuals were regarded as a third 292 variable that should be adjusted when comparing the amplitude with a graph measure. The 95% 293 confidence intervals and significances of the Pearson coefficients were estimated using the psych 294 1.8.12 package (Revelle, 2019) of the R software. To explore the entire continuum of m-island 295 graphs and select an optimal m value, we plotted all coefficients on a coordinate system for 296 which the x-axis denoted the maximum island size (see Supplementary Figures S1, S2). The left 297 pole included m-island graphs having small but strongly connected clusters (i.e., the "rich-club" 298 structures). The right pole contained m-island graphs having both large and highly connected 299 clusters (i.e., large island structures with a wide range of edge weights from weak to strong). If a 300 correlation were significant (p<0.05), it could be regarded as a coupling correlation.
301 Conversely, a non-significant correlation could be termed an uncoupling correlation. We also 302 did a permutation test on inter-group correlation coefficients with 1,000 randomizations by 303 shuffling the group assignments of individuals [i.e., the 10 individuals in a permutation were 304 randomly reassigned into two groups (5 ones per group) without replacement]. For each 305 permutation, an inter-group difference value of partial correlation coefficients were calculated.
306 The 1,000 values formed an estimation for the distribution of inter-group differences. The 307 statistics of correlation coefficients followed the estimation approach with 95% confidence 308 intervals (Calin-Jageman & Cumming, 2019). The brain networks were visualized using Pajek  Supplementary Table S2). Therefore, Figure 5 reports the 357 regions in which hothubs occurred. We also marked eight functional systems in this figure using 358 different colors. As detailed in Figure 5, the Broca group scores for InfOcciGyr_VenPst_R   Figure 3 also showed that the Broca 425 group had more coupling relationships than did the control group. For example, the t2 and t3 of 495 Broca group. However, during the entire naming process, the Broca group used specific hothubs 496 for which the activation levels did not differ from the control group. Third, both groups 497 commanded more than one functional system at each stage. This suggests that naming should be 498 a cross-modular task. Because our Broca participants were tested at least 5 months after their 499 onset (see Table 1

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Fourth, the stroked structure should be considered in the study. There were brain volumes 555 with encephalomalacia that could influence the results of source reconstruction. This is a 556 technical problem without a satisfactory solution in the head-modeling and brain parcellation.
557 The stroked-out areas remained part of the source space. Therefore, the results of stroke persons 558 were estimates based on virtual structures of the brain. Nevertheless, the control group should 559 not be influenced by this problem, and results from them should make sense for our hypothesis.
560 Besides, the amplitude-connectivity relationships between groups remained unchanged after 561 removing the stroked left hemisphere in both groups (see Supplementary Figures S6 and S7).     120-150 ms, object recognition; t3: 151-190 ms, memory access; t4: 191-320 ms, semantic processing; t5: 321-480 ms, phonological encoding; t6: 481-535 ms, articulation. A positive coefficient marked with an asterisk denotes that strongly activated brain regions are more likely to be highly connected hubs. A negative coefficient marked with an asterisk suggests that highly connected hubs are more likely to be with weak intensities of activation. The separation of the confidence intervals with opposite values of coefficients infers that the two groups have significantly different amplitude-connectivity relationships. One significant correlation with another nonsignificant correlation also implies that there are interconditional differences of amplitude-connectivity relationships. 1