Awake cortex stabilizes traveling waves for global and reliable information routing

Summary

How does the brain organize neural information for perception during wakefulness, yet lose such organization under anesthesia? Theories on consciousness hypothesize that perceptual experience arises from global communication across the cerebral cortex. However, the neural substrate that mediates information transfer between cortical regions remains uncertain. Here, developing large-scale and high-density electrocorticography arrays, we demonstrated that traveling waves serve as a fundamental mode for global information transfer. Compared with the anesthetized state, visual-evoked traveling waves during wakefulness exhibited greater stability. Hierarchical clustering uncovered the emergence of widespread waves with a rich repertoire of motifs only in the awake state. By quantifying the fidelity of information routing, we found that information flows more reliably along the direction of wave propagation during wakefulness than under anesthesia. This study provides meso- and macroscopic evidence consistent with theories of consciousness and introduces a framework, informational tuning, for characterizing the geometrical relations between neural and informational flows.

Graphical abstract

Highlights

• •In simulations, traveling waves do not guarantee directional information flow
• •We propose informational tuning to reveal the fidelity of information flow via waves
• •Wakefulness sharpens informational tuning compared with anesthesia
• •Wave-guided information routing offers a multiscale link to theories of consciousness

Biological sciences

Introduction

During wakefulness, we experience perception, which disappears under general anesthesia. Sensory information processing relies on the brain’s ability to efficiently encode features of the external world and transmit information between cortical areas.^1,2,3 Classical studies have established a fundamental principle of encoding: the property of “neuronal tuning” in sensory cortices. These neurons exhibit a preference for specific stimulus features, such as orientation, color, and frequency, with responses diminishing as stimuli deviate from the optimal feature.^4,5,6 However, the principles of large-scale communication that govern how information is organized and propagates across the entire cortical network remain unknown. Numerous theories of consciousness suggest that widespread information processing across the cortex, a hallmark of the awake state, is disrupted under anesthesia.^{7,8,9,10,11,12} Determining the neural basis of consciousness requires a comprehensive understanding of large-scale information transmission during the awake state.¹³

Traveling waves, spatiotemporally organized patterns of propagating neural activity, have been observed in various cortices.¹⁴ Previous studies showed that traveling waves contributed to diverse brain functions, such as memory consolidation,¹⁵ perceptual detection,¹⁶ and working memory.^17,18 Yet, the majority of studies on stimulus-evoked traveling waves have confined their recording sites to a lower-order sensory area.^{19,20,21,22,23,24,25} Therefore, whether these waves can propagate beyond lower sensory cortices to encompass widespread cortical regions remains elusive. To address this gap, we developed high-density custom electrocorticography (ECoG) arrays that cover nearly the entire cortical surface of rats and recorded visual-evoked responses in both awake and anesthetized conditions. To extract traveling waves with minimal waveform distortion, we applied the generalized phase (GP) method^16,26 to broadband signals (4–40 Hz) (Figures 1A–1D). As a result, we found that traveling waves in the awake state propagated more extensively and stably than those under anesthesia.

Figure 1.

Capturing widespread waves and a hypothesis on the role of broadband waves

(A) A 116-channel electrocorticography (ECoG) array covering most of the right cortex. Circles represent individual electrodes, and colors denote different cortical areas based on Paxinos atlas.

(B) Example of raw single-trial waveforms of visual-evoked local field potentials in awake state.

(C) Example of a broadband signal and its corresponding generalized phase (GP). The black trace shows a magnified view of the signal from the channel highlighted by the red box in (B). The same signal after being bandpass filtered (4–40 Hz) is plotted with the color representing the GP. Stimulus onset is at 0 ms.

(D) Single-trial example of a visual-evoked traveling wave in awake state. (Top) Spatial maps of the broadband signal amplitude following stimulus onset. (Bottom) Corresponding maps of the GP at the same time points, accompanied by a gradual spatiotemporal phase shift.

(E) Schematic of the hypothesis on the information-theoretical role about traveling waves. (Left) If a traveling wave propagating from channel X to Y contributes to information transmission, it should be reflected as directed information flow, measured by transfer entropy (TE). (Right) A Venn diagram representation of TE in terms of entropy (H). The TE from channel X to Y is quantified as the information that the current state t of X provides about the future state of Y (at a time lag of τ), beyond the information that is already provided by the current state of Y (indicated by the pink shaded area).

Beyond the physical properties of traveling waves lies an information-theoretical question: whether traveling waves mediate information flow along their propagation direction (Figure 1F). Although traveling waves are thought to modulate firing probability by spatiotemporally coordinating the phase of extracellular potentials,^14,27 their role in information transfer between cortical areas remains unexplored. To address this question, we first conducted simulations and calculated transfer entropy (TE)²⁸ to evaluate predictive information flow. Notably, the modeling results showed that traveling waves are not necessarily accompanied by information transfer. However, information-theoretical analysis of our experimental data revealed that in vivo traveling waves do transfer information along the direction of wave propagation. To quantify this directional selectivity, we devised a framework, “informational tuning.” Consequently, we found that the selectivity of information tuning during wakefulness was higher than that under anesthesia.

Results

We developed an ultra-thin, 116-channel sheet ECoG electrode that covered almost the entire cerebral cortex of the rat right hemisphere (Figures 1A and S1). Using this electrode, we recorded visual evoked potentials in response to light-emitting diode stimulation of the left eye from head-fixed rats under both awake and isoflurane-anesthetized conditions (n = 45) (Figure 1B). The GP method effectively detected the major fluctuations of the raw signal, where peaks and troughs were assigned phases of 0 and π, respectively (Figure 1C). Based on the direction of the GP phase gradient, we captured traveling waves (Figure 1D). During traveling waves, consistent phase delays between adjacent electrodes were observed. To determine whether such phase delays necessarily correspond to directional information transfer (Figure 1F), we first conducted simulations before analyzing our experimental data.

Simulations reveal that traveling waves do not necessarily entail information transfer

We constructed two simulation models. The models generated event-related potential (ERP)-like waveforms with brown noise, which were designed to imitate the temporal dynamics of visual evoked responses and ongoing cortical activity. In the “connected” condition, the activity at node X propagated to node Y with a fixed time delay, representing direct transmission (Figure 2A). In the “disconnected” condition, nodes X and Y independently received the same underlying ERP-like waveform with a fixed time delay but no direct relationship (Figure 2B). For both conditions, we generated 45 sessions of data, each consisting of 100 trials, which mirrored our experimental design. Session-averaged signals revealed that the activity at node Y exhibited nearly identical waveforms in the connected and disconnected conditions, with a clear delay relative to the activity at node X. This suggested the presence of a traveling wave from X to Y (Figure 2C, top). Visual inspection confirmed that the single-trial waveforms resembled that of our ECoG signals (Figure 2C, bottom).

Figure 2.

Simulation shows that traveling waves do not guarantee information transfer

(A) Schematic of the “connected” condition. Node X receives an ERP-like waveform as stimuli and brown noise. Node Y receives the activity transmitted from channel X with a delay, plus independent noise.

