Neural assemblies coordinated by cortical waves are associated with waking and hallucinatory brain states

SUMMARY

The relationship between sensory stimuli and perceptions is brain-state dependent: in wakefulness, suprathreshold stimuli evoke perceptions; under anesthesia, perceptions are abolished; and during dreaming and in dissociated states, percepts are internally generated. Here, we exploit this state dependence to identify brain activity associated with internally generated or stimulus-evoked perceptions. In awake mice, visual stimuli phase reset spontaneous cortical waves to elicit 3–6 Hz feedback traveling waves. These stimulus-evoked waves traverse the cortex and entrain visual and parietal neurons. Under anesthesia as well as during ketamine-induced dissociation, visual stimuli do not disrupt spontaneous waves. Uniquely, in the dissociated state, spontaneous waves traverse the cortex caudally and entrain visual and parietal neurons, akin to stimulus-evoked waves in wakefulness. Thus, coordinated neuronal assemblies orchestrated by traveling cortical waves emerge in states in which perception can manifest. The awake state is privileged in that this coordination is reliably elicited by external visual stimuli.

Graphical Abstract

In brief

During wakefulness, visual stimuli elicit perceptual experiences, while under the influence of hallucinogens, perceptual experiences unrelated to stimuli arise spontaneously. Aggarwal et al. show that in awake mice, visual stimuli elicit cortical traveling waves. Under ketamine—a potent hallucinogen—similar cortical waves arise spontaneously and are unaffected by stimuli.

INTRODUCTION

Visual stimuli appear to us as integrated scenes with an arrangement of objects, each one of which is a constellation of multiple features, such as position, shape, texture, and color. This integration happens subconsciously and is a sine qua non of our perceptual experiences. Neurons encoding different features of the sensory world, however, are distributed among many cortical regions. Thus, to give rise to integrated perceptual experiences, neuronal activity across multiple cortical areas must be coordinated. Zero phase lag synchrony across different regions has long been hypothesized to play a role in mediating this coordination.^1-6 However, recent studies revealed that oscillatory brain signals exhibit a rich repertoire of phase relationships and can resemble traveling waves traversing the cortex in different directions and at different frequencies.^7,8

Mounting evidence suggests that traveling waves coordinate activity within neuronal networks involved in sensory perception. Subthreshold waves of synaptic inputs are elicited in the primary visual cortex (V1) by stimuli outside the receptive field.⁹ Traveling waves are reliably evoked by stimuli^10-14 and coordinate firing of individual neurons across different cortical regions,¹¹ switch during spontaneously alternating perceptions during binocular rivalry,¹⁵ are associated with perceptual echoes,¹⁶ and can be used to implement predictive coding in naturalistic settings.^17,18 However, several observations complicate the relationship between traveling waves and perception. Traveling waves are observed in states where conscious perception occurs reliably, such as during normal wakefulness,^10-12,19 but also during sleep^20,21 and general anesthesia.^19,22 Traveling waves are evoked by sensory stimuli^11,12,23 but can also arise spontaneously.^23,24 Yet, a detailed understanding of the essential differences between spontaneous and evoked traveling waves in different states of consciousness is lacking.

To address this knowledge gap, here we study spontaneous and visual evoked traveling cortical waves and their relationship to firing of individual neurons in the visual and parietal cortices in mice across three distinct states of consciousness. During wakefulness, sensory perceptions are reliably evoked by suprathreshold stimuli. Under isoflurane anesthesia, subjects are unresponsive to all stimuli, exhibit slowing of cortical activity, and rarely report having perceptual experiences.²⁵ During the third state of ketamine-induced dissociative anesthesia, subjects are unresponsive to external stimuli but exhibit wake-like cortical levels of activity^26-30 and report having vivid hallucinations.^31-36 While it is difficult to be certain about the specific timing of these hallucinations, the conjunction of behavioral reports and neurophysiological recordings suggests that these perceptual experiences likely occur during ketamine-induced unresponsiveness.

While investigations of the neurophysiological underpinnings of hallucinations and dreams is of fundamental importance for the study of perception in general, these phenomena are difficult to study in animal models. Here, we chose to use ketamine to induce a dissociated state in mice based on several lines of evidence. Ketamine, at both anesthetic and sub-anesthetic doses, reliably induces sensory hallucinations in humans.^31-36 Ketamine-induced neuronal oscillations in the mouse³⁷ and human³⁸ brain are similar. Neuronal oscillations in humans who experience sensory hallucinations during the prodromal stage of seizures³⁷ are also similar to those induced by ketamine. While most conventional sedatives and anesthetics induce brain activity resembling slow-wave sleep,³⁹ activity induced by ketamine has some similarities to rapid eye movement (REM) sleep⁴⁰—a sleep stage associated with vivid dreaming.⁴¹ Much like REM sleep, the ketamine-induced state is associated with decreased responsiveness to external stimuli.^27,37 Stereotypical behaviors exhibited by mice under ketamine share similarities with behavioral signatures of other hallucinogens in rodents.²⁷ Thus, while one can never directly test for the existence of hallucinations, or any other subjective experience,⁴² in an animal model, the ketamine-induced neurophysiological state in mice exhibits essential similarities to states associated with dreaming and hallucinations in humans.

RESULTS

Head-fixed mice (n = 32) received stimuli consisting of either a 100 ms full-screen white flash of varying luminance (STAR Methods) or a 10 ms flash of a green LED (Figure 1A, STAR Methods). A 64-channel electrocorticography (ECoG) grid placed over the dural surface of the contralateral (left) hemisphere was used to record local field potentials (LFPs) from the visual, association, retrosplenial, somatosensory, and motor/frontal areas. In a subset of animals (n = 14), two 32-channel laminar probes were inserted perpendicularly into the cortex through holes in the ECoG grid to target V1 and the posterior parietal area (PPA). In these animals, histological localization of the laminar probes was used to determine the stereotaxic locations of ECoG electrodes and enabled comparisons of activity across mice (STAR Methods).

Figure 1. Spontaneous cortical waves exist during wakefulness, under isoflurane, and under ketamine, but are exclusively phase reset by visual stimuli in the awake brain.

(A) Experimental design: 64-channel electrocorticography (ECoG) grid used to record local field potentials (LFPs) from the cortical surface of the left hemisphere (n = 32 mice). Thirty-two-channel laminar probes were placed in the primary visual cortex (V1) and the posterior parietal area (PPA) in n = 14 mice. Stimuli consisted of 100 ms of screen flashes (44% brightness, 33 cd/m²) delivered by a CRT monitor placed in front of the right eye (STAR Methods).

(B) Five seconds of spontaneous V1 LFPs in the same mouse in the awake state (top), under isoflurane (middle), or under ketamine (bottom).

(C) Forty single trials (gray) and average (red) visual evoked potentials (VEPs) from a representative mouse during wakefulness (left), under isoflurane (middle), and under ketamine (right). The vertical green line denotes stimulus onset.

(D) Stimulus-evoked changes in spectral power (relative to pre-stimulus baseline) in V1 averaged over animals during wakefulness (left), under isoflurane (middle), or under ketamine (right). The vertical gray line denotes stimulus onset.

(E) Intertrial phase coherence in V1 averaged over animals during wakefulness (left), under isoflurane (middle), or under ketamine (right). The vertical gray line denotes stimulus onset.

(F) Single trial of LFPs filtered at 3–6 Hz recorded in a column of electrodes (each row is a single channel) at −2.0 mm lateral from bregma from the same representative mouse as in (A).

(G) Intertrial average VEP filtered at 3–6 Hz from the same representative mouse as in (A) and (F).

To determine how the traveling waves of cortical activity evoked by visual stimuli¹¹ are affected by the state of the brain, we recorded visual evoked activity in the same mice during wakefulness, under isoflurane, and under ketamine (STAR Methods; Figure S1). Spontaneous cortical activity during these three states is shown in Figure 1B. Consistent with previous findings,^27,43 isoflurane increases low-frequency oscillations, while brain activity under ketamine is similar to that observed in the awake state, albeit with moderately increased gamma oscillations (Figures 1B and S1).

