Human cognition requires the coordination of neural activity across widespread brain networks. Here, we describe a new mechanism for large-scale coordination in the human brain: traveling waves of theta and alpha oscillations. Examining direct brain recordings from neurosurgical patients performing a memory task, we found contiguous clusters of cortex in individual patients with oscillations at specific frequencies within 2 to 15 Hz. These oscillatory clusters displayed spatial phase gradients, indicating that they formed traveling waves that propagated at ∼ 0.25–0.75 m/s. Traveling waves were relevant behaviorally because their propagation correlated with task events and was more consistent when subjects performed the task well. Human traveling theta and alpha waves can be modeled by a network of coupled oscillators because the direction of wave propagation correlated with the spatial orientation of local frequency gradients. Our findings suggest that oscillations support brain connectivity by organizing neural processes across space and time.

We re-examined the potential role of cortical traveling waves in human cognition by analyzing electrocorticographic (ECoG) brain recordings from 77 neurosurgical patients. We analyzed the data with a new technique that identifies traveling waves at the single-trial level across various frequencies and electrode configurations. As we describe below, we found traveling waves in 84% (65 of 77) of subjects (for subject details, see Table S1 ). Traveling waves were present across a wide frequency range (2 to 15 Hz) that included the theta and alpha bands and were relevant behaviorally, as their propagation correlated with subject performance and events in a memory task. Our results indicate that human behavior is supported by traveling waves of theta- and alpha-band oscillations that propagate across the cortex.

There were some reports of traveling-wave-like patterns in humans, but these patterns were generally observed during sleep or rest (). Given the potential importance of spatially coordinated brain oscillations for distributed cortical processes, several studies tested for large-scale synchronized oscillations in the human cortex during cognition. However, this oscillatory synchrony was rare or present only on a small scale in humans (). These results shed doubt on the possibility that large-scale spatially coordinated oscillations, such as traveling waves, figured prominently in human cortical processing.

One such pattern is a traveling wave, which consists of a spatially coherent oscillation that propagates progressively across the cortex, reminiscent of a wave moving across water. Traveling waves have been studied most extensively in animal models, where they were observed most often in fine-scale recordings and were shown to be functionally important to various behaviors, including visual perception (), spatial navigation (), and movement (). In conjunction with predictions of computational models, these findings suggest that traveling waves are a key mechanism for guiding the spatial propagation of neural activity and computational processes across the brain ().

The human cortex displays oscillations at various frequencies during cognition (). To understand how these patterns relate to behavior, researchers have generally examined the properties of oscillations at individual frequencies in local networks () or in point-to-point links between distinct regions (). These approaches ignore a key feature of cortical oscillations that emerged from animal studies—that oscillations at multiple frequencies form spatially continuous neural patterns ().

Oscillations have a distinctive role in brain function because they coordinate neuronal activity on multiple scales. Brain oscillations are important at the microscale, because they modulate the timing of neuronal spiking (), and at the macroscale, where they synchronize distributed cortical networks that are communicating (). Owing to oscillations’ ability to coordinate neural processes across multiple scales, characterizing their spatiotemporal properties may reveal how neurons across multiple regions are dynamically coordinated to support behavior ().

In summary, these results indicate that the WCO model provides a good model for human cortical traveling waves because it illustrates how the direction and speed of traveling waves can be predicted by the local oscillatory frequency gradients. The WCO model suggests that the existence and direction of traveling waves are modulated by two factors: the strength of local phase coupling and spatial gradients of intrinsic oscillation frequencies (). When phase coupling is absent, there are no traveling waves because oscillation frequencies differ between electrodes ( Figure 7 E). When phase coupling is present, traveling waves emerge, propagating in the direction of decreasing oscillation frequency ( Figures 7 F and 7G).