(B) Schematic of the “disconnected” condition. Node X is identical to the connected condition. Node Y independently receives the same ERP-like waveform with a delay, plus independent noise.

(C) (Top) Simulated evoked potentials. Session-averaged ERPs (n = 45 sessions) for node X (violet) and node Y (connected, orange; disconnected, dotted green). Note the nearly identical waveforms for Y in both conditions. (Bottom) Example single-trial waveforms in both conditions. Shading indicates SEM. Scale bar, 100 ms.

(D) Time course of the inter-site phase coherence (ISPC) between nodes X and Y for the connected (orange) and disconnected (dotted green) conditions. Shading indicates SEM.

(E) TE for the connected condition. The left orange plot shows TE from X to Y, and the right violet plot shows TE from Y to X for each of the 45 sessions. The horizontal dashed line represents the 99th percentile of the null distribution from surrogate data. TE from X to Y was significantly above the surrogate threshold (p < 0.001, permutation t test), while TE from Y to X was not significant (p > 0.05).

(F) TE for the disconnected condition. Same plots as in (E). Neither direction showed significant TE (both p > 0.05, permutation t test).

Inter-site phase coherence analysis revealed stable phase relationships between nodes X and Y during the stimulus period in both conditions (Figure 2D). These results indicate that phase-based analyses detect a traveling wave in both scenarios but cannot distinguish between them. We then examined directional information transfer using TE.²⁸ Given the non-stationarity of evoked responses, we applied an ensemble method to calculate TE²⁹ and constructed probability distributions across trials (see STAR Methods). In the connected condition (Figure 2E), TE from X to Y was significantly higher than that of surrogate data (p < 0.001, permutation t test), whereas TE from Y to X was not significant (p > 0.05, permutation t test). In the disconnected condition (Figure 2F), TE was not significant in either direction (p > 0.05, permutation t test). These simulations indicate that the presence of traveling waves does not guarantee information transfer in the direction of wave propagation.

In vivo, awake state enhances the consistency of visually evoked traveling waves

We next examined our experimental data. We quantified the effect of the cortical state on the stability of traveling waves by assessing two types of consistency. First, to measure how consistently traveling waves were time-locked to the visual stimulus and how consistent their direction was across trials, we calculated the inter-trial wave consistency (iTWC) for each electrode (Figure S2A). The iTWC is an index that equals 1 if the direction of the broadband GP gradient is perfectly consistent across trials and 0 if it is completely random. When comparing the post-stimulus, electrode-averaged iTWC values to baseline, the anesthetized condition showed a significant increase only in the time window of 25–267 ms (Figure 3A, p = 0.0212, cluster-based permutation one-sided paired t test). By contrast, the awake condition exhibited a significant increase over a much broader time window of 20–450 ms (p < 0.001, cluster-based permutation one-sided paired t test). A direct comparison of the change in iTWC from baseline between the two states revealed significantly higher values in the awake condition than in the anesthetized condition (Figure 3B; p < 0.001, permutation paired t test). This result indicates that visual stimuli evoke more reproducible traveling waves across trials in the awake state than in the anesthetized state.

Figure 3.

Consistency of traveling waves differs between awake and anesthetized states

(A) iTWC from baseline in the awake (red) and anesthetized (blue) states. Stimulus onset is at 0 ms. The bottom horizontal line marks the time window where iTWC was significantly higher than baseline (p < 0.05, cluster-based permutation one-sided paired t test). Shaded areas represent the SEM.

(B) Post-stimulus iTWC (0–300 ms) was significantly higher in the awake state compared to the anesthetized state (p < 0.001, permutation paired t test). Gray lines connect paired data from the same session. The white circle represents the median.

(C) iSWC from baseline in the awake (red) and anesthetized (blue) states, Same as (A).

(D) Post-stimulus iSWC (0–300 ms) was significantly higher in the awake state compared to the anesthetized state (p < 0.001, permutation paired t test). Same as (B).

Second, as an index of how spatially coordinated the traveling waves are among neighboring electrodes, we calculated the inter-site wave consistency (iSWC) (Figure S2B). The iSWC is an index that equals 1 if the direction of the phase gradient is perfectly aligned between a given electrode and its eight adjacent electrodes, and 0 if the directions are completely random. Under the anesthetized condition, the post-stimulus increase in iSWC was monophasic, peaking at 66 ms and returning to baseline by 128 ms (p = 0.0340, cluster-based permutation one-sided paired t test). By contrast, under the awake condition, the iSWC showed a stepwise increase, peaked at 132 ms, and then gradually decreased, returning to baseline by 285 ms (p = 0.0080, cluster-based permutation one-sided paired t test; Figure 3C). A comparison of the change in iSWC from baseline revealed significantly higher values in the awake condition than in the anesthetized condition (p < 0.001, permutation paired t test; Figure 3D). This result indicates that the cortex in the awake state generates more spatially organized and widespread traveling waves in response to sensory input.

Spatial patterns of traveling waves exhibit state-dependent dynamics

To investigate the spatial propagation patterns of visual-evoked traveling waves, we applied hierarchical clustering to the iTWC vector fields during the 1- to 300-ms post-stimulus period (a time window in which iTWC was higher than baseline). This allowed us to extract the spatiotemporal structure of traveling waves under both awake and anesthetized conditions (see STAR Methods). The number of clusters, k, was selected as 7 from a range of 2–20 using the silhouette method (Figure S3). As a result, we identified wave motifs that were common to both states, as well as state-dependent motifs (Figure 4).

Figure 4.

Temporal evolution of wave motifs in awake and anesthetized states

(Top) Spatial patterns of traveling waves (wave motifs) within the 0- to 300-ms post-stimulus period in awake and anesthetized states, classified by hierarchical clustering. (Bottom) The identified motif at each time point is plotted for the awake (red) and anesthetized (blue) states. In the awake state, traveling waves exhibit spatiotemporal diversity persisting beyond 100 ms.

Under anesthesia, activity started with a spontaneous motif 0. Following stimulus onset, motif 1 propagating from the primary visual cortex to the secondary visual cortex was observed between 25 and 55 ms, followed by motif 2 from 56 to 80 ms. Both of these early responses were largely confined to the visual areas. In the awake state, activity also began with the spontaneous motif 0, followed by motif 1 from 18 to 42 ms post-stimulus. Subsequently, motif 3, which propagated from anterior to posterior within the visual areas, appeared from 43 to 64 ms. Next, the waves transitioned to motifs 4, 5, and 6, which propagated not only within the occipital regions but also into the temporal, parietal, auditory, and somatosensory areas. Thus, although traveling waves confined to the visual areas were observed in the early post-stimulus period under both anesthetized and awake conditions, only the awake condition showed waves that propagated beyond the visual areas to widespread brain regions in the late period. To assess the consistency of these motif dynamics across individual recording sessions, we performed hierarchical clustering independently for each session and matched the resulting motifs to the pooled reference using the Hungarian algorithm. The session-level motif sequences were largely consistent with pooled results, and correspondence substantially exceeds chance levels in both states (Figure S4).

