Fig 1.
Dynamic Connectivity, Single and Higher Dimensional Representations (A) Example of two network timecourses whose correlation evaluated over their entire duration is 0.4; (B) One of the many different ways that a pair of long timecourses can have correlation coefficient of 0.4 is to pass through the two distinct, identifiable connectivity regimes shown here. The existence of the two connectivity regimes and the transitions between them are completely obscured by looking at correlation on a longer timescale; (C and D) Too crude a dimensionality-reduction of the state space can create serious distortions of the dynamics being analyzed. Dynamically active and mobile trajectories (C) can appear constant under the reduction, while those barely moving from their starting position (D) can seem highly dynamic; (E) Shifting up one dimension and characterizing the same trajectories by vectors reflecting their position In a discrete 2-dimensional state space yields much better qualitative agreement between the geometric trajectories and their symbolic representations.
Fig 2.
Meta-State Dynamic FNC: High Level Schematics (A) Schematic showing connectivity decomposed into, for simplicity, binary weighted sums of connectivity patterns, yielding meta-states in {0,1}s4; (B) Histograms of maximal uninterrupted periods spent in any fixed meta-state for patients (red) and controls (blue) (C) A connectivity pattern in which network-pair connections are signed and non-binary (for example, given by correlations) and in graph (right) and matrix (left) forms; (D) Schematic illustration of differences in dynamical patterns of network connectivity between schizophrenia patients and healthy controls. Controls exhibit more, and more diverse, connectivity states changing from one connectivity pattern to another more often than patients.
Fig 3.
Temporal ICA Schematic with Examples of Single Window Weighted CPs and Discretized Time-Varying CP Weights (A) Schematic displaying stages involved in producing CPs; top row illustrates the initial decomposition of fMRI data into network spatial maps and corresponding timecourses using group spatial ICA (GICA); bottom row shows decomposition of window-indexed correlation matrices computed on sliding windows through the network timecourses (left-hand side of equation) produced by spatial ICA on fMRI data summarized in the top row into temporally independent CPs (matrix W on right hand side of equation) using temporal ICA; (B) Example of an observed wFNC expressed as weighted sum of the five displayed tICA CPs; (C) One subject's CP timecourses (top left) transformed into the signed quartile discretization (top right) with times at which each discretized timecourse changes from one level to another (bottom and example of one time-indexed 5-vector of timecourse values converted into a meta-state of signed quartile values (bottom right).
Table 1.
Demographic Information.
Fig 4.
Correlation Patterns Produced by Different Algorithms and by Temporal ICA at Different Model Orders (A) Different data-driven decompositions of the wFNCs yield different sets of correlation patterns; correlation patterns produced, from top to bottom, by tICA, sICA, PCA, K-means, all with model order five; (B) Different model-orders of tICA applied to the wFNCs yield growing collections of correlation patters with two recurring patterns (Row 1, Columnss 1 and 3); tICA correlation patterns, from top to bottom, for model orders three through seven.
Fig 5.
Planar projection of the discrete five-dimensional state space.
Fig 6.
Effect of Schizophrenia on Dynamic Fluidity Measures (A) Number of meta-states realized; (middle column) boxplot showing median, quartiles and outliers plus mean for each group, and diagnosis effect from regression model specified in the Methods section with associated p-value; (leftmost column) The time-indexed meta-states of a sample healthy subject, with the 88 distinct meta-states shown underneath; (rightmost column) The time-indexed meta-states of a sample schizophrenia patient, with the 23 distinct meta-states shown underneath; (B) Number of timepoints at which subjects change between meta-states; (middle column) boxplot showing median, quartiles and outliers plus mean for each group, and diagnosis effect from regression model specified in the Methods section with associated p-value; (leftmost column) The time-indexed meta-states of a sample healthy subject, with the 87 timepoints at which meta-state changes shown above; (rightmost column) The time-indexed meta-states of a sample schizophrenia patient, with the 33 timepoints at which meta-state changes shown above.
Fig 7.