Although most traveling waves showed posterior-to-anterior propagation, some exceptional clusters reliably propagated in other directions (e.g., Figures 1 A–1D). We compared the directions of frequency gradients and propagation across clusters to test whether these factors were correlated, as predicted by the WCO model. If such a correlation existed, it would suggest that the exceptional propagation directions of some traveling waves were caused by corresponding distinctive frequency gradients. Such a pattern was evident in patient 1, as seen in Figures 7 B and 7C , which show that the mean directions of the wave propagation and the frequency gradients both had anterior-to-posterior orientations. We assessed this correspondence statistically at the group level by testing for a correlation in the mean directions of frequency gradients and wave propagation across clusters from all patients. Across clusters, the distribution of pairwise directional differences was clustered near zero (Rayleigh test Figure 7 D), which indicates that the direction of traveling wave propagation is positively correlated with the orientation of the local oscillatory frequency gradient.

(E–G) Illustration of a model of weakly coupled oscillators () with parameters matched to our findings. Color warmth increases with intrinsic frequency. When there is no phase coupling (E), individual oscillators demonstrate their intrinsic oscillation frequencies from 2 Hz (anterior) to 16 Hz (posterior). When phase coupling is present (F and G), all oscillators have the same temporal frequency (F) and a traveling wave emerges (G).

(D) Distribution of angular differences, across oscillation clusters, between the mean direction of traveling wave propagation and the mean direction of spatial frequency gradients.

(C) Distribution of the directions of the spatial frequency gradients across this cluster. In (B) and (C), black lines indicate the mean directions, thus demonstrating a correspondence between the directions of phase and frequency gradients.

(A) The instantaneous frequency distribution across an oscillation cluster from patient 1 on one trial (same as Figure 1 B), demonstrating an anterior-to-posterior decreasing spatial frequency gradient ().

Furthermore, we found that the WCO model predictions matched the direction of wave propagation in our data. In the WCO model, traveling waves propagate toward oscillators with the slowest intrinsic frequencies (). Similarly, in our data, we observed a systematic decrease in mean oscillation frequency along the posterior-to-anterior axis ( Figure 6 F), which also followed the mean direction of traveling wave propagation ( Figure 2 A). These patterns indicate that human cortical traveling waves generally propagate in a posterior-to-anterior direction because they are coordinated by an overall decrease in intrinsic frequency from posterior to anterior regions ().

A third theoretical model is a network of weakly coupled oscillators (WCOs) (), which have been used to model traveling waves in both neural and non-neural systems (). Traveling waves appear in a network of weakly coupled Kuramoto oscillators () when their arrangement shows two properties. First, the oscillators must be arranged in a linear array with the strength of interoscillator phase coupling decreasing with distance. Second, there must be a spatial gradient in intrinsic frequency across the array. When these two criteria are satisfied, traveling waves appear and propagate toward oscillators with slower intrinsic frequencies (). Critically, the WCO model predicts that oscillations with faster temporal frequencies propagate more rapidly ( Figures 6 A–6C), because the traveling wave is derived from coupling based on oscillatory phase rather than fixed time shifts (). Because we found a positive correlation between propagation speed and oscillation frequency ( Figures 6 D and 6E), it supports the idea that human cortical traveling waves are driven by WCOs.

Two notable theoretical neural models for traveling waves are the single-oscillator (SO) and excitable-network (EN) models (). Critically, both SO and EN models predict that traveling waves have a constant propagation speed, because the propagation is caused by neural conduction delays, which are constant. In contrast to the prediction of these models, we found a positive correlation between propagation speed and oscillation frequency—waves with faster temporal frequencies propagated more rapidly—which seemingly rejects these models. This positive correlation between frequency and speed could be seen both at the trial level, by comparing propagation speed and frequency across trials from the same electrodes ( Figure 6 C), and at the group level, by comparing the mean properties of traveling waves between electrode clusters ( Figure 6 E).