To evaluate the state-dependent difference in the complexity of neural responses, we calculated the perturbational complexity index (PCI).^30,31 The PCI is a measure developed to distinguish between conscious (such as wakefulness) and unconscious states (such as anesthesia), and it increases as the neural response to a brain perturbation becomes wider and more diverse. Consistent with our observations of wave propagation, when we treated the visual stimulus as a perturbation, the calculated PCI was higher in the awake state than under anesthesia (p < 0.001, permutation paired t test; Figure S5). The PCI derives from integrated information theory.³² These findings suggest that traveling waves can function as an effective medium for the global informational communication that supports consciousness.

Cortical traveling waves transfer information along the propagation directions

To quantitatively evaluate whether the traveling waves observed in our experiments were accompanied by directional information transfer, we calculated the TE from a seed electrode to its eight surrounding electrodes. For this analysis, we defined the direction of wave propagation as 0 rad and plotted the TE to each surrounding electrode as a function of its counterclockwise angular distance from this reference (Figure 5A). The resulting tuning curves show that, under both awake and anesthetized conditions, TE peaked in the direction of wave propagation and decreased as the angle of the target electrode deviated from it (Figure 5B). A polar histogram of the angle of maximum TE for each session revealed a significant concentration around the 0 rad direction in both states (Figure 5C; circular V-test, p < 0.001 for both awake and anesthesia conditions, false discovery rate [FDR] corrected), indicating that information flows along the direction of wave propagation.

Figure 5.

Awake wave motifs modulate informational tuning to the wave directions

(A) The analysis for informational tuning. (Left) For a given seed electrode (black circle), transfer entropy (TE) is calculated to each of its eight neighbors (white circles). TE magnitude to each neighbor is represented by the radial distance of the green dots. The direction of traveling wave is indicated by the black arrow. (Center) The coordinate system is rotated to align the wave direction to 0 rad. (Right) An interpolated tuning curve is generated by plotting TE as a function of the angle relative to the wave propagation direction.

(B) Session-averaged TE tuning curves for the awake and anesthetized states. The x axis represents the angle from the wave propagation direction (0 rad). The gray dashed line shows the tuning curve computed from surrogate data with shuffled electrode locations. Shading indicates SEM.

(C) Polar histograms of the peak TE direction for all sessions in the awake and anesthetized states. The distribution is significantly concentrated at 0 rad in both conditions (V-test, p < 0.001 for both, FDR corrected).

(D) TE tuning curves during each of the wave motifs in the awake state.

(E) Same as (A) but during the wave motifs in the anesthetized state.

(F) Matrix showing t-values from pairwise statistical comparisons of the tuning selectivity index between all motifs. Asterisks indicate significant differences (∗p < 0.05, ∗∗p < 0.01, permutation paired t test, FDR corrected).

To test whether this selectivity of information transfer is specific to the broadband signal, we performed the same analysis on traveling waves defined in conventional narrowband frequency bands (delta [0.5–4 Hz], theta [4–8 Hz], alpha [8–16 Hz], beta [16–30 Hz], and gamma [30–90 Hz]) (Figure S6). We directly compared the selectivity of the TE tuning obtained from the broadband GP with that from each narrowband. In the awake state, the selectivity of the broadband GP was significantly higher than that of all narrowband frequency bands (permutation paired t test, p < 0.05, FDR corrected). Under anesthesia, the selectivity of the broadband GP was also higher than that of all narrowband frequency bands except the beta band (permutation paired t test, p < 0.05, FDR corrected), with which there was no significant difference in selectivity. Together, these results indicate that broadband GP traveling waves observed in the cortex are accompanied by information flow along their direction of propagation.

Enhanced selectivity of informational tuning for wave motifs in awake state

Finally, we examined whether the tuning of TE to the direction of broadband traveling waves differed for each motif identified in Figure 3. The tuning curves changed dynamically with the transition of motifs in the awake condition (Figure 5D) but remained unchanged across motifs in the anesthetized condition (Figure 5E). When we compared the tuning selectivity between motifs across the awake and anesthetized conditions, motif 5 in the awake condition exhibited significantly higher selectivity than all other motifs, including those in the anesthetized condition (Figure 5F, permutation paired t test, p < 0.05, FDR corrected). This result indicates that the cortex in the awake state uses widespread traveling waves in the late period to achieve effective information transfer. Notably, the overall TE magnitude was significantly higher under anesthesia than during wakefulness (Figure S7A), indicating that the enhanced selectivity in the awake state cannot be attributed to greater TE values. Furthermore, linear mixed-effects models controlling for signal power or signal-to-noise ratio confirmed that all motifs remained significantly less selective than awake motif 5 (Figures S7B and S7C), indicating that the selectivity differences reflect genuine differences in directional information flow. These findings were robust to the choice of time lag parameter (τ = 5, 10, 15, and 20 ms); awake motif 5 consistently exhibited the highest selectivity among all motifs across all tested values (Figure S8).

Discussion

By applying a combination of GP-based phase gradient analysis and information-theoretical analysis to large-scale ECoG data with high spatiotemporal resolution, the present study demonstrated that traveling waves function as an effective medium for information transfer along their propagation path. Compared with the anesthetized state, traveling waves in the awake state propagated over a wider cortical area. During specific wave motifs that appeared in the late period, we observed a highly directional information flow that did not emerge under anesthesia.

The spatiotemporal characteristics of broadband traveling waves differed between the awake and anesthetized states. Compared with the anesthetized state, traveling waves in the awake state exhibited less trial-to-trial variability (i.e., higher iTWC) (Figure 3B) and propagated over wider cortical areas (Figure 4). This characteristic is consistent with the recent findings.^33,34 Furthermore, our study shows that traveling waves in the awake state exhibited greater coordination with adjacent regions (i.e., higher iSWC) (Figure 3D) and that their spatial propagation patterns were more diverse compared with the anesthetized state (Figure 4). These state-dependent characteristics of visual-evoked cortical traveling waves are consistent with seminal transcranial magnetic stimulation–electroencephalography (TMS-EEG) studies to investigate effective connectivity.^35,36 These studies showed that direct cortical perturbation during wakefulness triggers complex spatiotemporal patterns of activation that propagate broadly, whereas the response becomes local and brief during loss of consciousness. The PCI is designed to quantify the spatiotemporal complexity of neural responses to a perturbation, and a higher PCI value likely reflects a greater degree of communication in the information network of the brain.^30,31 Taken together with the previous and current (Figure S5) findings in PCI, our result that the selectivity of information transfer via traveling waves was higher in the awake state suggests that communication between network nodes is tighter during consciousness.

We propose that directional selectivity of information flow via traveling waves be called “informational tuning.” The conventional concept of neuronal tuning refers to a property in which the activity of a single neuron selectively responds to specific sensory features (e.g., orientation or frequency). By contrast, informational tuning is a framework capturing the dynamic directional selectivity that is inherent in the information transmission pathways between cortical regions themselves, rather than the response characteristics of individual cells. Namely, it describes how the flow of information is efficiently sculpted through the propagation of traveling waves.