Waves of 3–6 Hz are present in spontaneous activity in all states, but visual evoked 3–6 Hz waves are observed only during the waking state

Prior work¹¹ has shown that the visual evoked potential (VEP) in mice can be decomposed into two oscillations: early gamma (30–50 Hz) oscillations and late 3–6 Hz oscillations. The 3–6 Hz oscillations are a dominant rhythm in the rodent V1 and share essential similarities with the alpha oscillations in the visual system of primates.^44,45 Thus, we first investigated the power in the 30–50 and 3–6 Hz ranges evoked by stimuli delivered at six different brightness levels during wakefulness as well as under isoflurane and ketamine (STAR Methods). Figure 1C shows that the early gamma oscillations (highlighted in the time-frequency analysis in Figure 1D) are consistently observed in response to stimuli with intermediate brightness within the first 100 ms of the stimulus in all three states. Gamma power (Figure 1D) in the first 100 ms is increased during wakefulness and under ketamine as assessed by comparing power in the 800–600 ms prior to stimulus onset with the power in the window spanning 50–150 ms after the stimulus delivered at one of six levels (Kruskal-Wallis: ketamine, df = 6, χ² = 24.7, p = 3.6140e–4; awake, df = 6, χ² = 47.16, p = 1.73e–8). Increase in gamma power under isoflurane did not reach statistical significance (Kruskal-Wallis: df = 6, χ² = 2.39, p = 0.8). However, bright LED stimuli reliably evoke gamma power under isoflurane and other anesthetics.⁴³ A similar analysis was performed for the 3–6 Hz frequency band, this time using the 200–400 ms window after the stimulus. The power in the 3–6 Hz range was significantly increased in all three states after the presentation of the visual stimulus (Kruskal-Wallis: df = 2, χ² = 19.24, p = 6.7e–5). Post hoc analysis (Dunn-Sidak) confirmed a larger increase in 3–6 Hz power in the awake state than under isoflurane (p = 0.0003) or under ketamine (p = 0.0007), but failed to detect differences between ketamine and isoflurane (p = 0.99). Thus, to a variable degree, spectral power both in the gamma and in the 3–6 Hz range is increased following presentation of the visual stimuli during normal wakefulness and under the influence of pharmacological agents that disrupt perception.

Analysis of power changes does not directly address whether the visual stimulus elicits spatially and temporally coherent oscillations. To test this possibility, we compared the intertrial phase coherence (ITPC) evoked by visual stimuli during wakefulness and under isoflurane or ketamine in V1. Post-stimulus gamma ITPC induced by intermediate-intensity stimuli under isoflurane is reduced relative to wakefulness and ketamine. More intense stimuli, however, reliably evoked early coherent gamma under isoflurane (Figure S2). With some notable exceptions,⁴⁶ multiple studies^11,47 have shown that these gamma oscillations originate in cortical input layer 4 and then propagate to supra- and infragranular layers. Consistent with this, the initial layer 4 sink supra- and infragranular sources pattern is observed in all three states in V1 (Figure S3). Thus, in all studied states, V1 continues to receive and respond to inputs from the thalamus. Inputs into the higher-order parietal area (PPA) and neuronal responses to stimuli in both V1 and the PPA are also observed in all three states (Figures S3 and S4).

The 3–6 Hz ITPC robustly increased after the stimulus in awake mice compared with mice under both ketamine and isoflurane. No differences in 3–6 Hz ITPC were detected between isoflurane and ketamine (Kruskal-Wallis: df = 2, χ² = 20.77, p = 3.09e–5; Dunn-Sidak post hoc comparisons: isoflurane [Iso] vs. awake, p = 0.0001; ketamine [Ket] vs. awake, p = 0.0016; Ket vs. Iso, p = 0.8621) (Figures 1D and 1E). This population-based analysis of evoked ITPC in the 3–6 Hz range is closely mirrored at the level of individual animals and is also observed in the PPA in the awake brain (Figure S5).

Because the stimulus-evoked coherence of the 3–6 Hz oscillation is strongly affected by the state of the animal, we focus the rest of our analysis on the relationship between the spontaneous and the stimulus-evoked 3–6 Hz activity in wakefulness, under isoflurane anesthesia, and during the ketamine-induced dissociative state.

Spontaneous and evoked 3–6 Hz wave activity is organized into standing and traveling waves

In wakefulness, visual stimuli evoke 3–6 Hz waves propagating in the feedback direction from the higher-order cortices toward V1.¹¹ To better appreciate how these waves are affected by the state of the animal, we start with a representative example. Figure 1F shows an example surface recording of 750 ms of pre- and post-stimulus LFPs filtered at 3–6 Hz across a column of electrodes along the anterior-posterior (AP) axis in the same mouse during wakefulness as well as under isoflurane and ketamine. Note that wave-like activity patterns in this frequency range are observed spontaneously in this mouse in all three states. In some instances, these patterns resemble a standing wave—oscillations are in opposite phases in the anterior and posterior aspects of the cortex and no systematic phase progression is observed (e.g., Figure 1F, isoflurane). In other cases, there is an orderly phase progression from anterior to posterior electrodes, and the overall pattern forms a traveling wave that propagates in the caudal direction (e.g., Figure 1F, ketamine).

During wakefulness, after the visual stimulus presentation, the 3–6 Hz oscillations increase in power and are phase reset to organize into a feedback traveling wave. However, the same stimulus fails to restructure the 3–6 Hz activity under isoflurane or ketamine. Consistent with this observation, the average of single-trial LFPs filtered at 3–6 Hz shows a coherent visual evoked wave traveling posteriorly in the awake mouse (Figure 1G). In contrast, under both isoflurane and ketamine, the oscillations are not phase locked to the stimulus, resulting in an attenuated average signal. These observations led us to hypothesize that, while spontaneous waves of 3–6 Hz are observed in all states, visual stimuli consistently reset the phase of these waves only in the awake brain.

Spontaneous feedback waves under ketamine are similar to visual evoked feedback waves in awake mice

To compare the features of spontaneous and visual evoked waves across different animals and trials, we performed complex-valued singular value decomposition (SVD) separately on single trials of pre- and post-stimulus activity periods.¹¹ SVD factorizes the signals from the surface electrode grid into a set of spatiotemporal modes (STAR Methods). Each SVD mode is composed of a spatial and a temporal component that, when multiplied, yield a single spatiotemporal pattern (Figure S6). To identify the most dominant spontaneous activity pattern, we examined the mode that captures the greatest fraction of the signal. The first mode captures a similar fraction of variance in all three states (medianVariance_Awake = 42.17%, IQR_Awake = 47.07%; medianVariance_Iso = 44.77%, IQR_Iso = 8.37%; medianVariance_Ket = 45.17%, IQR_Ket = 48.54%). The spatial phase (color) and the spatial-phase gradient (arrows) of the first spontaneous mode averaged across mice and trials in each of the three states are shown in Figure 2A. Each arrow points in the direction of the phase gradient. The length of the arrow is 1 minus variance. Thus, longer arrows mark locations where the distribution of spatial-phase gradients departed further from the uniform distribution. During wakefulness and under isoflurane, spontaneous oscillations in the anterior and posterior regions are in opposite phases, and the phase gradients do not point in a consistent direction. Thus, on average, spontaneous activity during wakefulness and under isoflurane resembles a standing wave (Figure 2A). In contrast, in the same mice under ketamine, phase progression from anterior to posterior aspects of the cortex is clearly observed, resulting in spatial gradients that consistently point in the posterior direction. Thus, consistent with the example in Figure 1F, spontaneous 3–6 Hz oscillations under ketamine resemble a feedback traveling wave percolating across the cortical surface (Figure 2A).

Figure 2. Spontaneous waves under ketamine and visual evoked waves in the awake brain both travel in the feedback direction.

(A) The phase (relative to V1 shown by red diamond) averaged across trials and animals (n = 14) of the largest spontaneous 3–6 Hz spatiotemporal mode (STAR Methods) is shown by color (gray shows locations that did not meet statistical significance for phase coherence). PPA is shown by the blue diamond. The arrows show the spatial-phase gradient averaged across trials and animals. The length of the arrows encodes phase coherence (STAR Methods).

(B) Same analysis as in (A) performed on the most visually responsive 3–6 Hz spatial mode (STAR Methods).

The analysis presented in Figure 2A includes all SVD modes. However, the modes identified by the SVD need not necessarily be wave-like (Figure S6). Traveling wave-like modes are distinguished from others by the fact that the spatial-phase gradient points in a consistent direction across space. To test for wave-like features of each SVD mode, we computed a circular average of spatial-phase gradients across electrodes on a single-trial basis. The deviation from a uniform circular distribution, as assessed with a Rayleigh test (STAR Methods), was used as a testing criterion. With this approach, we determined the fraction of spontaneous trials on which SVD modes resembled traveling waves (Iso, median 0.68, IQR 0.20; Ket, 0.53, IQR 0.16; awake 0.67, IQR 0.10). While the fraction of wave-like modes differed between the three states (Kruskal-Wallis: df = 2, χ² = 10.99, p = 0.0041), in all three states a significant fraction of all spontaneous modes resembled traveling waves. The direction of propagation of the wave-like modes differed among states (Iso, 2.3 [2.09, 2.51]; Ket, −1.14 [−1.26, −1.08]; awake, 2.12 [1.82, 2.43], reported as circular mean in radians relative to the medial-lateral [M-L] axis and 95% confidence bounds). Negative values denote posterior propagation. The tendency of wave-like modes to propagate in a specific direction was additionally quantified by the modulus of the mean resultant vector (STAR Methods) across all wave-like spontaneous SVD modes (Iso, 0.21 [0.18, 0.26]; Ket, 0.42 [0.37, 0.56]; awake, 0.16 [0.11, 0.22], reported as mean [dimensionless] and 95% confidence intervals). A larger modulus of the mean resultant vector denotes greater departure from uniform circular distribution. Thus, single-trial analyses (Figure S7) confirm that approximately half of all SVD modes extracted from spontaneous LFPs are traveling waves. Exclusively under ketamine, spontaneous waves propagate predominantly in the posterior direction. In contrast, in wakefulness and under isoflurane, the comparatively weaker direction preference points in the anterior direction.