Effect of Schizophrenia on Dynamic Range Measures (A) Maximally different (in the L1 sense) meta-states that subjects realize; (middle column) boxplot showing median, quartiles and outliers plus mean for each group, and diagnosis effect from regression model specified in the Methods section with associated p-value; (leftmost column) The time-indexed meta-states of a sample healthy subject, with the two most divergent realized meta-states (L1 distance = 21) shown underneath; (rightmost column) The time-indexed meta-states of a sample schizophrenia patient, with the two most divergent realized meta-states (L1 distance = 8) shown underneath; (B) Total distance traveled (summed L1 distance between successive meta-states) in the state space; (middle column) boxplot showing median, quartiles and outliers plus mean for each group, and diagnosis effect from regression model specified in the Methods section with associated p-value; (leftmost column) The time-indexed meta-states of a sample healthy subject, with the timeseries of cumulative distance traveled (increasing to 117 at final timepoint) shown above; (rightmost column) The time-indexed meta-states of a sample schizophrenia patient, with timeseries of cumulative distance traveled (increasing to 37 at final timepoint) shown above.
Table 2.
Age and gender-corrected effects of SZ on four general dynamism measures (rows) under four different decompositions of the wFNC data into sets of five correlation patterns (columns).
Table 3.
Age and gender-corrected effects of SZ on four general dynamism measures (rows) computed over tICA decompositions of different model orders (columns).
Displayed effects and p-values are from the regression model specified in the Methods section.
Fig 8.
Effect of Main Psychotic Symptoms of Schizophrenia on Connectivity Dynamism Measures Significant (α<0.05) effects of hallmark psychotic symptoms of SZ on each of the four dynamism measures from regression on all thirty symptom scores from the PANSS scale along with gender and age as covariates.
The effect of delusions on L1 Span of Realized Meta-States has p-value = 0.023. The p-values associated to the effects of hallucinatory behavior on each of the four measures given along the x-axis are, from left to right: 0.005, 0.003, 0.003, and 0.010.
Fig 9.
Basic Results on Hub Meta-States and Schizophrenia (A) Bar plots for HC and SZ of number of subjects (y-axis) with hubs of exactly the indicated levels (x-axis); (B) Bar plots for HC and SZ of number of subjects (y-axis) with hubs of at least the indicated level (x-axis).
Fig 10.
Results of Comprehensive Investigation of Hub Meta-States and Schizophrenia (A) Histograms of within-subject mean meta-state recurrence rate (average number of re-visitations made to the meta-states realized) and SZ regression effect on this quantity (SZ effect = 0.86, p-value = 0.0001); (B) SZ effect on number of distinct meta-states with indicated within-subject recurrence rate (inset zooms on rates 3–18) along with SZ effect on the largest number of visits to the same state (SZ effect = 1.42, p-value = 4.96e-005 (also see (C) for distribution)); (C) Number of subjects whose most visited meta-state had indicated recurrence rate; (D) Mean longest uninterrupted period of hub state occupancy (recall that level k hubs are occupied k times, not necessarily in uninterrupted stretches) and SZ regression effect (SZ effect = 1.18, p-value = 4.60e-005); (E) Effect of SZ on hub saturation, evaluated separately for hubs of each level k, k = 4,5,…,36. Saturation positively correlated with SZ in red (dark red indicates effects significant 0.05 level after FDR correction), negatively correlated with saturation in blue. (F) Boxplot of saturation index over all hubs for HC and SZ with group means (μSZ = 5.2, μHC = 5.6) and SZ regression effect on this quantity (SZ effect = 0.34, p-value = 4.88e-005); All SZ effects and associated p-values are from the regression model specified in the Methods section. The reported regressions include the patient with an order-36 hub (ie, they are for the displayed data, and we did want to provide evidence that hubs of higher order are achievable). In regressions omitting this extreme observation, both the direction and significance level of displayed effects were preserved (p-values were on order e-005 or e-006).
Fig 11.
Number of Distinct Meta-States Occupied Multiple Times by any Subject (A) Bar plot of number of meta-states with indicated within-subject recurrence rates for full population with fitted power law (α = -323); (B) Power laws fitted separately for HC(α = -3.36) and SZ (α = -2.30) to number of meta-states with given within-subject recurrence rates.
Fig 12.