The relationship between traveling waves and information transfer has been suggested previously.^37,38 However, it has never been directly examined whether traveling waves preferentially enhance information flow along their propagation direction (the phase gradient) compared to the other directions. For example, Rubino et al. showed that the amplitude and phase of beta-band traveling waves in the motor cortex encode features of visual targets during motor tasks.³⁷ Besserve et al. reported that the gamma-band phase lead between two electrodes in the V1 of anesthetized monkeys reflects directional information, as measured by TE.³⁸ Although these studies suggest a link between traveling waves and information flow, their analyses were restricted to single-electrode phases or pairwise phase differences. Conversely, the present study directly defines the propagation direction as a “plane of waves” based on the spatial phase gradient calculated from ECoG grids and systematically relates this direction to the direction at which TE reaches its maximum. The resulting TE tuning curve, which peaks in the direction of the traveling wave (Figures 5A–5C), provides direct evidence that the traveling wave selectively transmits information along its propagation direction.

The informational tuning curves allowed us to quantify the selectivity of information transfer. This selectivity also varied with the state of consciousness. It was higher in the awake state than under anesthesia. In general, the power spectrum of cortical oscillations differs significantly between conscious states; the low-frequency band becomes dominant under anesthesia, whereas the power in high-frequency bands is associated with various cognitive variables in the awake state.^39,40,41 When we calculated informational tuning for each narrowband frequency, we revealed that in the awake state, the selectivity of the broadband GP was significantly higher than that of all narrowband frequency bands. Under anesthesia, the selectivity of the broadband GP was also higher than that of all other narrowband frequency bands, although there was no significant difference with the beta band. This superiority of the broadband signal is consistent with a previous report demonstrating that spike firing correlates more strongly with the GP of broadband local field potential than with the narrowband phase.²⁶

Although our analyses focused on broadband waves and thus cannot be directly compared with recent studies examining narrowband traveling waves,^33,34 the temporal profiles of frequency-specific power in our data are consistent with these findings. The recent studies reported that the gamma waves appeared early after visual stimulus presentation, whereas theta waves emerged later during wakefulness. In this study, gamma-band power showed an early post-stimulus peak, whereas theta-band power exhibited a pronounced increase during the late period in the awake state (Figure S9). Under anesthesia, the early gamma component was preserved, but the late theta increase was substantially attenuated. This pattern aligns with the view that the late components of evoked responses, which may involve feedback processing, contribute more to conscious awareness than the early feedforward component.^{11,12,13,34,35,36}

Which neural mechanisms might account for the profound differences observed in the spatiotemporal dynamics of traveling waves between the awake and anesthetized states? A key finding of our study is the stable emergence of late-component waves that propagate widely, observed exclusively in the awake state (Figure 6A). Such late timing suggests the involvement of time-consuming feedback loops. Indeed, feedback from higher-order areas, which sparsifies activity in cortical layers 2/3, is reportedly crucial for the propagation of late-component traveling waves (Figure 6B).²⁰ Furthermore, feedback signals contribute to the generation of calcium spikes in layer 5^42,43 and the activity of layer 5 pyramidal cells propagates to layers 2/3 within the same column,⁴⁴ which likely represents the origin of these late-component and widespread waves. Previous studies have shown that feedback signals become impaired under general anesthesia because inputs to the distal dendrites of layer 5 pyramidal cells, the primary target of top-down signals, are decoupled from the activity of the cell body.^12,45 Such disruption of feedback circuits likely leads to the absence of late-component traveling waves under anesthesia.

Figure 6.

Traveling waves link multiscale mechanisms underlying consciousness

(A) Macroscopic view: in the awake state, visual stimuli evoke globally propagating traveling waves. Under anesthesia, wave propagation remains locally restricted, reflecting a breakdown in large-scale communication (lower PCI) that theories of consciousness posit as essential. We hypothesize that such large-scale difference arises from impaired feedback from higher-order cortical areas under anesthesia.

(B) Microscopic view: top-down feedback creates a sparse network in layers 2/3 during wakefulness. This sparseness allows Ca²⁺ spikes from layer 5 pyramidal cells to propagate widely through layer 2/3. Under anesthesia, the loss of this feedback results in an unregulated, dense network where Ca²⁺ spikes in layer 5 pyramidal cells fail to trigger.

(C) Mesoscopic view: the sparse network in the awake state enables reliable neural population responses by preventing excessive excitation, resulting in stabilized wave propagation. Absence of inhibitory control under anesthesia leads to unstable wave propagation.

(D) Informational view: the stable traveling waves in the awake state consequently provide a substrate for efficient information transfer along their propagation path. Such directional information flow is significantly reduced under anesthesia.

We hypothesize that feedback regulation not only facilitates widespread wave propagation in the awake state but also contributes to highly directional information tuning by adjusting the E/I balance in the cortical network. In the awake state, feedback-mediated sparsification of cortical network activity²⁰ enhances the temporal precision and reliability of neural responses,⁴⁶ which in turn stabilizes the wave’s direction and sculpts its spatiotemporal profile more precisely (Figure 6C). This refined wave dynamics may enable the organization of efficient information routing. By contrast, the lack of feedback control under anesthesia^12,45 results in less-reliable neural responses⁴⁷ and more passive, uncontrolled wave propagation that primarily reflects feedforward connections within the visual cortex. This presumably attenuates the efficacy of information transfer via traveling waves (Figure 6D). This hypothesized mechanism is further supported by observations that the spatial and directional selectivity of V1 neurons in layer 2/3 is higher in the awake state than under anesthesia.^{48,49,50,51,52}

Together, we conclude that traveling waves serve as a vehicle for information transfer in the brain and that the emergence of reliable information routing, supported by widespread and stable waves, is a hallmark of the awake state compared to isoflurane anesthesia. The informational tuning framework introduced here offers a promising approach to elucidate how neural signal propagation translates into directional information flow across the cortex and how this flow supports consciousness and diverse cognitive functions.

Limitations of the study

First, the present work relies on a contrastive design comparing awake versus isoflurane-anesthetized conditions. To generalize our conclusions regarding the relationship between traveling wave dynamics and consciousness, it will be essential to examine how these findings extend to graded levels of awareness and different conscious states such as other anesthetized or sleeping conditions. Second, this study uses TE as a measure of information transfer. Although TE quantifies directional information flow between electrode pairs, it does not establish causal dependence. This is because pairwise TE can be influenced by common inputs from unobserved sources or other multivariate confounds. The simulation and surrogate analyses in the present study mitigate but do not entirely eliminate these concerns. Finally, the multiscale mechanisms illustrated in Figure 6 remain hypothetical at this stage. These schematics are motivated by previous cellular-level findings and represent testable predictions rather than direct evidence from the current study. Future experiments combining cellular-level manipulations with whole-brain recordings will be important to directly test these hypothesized mechanisms and to determine how they shape the traveling wave properties and TE tuning selectivity across states of consciousness.

Resource availability

Lead contact

Further information and requests for resources should be directed to and will be fulfilled by the lead contact, Yutaka Komura (komura.yutaka.6a@kyoto-u.ac.jp).

