Functional hierarchies in brain dynamics characterized by signal reversibility in ferret cortex

Abstract

Brain signal irreversibility has been shown to be a promising approach to study neural dynamics. Nevertheless, the relation with cortical hierarchy and the influence of different electrophysiological features is not completely understood. In this study, we recorded local field potentials (LFPs) during spontaneous behavior, including awake and sleep periods, using custom micro-electrocorticographic (μECoG) arrays implanted in ferrets. In contrast to humans, ferrets remain less time in each state across the sleep-wake cycle. We deployed a diverse set of metrics in order to measure the levels of complexity of the different behavioral states. In particular, brain irreversibility, which is a signature of non-equilibrium dynamics, captured by the arrow of time of the signal, revealed the hierarchical organization of the ferret's cortex. We found different signatures of irreversibility and functional hierarchy of large-scale dynamics in three different brain states (active awake, quiet awake, and deep sleep), showing a lower level of irreversibility in the deep sleep stage, compared to the other. Irreversibility also allowed us to disentangle the influence of different cortical areas and frequency bands in this process, showing a predominance of the parietal cortex and the theta band. Furthermore, when inspecting the embedded dynamic through a Hidden Markov Model, the deep sleep stage was revealed to have a lower switching rate and lower entropy production. These results suggest functional hierarchies in organization that can be revealed through thermodynamic features and information theory metrics.

Fig 1

Analysis summary: (A) Data was recorded from 64 custom micro-electrocorticographic (μECoG) electrodes placed in the ferret cortex. The number of electrodes in each cortical functional system (auditory, visual, parietal) is depicted in the insert, which sum to 64 total electrodes. (B) Raw signal level of irreversibility was obtained by calculating for each time window (1 second) the time-shifted forward correlation difference with the time-shifted backward correlation. (C) Frequency spectra, classification of behavioral states and irreversibility values (difference between forward and backward matrix) at each time point across the whole recording (> 2 hours). Irreversibility value was calculated for each behavioral state showing the AA/REM as the one with the highest level. (D) PCA was calculated for each brain region and the three first components (one from each area) were used as the input signal for the Hidden Markov Model Analysis (HMM). The HMM resulting network states are presented with their corresponding transitions. (E) The switching rate between the obtained network states was grouped by behavioral states, showing the AA/REM as the state with the highest switching rate (AA/REM: 0.15; QA: 0.13; SWS:0.12). (F) The maximal fractional occupancy of the 5 network states was calculated for each behavioral state, showing the SWS as the one with the highest value (AA/REM: 0.32; QA: 0.37; SWS:0.45). (G) We applied a deep autoencoder to reduce the dimensionality of the source data in order to explore the embedded dynamics of the system. (H) The distinction between the three behavioral states was assessed through a classifier at each reduced dimension, showing the highest level of performance at dimension 7. (I) The entropy production of each behavioral state is displayed at dimension 7 revealing that the greatest departure from equilibrium occurs in the stage AA/REM ([F(2, 1787) = 390,p < .01]). The highest entropy production was at the AA/REM state (mean = 0.0034, std = 0.0012), followed by the SWS state (mean = 0.0023, std = 0.001) and QA state (mean = 0.0017, std = 0.0011).

Fig 2

Irreversibility level across time and regions: (A) The irreversibility level was assessed at each time point, displayed next to the behavioral state at the corresponding moment. Over time, a significant increase in irreversibility can be observed during the Active-Awake(AA)/REM stages. (B) Signal irreversibility was calculated for the three different behavioral states. AA/REM (left), Quiet-Awake (QA) (center) and Slow-wave-sleep (SWS) (right). For each state, it is displayed the level of irreversibility for each functional system (Visual, auditory, and parietal) and the level corresponding to the within-system relations and the between-system relations. Across sleep stages, the parietal cortex and within-system relations were revealed to be the drivers of the irreversibility in the system. At the bottom, the irreversibility level was measured at bins of 1 Hz between 0 and 50 Hz. The analysis was also performed for all the different behavioral states. Bar figures indicated the level of irreversibility when grouping the frequencies by previously reported frequency bands being the theta range the one with the highest irreversibility value.

Fig 3

HMM analysis: (A) Principal component analysis was calculated for each functional system and the three first components (one from each system) were used as the input signal for the Hidden Markov Model Analysis (HMM). (B) At each time point, the probability of occurrence of each network-state is displayed, next to the predominant one for the corresponding moment. (C) The average life-time (time spent at each network state) was calculated for each behavioral state and displayed together to observe the similarities between them (D) Entropy production was calculated by observing how asymmetrical the transitions between the network-states were. (E) The results, grouped by behavioral state indicated a higher level of transfer entropy in the AA/REM state (F) The joint transition probability between the network states is displayed for each behavioral state. Furthermore, the difference matrix (upper triangle minus lower triangle) is displayed to enhance the visualization of the effect (G) The level of determinism was calculated showing the highest value for the SWS state (H) The level of degeneracy was calculated showing the highest value for the SWS state (I) The level of mutual information was calculated showing the highest value for the SWS state.