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. 2014 Dec;35(12):5984-95.
doi: 10.1002/hbm.22599. Epub 2014 Jul 31.

Disentangling dynamic networks: Separated and joint expressions of functional connectivity patterns in time

Nora Leonardi  1 , William R Shirer, Michael D Greicius, Dimitri Van De Ville
Affiliations

Disentangling dynamic networks: Separated and joint expressions of functional connectivity patterns in time

Nora Leonardi et al. Hum Brain Mapp. 2014 Dec.

Abstract

Resting-state functional connectivity (FC) is highly variable across the duration of a scan. Groups of coevolving connections, or reproducible patterns of dynamic FC (dFC), have been revealed in fluctuating FC by applying unsupervised learning techniques. Based on results from k-means clustering and sliding-window correlations, it has recently been hypothesized that dFC may cycle through several discrete FC states. Alternatively, it has been proposed to represent dFC as a linear combination of multiple FC patterns using principal component analysis. As it is unclear whether sparse or nonsparse combinations of FC patterns are most appropriate, and as this affects their interpretation and use as markers of cognitive processing, the goal of our study was to evaluate the impact of sparsity by performing an empirical evaluation of simulated, task-based, and resting-state dFC. To this aim, we applied matrix factorizations subject to variable constraints in the temporal domain and studied both the reproducibility of ensuing representations of dFC and the expression of FC patterns over time. During subject-driven tasks, dFC was well described by alternating FC states in accordance with the nature of the data. The estimated FC patterns showed a rich structure with combinations of known functional networks enabling accurate identification of three different tasks. During rest, dFC was better described by multiple FC patterns that overlap. The executive control networks, which are critical for working memory, appeared grouped alternately with externally or internally oriented networks. These results suggest that combinations of FC patterns can provide a meaningful way to disentangle resting-state dFC.

Keywords: dynamic functional connectivity; functional magnetic resonance imaging; matrix factorization; resting state.

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Figures

Figure 1
Figure 1
(a) dFC is temporally concatenated across multiple subjects to form matrix C. (b) k‐Means clustering separates the data into K clusters, thereby approximating C by a succession of the cluster centroids, for example, the first dFC estimate is approximated by centroid 1, the second and third by centroid 2,…. This can be seen as decomposing the dFC matrix C into K FC patterns (D) and associated sparse weights (A), where only one FC pattern may have a nonzero weight at each instance in time ( ∥a:t∥0=1). (c) PCA or SVD decomposes the dFC matrix into K FC patterns and associated nonsparse, orthogonal weights ( ∥a:t∥0= K). [Color figure can be viewed in the online issue, which is available at http://wileyonlinelibrary.com.]
Figure 2
Figure 2
(a) k‐Means clustering assigns each dFC network to one of three clusters. (b) This assignment is guided by the similarity of each dFC network to all three FC patterns. We interpret the similarity of each dFC network to all FC patterns as a nonsparse weight matrix A*. (c) The histogram of A* distinguishes separated (left) and joint (right) expression of FC patterns. [Color figure can be viewed in the online issue, which is available at http://wileyonlinelibrary.com.]
Figure 3
Figure 3
(a) Average correlation coefficient of true FC patterns with those estimated using k‐means clustering (K = 3), sparse matrix factorizations (k‐SVD with K = 3, S = 1; K = 3, S = 3; K = 2, S = 1, and K = 2, S = 2), and PCA (K = 2) for both simulated separated and joint expression of FC patterns. Error bars represent standard deviation across simulations. (b) Split‐half reproducibility for K = 1, 2,…, 8 for simulations (separated, joint, and null), subject‐driven task‐based and resting‐state dFC. Error bars represent standard deviation across splits. (c) Skewness of time‐dependent weights A* for simulations and experimental subject‐driven task‐based and resting‐state dFC. [Color figure can be viewed in the online issue, which is available at http://wileyonlinelibrary.com.]
Figure 4
Figure 4
(a) Average dFC of the three subject‐driven tasks: subtraction, memory and music. (b) Estimated FC patterns (K = 3), correlation between average dFC of each task and the estimated FC patterns, and correlation coefficients of windowed FC with all 3 FC patterns across windows and subjects. The x‐axis is arranged by task, rather than by subject. (c) Same as b for K = 4 (only the two music‐related FC patterns are shown as the others do not change). [Color figure can be viewed in the online issue, which is available at http://wileyonlinelibrary.com.]
Figure 5
Figure 5
FC patterns estimated during resting‐state (1–3) and dFC averaged across all windows and subjects. [Color figure can be viewed in the online issue, which is available at http://wileyonlinelibrary.com.]
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