Materials availability

This study did not generate new unique reagents.

Data and code availability

• •The analyzed datasets and all original codes have been deposited at Zenodo and are publicly available as of the date of publication. The DOI assigned to this repository is https://doi.org/10.5281/zenodo.20759618.
• •This study did not generate RNA-seq or other sequencing datasets.
• •Any additional information required to reanalyze the data reported in this paper is available from the lead contact upon request.

Acknowledgments

We thank T. Okubo, M. Onodera, and M. Takahashi for technical assistance and M. Oizumi and S. Ishii for helpful discussions. This work was supported by Core Research for Evolutional Science and Technology (CREST JPMJCR1864) from Japan Science and Technology Agency, Japan, Naito Foundation, and Grant-in-Aids for Scientific Research (A) (KAKENHI 21H04423) from Ministry of Education, Culture, Sports, Science and Technology, Japan (all to Y.K.).

Author contributions

Conceptualization, K.M., K.C., and Y.K.; methodology, K.M., K.C., T.K., and T.S.; software, K.M., A.K., and K.C.; investigation, K.C. and K.M.; data curation, K.M., K.C., and A.K.; formal analysis, K.M. and Y.K.; writing draft, K.M. and Y.K.; supervision, Y.K.; project administration, Y.K.

Declaration of interests

The authors declare no competing interests.

STAR★Methods

Key resources table

REAGENT or RESOURCE	SOURCE	IDENTIFIER
Deposited data
Analyzed datasets for all figures	This paper	https://doi.org/10.5281/zenodo.20759618
Experimental models: Organisms/strains
Rat: Long Evans	Shimizu Laboratory Supplies, Japan	RGD_18337282
Software and algorithms
MATLAB R2025a	Mathworks	RRID: SCR_001622
Psychophysics Toolbox v3	Brainard53	RRID: SCR_002881
Python	Python Software Foundation	RRID: SCR_008394
Custom code for all figures	This paper	https://doi.org/10.5281/zenodo.20759618
Other
116-channel ECoG array (Parylene-C, gold electrodes)	This paper	N/A
RHD2132 amplifier board	Intan Technologies, CA, USA	https://intantech.com/products_RHD2000.html
STG4002	Multi Channel Systems MCS GmbH, Kusterdingen, Germany	https://www.multichannelsystems.com/
Stereotaxic apparatus SR-10	Narishige, Tokyo, Japan	N/A

Experimental model and subject participant details

Animals

We used ten Long Evans rats (300–400 g, 9–13 weeks old), which were obtained from Shimizu Laboratory Supplies, Japan. Only males were used; therefore, sex-based analyses were not performed. The animals were healthy and experimentally naive. Rats was individually housed in a sufficiently spacious cage within an animal facility where was maintained on a 12-hour light/dark cycle. Food and water were freely accessible at all times. All experiments were conducted during the active period and details of the procedures used in the present study are similar to those previously described.^54,55,56 After completion of all experimental procedures, rats were deeply anesthetized with medetomidine hydrochloride, midazolam, and butorphanol tartrate, and were then euthanized by transcardial perfusion with saline followed by 4% paraformaldehyde. All procedures involving animals were approved by the Animal Research Committee at Kyoto University (23-A-9), and were conducted in accordance with the guideline for the care and use of laboratory animals at the institute and ARRIVE (Animal Research: Reporting of In Vivo Experiments) guidelines.

Multi-electrode array

We developed a custom multi-electrode array to cover a wide area of the rat cortex (Figure S1). This array consisted of 116 gold electrodes (diameter: approx. 113 μm) embedded in flexible and biocompatible Parylene-C [poly(chloro-paraxylylene)] sheet. The thickness of a base layer was 10 μm. It was designed so that, when placed on the cortical surface, each electrode was positioned at the intersection of a 1-mm grid. A previous study using a ECoG array made of similar material reported that meshing the Parylene-C sheet improves its conformity to curved surfaces.⁵⁷ On the basis of this finding, we designed the parts of the Parylene-C sheet corresponding to the highly curved areas of the rat brain using a partial claw-like structure to enhance its fit. The arrays were fabricated using photolithography process as shown in our previous work.⁵⁸ The arrays were connected to a custom printed circuit board (PCB) with four 36-pin miniature connectors (Omnetics Connector Corporation, MN, USA). The ground and reference wires were also attached to the PCB.

Surgery

All surgical procedures were performed under general anesthesia with isoflurane (4% for induction, 1.5%–3.0% for maintenance) while the animal was secured in a stereotaxic apparatus (SR-10, Narishige, Tokyo, Japan). The body temperature of each animal was maintained at ≥37.5°C using a closed-loop heating pad (TCAT-2LV, Physitemp, Clifton, NJ, USA), and pulse was monitored in real time as a vital sign. The anchor screws (diameter: 1 mm, length: 3 mm) were implanted into the skull and secured with dental adhesive (Super Bond C&B, Sun Medical, Shiga, Japan). A craniotomy was then performed over the right hemisphere (anteroposterior, +6 mm to −10 mm; mediolateral, +0.5 mm to just superior to the zygomatic process; relative to bregma). The multi-electrode array was placed on the cortex with its medial edge parallel to the midline (the innermost electrode at +1.5 mm lateral from the midline, and the rearmost electrode at +0.5 mm anterior to the transverse sinus). A chamber frame for head fixation (CFR-1, Narishige, Tokyo, Japan) was secured onto the skull with dental cement for the awake recordings.

Method details

Experimental procedures

Experiments were conducted after a post-surgery recovery period and an acclimation period for head fixation. Using the above ECoG array, we recorded neural activities in awake and anesthetized conditions. For each session (n = 45 sessions), recording experiments in two conditions were conducted in separate blocks. In anesthetized blocks, we maintained isoflurane at 0.5%–2.0% and confirmed the anesthetic state by monitoring the absence of motor reflexes. In awake blocks, we confirmed the awake state by checking motor responses and power spectrum in LFPs. For each trial, visual stimulus (duration: 50 ms, inter-stimulus interval: 5.0–6.0 s) was delivered to the left eye of the rat using a white LED (φ 5 mm, 30° beam) positioned 2 cm from the front of the eye. The light stimulus was controlled using an STG4002 (Multi Channel Systems MCS GmbH, Kusterdingen, Germany), and the experiment was controlled using MATLAB (MathWorks Inc., USA) with Psychtoolbox.⁵³

Electrophysiological recordings

Visual responses across were measured using the 116-channel multi-electrode array. The signals were amplified using an RHD2132 amplifier board (Intan Technologies, Los Angeles, CA, USA) and recorded with an Open Ephys Acquisition Board. The sampling frequency was 1 kHz. A screw over the left cerebellum contacting the dura mater served as the reference electrode. Signal preprocessing was performed using MNE-Python and custom-built Python code. Trials with motion artifacts were excluded by visual inspection, leaving 100 trials per session for both the awake and anesthetized conditions. When data from all sessions were analyzed together, the signals from each electrode were grouped into 1 mm² grid units based on their stereotaxic coordinates. For two animals, the electrode positions were observed to be shifted by more than 0.5 mm from the intended location; for these animals, the electrode positions were corrected in the anteroposterior and mediolateral directions before data aggregation.