We next considered the neural mechanisms underlying traveling wave propagation. In animal model systems, identifying the mechanisms of traveling wave propagation is an area of active research (). At first blush, examining this issue in humans might be even more challenging than in animals, because human brain oscillations are rather variable across time and frequency () and because oscillations at neighboring frequencies in humans, like alpha and theta, are often considered to have different physiological roles (). Nonetheless, we considered the possibility that a single physiological mechanism could support traveling waves at multiple frequencies (). We would be confident in identifying such a mechanism if it could predict the properties of wave propagation across the range of traveling waves we observed, including signals that varied in frequency and speed across trials (e.g., Figures 6 A and 6B ).

(F) Population analysis of the relation between traveling wave frequency and cluster position along the anterior-posterior axis (Talairach coordinates, mm).

(E) Population analysis of the relation between traveling wave propagation speed and frequency across clusters. Each point indicates the mean frequency and mean propagation speed of the traveling waves from a given oscillation cluster.

(D) Histogram of within-cluster correlations between propagation speed and frequency. Each correlation coefficient is computed separately for each cluster.

(C) Across-trial analysis of the relation between traveling wave propagation speed and frequency for the electrode cluster whose signals are shown in (A) and (B). Each point indicates one trial. Black line is a least-squares fit.

(B) A traveling wave for these electrodes from a different trial when there was a slower temporal frequency. Same format as (A).

(A) A traveling wave on one trial for four electrodes in an oscillation cluster from patient 1 (see Figure 1 B).

In addition to DC, we also examined how other properties of traveling waves correlated with performance ( Table S3 ). On trials in which patients had fast reaction times, traveling waves showed increased PGD () and power (). Traveling waves did not show reliable performance-related correlations with temporal frequency, spatial frequency, or propagation speed (p values). Because the primary behavioral correlates of traveling waves are increased DC and PGD, it indicates that efficient cognitive processing is predicted by traveling waves maintaining their optimal propagation direction as opposed to moving at a faster speed or oscillating at a different temporal frequency.

We next examined whether traveling waves correlated with the efficiency of memory processing. We compared the DC of the traveling waves on each electrode cluster between trials where patients had fast versus slow reaction times (median split). Overall, DC positively correlated with performance, such that traveling waves moved more reliably in the preferred direction for each cluster on trials with fast reaction times ( Figure 5 ). This effect was significantly stronger for traveling waves in the frontal lobe ( Figure 5 A). This result is consistent with the notion that frontal theta oscillations are implicated in working memory (), although we have not ruled out the possibility that frontal traveling waves support a broader function, such as attention.

(E) Time course of DC for data from patient 3 that demonstrated elevated DC during trials in which the patient responded rapidly. Shading indicates p values from a non-parametric circular direction comparison test () between fast and slow response trials. Post hoc test:p < 0.001;p < 0.05;p < 0.1.

(D) Same as (C), for trials in which the patient responded slowly.

(C) Brain plot showing the mean relative phase distribution across an oscillation cluster in patient 3. Inset plot shows distribution of propagation directions across trials 340 ms after probe onset.

(B) Time course of mean DC in the frontal lobe between fast and slow trials. Gray shading indicates significance (paired t tests).

(A) Mean difference in DC between fast and slow trials for 1 s after cue onset, separately calculated for each region.

Given that it can be challenging to measure an oscillation’s phase when amplitude is low (), it is theoretically possible that our ability to measure traveling waves was diminished due to decreases in oscillatory power. We examined this possibility by comparing the time courses of power and DC between traveling waves from different areas ( Figure S5 ). In the frontal and temporal lobes, these time courses diverged dramatically, indicating that the increases in DC that we observed in these areas were not artifacts of task-induced power changes.

After a person views a stimulus, the brain exhibits stimulus-locked neural patterns, including phase resets of ongoing brain oscillations and evoked activity (). Because these can have oscillatory components (), we considered the possibility that stimulus-locked signals affected observations of traveling waves. We identified time- (evoked) and phase-locked signals on each electrode cluster and then compared the timing of these signals to the time course of the traveling waves on the same channels ( Figure S4 ). Evoked signals and phase resets were prominent200–400 ms post stimulus whereas traveling wave DC peaked later (800 ms). There were no correlations between the time points of peak DC and of the strongest evoked or phase-reset activity (p values). These results suggest that the traveling waves we measured were not artifacts of previously known stimulus-locked signals.