Visual evoked modes were identified on a single-trial level as the mode with the greatest increase in temporal amplitude during the post-stimulus period relative to the pre-stimulus baseline¹¹ (STAR Methods). While in awake animals, the phases of the evoked modes are consistent across trials and mice,¹¹ in animals under isoflurane or ketamine, the intertrial and interanimal variability dominates. Consequently, no consistent traveling wave is observed outside of V1 when animals are under isoflurane or ketamine (Figure 2B). This confirms our observation (Figure 1) that, in contrast to the awake state, visual stimuli under both ketamine and isoflurane do not consistently affect the phase of spontaneous cortical waves. Figure S8 shows single-trial analyses specifically focusing on evoked visual modes that have been classified as waves in all three states. The fraction of trials where evoked waves were detected was higher in the awake state than under ketamine or isoflurane. The probability of observing evoked waves under isoflurane and ketamine was not statistically different (Kruskal-Wallis: df = 2, χ² = 14.6, p = 6.8e–4; post hoc Dunn-Sidak comparison: Iso vs. awake, p = 0.026; Ket vs. Awake, p = 0.006; Iso vs. Ket, p = 0.61). The direction of propagation of evoked waves also differed among the different brain states. Under isoflurane, the direction of wave propagation was not significantly different from a uniform distribution (Rayleigh test, p = 0.19), while under ketamine, the direction of wave propagation deviated from uniform distribution (Rayleigh test, p = 4.0e–6). The degree of this deviation was significantly less than during wakefulness as measured by the modulus of the mean resultant vector (Ket, 0.20 [0.14, 0.27]; awake, 0.54 [0.50, 0.59]; mean and 95% confidence intervals). Altogether these data suggest that, in the awake state, visual stimuli more reliably elicit feedback cortical traveling waves at 3–6 Hz. Interestingly, spontaneous waves under ketamine and stimulus-evoked waves in the awake state exhibit similar propagation patterns.

Visual evoked 3–6 Hz feedback waves in awake mice and spontaneous 3–6 Hz waves in mice under ketamine entrain single-unit neuronal firing in V1 and PPA

Low-frequency LFPs recorded from the cortical surface are thought to be dominated by post-synaptic potentials in the superficial cortical layers.⁴⁸ Indeed, we observe an oscillatory sink and source pattern in the superficial cortical layers of V1 at the 3–6 Hz range¹¹ (Figure S3A). This raises the possibility that a wave of synaptic inputs percolating across the cortical surface may coordinate firing of neurons in different cortical areas. If this coordinated firing plays a role in perception, we would expect that (1) neuronal activity should transiently become coordinated by the 3–6 Hz wave after the stimulus only in the awake state, (2) 3–6 Hz waves should not entrain neurons under isoflurane either before or after the stimulus, and, conversely, (3) spontaneous waves should entrain neurons in mice under ketamine. Results in Figure 3 confirm these predictions. The fraction of entrained neurons (either pre- or post-stimulus) was significantly lower under isoflurane than under ketamine or during wakefulness (Tukey’s honestly significant difference: p_Iso-wake Diff. 10.50; SE 1.381; q = 7.607, qc = 3.314, p = 0; p_Iso-ket Diff. 12.01; SE 1.7; q = 7.07, qc = 3.314, p = 0). No differences between the total fraction of entrained neurons were observed between the ketamine and the awake state (Diff. 1.51; SE 1.38; q = 0.85, qc = 3.314, p = 0.99). In wakefulness, the number of entrained neurons is significantly increased after the visual stimulus in both V1 and the PPA (Figures 3A and 3B, χ²_V1 = 185.9201, p_V1 < 10⁻¹⁰, χ²_PPA = 25.9103, p_PPA = 9.2883 × 10⁻⁶, χ²; p_AwakeV1 < 10⁻¹⁰, p_AwakePPA = 0.034, Tukey’s post hoc). In contrast, under both ketamine and isoflurane, the number of entrained neurons is unaffected by the stimulus (Figures 3A and 3B, p_IsoV1 = 0.987, p_IsoPPA = 0.998, p_KetV1 0.435, p_KetPPA = 1, Tukey’s post hoc). While the number of entrained neurons under isoflurane is consistently low both before and after the stimulus, the number of entrained neurons under ketamine is consistently high. The fraction of entrained neurons entrained to the spontaneous 3–6 Hz wave under ketamine is similar to that entrained by the stimulus-evoked wave during wakefulness in V1 (awake post-stimulus vs. Ket pre-stimulus, p = 0.1, Tukey’s post hoc) and in the PPA (awake post-stimulus vs. Ket pre-stimulus, p = 0.78, Tukey’s post hoc).

Figure 3. V1 and PPA neurons are entrained to the 3–6 Hz visual evoked wave during wakefulness and to the spontaneous 3–6 Hz under ketamine.

(A) Fraction of single units entrained to the 3–6 Hz oscillation in V1 averaged across animals (n = 11) in the awake state, as well as under isoflurane or ketamine anesthesia. Hashed bars show pre-stimulus, solid bars show post-stimulus. Error bars show standard error computed across animals. In the awake state, the fraction of entrained neurons is increased relative to the pre-stimulus baseline (χ²_V1 = 185.9201, p_V1 < 10⁻¹⁰, χ²; p_AwakeV1 < 10 ⁻¹⁰, Tukey’s post hoc). Under ketamine (p_KetV1 = 0.435, Tukey’s post hoc) or isoflurane (p_IsoV1 = 0.987, Tukey’s post hoc), no statistical differences in the fraction of entrained neurons are detected. Under ketamine, but not isoflurane anesthesia, the fraction of entrained neurons is comparable to that observed after the stimulus in the awake state (p_AwakeKetV1 = 0.999, Tukey’s post hoc).

(B) Similar to (A), but for cells in the PPA. The fraction of PPA neurons entrained to the 3–6 Hz wave increases after the stimulus presentation in awake mice (χ²_PPA = 25.9103, p_PPA = 9.2883 × 10 ⁻⁶, χ²; p_AwakePPA = 0.034, Tukey’s post hoc), but not under isoflurane (p_IsoPPA = 0.998, Tukey’s post hoc) or ketamine (p_KetPPA = 1, Tukey’s post hoc). The fraction of PPA neurons entrained by the spontaneous wave under ketamine is similar to that in the post-stimulus period in the awake state (p_AwakePPA = 0.034, Tukey’s post hoc).

(C) Example raster plots (top row) showing 100 trials (y axis) from a representative V1 neuron firing in relation to the visual stimulus (time t = 0 ms) in mice that are awake (left column), under isoflurane (middle column), or under ketamine (right column). Spike histogram is shown below the raster (bars show probability). The second row shows raster plots of the same neuron, after time warping to match the phases of the 3–6 Hz oscillations in the pre-stimulus period (STAR Methods). The third row shows a similar time-warped raster for the post-stimulus period 3–6 Hz.

The raster plot in Figure 3C shows example V1 neurons from the same representative mouse, reliably activated by the stimulus in all three states. In aggregate, the numbers of neurons that change their firing rate in response to the visual stimulus in V1 and PPA are similar in all three states (Figures S3 and S4). The key distinction between different states thus appears to be the coordination of neural firing (Figure 3A) to the phase of the wave. To better illustrate the spike-wave entrainment, we time warped the recordings (STAR Methods) to align the phases of the 3–6 Hz wave (Figure 3C). In the awake brain, the firing is uncorrelated to the phase of the wave before the stimulus presentation, but becomes phase locked to the wave after the stimulus. In the animal under isoflurane, there is no association between the phase of the 3–6 Hz wave and firing either before or after the stimulus. Under ketamine, in contrast, action potentials are phase locked to the 3–6 Hz oscillation both before and after the stimulus. Thus, exclusively under ketamine, spontaneous waves entrain neuronal firing. Only in the awake state can stimulus-evoked waves transiently entrain neuronal firing. This further underscores the essential physiological similarity between spontaneous activity under ketamine and stimulus evoked activity in the waking state.