Quantification and statistical analysis

Statistical analysis

All analyses in this study were performed using Matlab 2024b. All statistical tests were performed on n = 45 sessions from 10 rats, and reported p-values can be found in the figure legends and main text for each data comparison. The significance level was set at p < 0.05 for all tests. To compare iTWC and iSWC against baseline (Figures 3A and 3C), we used a cluster-based permutation approach. Clusters were defined as consecutive time points where one-sided paired t-tests yielded p < 0.05. The sum of t-values within each cluster was then compared against a null distribution generated from 1000 Monte Carlo permutations to calculate the final p-value. The ft_timelockstatistics function from the FieldTrip toolbox was used for this analysis. For comparisons between awake and anesthetized conditions (Figures 3B and 3D), and for comparisons of tuning selectivity indices between wave motifs (Figure 5F), we used permutation-based paired t-tests with 5000 shuffles to generate the null distribution. When multiple comparisons were performed, p-values were corrected using the FDR method. To test whether the peak direction of TE tuning curve was significantly concentrated around the wave propagation direction (0 rad), we applied the circular V-test (Figure 5C). For the simulation study (Figures 2E and 2F), we assessed the statistical significance of TE by comparing observed values against surrogate data generated by trial-shuffling the activities of nodes X and Y, repeated 1000 times to establish the null distribution. To show the TE tuning under spatially shuffled conditions (Figure 5B), we generated surrogate data by randomly shuffling adjacent electrode locations across the ECoG array while preserving the temporal structure of the signals. Asterisks in Figure 5F indicate statistical significance (p < 0.05, p < 0.01) based on permutation paired t-tests with FDR correction.

GP calculation

To extract the phase information of the visual response, the GP was calculated according to the following procedure.¹⁶ Broadband signals of 4–40 Hz were extracted from the data spanning −2500 to 2499 ms relative to stimulus onset, using a second-order Butterworth filter. This frequency range was selected following previous studies employing the GP method.^16,20 These studies excluded lower-frequency components (below 3–5 Hz) and higher-frequency components (above 40–50 Hz) to avoid phase distortions, thereby enabling accurate detection of the major fluctuations in raw field potentials. The broadband GP approach has been shown to be more predictive of spike timing and animal behavior than narrowband phase approach.^16,26 The GP was calculated using generalized_phase_vector.m (available at: https://github.com/mullerlab/generalized-phase) by detecting and interpolating the time points at which negative frequencies were observed.

Clustering to extract the spatiotemporal structure of evoked waves

Hierarchical clustering was used to investigate whether visual evoked potentials form systematically organized spatiotemporal traveling waves and to determine whether their spatiotemporal patterns are similar between states (Figure S3). For the 1–300 ms post-stimulus period, we generated a 232-dimensional vector at each time point by concatenating the x and y components of the session-averaged vectors from all 116 channels. This resulted in a (232, 300) matrix. After concatenating the data matrices from the awake and anesthetized conditions, hierarchical clustering was performed using Euclidean distance and Ward’s method. Time points with high similarity in their phase gradient consistency maps were thus classified into the same cluster. The optimal number of clusters, k = 7, was selected from a range of 2–20 using the silhouette method.

To assess the consistency of the wave-motif temporal dynamics across recording sessions, we performed hierarchical clustering separately for each of the 45 sessions. The resulting session-specific clusters were subsequently matched to the seven pooled motifs (Figure 4) using the Hungarian algorithm, which finds the optimal one-to-one assignment by minimizing the total Euclidean distance between session-level and pooled cluster centroids. At each time point, we computed the motif frequency (number of sessions assigned to each motif). The chance level for motif frequency was 45/7 ≈ 6.43 sessions (Figure S4).

TE analysis

To quantify directional information flow between adjacent electrodes, we used TE,^28,59,60,61 an information-theoretic measure that quantifies statistical relationship in the Wiener–Granger sense. Unlike simple correlation-based measures, TE specifically measures how much the past activity of a source signal X reduces uncertainty about the future state of a target signal Y, beyond what Y’s own past provides.

For each session (n = 45 sessions), we computed TE between all pairs of the seed electrode and eight adjacent electrodes at 1 ms temporal resolution across the entire post-stimulus period, resulting in a comprehensive spatiotemporal map of information flow. Electrodes located on the edges of the ECoG sheet were excluded from the analysis. Visual responses exhibit highly non-stationary dynamics, with both signal amplitudes and information flow changing rapidly over time following stimulus onset. Given the non-stationary nature of the signals, we used an ensemble method to estimate probability distributions across trials within each session at each time point.²⁹ This ensemble approach enabled the robust estimation of probability distributions by leveraging trial-to-trial variability, thereby allowing us to track time-resolved changes in information transfer without requiring stationarity assumptions over time. TE calculations were performed using ECoG amplitude without GP filtering to prevent filtering artifacts.^62,63 Furthermore, TE was normalized to 0–1 using the mutual information between electrode pairs.

We defined TE from signal X to signal Y at time t as

$$\begin{array}{c}{TE}_{X\to Y}\left(t\right)=\\ \sum _{Y_{future\left(t\right)},{\mathit{Y}}_{\mathit{p}\mathit{a}\mathit{s}\mathit{t}\left(\mathit{t}\right)}^{\left(\mathit{m}\right)},{\mathit{X}}_{\mathit{p}\mathit{a}\mathit{s}\mathit{t}\left(\mathit{t}\right)}^{\left(\mathit{m}\right)}}p\left(Y_{future\left(t\right)},{\mathit{Y}}_{\mathit{p}\mathit{a}\mathit{s}\mathit{t}\left(\mathit{t}\right)}^{\left(\mathit{m}\right)},{\mathit{X}}_{\mathit{p}\mathit{a}\mathit{s}\mathit{t}\left(\mathit{t}\right)}^{\left(\mathit{m}\right)}\right)\log \frac{p\left(Y_{future\left(t\right)}|{\mathit{Y}}_{\mathit{p}\mathit{a}\mathit{s}\mathit{t}\left(\mathit{t}\right)}^{\left(\mathit{m}\right)},{\mathit{X}}_{\mathit{p}\mathit{a}\mathit{s}\mathit{t}\left(\mathit{t}\right)}^{\left(\mathit{m}\right)}\right)}{p\left(Y_{future\left(t\right)}|{\mathit{Y}}_{\mathit{p}\mathit{a}\mathit{s}\mathit{t}\left(\mathit{t}\right)}^{\left(\mathit{m}\right)}\right)}\end{array}$$ (Equation 1)

$$\begin{array}{c}past\left(t\right)=t-\frac{1}{2}\tau \end{array}$$ (Equation 2)

$$\begin{array}{c}future\left(t\right)=t+\frac{1}{2}\tau \end{array}$$ (Equation 3)