Meta-States Realized at Least Once by Multiple Subjects (A) Bar plot of number of meta-states realized by two or more subjects (number of subjects in the collection jointly realizing some meta-state on the x-axis), shown separately for patients and healthy controls. No meta-state whatsoever is realized by more than 7 different healthy subjects. Fewer than 50 (of 32,768) meta-states are realized by more than 6 patients. A two-sample T-test shows that the number NSZ of patients jointly realizing some meta-state is significantly larger than the number NHC of controls respectively jointly realizing some meta-state; (B) Bar plot of the number of subject-pairs that jointly realize indicated (x-axis) number of meta-states, shown separately for pairs of controls, pairs of patients and mixed pairs consisting of one patient and one control. A two-sample T-text shows that the average number of intersection points (jointly realized meta-states) for SZ subject pairs is significantly larger than the average number of intersection points for HC subject pairs.
Fig 13.
Dynamism measures restricted to immediate neighborhoods of higher-level hubs.
We examine the number and the span of incoming and outgoing meta-states connected to each hub of level 8 and over. The interval was selected so that more than a third of HCs and of SZs have level-k hubs for k≥the lower bound of the interval. The values are not integers because we average over each segment during which a given hub is occupied for a subject, ie. the subject first visits some level k hub for 3 consecutive timepoints and then later visits the same hub again for k-3 consecutive timepoints. Each separate occupancy has its own outgoing target, which might or might not be identical. Since the number of distinct segments of occupancy of a given hub affect the overall number and range of the targets of that hub, we rescale by resulting in non-integer valued measures. (A) The number (rescaled as indicated) of distinct target meta-states of fixed hubs; (B) The span (maximal L1 distance between, also rescaled as indicated above) of target meta-states of fixed hubs.
Fig 14.
Effect of Schizophrenia on Dynamic Roles of Individual tICA Correlation Patterns (Fig 4(A), Row 1).
Red (or bars pointing upward) indicate positive correlation with SZ. Only effects significant at the 0.05 level following FDR-correction are displayed. (A) SZ effects on the number of times each discretized CP timecourse (y-axis), assumes values indicated on the x-axis; (B) SZ effects on binned counts (x-axis) of the number of timepoints each discretized CP timecourse spends consecutively the most negative level, -4; (C) SZ effect on the number of correlation patterns simultaneously contributing in their anti-state form, ie. on the number of timepoints at which a subject's meta-state contains the indicated number (x-axis) of negative values; (D) SZ effects, component-wise for CPs that exhibit strong positive AVSN correlations, on the number of transitions between levels indicated on x-axis and y-axis; All diagnosis effects and p-values are from the regression model specified in the Methods section.
Fig 15.
Effect of Schizophrenia on Spectral Power as Data is Transformed from Voxels to Networks to Meta-States SZ effects on the spectral power for inputs (Columns 1–4) to the meta-state dynamic connectivity framework and its output (Column 5) (red indicates positive correlation with SZ); (Column 1) (A) SZ effects on network TC spectra; (F) Effects from (A) that survive FDR correction at 0.05 significance level; (J) SZ effect on average spectral power over all network TCs; (O) Effects from (J) that survive FDR-correction at 0.05 significance level; (Column 2) (B) SZ effect on windowed network TC spectra; (G) Effects from (B) that survive FDR-correction at 0.05 significance level; (K) SZ effect on the average spectral power over all windowed network TCs; (P) Effects from (K) that survive FDR correction at the 0.05 significance level; (Column 3) (C) SZ effects on wFNC network-pair correlation spectra; (H) Effects from (C) that survive FDR-correction at the 0.05 significance level; (L) SZ effect on average spectral power over all wFNC network-pair correlations; (Q) Effects from (L) that survive FDR-correction at the 0.05 significance level; (D) SZ effects on tICA correlation pattern TCs; (I) Effects from (D) that survive FDR-correction at the 0.05 significance level; (M) SZ effect on average spectral power over all tICA correlation pattern TCs; (R) Effects from (M) that survive FDR-correction at the 0.05 significance level; (E) SZ effect on spectral power of the timeseries that is '1' when a five-dimensional meta-state changes to a different meta-state and '0' otherwise; (N) Effects from (E) that survive FDR-correction at the 0.05 significance level; All diagnosis effects and p-values are from the regression model specified in the Methods section.