Altered resting state complexity in schizophrenia

Abstract

The complexity of the human brain's activity and connectivity varies over temporal scales and is altered in disease states such as schizophrenia. Using a multi-level analysis of spontaneous low-frequency fMRI data stretching from the activity of individual brain regions to the coordinated connectivity pattern of the whole brain, we investigate the role of brain signal complexity in schizophrenia. Specifically, we quantitatively characterize the univariate wavelet entropy of regional activity, the bivariate pairwise functional connectivity between regions, and the multivariate network organization of connectivity patterns. Our results indicate that univariate measures of complexity are less sensitive to disease state than higher level bivariate and multivariate measures. While wavelet entropy is unaffected by disease state, the magnitude of pairwise functional connectivity is significantly decreased in schizophrenia and the variance is increased. Furthermore, by considering the network structure as a function of correlation strength, we find that network organization specifically of weak connections is strongly correlated with attention, memory, and negative symptom scores and displays potential as a clinical biomarker, providing up to 75% classification accuracy and 85% sensitivity. We also develop a general statistical framework for the testing of group differences in network properties, which is broadly applicable to studies where changes in network organization are crucial to the understanding of brain function.

Figure 1. Examination of Functional Activity and Connectivity

(A) Diagnostics. We characterized the fMRI data using both univariate and bivariate properties. We used the univariate property of wavelet entropy to characterize the average time series extracted from 90 cortical and subcortical regions defined by the AAL atlas. To estimate pairwise relationships, we computed the functional connectivity between any pair of regions using the Pearson correlation coefficient. Bivariate properties (strength and diversity) were estimated on the matrix of correlations between all possible pairs of ROIs. Strength is defined as the average of the column sum of the correlation matrix, while diversity is defined as the average of the column variance. Note that for ease of visualization, ROIs are ordered within the correlation matrices according to left and right hemisphere and then according to the respective functional module as defined by Salvador et al. (2005). (B) Group differences. While wavelet entropy was not significantly different between the two groups (2-sample t-test: t = −0.77, p = 0.44), strength was significantly higher in the controls (t = 4.86, p = 9.69 × 10⁻⁶) and diversity was significantly higher in the people with schizophrenia (t = 2.76, p = 0.007). Note: The edges of each box in these boxplots represent the 25th and 75th percentiles.

Figure 2. Anatomy of Activity and Connectivity

(Left) Spatial distribution of average wavelet entropy (A) as well as strength and diversity (B) in the healthy control group. (Right) Group differences in average wavelet entropy (A; regions for which p < .05 uncorrected), strength (B; p < .05, Bonferroni corrected) and diversity (B; p < .05, Bonferroni corrected).

Figure 3. Relationship Between Activity and Connectivity

(A) Correlations between the complexity of activity (as measured by the time series wavelet entropy) and connectivity (as measured by the strength (Left) and diversity (Right) of the whole brain correlation matrices) for healthy controls (black) and people with schizophrenia (red). The correlation between group median wavelet entropy and mean strength was r = 0.39, p = 1 × 10⁻⁴ for the healthy controls and r = 0.51, p = 3 × 10⁻⁷ for the people with schizophrenia, while the correlation between wavelet entropy and diversity was r = −0.10, p = 0.34 for the controls and r = 0.31, p = 0.002 for the patients. Data points represent individual brain regions. (B) Boxplots showing significant group differences in Pearson’s r between strength and wavelet entropy (Left; two-sample t-test, t = 2.34, p = 0.022) and diversity and wavelet entropy (Right; t = 3.40, p = 0.001), computed for each individual. Note: the edges of each box are the 25th and 75th percentiles.

Figure 4. Group Differences in Patterns of Connectivity

(A) The size of the largest connected component in brain graphs as a function of graph density for healthy controls (black) and people with schizophrenia (red). Error bars indicate standard deviation of the mean. Insets show binary matrices at three different graph densities; matrix elements shown in white indicate the existence of connections, while matrix elements shown in black indicate the absence of connections. Bars along the bottom indicate graph densities at which the p-value for a two-sample t-test showed significant group differences at p < .05 uncorrected. (B) P-values for the correlations between the size of the connected component and six more complex graph diagnostics (global efficiency, betweenness centrality, small-worldness, modularity, local efficiency, and clustering coefficient) as a function of density. For the majority of graph densities, the size of the connected component is a highly significant predictor of more complex graph measures: significant p-values are given by colors ranging from purple (p ~ .05) to white (p ~ 10⁻⁴⁰) while non-significant p-values are show in black (p > 0.05). (C) & (D) Functional Data Analysis (FDA) can be used to test for group differences in graph metric curves like the size of the connected component as a function of graph density. (C) In order to determine the differences between the group curves shown in (A), we compute the area between the group mean curves. (D) We then permute group membership among the subjects to construct a permuted distribution (histogram shown in gray) and compare that to the ’empirical area value’ determined in (C). We find that the area between the two curves is significantly larger than expected in the null distribution: p = 0.004.

Figure 5. Examining Graph Structure

(A) We can construct graphs using one of two methods: cumulative or windowed thresholding of the correlation matrix. In the commonly used cumulative thresholding procedure (top), matrix elements (graph links) with lower and lower correlation values are retained in the graph, such that the density (number of links) of the graph increases. In a windowed thresholding procedure (bottom), matrix elements (graph links) whose correlation values lie within a given correlation range (or window) are retained in the graph. The density of each graph is therefore determined by the correlation range. (B) Curves for the size of the largest connected component for both healthy controls (black) and people with schizophrenia (red) derived via the windowed thresholding procedure showed significant group differences (p < 5 × 10⁻⁵, via FDA permutation testing). (C) Using a support vector machine, the classification accuracy, sensitivity, and specificity of the size of the connected component as a function of window (data shown in (B)) were determined to be highest for windows that included weak correlations. Color bar indicates percent. (D) The median wavelet entropy (top) of nodes and the mean connection distance of the edges (bottom) present in the windows shown in (B). Windows constructed from weak correlations on average contain nodes of low wavelet entropy and edges linking distant regions. Node connectivity (E),(G) and average graph (F),(H) in a weak correlation window for healthy controls and people with schizophrenia, respectively. Color indicates average degree. The window chosen for this figure is the window that provided the highest classification accuracy and sensitivity shown in (C); however, results are consistent for a range of windows constructed from weak correlations. Note in comparing (A) and (B): While graph diagnostics are often plotted as a function of density when constructed by cumulative thresholding (networks of strong correlations lying on the left of the plot), when constructing graphs from windowed thresholding, diagnostics can be plotted as a function of average correlation (networks of strong correlations lying on the right of the plot).

Figure 6. Cognitive Variables and Symptoms Scores

Composite attention (A), composite memory (B), and SANS (C) scores as a function of the size of the connected component for healthy controls (black) and people with schizophrenia (red). For the two groups combined, the size of the connected component was significantly correlated with both attention (r = 0.50, p = 4.5 × 10⁻⁵ (A)) and memory (r = 0.27, p = 0.036 (B)); best fits are shown with a solid gray line. No significant correlations were found within the two groups separately; best fits are shown in the dotted black (red) line for the control (schizophrenia) population. The size of the connected component was also significantly correlated with the SANS scores in the schizophrenia population (r = −0.43, p = 0.018); best fit shown in the solid red line in (C). No significant correlations were found with the SAPS scores. Network size estimates are taken from the window in which the maximum classification accuracy and sensitivity were identified (see Fig 5C).