where τ and m denote the time lag (ms) and embedding dimensions of the ECoG signal. Equation 1 represents the deviation from the Markov condition calculated by Kullback–Leibler divergence between the two probability distributions.^28,59 In accordance with previous studies, we applied a commonly used approximation.^64,65,66 Instead of incorporating the full past activity ${\mathit{X}}_{\mathit{p}\mathit{a}\mathit{s}\mathit{t}\left(\mathit{t}\right)}^{\left(\mathit{m}\right)}$ and ${\mathit{Y}}_{\mathit{p}\mathit{a}\mathit{s}\mathit{t}\left(\mathit{t}\right)}^{\left(\mathit{m}\right)}$, we used single-latency observations at time ${\mathit{X}}_{\mathit{p}\mathit{a}\mathit{s}\mathit{t}\left(\mathit{t}\right)}^{\left(\mathit{m}\right)}=X_{past\left(t\right)}$ and ${\mathit{Y}}_{\mathit{p}\mathit{a}\mathit{s}\mathit{t}\left(\mathit{t}\right)}^{\left(\mathit{m}\right)}=Y_{past\left(t\right)}$. This approximation reduced Equation 1 to

$$\begin{array}{c}{TE}_{X\to Y}\left(t\right)=H\left(Y_{future\left(t\right)}|Y_{past\left(t\right)}\right)-H\left(Y_{future\left(t\right)}|Y_{past\left(t\right)},X_{past\left(t\right)}\right)\end{array}$$ (Equation 4)

where H(Y_future(t)|Y_past(t)) represents the conditional entropy of Y at time future(t) ms given its past(t) ms states, and H(Y_future(t)|Y_past(t),X_past(t)) represents the conditional entropy of Y when the pasts of both Y and X are observed. Thus, TE quantifies the reduction in uncertainty about Y_future(t) by observing X_past(t) in addition to Y_past(t).

Using the relationship between conditional entropies and joint entropies:

$$\begin{array}{c}H\left(Y_{future\left(t\right)}|Y_{past\left(t\right)}\right)=H\left(Y_{future\left(t\right)},Y_{past\left(t\right)}\right)-H\left(Y_{past\left(t\right)}\right)\end{array}$$ (Equation 5)

TE can be rewritten as:

$$\begin{array}{c}{TE}_{X\to Y}\left(t\right)=\\ H\left(Y_{future\left(t\right)},Y_{past\left(t\right)}\right)-H\left(Y_{past\left(t\right)}\right)-H\left(Y_{future\left(t\right)},Y_{past\left(t\right)},X_{past\left(t\right)}\right)+H\left(Y_{past\left(t\right)},X_{past\left(t\right)}\right)\end{array}$$ (Equation 6)

This corresponds to the shaded area in Figure 1.

In addition, TE can be expressed using conditional mutual information I:

$$\begin{array}{c}{TE}_{X\to Y}\left(t\right)=I\left(Y_{future\left(t\right)};X_{past\left(t\right)}|Y_{past\left(t\right)}\right)\end{array}$$ (Equation 7)

which emphasizes that TE measures the information shared between X_past(t) and Y_future(t) that is not already explained in Y_past(t).

Given that traveling wave speeds at the mesoscopic scale typically range from 0.1–0.8 mm/ms, and adjacent electrodes are separated by 1 or √2 mm, we set the time lag τ to 10 ms. For the entropy estimation, we used a parametric approach, which enables TE calculation at 1 ms resolution across all electrode pairs within feasible time and provides statistical robustness given our moderate sample sizes rather than non-parametric alternatives.⁶⁷ In simulation, TE was also computed at 1 ms temporal resolution using the ensemble method across trials within each session. Significance was assessed using surrogate data generated by trial-shuffling the activities of X and Y, which was repeated 1000 times to establish the null distribution. The 99th percentile of this distribution served as the significance threshold (p < 0.01).

TE tuning curve

To examine whether information flows preferentially along the direction of traveling waves, we constructed TE tuning curves that were aligned to the phase gradient direction. For each seed electrode (excluding edge electrodes), we calculated TE to its eight adjacent electrodes, positioned at π/4 rad intervals. At each time point t, these TE values were plotted in polar coordinates, where the radial distance represents TE value and the angular position (θ) corresponds to the relative electrode position. We then rotated these data points to align with the phase gradient vector at the seed electrode, setting the wave propagation direction to 0 rad. Linear interpolation between the eight data points (spaced at π/4 rad intervals) generated continuous tuning curves from 0 to 2π rad, where 0 rad represents information flow along the wave direction and π represents information flow along the opposite direction. For inter-motif comparisons (Figure 5), tuning curves were normalized to the unit area for each electrode, and were then averaged across electrodes and time windows within each motif to obtain tuning curves per session.

To evaluate the selectivity of TE tuning curves, we calculated the selectivity index as follows:

$$\begin{array}{c}Selectivityindex=\frac{{TE}_{pref}-{TE}_{nonpref}}{{TE}_{pref}+{TE}_{nonpref}}\end{array}$$ (Equation 8)

TE_pref represents the mean value within 0 ± $\frac{\pi }{4}$ rad in the TE tuning curve, whereas TE_nonpref represents the mean value of $-\frac{\pi }{2}$ ±$\frac{\pi }{4}$ rad and $\frac{\pi }{2}$ ± $\frac{\pi }{4}$ rad.

Confound-control analysis for TE tuning selectivity

To test whether the observed differences in TE tuning selectivity between motifs could be explained by differences in signal amplitude or signal-to-noise ratio (SNR), rather than by genuine differences in directional information flow, we performed the following control analyses.

TE magnitude comparison

TE magnitude was computed as the mean TE across all angular directions, averaged over time points within all motif windows and electrodes for each session. This quantity represents the overall strength of information flow prior to the unit-area normalization used in the tuning curve analysis. Awake and anesthetized conditions were compared using a permutation paired t-test.

Signal power and SNR

Signal power was defined as the mean squared amplitude of the raw ECoG signal, averaged across trials, time points within each motif window, and electrodes. The SNR was defined as the ratio of the trial-averaged power to the across-trial standard deviation of instantaneous power, averaged over electrodes.

Linear mixed-effects models

We used linear mixed-effects models (LMMs) to assess whether motif-dependent differences in TE tuning selectivity persisted after controlling for signal power or SNR. 315 observations (45 sessions × 7 motifs: 5 awake + 2 anesthesia) were used. The model was: selectivity ∼ power + motif + (1|rat/session), which included signal power as a continuous covariate, motif as a categorical fixed effect, and nested random intercepts for rat and session. Awake motif 5, which exhibited the highest selectivity, served as the reference category. p-values for motif coefficients were corrected using the FDR method. An analogous model was fitted with SNR replacing power as the covariate.

Robustness of TE results to time lag parameter

To confirm that the main findings were not dependent on the specific choice of time lag τ = 10 ms, we repeated the TE tuning analysis for τ = 5, 10, 15, and 20 ms (Figure S8).