We confirmed that these patterns were reliable by measuring the time course of mean traveling wave DC at the group level. Following cue onset, traveling waves in the temporal and frontal lobes showed increases in DC above baseline levels ( Figure 4 E). Inversely, traveling waves from occipitoparietal clusters showed decreased DC during this same period, which was significantly different from the DC increase in the frontal and temporal lobes ( Figure 4 F; ANOVA,). Because frontal and temporal regions specifically show increased DC following cue onset, it indicates that traveling waves in these areas move more consistently during memory retrieval.

We computed each cluster’s directional consistency (DC), which measures the degree to which traveling waves on each cluster showed a consistent propagation direction at a particular time point relative to task events. DC, which is computed across trials, varies between 0 and 1, with 1 indicating that traveling waves always propagated in a single direction and 0 indicating that propagation directions were uniformly distributed. Figure 4 A illustrates the time course of mean DC during the cue response interval for the traveling waves in the frontal lobe of patient 26. This plot indicates that the traveling waves on this cluster were not directionally organized at the moment of cue onset, but 500 ms later, they reliably propagated anteriorly (DC = 0.34). A different pattern was present for the traveling waves on a posterior electrode cluster in patient 13 ( Figures 4 C and 4D), whereby the directional organization was consistent at cue onset and subsequently decreased.

(E) Time course of traveling wave DC. Bars indicate the mean DC for each region when patient is out of task.

(B) Brain plot showing the mean relative phase shift at each electrode at the time point of peak consistency for the same subject as (A).

(A) Time course of directional consistency (DC) for a traveling wave at 12.5 Hz from patient 26’s frontal lobe. Inset circular histograms indicate the distributions of propagation directions across trials at the labeled time points.

We hypothesized that the spatial propagation of traveling waves reflected the movement of neural activity across the cortex in a manner that was important for behavior. Although some previous studies had measured human cortical traveling waves during tasks, they did not show clear correlations to behavior (). We tested for a potential functional role for traveling waves by comparing their properties through the course of memory processing. In each trial of the memory task (), patients learned a list of stimuli and then viewed a retrieval cue. By comparing traveling wave properties during the task, we sought to identify functional properties of traveling waves and to test whether they differ across brain regions.

We computed additional properties of traveling waves at the group level. Although most subjects had only one or two electrode clusters with traveling waves, a small number of subjects showed up to five such clusters ( Figure 3 A). In most cases (99% of electrodes), the multiple clusters in a subject did not overlap. Traveling waves with frequencies near8 Hz had the highest power ( Figure 3 B). The electrode clusters with traveling waves ranged in size substantially ( Figure 3 C), having a median radius of 2.5 cm (20) up to a maximum of6 cm (113). Traveling waves had a median propagation speed of 0.55 m/s and a median wavelength of 11.7 cm, but these values varied substantially across the population ( Figures 3 D and 3E). Finally, we measured the prevalence of traveling waves at the single-trial level. Across the significant oscillation clusters, traveling waves were present on 61% of single trials (median), although some clusters showed traveling waves on 80%–100% of trials ( Figure 3 F).

(F) Distribution of the mean percentage of time when individual clusters showed reliable traveling waves at the single-trial level.

(C) Distributions of estimated spatial radius across traveling wave clusters. Purple bars indicate data from grid electrodes; other bars come from strips. Black line indicates median.

We also compared the temporal frequencies of the oscillation clusters that showed significant traveling waves ( Figure 2 C). Traveling waves were present at frequencies from 2 to 15 Hz. Traveling waves in the frontal lobe had a slower mean temporal frequency in the theta range (6 Hz). In contrast, traveling waves in occipital and temporal regions had faster alpha-band frequencies (mean 9 Hz; ANOVA,). It is notable that the frequencies of the traveling waves in these areas were similar to the frequencies of the oscillations that had been reported in these regions earlier () because it suggests that many previously reported neural oscillations could in fact be traveling waves.

