Lag threads organize the brain’s intrinsic activity

Abstract

The objective is to demonstrate the mapping between lag structure and PCA. The illustration is not intended as a model of propagation in neural tissue. Each lag thread is also shown as a multidimensional time series with spectral content duplicated from real BOLD rs-fMRI data. B shows the superposition of the three lag threads. C shows the time-delay matrix (TD) recovered by analysis of the superposed time series in B, using the technique illustrated in SI Appendix, Fig. S1 (27).The bottom row of C shows the latency projection of TD computed as the average over each column. D illustrates the latency projection as a node diagram. This projection represents nodes that are, on average, early or late. Critically, the projection fails to capture the full lag structure. E illustrates eigendecomposition of the covariance structure of TD z , derived from TD by removing the mean of each column (see SI Appendix, Eqs. S4-S8). There are three significant eigenvalues (33), indicating the presence of three lag threads. In an ideal case, eigenvalues 4-6 would be zero; in this example, imperfect superposition leads to a small fourth nonzero eigenvalue. The eigenvectors corresponding to the first three eigenvalues are the thread topographies (shown above the eigenvalues). The lag thread sequences defined in A were accurately recovered purely by eigen-analysis of TD z . It should be noted that the lag threads in this illustration were a priori constructed to be mutually orthogonal (see SI Appendix, Eq. S7). Hence, they were neatly recovered intact by eigendecomposition of TD z . Also, although the nodes in this illustration are represented as foci, the algebra applies equally well to voxels, ROIs, or extended, possibly disjoint, topographies.www.pnas.org PNAS | December 29, 2015 | vol. 112 | no. 52 | E7307 CORRECTION

How networks communicate: propagation patterns in spontaneous brain activity

“…between the DMN and DAN, upper right corner). The TD matrix in figure 1c is highly reproducible at the group level in awake adults, as previously shown using a cohort of nearly 1400 subjects [42] indicating that the propagation structure of rs-fMRI data is highly conserved across individuals.…”

“…We refer to these 'one-way street topographies' as 'lag thread motifs'. Comparing the propagation sequence correlation matrix (figure 1f ) against a conventional zero-lag (functional connectivity) correlation matrix (figure 1b), we find substantial agreement [42]. Thus, not only do we find evidence of 'one-way street' motifs in BOLD signal propagation, these lag thread motifs match the topographies of RSNs.…”

“…Second, lag threads are very consistent across independent groups of subjects. This replicability is demonstrated in two groups of 688 subjects in [42] and a group of 39 subjects in [45]. Thus, the propagation structure of rs-fMRI data is defined by a set of remarkably conserved, bilaterally symmetric propagation sequences.…”

“…Endnote 1 A co-author of our earlier lag threads paper [42] suggested examining spatial correlations across lag thread topographies. He had intended to suggest computing spatial correlations between RSNs and lag threads, but A.M. mistook his meaning, and thus surprised the group by finding that voxel-wise correlations across lag threads mimicked RSN organization.…”

Temporal dynamics in fMRI resting-state activity

“…In a significant new study, Mitra et al (1) demonstrate the existence of reproducible temporal patterns of spontaneous activity from human functional magnetic resonance imaging (fMRI) recordings. This finding and the novel methods used to demonstrate it bring the question of the role of temporally patterned activity into the domain of human cognition.…”