Traveling wave analysis

To capture traveling waves evoked by visual stimuli, we performed the analysis as follows. We calculated the spatial gradient for the phase at each electrode and time point¹⁹:

$$\begin{array}{c}\overrightarrow{g}\left(x,y,t,i\right)\equiv -\nabla \phi \left(x,y,t,i\right)\end{array}$$ (Equation 9)

where x and y represent the anteroposterior and mediolateral coordinates of the electrode, respectively, t represents a given time point, and i represents the trial. The phase differentiation to obtain the spatial gradient of phase ∇φ was implemented using multiplication in the complex plane.

To evaluate the cross-trial consistency and temporal locking of traveling wave direction, we calculated the following for each electrode and time point:

$$\begin{array}{c}{\overrightarrow{G}}_{mean}\left(x,y,t\right)\equiv \frac{1}{N}{\sum }_{i=1}^N\frac{\overrightarrow{g}\left(i\right)}{\left|\overrightarrow{g}\left(i\right)\right|}\end{array}$$ (Equation 10)

$$\begin{array}{c}\text{iTWC}\left(x,y,t\right)=\left|{\overrightarrow{G}}_{mean}\left(x,y,t\right)\right|\end{array}$$ (Equation 11)

Here, N = 100 is the number of trials. The magnitude of the resulting vector, which represents the alignment of phase gradient directions across trials, was defined as the iTWC. The angle of ${\overrightarrow{G}}_{mean}$ was defined as the wave direction. For visualization, these vectors were averaged across sessions. iTWC ranges from 0 (a completely uniform distribution of directions) to 1 (perfectly consistent direction across all trials).

To quantify the spatial coherence of traveling wave direction, we defined iSWC as the directional consistency between a seed electrode and its eight neighbors:

$$\begin{array}{c}\text{iSWC}\left(x,y,t\right)=\left|\frac{1}{9}{\sum }_{k=1}^9{e}^{i{\psi }_{tk}}\right|\end{array}$$ (Equation 12)

where i is the imaginary unit, e is Euler’s number, k represents the index of adjacent electrodes, including the seed electrode, and ψ_tk represents the wave direction (in radians) at electrode k at time t. iSWC equals 1 if the wave direction is perfectly aligned between a given electrode and its eight adjacent electrodes, and 0 if it is completely random.

To quantify whether signals generated by simulation at nodes X and Y have consistent phase differences across trials, we calculated inter-site phase coherence (ISPC). ISPC was calculated for GP according to the following equation for each session:

$$\begin{array}{c}{\text{ISPC}}_{\mathrm{t}}=\left|\frac{1}{n}{\sum }_{r=1}^n{e}^{i\left({\theta }_{tr}-{\varphi }_{tr}\right)}\right|\end{array}$$ (Equation 13)

where n is the number of trials, and θ_tr and ϕ_tr represent the phases of node X and node Y, respectively, for the r-th trial at time t.

Simulation of neural signal propagation

To test whether consistent temporal delays between two nodes necessarily imply directional information transfer, we performed numerical simulations comparing two scenarios.

We simulated 45 sessions of paired time-series data (X and Y), each containing 100 trials. Each trial was 2.4 s in duration, sampled at 1000 Hz. An ERP-like waveform was generated for each trial by modulating a 10 Hz sine wave with a Gaussian envelope. To simulate the trial-to-trial variability observed in neural recordings, we introduced amplitude variations (3% standard deviation) and latency jitter (3 ms standard deviation) to the ERP waveform on each trial. The base ERP waveform for trial i was constructed as:

$$\begin{array}{c}{ERP}_i\left(t\right)=A_i\exp \left(-\frac{{\left(t-t_{peak}-{\delta }_i\right)}^2}{2{\sigma }^2}\right)\sin \left(2\pi f\left(t-t_{peak}-{\delta }_i\right)\right)\end{array}$$ (Equation 14)

where A_i = 1 + 0.03ε_amp represents trial-specific amplitude modulation with ${\epsilon }_{amp}\sim \mathcal{N}\left(0,1\right),t_{peak}=1.2\mathrm{s}$ represents the peak time, δ_i = 0.003ε_lats represents latency jitter with ${\epsilon }_{lat}\sim \mathcal{N}\left(0,1\right),\sigma =0.05\mathrm{s}$ represents the Gaussian envelope width, and f = 10 Hz represents the oscillation frequency. Brown noise was added to approximate the spectral characteristics of cortical activity, and the noise level was adjusted to produce signals resembling those observed in our ECoG recordings.

We implemented two conditions that produced similar temporal relationships but differed in their underlying structure. In the connected condition, activity at node Y was generated from past activity at node X plus independent brown noise:

$$\begin{array}{c}{X}_{con}\left(t\right)=ERP\left(t\right)+{\eta }_X\left(t\right)\end{array}$$ (Equation 15)

$$\begin{array}{c}{Y}_{con}\left(t\right)=c{X}_{con}\left(t-\tau \right)+{\eta }_Y\left(t\right)\end{array}$$ (Equation 16)

where τ = 30 ms represents the propagation delay, c = 0.8 is the coupling strength, and η_X(t) and η_Y(t) represent independent brown noise processes. This model represents a scenario in which there is a direct anatomical connection from node X to node Y.

In the disconnected condition, both X and Y were independently generated from the base ERP waveform, with Y receiving the input delayed by τ = 30 ms:

$$\begin{array}{c}{X}_{dis}\left(t\right)=ERP\left(t\right)+{\eta }_X\left(t\right)\end{array}$$ (Equation 17)

$$\begin{array}{c}{Y}_{dis}\left(t\right)=cERP\left(t-\tau \right)+{\eta }_Y^{\prime }\left(t\right)\end{array}$$ (Equation 18)

This model represents a scenario in which both signals are driven by an external input with different latencies, thereby producing temporal delays without a direct connection from node X to node Y. Importantly, activity at node X was generated identically in both conditions (X_con(t) = X_dis(t)), thus ensuring that differences in information transfer were attributed solely to the different generative mechanisms for Y.

PCI calculation

To quantify the complexity of VEPs, we calculated the perturbational complexity index based on state transitions (PCIst).³¹ For the PCIst calculation, we utilized code from https://github.com/renzocom/PCIst. First, singular value decomposition was performed on the VEP for each electrode, yielding principal components explaining 99% of the VEP variance. The signal-to-noise ratio (SNR) was then calculated for these principal components, with only those exceeding 1.5 being selected for analysis. Subsequently, the number of state transitions (NST) was determined for the distance matrix of each principal component. Finally, the sum of the increase in NST for the response interval relative to the baseline interval across all analyzed principal components was designated as the PCIst.

Theta and gamma band power analysis

To examine the frequency-specific cortical dynamics, we computed instantaneous power in the theta and gamma bands based on the recent findings.^33,34 For each trial, the raw ECoG signals were bandpass-filtered using a second-order Butterworth filter applied with zero-phase filtering (MATLAB filtfilt). The analytic signal was then obtained via the Hilbert transform, and instantaneous power was computed as the squared magnitude of the analytic signal. Power was averaged across 100 trials and z-scored for each session and electrode, using the mean and standard deviation of the pre-stimulus baseline period (−800 to −300 ms). The z-scored power was then averaged across all electrodes within each session.

Additional resources

This study did not generate additional resources beyond those described in the STAR Methods sections.