Stimulus-evoked 3–6 Hz traveling waves orchestrate oscillatory neuronal assemblies spanning the visual and the parietal cortex

We hypothesized that because both V1 and PPA neurons become entrained to the visual evoked traveling wave in the awake brain, their firing ought to form a transient oscillatory assembly following the stimulus presentation. Analysis of correlations in V1 and PPA firing (Figure S9) before and after the stimulus in the time domain in all three states is consistent with the entrainment results in Figure 3C but does not directly address the possibility of an oscillatory cell assembly. To test for the emergence of an oscillatory cell assembly, we analyzed neuron correlations in the frequency domain using coherency. An example coherogram averaged across 100 trials of visual stimuli for a representative V1-PPA neuron pair (Figure 4A shows spike waveforms; Figure 4B shows the coherogram) recorded in the awake state is shown. As expected, prior to the stimulus, the firing of V1 and PPA neurons is essentially uncorrelated. Roughly 200 ms after the stimulus, the activity exhibits a peak in coherence at 3–6 Hz. This coherent activity lasts approximately 750 ms, after which the correlated firing of V1 and PPA neurons decays and becomes uncorrelated once again. To characterize the robustness of this finding, we computed coherence as a function of frequency in the pre-stimulus and post-stimulus periods (−600 to −100 ms and 100 to 600 ms, respectively) for all 218 V1-PPA neuron pairs recorded in 10 mice (Figure 4C). This average coherence exhibits a clear peak confined to the 3–6 Hz range (shading shows 95% confidence bounds). Thus, the correlations in firing between V1 and PPA neurons form an oscillatory assembly spanning V1 and PPA after the stimulus presentation in the awake brain.

Figure 4. V1 and PPA cells form a transient oscillatory assembly at 3–6 Hz after stimulus presentation in awake mice and spontaneously under ketamine.

(A) Single-trial (thin lines) and average (thick lines) waveforms from representative V1 (left) and PPA (right) single units in an awake mouse.

(B) Average coherence of spike times from the V1 and PPA units in (A), averaged over trials (black vertical line shows the stimulus). The solid black outline represents pre-stimulus time from −600 to −100 ms before the flash onset. The dashed black outline represents post-stimulus time from 100 to 600 ms after the flash onset. The white dashed line represents the cone of influence.

(C) Average coherence of all V1-PPA unit pairs over trials and animals in the −600 to −100 ms pre-stimulus (solid) and 100 to 600 ms post-stimulus (dashed) time frames in awake mice.

(D) Average 3–6 Hz coherence of V1-PPA unit pairs over trials in each condition (p = 1.1959 × 10⁻¹⁷², Kruskal-Wallis; p_{Awakepre-post} < 10 ⁻¹⁰; p_Isopre-post < 10⁻¹⁰, p_Ketpre-post = 0.9999, p_{KetPreAwakePost} = 0.0668, p_{KetPreAwakePost} = 0.3514, p_{KetPreAwakePost} = 0.0668, p_{KetPreAwakePost} = 0.3514, Dunn-Sidak post hoc).

To determine whether this oscillatory assembly emerges exclusively in the awake state after the stimulus, we computed coherence averaged across pre- and post-stimulus intervals in the time-frequency plane (solid and dashed rectangle, respectively, in Figure 4B) in all three conditions. Figure 4D shows this analysis pooled across 218 pairs from awake mice, 1,946 pairs from mice under isoflurane, and 208 pairs from mice under ketamine. Kruskal-Wallis test performed across all brain states both before and after the stimulus revealed significant differences (df = 5; χ² = 798.21, p = 2.82e–170). Post hoc analyses using Dunn-Sidak tests revealed that post-stimulus coherence in the awake state was significantly higher than under isoflurane (p = 7.38e–10). This implies that isoflurane impedes the ability of V1 and PPA to form oscillatory cell assemblies after presentation of the stimulus. In the awake brain, coherence increased significantly after the stimulus relative to pre-stimulus values (p = 0). This implies that the oscillatory assembly of V1 and PPA neurons is reliably evoked by the visual stimulus in the awake brain. The presence of a stimulus did not significantly affect coherence under ketamine (Ket_pre vs. Ket_post p = 0.92). Furthermore, the pre-stimulus coherence under ketamine was not significantly different from post-stimulus coherence observed in the awake state (p = 0.21). This implies that the propensity of V1 and PPA neurons to form an oscillatory assembly in the absence of stimuli under ketamine is similar to that evoked by the stimuli in the waking brain.

Characteristics of visual evoked 3–6 Hz feedback waves in the awake brain indicate their potential neurophysiological significance in sensory perception

If visual evoked 3–6 Hz waves were important for visual perception, these waves should have a high signal-to-noise ratio, be consistently evoked on most trials, and be phase locked to the stimulus. To determine if visual evoked 3–6 Hz waves have high signal-to-noise ratio, we quantified the fraction of trials in which the most visually evoked mode accounted for the largest total fraction of variance. Indeed, we find that that the most visually responsive 3–6 Hz wave is more likely be the first SVD-ranked mode in awake mice compared with mice under isoflurane or ketamine (p = 1.57 × 10⁻¹³⁰, Kruskal-Wallis; p_Awake-Iso < 10⁻¹⁰; p_Awake-Ket < 10⁻¹⁰, Dunn-Sidak post hoc) (Figure 5A). We failed to detect any statistically significant differences in the signal-to-noise ratio between isoflurane and ketamine (p_Iso-Ket = 0.85, Dunn-Sidak post hoc).

Figure 5. Visual evoked 3–6 Hz waves have high signal-to-noise ratio, have consistent phase, and are reliably elicited only in the awake mice.

(A) Distribution of ranks of the most visually responsive modes in each behavioral state. Visually responsive modes were more likely to be of lower rank in awake mice than in mice under isoflurane or ketamine (p = 1.5655 × 10⁻¹³⁰, Kruskal Wallis; p_Awake-Iso < 10⁻¹⁰, p_Awake-Ket < 10⁻¹⁰ , p_Iso-Ket = 0.8531, Dunn-Sidak post hoc).

(B) Real part of the temporal component of the most visually responsive mode in a representative animal in the awake (left), isoflurane (middle), or ketamine (right) state. Each trace shows a single trial. The temporal components across trials align transiently after the stimulus in the awake animal, but not under ketamine or isoflurane.

(C) Deviations of phases of the most visually responsive mode from uniform circular distribution averaged across trials and animals expressed as Z score (shading represents 95% confidence intervals).

(D) Distribution of mean earth mover’s distance (EMD) between spatial amplitudes of the most visually responsive modes across trials and animals in the awake state (red), under isoflurane (purple), or under ketamine (green). Shading represents 95% confidence intervals.

(E) Probability that a visually responsive mode was detected in all three states shown as a violin plot (each point is a probability estimated across all trials in a single animal) (p = 3.966 × 10⁻⁷, Kruskal-Wallis; p_Awake-Iso = 1.6435 × 10⁻⁶; p_Awake-Ket = 2.4853 × 10⁻⁵, p_Iso-Ket = 0.9999, Dunn-Sidak post hoc).

To determine if the spatial activation profile of visual evoked 3–6 Hz waves is consistent across trials, we calculated the distribution of the earth mover’s distance (EMD) (Figure 5D) and cosine distance (Figure S10) between the spatial amplitude of the most visually responsive modes. We found that the spatial activation patterns of visual evoked 3–6 Hz waves during wakefulness are more consistent on a trial-by-trial basis than those found in mice under isoflurane or ketamine. Finally, to test for reliability, we quantified the number of trials in which at least one visually evoked mode was detected (a mode in which the post-stimulus temporal amplitude exceeds pre-stimulus temporal amplitude by at least 6 standard deviations). We found that visual evoked 3–6 Hz waves are more reliably elicited when animals are awake compared with when they are under isoflurane or ketamine (Figure 5E, p = 3.966 × 10⁻⁷, Kruskal-Wallis; p_Awake-Iso = 1.6435 × 10⁻⁶; p_Awake-Ket = 2.4853 × 10⁻⁵, Dunn-Sidak post hoc). We failed to detect any significant differences in reliability between ketamine and isoflurane states (p_Iso-Ket = 0.99, Dunn-Sidak post hoc).

