Fig 1.
Diversity of phase-locking behavior.
A) Time-series of mode eigenvectors from two subjects from the HCPEP dataset. Top panel shows phase-locking behavior. Middle panel shows instantaneous magnetization which is the ratio of in-phase to antiphase regions. Bottom panel shows the mode assigned to the timepoint from k-means clustering. Interesting behavior is indicated with numbered circles. B) Blow-outs for points 1 to 5. C) Legend for the numbered circles. MAG, magnetization; M, mode. Gray dotted line shows where phase-locking is equal to zero.
Fig 2.
Spatial patterns of recurrent phase-locked connectivity in RUN3 for controls.
A) Phase-locking patterns for the 5 modes in sagittal view. B) Phase-locking patterns for the 5 modes in axial view. C) Respective FC presented as connectograms color-coded as in Yeo [63] with the addition of dark blue for subcortical regions, and black for cerebellar regions. In Mode ψ1 all regions are aligned in-phase and so there is no antiphase connectivity. FC computed as the outer product of the leading eigenvector for each mode. D) Color coded legend for the Yeo resting-state networks, subcortical and cerebellar regions. VIS, Visual; SMT, Somatomotor; DAT, Dorsal attention; VAT, Ventral attention; LBC, Limbic; FPA, Frontal parietal; DMN, Default mode network; SC, Subcortical; CB, Cerebellar.
Table 1.
Effects of group, run, and interactions between group and run, on contributions to mode ψ4 connectivity in the bilateral caudate, putamen, pallidum, and thalamus.
Fig 3.
Group differences in regional contribution to the leading eigenvector for Mode ψ4.
Regional contribution was calculated as the mean value of instantaneous phase-locking over time for a particular anatomical region of interest. Raincloud plots show from left to right scatter plot for the raw data, boxplots showing the median, upper and lower quartiles, upper and lower extremes, and the distributions of the raw data. iPL, instantaneous phase-locking, * = 0.05, ** = 0.01, *** = 0.001, ****<0.001. Red * effect size between groups greater than effect size between runs. Blue * effect size between groups less than largest effect size between runs.
Table 2.
Effects of group, run, and interactions between group and run, on global VAR.
Table 3.
Effects of group, run, and interactions between group and run, on local VAR in modes ψ1, ψ2, ψ3, ψ4, ψ5.
Fig 4.
Most significant group differences in local VAR in the modes for HCPEP and Cobre datasets.
Raincloud plots show from left to right the raw data, boxplots showing the median, upper and lower quartiles, upper and lower extremes, and the distributions of the raw data. A) HCPEP RUN1. B) HCPEP RUN2. C) Cobre dataset. * = 0.05, ** = 0.01, *** = 0.001, ****<0.001. Red * effect size between groups greater than effect size between runs. Blue * effect size between groups less than largest effect size between runs.
Fig 5.
Connectograms and word clouds for Mode ψ4 in RUN2.
A) Group-level FC in Mode ψ4 for HCPEP controls. B) Group-level FC in Mode ψ4 for HCPEP Non-affective psychosis. C) The word cloud presents the top terms derived from Neurosynth using reverse inference for the regions in Mode ψ4 for HCPEP controls. Word size represents the strength of the probabilistic association of the term to the regions. D) Top terms for Mode ψ4 in HCPEP Non-affective psychosis. E) Group-wide FC in Mode ψ4 for Cobre controls. F) Group-wide FC in Mode ψ4 for Cobre Schizophrenia. G) Top terms for Mode ψ4 in Cobre controls. H) Top terms for Mode ψ4 in Cobre Schizophrenia. I) Color coded legend for the Yeo resting-state networks, subcortical and cerebellar regions. VIS, Visual; SMT, Somatomotor; DAT, Dorsal attention; VAT, Ventral attention; LBC, Limbic; FPA, Frontal parietal; DMN, Default mode network; SC, Subcortical; CB, Cerebellar.
