Untangling Brain-Wide Dynamics in Consciousness by Cross-Embedding
Fig 3
Cross-embedding analysis reveals large-scale cortical interaction, which can be missed by correlation-based statistics.
(A) ECoG electrode loci in a representative subject. (B) Illustration of cortical areas covered by the present recording system. (C) Example of ECoG signals. Gray traces represent the signal from the all electrodes superimposed; green and magenta traces show the signals in an example electrode pair (electrodes 41 and 118). (D) Cross-embedding analysis based on the state-space reconstructions for the example electrode pair, corresponding to Fig 1E and 1F. (E) Relationship between coordinate dimensions and embeddedness in the example electrode pair, corresponding to Fig 1F. (F) Optimal embeddedness values as functions of data length (number of data points) used in the analysis. The line colors corresponds to those in panel E. Note that the embeddedness values improve as data length increases, which is a hallmark of causally coupled deterministic dynamics [21]. (G-K) Cross-embedding results. (G) The complexity of area-to-area interaction are shown in the matrix formats, which show the results of interaction from areas specifying columns to areas specifying rows. (H) Scatter plot of complexity in awake vs. anesthetized conditions; each dot represents a complexity value for each “effect” electrode, averaged across “cause” electrodes. Dashed red line shows equality. (I) (Top) The directionality of area-to-area interaction are shown in the matrix formats. (Bottom) The directionality among individual electrodes in a single subject. (J) Scatter plot of directionality in awake vs. anesthetized conditions; each dot represents the values for each electrode pair. (K) The same as panels I, except for that the directionality values were computed based on the cross-embedding analysis with limiting the embedding dimension to 1. (L-N) Correlation analysis of snapshot electrode signals. (L) (Top) Average correlation among areas. (Bottom) Correlation among individual electrodes in a single subject. (M) Scatter plots of complexity, directionality, and correlation coefficient in awake vs. anesthetized conditions; each dot represents the values for each electrode pair. (N) Comparison between cross-embedding-based directionality and correlation. Dashed red line shows zero value of correlation. Panels G-L, N and O show the pooled results across the four subjects. LVC: lower visual cortex; HVC: higher visual cortices; TC: temporal cortex; PC: parietal cortex; MSC motor and somatosensory cortex; PMC: premotor cortex; lPFC: lateral prefrontal cortex; mPFC: medial prefrontal cortex