Visual evoked 3–6 Hz feedback waves emerge in a stepwise function in awake mice, but fail to be evoked even at maximum intensity stimuli in mice under isoflurane or ketamine

Previously we have shown that, as the intensity of the visual stimulus is increased, there is a sharp increase in the spatial phase consistency of visual evoked 3–6 Hz feedback waves in the awake state.¹¹ Further, the sharp increase in the spatial extent of the wave occurs near the murine perceptual threshold.^49-51 After the lowest-intensity screen flash at 1.5 cd/mm², only 20% of electrodes exhibit a consistent phase in the awake state (Figure 6A). An electrode was defined as having consistent phase if the distribution of phases of the most visually evoked mode at this electrode (computed across trials and animals) deviated from a uniform circular distribution (STAR Methods). When the stimulus intensity is increased from 1.5 to 18 cd/mm², the number of coherent electrodes approximately doubles and remains insensitive to stimulus intensity up to 650 cd/mm² (Figure 6A). Remarkably, 3–6 Hz waves elicited by a maximum-intensity screen or even LED flashes in mice under isoflurane or ketamine resemble the curtailed pattern of 3–6 Hz waves mostly confined to V1. This pattern is similar to that evoked by the weakest stimuli in awake mice (Figures 6B and 6C). This similarity between responses to the weakest stimuli in the awake mice and strong stimuli in mice rendered unresponsive with either ketamine or isoflurane lends further evidence that supports the conclusion that perception of visual stimuli requires integration of activity across different cortical sites orchestrated by the 3–6 Hz wave.

Figure 6. Waves evoked by strong stimuli under isoflurane and ketamine resemble waves evoked by subthreshold stimuli in awake mice.

(A) Fraction of electrodes in which phase of the slow waves is coherent with V1 (y axis) across trials within each mouse (individual points), when animals are shown 100 ms screen flashes of varying intensities or an LED flash, during wakefulness (left), under isoflurane (middle), or under ketamine (right). Under both ketamine and isoflurane, the number of coherent electrodes is consistently low for stimuli of all intensities.

(B) At each stereotaxic location, the average phase offset of the most visually evoked mode from V1 (the red diamond) is plotted in color for lowest-intensity (1.5 cd/mm²) stimulus recorded in awake mice. The arrows depict the spatial gradient. Magnitude of the arrows show consistency of the phase angles over trials and animals. Gray locations were not statistically different from uniform circular distribution (Raleigh test) across trials and animals. The blue diamond denotes the PPA.

(C) Similar phase plots for maximum-intensity stimuli (640 cd/mm²) recorded in mice under isoflurane and ketamine. Awake data (in B) are adapted from data presented in Figure S8B of Aggarwal et al.¹¹ and are shown here for comparison to responses observed under ketamine and isoflurane.

DISCUSSION

In our previous work,¹¹ we determined that during wakefulness, visual stimuli evoke large-scale 3–6 Hz feedback traveling waves. These results established a correlation between traveling waves and visual perception. Building upon these previous findings, here we pharmacologically manipulated the animal’s ability to perceive internal or external stimuli to determine whether properties of these waves depend on the state of the brain. We show that, while 3–6 Hz traveling waves are observed spontaneously in awake mice, they do not entrain neuronal activity in V1 or PPA. Visual stimuli reliably reset the phase of spontaneous 3–6 Hz oscillations to form a visual evoked traveling wave propagating caudally. This wave entrains individual neurons and gives rise to correlations between V1 and PPA neuron firing specifically at 3–6 Hz. Under isoflurane anesthesia or in the ketamine-induced dissociative state, however, visual stimuli do not reset the phase of spontaneous waves at 3–6 Hz. During isoflurane anesthesia, V1 and PPA neurons are not correlated to the wave or to each other either spontaneously or after a stimulus presentation. In contrast, in the dissociative state, spontaneous waves resemble those evoked by visual stimuli in the awake brain in terms of both the propagation direction and the ability to coordinate V1 and PPA neuronal firing. In summary, we show that a hallmark of sensory responsiveness is the ability of a stimulus to perturb spontaneous traveling waves. The capacity for sensory perceptions, be they stimulus evoked or hallucinatory, on the other hand, may be related to the formation of the 3–6 Hz oscillatory assembly of neurons across the visual hierarchy.

The differences in the responses evoked by simple visual stimuli in different states of consciousness offer insights into the fundamental neurophysiological distinctions between them. Consistent with previous work,⁵² we find that the early component of the evoked potential is preserved in all states (Figures 1 and S2). This early component of the evoked response reflects thalamic input into V1.⁴⁷ Indeed, we find that the early pattern of sinks and sources in V1 is similar among the three states (Figure S3). Further, approximately the same number of V1 neurons alter their firing rate in response to the stimulus in all three states. Thus, in the state of diminished responsiveness, the transmission of thalamic sensory inputs into the cortex is not dramatically disrupted. Similar observations have been made with auditory stimuli during slow-wave sleep^53,54 and under anesthesia.⁵⁵ We also observe that PPA—a higher-order cortical region^56-58—continues to receive inputs in all states, and approximately the same fraction of PPA neurons alter their firing rate in response to visual stimuli (Figure S4). Thus, the failure of signal propagation from the primary to higher-order cortical areas does not readily account for the differences in the states of consciousness. The key distinguishing feature unique to normal wakefulness is that visual stimuli evoke a coordinated oscillatory assembly^59,60 of neurons orchestrated by the feedback traveling wave at 3–6 Hz.

There is an extensive body of literature linking correlated oscillations in brain signals to perception,^10,11,23 attention,⁶¹ cognitive control,⁶² representation of space,⁶³ etc. While the existence of traveling waves is not in question, whether these correlated oscillations play a functional role or are epiphenomenal remains a hotly debated issue. One of the major reasons for this confusion is that oscillations per se and correlations among them can arise generically in a broad class of systems.⁸ Thus, observing traveling waves does not directly point to their underlying mechanisms or behavioral significance. The waves that we and others¹⁰,¹⁴,²⁰,²³,⁴⁵,⁶⁰,^64-68 observe in the LFPs reflect the spatial patterns of synaptic potentials. The effect of this synaptic input, however, depends strongly on the specific network mechanisms that produce these synaptic inputs and the states of individual neurons that receive it.

The specific neuronal and circuit mechanisms were not the focus of this work. Nevertheless, recent computational modeling efforts⁶⁹ suggest a general class of mechanisms that may explain our experimental results. Networks with predominantly local connectivity and conduction delays naturally produce traveling waves over a broad range of parameters.⁶⁹ In the regime where coupling between neurons is weak, these spontaneous traveling waves do not strongly entrain firing. Thus, there is no inherent contradiction between traveling waves of synaptic activity and asynchronous irregular and weakly correlated neuronal firing.⁷⁰ This regime is reminiscent of spontaneous brain activity during wakefulness observed herein and in previous studies.²³

When the coupling strength between neurons is increased, neuronal firing becomes correlated and entrained to the phase of the traveling wave. Interestingly, only during wakefulness can a suprathreshold stimulus reliably switch the system from a weakly coupled to a more strongly coupled regime. The fact that neurons are spontaneously entrained to the wave and correlated to each other under ketamine may result from elevated baseline coupling between cortical neurons. One mechanism that can give rise to this increased coupling is the preferential suppression of inhibitory cortical interneurons by ketamine^27,71 and the consequent disinhibition of pyramidal cells.⁷² Conversely, isoflurane is thought to disrupt corticocortical synapses⁷³ and preferentially depress excitatory neurotransmission.⁷⁴ This may explain why, under isoflurane, cortical neurons are never entrained by the wave. Interestingly, while ketamine preserves the overall level of cortical activity, the population of spontaneously active pyramidal neurons switches.²⁷ Thus, while the overall excitability of the cortical neurons may explain why, under some circumstances, the wave is able to entrain neuronal firing, the identity of specific neurons that are recruited into the oscillatory assembly depends strongly on the state of the animal.

The idea that specific oscillatory LFP dynamics may accompany sensory dissociation has been previously suggested. Both ketamine administration in mice and spontaneously occurring hallucinations in patients are associated with coherent 1–3 Hz oscillations in brain activity.³⁷ Oscillations in the 3 Hz range were also identified under ketamine in patients implanted with ECoG electrodes for epilepsy localization.³⁸ It is impossible to know whether mice experience hallucinations. However, the fact that LFP oscillations in humans during both ketamine-induced and spontaneously occurring hallucinations resemble those observed here suggests that at the neurophysiological level, the state observed in mice under ketamine is similar to that associated with self-reported hallucinations in humans. Yet, it remained unclear why a specific oscillatory behavior should give rise to sensory dissociation. Here, we demonstrate that waves of activity evoked by suprathreshold stimuli in the waking mouse brain are similar to those observed spontaneously under ketamine. This provides a link between specific cortical waves at 3–6 Hz induced by ketamine and hallucinatory experiences unrelated to the environment.