Table 4.
Results of out of sample testing for each HCPEP run.
Fig 6.
naïve Bayes classifier results for discriminating cases from controls using a single a-priori feature VAR in Mode ψ4.
A) Results for HCPEP model trained and cross-validated in RUN2. B) Results for HCPEP model trained and cross-validated in RUN2 and tested in Cobre. C) Results for Cobre model trained and cross-validated. D) Results for Cobre model trained and cross-validated in Cobre and tested in HCPEP RUN2. AUC/Balanced accuracy/Sensitivity/Specificity; p value calculated from the binomial distribution. AUC, area under receiver operating characteristic curve.
Table 5.
Pserformance of additional classifiers in comparison to the classifier used in this study.
Fig 7.
Time-series for the relative phase order and the Kuramoto order parameter for one NAP subject.
A) Time-series for the cosine of relative phase or instantaneous phase-locking for a single subject. B) Time-series for the Kuramoto order parameter or average phase for a single subject. C) Blow-outs showing how relative phase is more informative than average phase for the dynamics of brain activity in one subject. MAG, magnetization ratio; KOP, Kuramoto order parameter, CHI, chimerality.
Fig 8.
Relationship between VAR and META with metrics of global integration, functional segregation, and a metastability index K.
A) HCPEP global integration versus META. B) HCPEP functional segregation versus META. C) HCPEP Metastability Index versus META. D) Cobre global integration versus META. E) Cobre functional segregation versus META. F) Cobre Metastability Index versus META. G) HCPEP global integration versus VAR. H) HCPEP functional segregation versus VAR. I) HCPEP Metastability Index versus VAR. J) Cobre global integration versus VAR. K) Cobre functional segregation versus VAR. L) Cobre Metastability Index versus VAR. R2 and R2adj results from linear regression. M) HCPEP Group-level differences in global integration. N) HCPEP Group-level differences in functional segregation. O) Cobre Group-level differences in global integration. P) Cobre Group-level differences in functional segregation. GINT, global integration; FSEG, functional segregations; K, Metastability Index.
Fig 9.
Simple scheme of basal ganglia connectivity.
A) Location of the basal ganglia in an axial cartoon view of the brain. B) Basal ganglia connectivity. Arrows indicate direction of connectivity. Glutamatergic (Glu) structures are shown in rose, GABAergic nuclei are shown in cyan, and the dopaminergic (DA) nucleus is shown in green. STN, subthalamic nucleus; SNC, substantia nigra pars compacta; GPe, global pallidus external; GPi, global pallidus internal; SNr, Substantia nigra; MLR, midbrain locomotor region; diencephalon locomotor region.
Table 6.
Comparison of classifier performance using FC and dFC.
Fig 10.
Attractor landscape for the extended HKB model of multi-adic coordination.
A plot of the relative phase potential function landscape for Aij = 2Bij = 1 for each i, j. Note the many valleys (marked with red asterisks) in which an oscillator moving around in this landscape will become trapped. These valleys are the local minima corresponding to the coordination states. There are two types of valleys in this landscape: in-phase valleys, which have relatively very deep and wide basins of attraction, and antiphase valleys, which are narrower and shallower, reflecting the fact that the in-phase state is more stable than the antiphase state. Each of these valleys is separated by a distance of Π, and repeats infinitely on the potential surface in a 2 Π -periodic pattern. A, B, effective coupling parameters; i,j, ith and jth oscillator. Reproduced with permission from [52].
Table 7.
Demographic characteristics of participant groups.
Fig 11.
Statistical flowchart for non-parametric testing of differences between groups across runs.
1) 2x4 non-parametric ANOVA using Align rank transform (ART). 2) Friedmann repeated measures test. 3) Paired Wilcoxon test. 4) Friedmann repeated measures test. 5) Paired Wilcoxon test. 6) Independent Wilcoxon test for each run. 7) Independent Wilcoxon test across all runs.