Fundamental dynamical modes underlying human brain synchronization

Abstract

Little is known about the long-term dynamics of widely interacting cortical and subcortical networks during the wake-sleep cycle. Using large-scale intracranial recordings of epileptic patients during seizure-free periods, we investigated local- and long-range synchronization between multiple brain regions over several days. For such high-dimensional data, summary information is required for understanding and modelling the underlying dynamics. Here, we suggest that a compact yet useful representation is given by a state space based on the first principal components. Using this representation, we report, with a remarkable similarity across the patients with different locations of electrode placement, that the seemingly complex patterns of brain synchrony during the wake-sleep cycle can be represented by a small number of characteristic dynamic modes. In this space, transitions between behavioral states occur through specific trajectories from one mode to another. These findings suggest that, at a coarse level of temporal resolution, the different brain states are correlated with several dominant synchrony patterns which are successively activated across wake-sleep states.

Figure 1

After a narrow band filtering of the intracranial EEGs in the delta (1–4 Hz), theta (4–8 Hz), alpha (8–13 Hz), beta 1 (13–20 Hz), beta 2 (20–30 Hz), and gamma (30–50 Hz) frequency bands, local- and long-range synchronizations were, respectively, estimated by the spectral power of each recording contact and by the mean phase-locking values (PLV) between every contact and all the others. This computation allows the characterization of the multifrequency synchronization patterns of each time window t as a vector S(t). (b) Scatter and density plots of 4 successive days (i.e., 96 hours, patient 1), in the space of the first principal components. (c, d) Distributions in the state space across several days and during waking and sleep states. (e) The spectral amplitudes were color coded in the state space, characterizing three main internal frequencies of individual regions in the delta, alpha, and gamma bands.

Figure 2

Correlation matrix showing the similarity of all the windows compared with each other over 4 successive days (upper map) and during one day (lower map).

Figure 3

(a) Same correlation matrix as in Figure 2, now sorted in order of similarity by the clustering algorithm. (b) Dendrogram of correlation matrix. Levels of the dendrogram correspond to different sets of clusters in the correlation matrix. At the top of the dendrogram, a single branch signifies that all avalanches are in one cluster. Just below this, the dendrogram divides into two branches, representing a set of two clusters. Branching continues further down the dendrogram until every window is in its own family. The red line crosses the dendrogram at minimum of the ratio between intracluster and intercluster distances and indicated that 5 clusters can be identified (note here that one small sized cluster was removed). The 5 corresponding clusters were reported in the sorted correlation matrix (a). (c) The corresponding 5 clusters were reported in the state space, coded by different colors. The probabilities of transition between the different clusters are depicted using different arrow sizes (small: 0.2 < P < 0.4 and large: P > 0.4). Direct cluster-to-cluster transitions were mostly identified between proximal modes in the state space. (c) Matrices of transition probabilities between the characteristic modes defined by clustering, for both the actual and shuffled data.

Figure 4

Global state space for 4 patients. For each patient, several characteristic clusters were identified by a hierarchical clustering algorithm and were coded by different colors (analyzed periods for patient 2: 103 hours; patient 3: 38.7 hours; patient 4: 86 hours; patient 5: 40 hours). The probabilities of transition between the different clusters are depicted using different arrow sizes (small: 0.2 < P < 0.4 and large: P > 0.4). Note that the global dynamic structures governing the trajectories across the state space are similar among all the different patients (insets: matrices of transition probabilities). In a comparable way, the color-coded spectral state spaces conserved three different segregated regions in the delta, alpha/beta, and gamma bands (first column).