Investigations of cortical dynamics⁷⁵ converge on the conclusion that loss of consciousness during dreamless sleep,⁷⁶ during general anesthesia,⁷⁷ and after neurological injury⁷⁸ results in disruption of functional connectivity and the decrease in the repertoire of available brain states. In this work, we focused on decomposing the overall spatiotemporal activity pattern into a set of modes. Each of these modes captures a specific pattern of pairwise correlations among electrodes. While it may appear that the existence of traveling waves contradicts the results on decreased connectivity, the relationship between waves and pairwise connectivity is not a priori obvious and should be investigated in future work. Another interesting contrast is to the studies of responses evoked by transient magnetic stimulation (TMS).^30,79-82 In states of diminished consciousness, TMS-evoked cortical responses are simplified relative to the waking state. This is in full agreement with our results on isoflurane. However, TMS responses in a dissociated state such as that induced by ketamine or during REM sleep are nearly as complex as those observed during wakefulness.³⁰ In contrast, we and others⁸³ find that under ketamine, responses to visual stimuli are strongly curtailed relative to the waking state. One critical difference is that TMS stimulation, in contrast to the visual stimuli, directly activates the cortex without relying on the endogenous thalamic input pathways. Whether this difference in input modality can account for the differences in evoked dynamics is an interesting question that could be addressed in the future.

Distilling which specific aspects of neuronal signals are associated with perception is a challenging task, because brain activity associated with perception, reward anticipation, and movement becomes difficult to disentangle in the setting of behavioral tasks, especially on a single-trial basis.^84-87 In altered states of consciousness, the behavior is further confounded by disruption of memory, motor coordination, and motivation. Nevertheless, our results have important implications for the role of traveling cortical waves in perception.

Classical theories assumed that the visual system processes stimuli in a hierarchical feedforward fashion.^88,89 In contrast, recent work suggests that the overall activity is heavily influenced by feedback.⁹⁰ In this view, the stimulus does not elicit a perception per se, but serves to modulate the spontaneous reciprocal feedforward-feedback dynamics in the brain.^41,91 Interestingly, this interactionist perspective applies not only to perception of the visual world but also to illusory perceptions. Identical circuitry seems to be required for both normal and illusory perceptions. Patients with Charles Bonnet syndrome exhibit activation of the visual cortex during visual hallucinations.⁹² Extensive damage to the cortical visual areas results in ablation of visual imagery during sleep.⁹³ Patients with more circumscribed lesions exhibit more specific visual deficits both during normal wakefulness and in dreams.^94,95 Computational modeling suggests that the symmetry of visual hallucinations induced by psychedelics reflects the architecture of V1.⁹⁶ Unlike spontaneous activity, direct electrical activation of the visual cortex in humans leads to the perception of highly artificial phosphenes.⁹⁷ These lines of evidence together suggest that visual perception relies upon the interactions between spontaneous dynamics and perturbations imposed onto them by the visual stimuli.

Our work suggests that the 3–6 Hz traveling waves span much of the cortical surface and can, under specific circumstances, entrain firing of broadly distributed neurons. This leads to a tantalizing suggestion that this traveling cortical wave coordinates neuronal activity ultimately required for perceptual awareness. Manipulations that prevent neurons from being entrained to the traveling wave are associated with states lacking perception. Conversely, manipulations that increase the coupling of individual neurons to the traveling wave may be associated with hallucinations. The awake state is delicately balanced between these two regimes such that stimuli evoke an increase in coupling among cortical neurons, which allows them to transiently form an oscillatory assembly spanning distant cortical regions.

Limitations of this study

The major limitation of this study is that one cannot be certain about the existence of hallucinations in mice. We describe the spatiotemporal oscillations in the LFPs as traveling waves extracted using SVD. Yet, these spatiotemporal oscillations are somewhat distinct from waves traveling through a uniform passive medium. While we provide extensive evidence for the existence of traveling waves in LFPs, better understanding of the nature of these spatiotemporal activity patterns can likely be obtained using a combination of conventional neurophysiology and imaging modalities.

STAR★METHODS

RESOURCE AVAILABILITY

Lead contact

Further information and requests for resources and reagents should be directed to and will be fulfilled by the lead contact, Alex Proekt (proekt@gmail.com).

Materials availability

Please see the data availability statement below. No new reagents/materials were generated in this study.

Data and code availability

• Data for this study are found at Zenodo: https://doi.org/10.5281/zenodo.10637601.

• All custom original code used in this study is deposited on GitHub: https://github.com/proektlab/WaveAnalysis.

• Any additional information required to reanalyze the data reported in this work paper is available from the lead contact upon request.

EXPERIMENTAL MODEL AND STUDY PARTICIPANT DETAILS

Animals

All experiments in this study were approved by Institutional Animal Care and Use Committee at the University of Pennsylvania and were conducted in accordance with the National Institutes of Health guidelines. Experiments were performed on 32 adult (12–32 weeks old, 20–30 g, 21 male and 11 female) C57BL/6 mice (Jackson Laboratories). Mice were housed under a reverse 12:12 h, light: dark cycle, and were provided with food and water ad libitum. Inclusion criteria for mice included the following: 1) presence of visual-evoked activity in which the absolute value of the first 100 ms of post-stimulus activity exceeds five standard deviations of pre-stimulus activity and 2) presence of spontaneous activity that was not characterized as burst suppression. 25 mice were recorded from under isoflurane, ketamine and during wakefulness. 7 mice were recorded from only under isoflurane.

METHOD DETAILS

Headplate implantation, habituation, and craniotomy

Headplate implantation, mouse habitation and craniotomy for mice performing isoflurane, ketamine, and awake recordings followed protocols described in Aggarwal et al., 2022.¹¹ Briefly, mice were anesthetized with 2.5% and maintained with 1.5% isoflurane and secured on a stereotaxic frame (Narishige). Periosteum was exposed and bregma, lambda, and the site of the future craniotomy were marked (+1mm to −5 mm AP, +0.25 mm to +6 mm ML of bregma) on the left hemisphere. The skull was then scored, and a custom designed headpiece was secured with dental cement (Metabond), cyanoacrylate adhesive (Loctite 495), and 3 skull screws (Fine Science Tools, Self-tapping skull screws, 19010-10). Mice received 0.5mg cefazolin, 0.125mg meloxicam, and 7 mL of normal saline SQ post operatively, and recovered for one week. Then, mice were habituated to head fixation with body restraint with visual stimuli during one 45-min session per day over the course of 4 days.

After completing the habituation protocol, mice were ready for recordings. Animals were anesthetized with 2.5% isoflurane in oxygen, secured onto the stereotaxic frame and maintained at 1.5% isoflurane. Before surgery, local anesthesia was injected subcutaneously in the face, scalp and neck muscles, targeting the trigeminal and occipital nerves (0.625 mg bupivacaine, 0.025%).⁹⁸ Analgesia was supplemented with subcutaneous injection of 0.125mg meloxicam. To reduce potential swelling, 0.006mg dexamethasone was also injected subcutaneously before surgery. A 4 mm ML by 6 mm AP craniotomy was then drilled through the dental cement along the markings. A bone screw (Fine Science Tools, Self tapping skull screws, 19010-10) on the right skull bone (+2 mm ML, −2mm AP) was used for a reference. A 64-electrode surface grid (E64-500-20-60, Neuronexus) was positioned over the dura (right most electrode anterior electrode at ~ 1mm lateral and 1mm posterior to bregma).

In 14 animals, two DiI coated (Sigma-Aldrich) laminar 32 channel probes (H4, Cambridge Neurotech) were also inserted 800um into the cortex. One targeted a hole in the ECoG grid closest to V1 (−3.25 AP, −2.25 ML). The other targeted a hole in the ECoG grid closest to PPA (−1.5 AP, −1.5 ML). Both were placed using a motorized micromanipulator (NewScale Technologies). The grid and exposed dura were then covered with gel foam soaked in mineral oil to prevent desiccation. Upon completing recordings, animals were deeply anesthetized (5% isoflurane) and sacrificed. Brains were extracted and fixed in 4% paraformaldehyde (PFA) over-night prior to sectioning and histology.

Anesthetic delivery protocol

After ECoG electrodes were positioned, animals were ready for electrophysiology recording. Mice were first given 0.6% isoflurane through a nose cone and presented with visual stimuli. Isoflurane was then turned off for 30 min before awake recordings when visual stimuli began. After awake recordings concluded, mice were re-induced with a transient 2 min inhalation of 2.5% isoflurane to allow for accurate administration of 100 mg/kg IP ketamine. Visual stimulation and recording under ketamine anesthesia began 2 min after ketamine administration. Acute surgeries for animals receiving only isoflurane (n = 7) were performed as described in Aggarwal et al. 2019.⁴³

Histology

Brains from the 14 animals in which laminar probes were inserted, were sectioned at 80μm on a vibratome (Leica Microsystems). Sections were mounted with a medium containing a DAPI counterstain (Vector Laboratories) and imaged with an epifluorescence microscopy (Olympus BX41) at 4× magnification. The stereotaxic locations of the laminar probes were determined using postmortem histology by comparison to the brain atlas.⁹⁹

Visual stimulation

Two sets of visual stimuli were used in the study. The first consisted of 100 trials of 10 ms flashes of a green LED (650 cd/m²), covering 100% of the mouse’s right visual field, delivered at a random interstimulus interval drawn from a uniform distribution between 3 and 4 s. In 17 animals, 240 trials of 100ms full flashes of a CRT monitor (Dell M770, refresh rate 60 Hz, maximum luminance 75 cd/m²), placed 23 cm away at an angle of 60% from the mouse’s nose, thereby covering 70% of the mouse’s right field of view. The monitor full field flashes varied in luminance’s (2%, 11%, 25%, 44%, 75%, 100%) in random order at a random interstimulus time interval between 3 and 5 s. The corresponding luminance values are shown in Figure 6.

