Decoding brain states on the intrinsic manifold of human brain dynamics across wakefulness and sleep

Abstract

Current state-of-the-art functional magnetic resonance imaging (fMRI) offers remarkable imaging quality and resolution, yet, the intrinsic dimensionality of brain dynamics in different states (wakefulness, light and deep sleep) remains unknown. Here we present a method to reveal the low dimensional intrinsic manifold underlying human brain dynamics, which is invariant of the high dimensional spatio-temporal representation of the neuroimaging technology. By applying this intrinsic manifold framework to fMRI data acquired in wakefulness and sleep, we reveal the nonlinear differences between wakefulness and three different sleep stages, and successfully decode these different brain states with a mean accuracy across participants of 96%. Remarkably, a further group analysis shows that the intrinsic manifolds of all participants share a common topology. Overall, our results reveal the intrinsic manifold underlying the spatiotemporal dynamics of brain activity and demonstrate how this manifold enables the decoding of different brain states such as wakefulness and various sleep stages.

Fig. 1. Intrinsic manifold framework.

a–d A classic example that illustrates manifold embedding; i.e., manifold learning applied to the swiss roll data, which is intrinsically a two-dimensional dataset yet represented in a higher (three-dimensional) space. To estimate the low dimensional embedding of the sampled dataset (b), we first create a graph representation (c), where the nodes represent the data points shown in (b), which are sampled from the underlying manifold illustrated in (a), and the edges indicate the relations (distances and/or similarities) between data points. d The manifold is embedded into the low-dimensional representation that matches its intrinsic dimensionality using the Laplacian eigenmaps manifold learning. e–g Our framework applying the same manifold learning approach, i.e. Laplacian eigenmaps, to extract the manifold underlying brain dynamics measured in fMRI data. e For each time point, the fMRI BOLD signal is parcellated into the 90 brain areas defined by the AAL template and pre-processed as explained in the “Methods“ section. f Using the parcellated fMRI data, the instantaneous phase is computed via Hilbert transform and the phase coherence among brain areas is estimated. This phase coherency matrix characterizes the pairwise synchrony relations between each pair of brain areas at any given time point. g The intrinsic manifold (here illustrated as two-dimensional) underlying the set of all instantaneous phase coherence states is estimated using the Laplacian eigenmaps method. To visualize the changes in phase coherency throughout the intrinsic manifold, for illustration purposes we defined 2-dimensional (2D) bins using the two manifold dimensions, and computed the average phase coherency of data points in those bins. Different colors indicate different sleep stages and wakefulness as defined by polysomnography.

Fig. 2. Representation of the brain activity fMRI BOLD data during wakefulness and sleep embedded in lower-dimensional spaces.

The plots show the data embedded into the three first dimensions of the intrinsic manifold (large coordinate system) and into the three principal components derived from PCA (small coordinate system). a–h Each separate coordinate system corresponds to the data of eight different participants, embedded individually. i Intrinsic manifolds from all 18 participants, aligned jointly into the group manifold. For all cases, nonlinear embedding of the data into their intrinsic manifold led to well-structured intrinsic manifolds with a clearer separation of different sleep stages (as defined through polysomnography) compared to the linear embedding given by PCA.

Fig. 3. Accuracy of brain state decoding on the intrinsic manifold of brain dynamics and on PCA.

Decoding accuracies in the feature space defined by the intrinsic manifold (IM) and PCA space for different experiments. a–f The accuracies of the SVM 1-vs-1 classification between a wakefulness and N1, b wakefulness and N2, c wakefulness and N3, d N1 and N2, e N1 and N3, and f N2 and N3. g–j The accuracies of the SVM 1-vs-all classification for each stage: g wakefulness, h N1, i N2 and j N3. The accuracy is defined as the ratio between the number of true positives and the total number of tested time points. The boxplots’ centrality is indicated by the median, and the boxes extend between 25th and 75th percentiles. Each colored circle corresponds to the classification accuracy for each single subject (in the case of individual analysis, left of the dashed line) and to the accuracy of each leave-one-subject-out round (in the case of group analysis, right to the dashed line). The classification accuracies on the intrinsic manifold and in PCA space are represented by green and red dots, respectively. Classifications are performed in spaces of dimensionality d = 7 (see Supplementary Fig. 3 for d = 3). For all classifications, intrinsic manifold classification yields significantly higher accuracies (for all comparisons, p-value < 0.001, Wilcoxon Rank-sum two-sided test, corrected for multiple comparisons via FDR). k Confusion matrices obtained from the 1-vs-all classification experiments (shown in g–j. l, m show the average accuracy across all stage-to-stage (1-vs-1) classifications for varying dimensionality of the embedding spaces for individual participants (l) and for group analysis (m), respectively. n, o show the average accuracy for all stages (1-vs-all) classifications for varying dimensionality of the embedding spaces for individual participants (n) and for group analysis (o), respectively. The solid lines indicate the median of the distribution across classifications and shaded areas indicate 25th and 75th percentiles.

Fig. 4. Receiver operating characteristic (ROC) for all pairwise comparisons between brain states on the intrinsic manifold of brain dynamics and compared to PCA.

ROC reveals the relationship between sensitivity and 1-specificity. The area under the curve (AUC) indicates how accurately the two compared states can be classified using only one dimension of the embedding space. ROC curves of the classifications performed on the intrinsic manifold (shown in green) and on PCA (shown in red) are illustrated for all pairwise stage comparisons: a between wakefulness and N1, b between wakefulness and N2, c between wakefulness and N3, d between N1 and N2, e between N1 and N3, f between N2 and N3. For all stage pairwise comparisons between wakefulness, N1, N2, and N3, intrinsic manifold yield significantly higher AUC (for all comparisons, p-value < 0.001, Wilcoxon Rank-sum two-sided test, corrected for multiple comparisons via FDR) in the first three-manifold dimensions. Shaded areas indicate the distribution of AUC values across different participants, for performed on their intrinsic manifold, whereas red dots correspond to the AUC values in the PCA space. The solid lines indicate the mean of the distribution across classifications and shaded areas indicate their standard error of the mean (N = 18).