Electrode registration

Histological localization of laminar probes was used to align the ECoG grid to stereotaxic coordinates. The angle of the line formed by two laminar probe insertion sites and the AP axis was defined as $\theta$. Each electrode on the ECoG grid was then assigned a location based on its Euclidean distance from the two laminar probe sites. Finally, the resultant grid location matrix was multiplied by a rotation matrix ($R$) to convert the electrode location within the grid to stereotaxic coordinates.

$$R=\left[\begin{array}{cc}\hfill cos\theta \hfill & \hfill -sin\theta \hfill \\ \hfill sin\theta \hfill & \hfill cos\theta \hfill \end{array}\right]$$

The resulting ECoG coordinates were then compared to photographs of the ECoG grid relative to bregma and lambda to verify coordinate assignment.

Electrophysiology and preprocessing

In 6 mice, signals were amplified via a Neuralynx headstage (HS36), digitized with a Cheetah 64 acquisition system (Neuralynx, ERP-27, Lynx-8), and collected at a rate of 3030.3Hz/channel. In the remaining mice, signals were amplified and digitized on an Intan headstage (Intan, RHD2132) connected to an Omniplex acquisition system (Plexon, Omniplex), and collected a sampling rate of 40KHz/channel.

The LFP data were first downsampled to 1 kHz and then filtered between 0.1 Hz and 325 Hz using firls.m and filtfilt.m functions in MATLAB, to minimize phase distortions. Channels that contained line noise and trials with excessive movement artifacts were eliminated manually. To minimize the impact of volume conduction, the average signal across all electrodes was subtracted from the LFP. All subsequent analyses were conducted using custom-made MATLAB code unless otherwise specified.

Selection of V1 ECoG electrode

In 18 mice, laminar probes were not inserted and therefore grid electrodes were not aligned to stereotaxic coordinates. In these mice, the V1 electrode was identified neurophysiologically 11,43. The latency of onset of the visual-evoked potential was calculated for each ECoG electrode as the time point at which the post-stimulus average LFP exceeded 3 standard deviations above the pre-stimulus baseline for 3 consecutive time points. The electrode which had the lowest latency of onset was defined as V1.

In the 14 mice in which laminar probes were inserted and the stereotaxic positions of the ECoG probes were inferred, the electrode closest to stereotaxic V1 (−3.25 AP, −2.25 ML) was chosen for each animal. To confirm that the chosen electrode neurophysiologically corresponded to V1, the latency of onset of the VEP at each grid electrode was also computed as above. The position of the stereotaxically identified V1 electrodes was within 1–2 electrodes (<1000um) in distance and the onset was within 2 ms of the electrode with the earliest latency of onset in all mice.

Current source density analysis (CSD)

LFP from the laminar probes was converted in CSD by computing the second spatial derivative ¹⁰⁰:

$$\frac{d^2\phi }{d{z}^2}=\frac{-[\phi (z+2\Delta z)-2\phi (z)+\phi (z-2\Delta z)]}{{(2\Delta z)}^2}$$

where $\phi$ is the LFP, $\mathsf{z}$ is the vertical coordinate depth of the probe, and $\Delta \mathsf{z}$ is the interelectrode distance (25 μm). Estimation of the CSD at the boundary electrodes was projected using the Vaknin estimation procedure.¹⁰¹ Channels with the earliest current sink in the V1 probe were assigned as layer 4 (granular layer). Subsequent sinks were found above and below layer 4 in layers 2/3 and layer 5 of the V1 probe. The channels of the PPA probe were assigned a laminar structure based on their distance from the cortical surface as described in Aggarwal et al. 2022.¹¹ Laminar data was only included in analysis if the channels could clearly be assigned to layers in this manner (11 out of 14 mice).

Wavelet analysis

Continuous wavelet transform with Morlet wavelets implemented in contwt.m (0.1 Hz–150 Hz, with a step-width 0.25 Hz and normalized amplitude) was used to calculate the power, phase, and frequency characteristics of LFP or CSD (http://paos.colorado.edu/research/wavelets/).¹⁰²

Inter-trial phase coherence (ITPC) analysis

Intertrial phase coherence (ITPC) is a measure of phase consistency of LFP filtered at specific frequency bands. The phase of the LFP in each frequency band was extracted using continuous wavelet transform. The ITPC was computed as the circular across trial average of such unit length phase vectors.¹⁰³

Filtering data for wave analysis

LFP or CSD data was filtered into (3-6Hz) using the inverse wavelet transform, invcwt.m, (available at: http://paos.colorado.edu/research/wavelets/).¹⁰² All wavelet coefficients outside the desired frequency band were set to zero. As we have shown previously¹¹ the results are largely unaffected by the choice of the filtering method.

Construction of analytical 3-6 Hz signals

Hilbert transform was used to extract the analytical signal of LFPs or CSDs filtered for 3–6Hz frequencies. This resulted in series of complex numbers, in which the modulus of the analytical signal corresponds to the instantaneous amplitude and the arctan of the analytical signal corresponds to the instantaneous phase.

Complex singular value decomposition (SVD)

Detailed methods and examples describing complex SVD analysis of filtered LFP can be found in Aggarwal et al.¹¹ Briefly, analytical signal (spanning from 1600ms to 100 ms of pre-stimulus activity for spontaneous trials 500ms of pre-stimulus to 1000 ms of post-stimulus activity for stimulus evoked trials) from ECoG electrodes formed matrix $\mathbf{A}$ for each trial. Oscillatory modes were extracted from $\mathbf{A}$ by performing singular value decomposition, which factorizes $\mathbf{A}$ into mutually orthogonal modes: $A={USV}^T$

$U$ and $V$ are the matrices that encode the spatial and temporal components of each mode, respectively. The diagonal real-valued S contains singular values (${\lambda }^{\prime }s$) which encode the fraction of the total variance explained by each mode.

The spatial amplitude and spatial phase of the $i-th$ mode is the modulus and the arctan of $U_{(\ast ,i)}\ast {\lambda }_i$ respectively. Temporal amplitude and temporal phase are the modulus and the arctan of $V_{(\ast ,i)}\ast {\lambda }_i$ respectively.

Reliability of visually responsive modes

The temporal amplitudes of the first ten singular modes were computed for each single trial, as above, and then normalized to their mean and standard deviation over 400 ms of pre-stimulus activity. Modes in which the temporal amplitude exceeded 6 standard deviations above pre-stimulus activity within the post-stimulus window (1000ms post-stimulus for 3-6Hz activity), were defined as visually responsive modes.

Defining the most visually responsive mode

The mode that displayed the greatest increase in temporal amplitude during the post-stimulus period compared to pre-stimulus activity, was defined as the most visually responsive mode.

Consistency of spatial amplitude loading using Earth Movers Distance

Earth Movers Distance was calculated for the spatial amplitude of the most visually evoked modes for each pair of trials using the MATLAB function emd.m. This was done for each mouse in each experimental condition. Next, the probability density function (PDF) of the Earth Movers Distance was calculated. 95% confidence intervals obtained through bootstrapping.

Consistency of spatial amplitude loading using cosine similarity

To determine the similarity in the spatial activation of the most visually evoked modes across trials, the cosine distance of the spatial amplitude of the most visually evoked mode was computed between pairs of single trials, within each mouse in each condition. Subsequently, the PDF of the cosine similarity (1-cosine distance) was computed for all pairs of trials across all mice for each state. The cosine similarity of spatial amplitudes in mice under anesthesia is subtracted from the PDF of the cosine similarity of spatial amplitudes in awake mice.

Spatial phase offset from V1

For each single trial, the phase offset from V1 was computed by extracting the spatial phase of the most visually responsive mode at each electrode and projecting it onto a unit circle. To find the average phase angle and consistency of each channel’s phase offset relative to V1, the circular mean was computed across trials within each animal.¹⁰⁴ The direction of the mean vector corresponds to the angle of phase offset whereas the magnitude corresponds to 1 variance.

In the 14 animals in which ECoG electrode stereotaxic positions were identified, the circular mean and variance were computed across trials and animals at each stereotaxic location.

Spatial phase gradient

Using phase_gradient_complex_multiplication.m, written by Lyle Muller (available at: https://github.com/mullerlab/wave-matlab), the spatial phase gradient was calculated on a single trial basis by iteratively multiplying the complex valued spatial component of the most sensory evoked mode at one electrode location to the complex conjugate of the spatial component of the next electrode in the medial-lateral and anterior-posterior directions.¹⁰ The average gradient over trials was calculated by projecting each trial’s gradient vector at each position onto a unit circle and computing the circular mean. The angle of the resultant vector corresponds to the direction of spatial phase advancement, whereas the magnitude of the resultant vector corresponds to 1 variance in the direction of the gradient over trials.

Defining traveling waves

SVD modes were classified as traveling-wave like or not using the spatial phase gradient. Spatial phase gradient for each mode of interest was computed as described above. Spatial gradients at each electrode were subjected to the Rayleigh test (implement as circ_rtest.m from the circular statistics toolbox for MATLAB: https://www.mathworks.com/matlabcentral/fileexchange/10676-circular-statistics-toolbox-directional-statistics). All modes that reached statistical significance at or below p value 0.01 were considered to be traveling wave-like.

Mean resultant vectors

For each wave-like SVD mode (defined above), we obtain the direction of propagation as the circular mean of the phase gradients estimated from each electrode. To determine whether waves detected on different trials tend to propagate in a preferred direction, we computed the mean resultant vector: $r=\frac{1}{T}{\sum }_{t=1}^T{e}^{i{\omega }_t}$ where $t$ indexes the wave-like trials from 1 to T, T is the total number of wave-like trials and ${\omega }_{\mathsf{t}}$ is the direction of propagation of the $t\text{-}th$ wave-like mode. The mean direction of propagation is then: $\langle \omega \rangle ={\tan }^{-1}r$. The resultant vector (between 0 and 1) is defined as the modulus of $r$. Note that the circular variance is defined as: $\overline{var}(e^{i\omega })\stackrel{\text{def}}{=}1-\mid r\mid$. Thus, larger $\mid r\mid$ denotes greater tendency to depart from a uniform distribution. To estimate 95% confidence bounds on $\mid r\mid$ we generated 1000 independent samples with replacement among all wave-like trials and repeated the above calculation. 95% bounds were then estimated empirically from these bootstrap samples.

Averaging stereotaxic coordinates over animals

This procedure was implemented in order to average signals from different animals while taking into account the precise electrode location which varied from animal to animal. A grid of stereotaxic locations was defined from −5 to 0 mm AP and −3.5 to 0 mm ML, with 0.5mm spacing. Stereotaxic locations of each ECoG electrode in each mouse were identified as described above. The weight of each electrode at each stereotaxic location was computed as a Gaussian function of the distance between the stereotaxic location of the electrode and the nearest stereotaxic grid location:

$$W=\frac{1}{\sigma \sqrt{2\pi }}{e}^{\frac{\Vert pq\Vert }{\sigma }}$$

Where ${\mathsf{p}}_{\mathsf{q}}$ is the Euclidean distance between the electrode p and nearest location on the stereotaxic grid q, $\sigma =0.15$ is the standard deviation. The weight of all electrodes outside of two standard deviations (0.3 mm radius) was set to zero. The average signal (computed across mice) is a weighted spatial average at each stereotaxic grid location.

Spike sorting

The same 11 mice that were used for laminar analysis also had their probe data analyzed to identify individual neurons. Kilosort¹⁰⁵ was used for spike sorting, and then the resulting spikes were visually checked for accurate waveform clustering using Phy. Neurons with a firing rate below 0.5 spikes per second were removed from the analysis.

Spike field coherence (SFC)

Was computed using the method by Tort et al.¹⁰⁶ CSD (filtered at 3-6Hz) from the same electrode as the action potential was used for phase. Briefly, a distribution of spike times as a function of phase of the wave was estimated. Deviations from uniform distribution of spike times is considered as evidence that the phase of the wave influences the probability of firing. Deviations from uniform distribution were quantified as Kullbach-Leibler (KL) divergence. To establish the statistical significance of an experimentally observed KL divergence, it was compared to surrogate data. Surrogates consisted of non-homogenous Poisson models in which firing rate was constrained to mimic experimental observations. KL divergence of the surrogate spike trains was computed as described above for experimental data. p-value was then computed empirically as the integral of the right tail of the KL divergence distribution of the surrogates. Significance level was set at 0.05. All neurons exceeding this significance threshold were considered to be entrained.

Time-warped raster generation

For each neuron, time-warped raster plots were created with three cycles of 3-6Hz filtred CSD from each trial. A horizontal stretch and shift value was found for every trial’s CSD such that its correlation with the first trial is maximized. Optimization was implemented in fminsearch.m function (MATLAB 2020b, Mathworks). Once the optimal stretch and shift values were obtained for each trial, the transformations were applied to the trial’s corresponding spike times.

Spike coherence

Coherence between spike trains of each pair of V1 and PPA neurons within the same mouse were calculated on a single trial basis using the MATLAB function wcoherence.m, (MATLAB 2020b, Mathworks). Spike coherence was then averaged over all trials for each pair of neurons.

QUANTIFICATION AND STATISTICAL ANALYSIS

Statistical analysis

In all cases, the threshold for statistical significance was set at p < 0.05 unless otherwise stated. To determine the statistical significance of the ITPC, the observed ITPC were compared to time shifted surrogates (n = 100 sets, 100 trials per set), using a one tailed t test.

To determine the effects of brain state on the wave distributions, reliability of visually evoked modes, SVD rank of most visually evoked mode, consistency in phase offset from V1 of most visually responsive mode across luminance, and spike coherence, a Kruskal Wallis test was first performed. If there was a statistically significant effect of brain state, pairwise hypotheses were tested using Dunn-Sidak post hoc analysis, thus correcting for multiple comparisons.

To determine if the proportion of neurons entrained to the phase of the slow wave was different across brain states, a Chi Square test for Homogeneity was preformed. Pairwise hypotheses were tested using the post hoc Tukey’s Honest Significant Differences Test among Proportions, thus correcting for multiple comparisons.

To assess the significance of the spatial phase and gradients at each location, a Rayleigh test was conducted to determine whether there was a deviation from circular uniformity. The p values resulting from this test were then corrected for multiple comparisons using the Bonferroni method (64 ECoG channels within individual mice and 77 query stereotaxic locations across mice).

KEY RESOURCES TABLE

REAGENT or RESOURCE	SOURCE	IDENTIFIER
Chemicals, peptides, and recombinant proteins
DAPI stain	Vector Laboratories	RRID:SCR_000821 https://vectorlabs.com/
DiI	Sigma Aldrich	N/A
Isoflurane	Hospira Inc	N/A
Ketamine	Zoetis	N/A
Deposited data
https://doi.org/10.5281/zenodo.10637601	N/A	N/A
Experimental models: Organisms/strains
Wild type (C57/Bl/6J) (strain number 000664)	Jackson Labs	https://www.jax.org/strain/000664
Software and algorithms
MATLAB 2020a	Mathworks	RRID:SCR_001622 https://www.mathworks.com/products/new_products/release2020a.html
Plexon Data Acquisition System	Plexon	RRID:SCR_003170 http://www.plexon.com/products/map-software
Neuralynx Data Acquisition System (Cheetah)	Neuralynx	https://neuralynx.fh-co.com/
Kilosort	N/A	RRID:SCR_016422 https://github.com/cortex-lab/Kilosort
Phy	N/A	https://phy.readthedocs.io/en/latest/
Wave Statistics Package	Lyle Muller Lab	https://www.mathworks.com/matlabcentral/fileexchange/10676-circular-statistics-toolbox-directional-statistics
Psychophysics Toolbox	N/A	RRID:SCR_002881 http://psychtoolbox.org/
Circular Statistics Toolbox for MATLAB	N/A	https://www.mathworks.com/matlabcentral/fileexchange/10676-circular-statistics-toolbox-directional-statistics
Other
E64-500-20-60 (surface grid electrode)	Neuronexus	www.neuronexus.com
H4 (laminar 32 channel probes)	Cambridge Neurotech	www.cambridgeneurotech.com

Highlights.

• In wakefulness, visual stimuli reliably elicit feedback traveling cortical waves

• Stimulus-evoked traveling waves coordinate firing of individual neurons across the cortex

• Under anesthesia and in dissociative states, stimuli do not disrupt spontaneous waves

• In dissociative states, spontaneous activity resembles stimulus-evoked waves in wakefulness