Having established that human cortical traveling waves were widespread, we next studied their properties in more detail at the population level. First, we compared the properties of traveling waves from oscillation clusters identified in different brain areas ( Figures 2 A and 2B ; Video S2 ). Traveling waves in the frontal and temporal lobes generally propagated in a posterior-to-anterior direction (p values, Rayleigh tests). In addition, frontal traveling waves had a tendency to propagate toward the midline. In the occipital and parietal lobes, the propagation direction of traveling waves varied and were not reliably clustered ().

(C) Distributions of temporal frequencies for traveling waves from different regions; shaded region indicates probability density. Black dots indicate the mean frequency from individual electrode clusters.

(B) Distribution of the mean direction of traveling waves from each lobe. The orientations of the polar histograms are projected to match the lateral brain view.

(A) Spatial topography of mean traveling wave direction and frequency. Colored arrows indicate the mean direction and frequency of traveling waves observed at an electrode within 1.5 cm.

We applied this methodology across our dataset and found that 140 (of 208; 67%) oscillation clusters had consistent traveling waves, defined as showing both reliable plane waves at the single-trial level and having a consistent propagation direction (see STAR Methods ). 30 (14%) oscillation clusters showed reliable plane waves at the single-trial level but did not have a consistent propagation direction across trials; the remaining 38 (18%) clusters did not show reliable single-trial plane waves. Traveling waves involved 47% of all electrodes and were present in all lobes of the neocortex across both left and right hemispheres ( Table S2 ). Thus, traveling waves are a broad phenomenon across the human brain.

We assessed whether each oscillation cluster exhibited a reliable traveling wave using a permutation procedure. Here, we compared each electrode cluster’s median PGD value to the distribution of PGD values expected by chance ( Figure 1 E). This analysis demonstrated that traveling waves on the cluster in Figures 1 A–1D were statistically reliable on a single-trial basis (mean). Furthermore, by assessing the distribution of propagation directions across trials for this cluster, we determined that these traveling waves consistently moved in an anterior-to-posterior direction (, Rayleigh Figure 1 F). The traveling wave on this cluster is also visible by using a simpler approach based on temporal averaging ( Figure 1 G). Figures 1 H–1J shows example electrode clusters in other patients that also showed robust traveling waves.

We used circular statistics () to first identify human cortical traveling waves at the single-trial level and then to compare their properties at the group level. For each oscillation cluster, at each time point within a trial, we used a circular-linear model to characterize the relation between electrode position and oscillation phase ( Figure 1 C). This procedure models each cluster’s instantaneous phase distribution as a plane wave, finding the best-fitting spatial phase gradient. The fitted phase gradient provides a quantitative estimate of the speed and direction of traveling wave propagation ( Figure S3 ). We compute the instantaneous robustness of the traveling wave on each electrode cluster by computing, for each trial, the proportion of phase variation that is explained by the circular-linear model, which we call the phase-gradient directionality (PGD).

We quantified this phenomenon by calculating the relative phase of the oscillation on each electrode and trial. On this trial, the electrodes in this cluster showed a continuous spatial phase shift across a range of240° ( Figure 1 B). In this scheme, positive phase shifts correspond to oscillators that have been advancing for a longer period of time. Thus, because the phase was largest at posterior electrodes, it indicates that the electrode cluster showed an anterior-to-posterior traveling wave on this trial (see Video S1 ).

Visual inspection of the signals across many oscillation clusters indicated that the timing of individual oscillation cycles varied systematically with the electrode location, which is indicative of a traveling wave. As an example, Figures 1 A–1D show the activity on one trial across an 8.3-Hz oscillation cluster in an electrode grid from patient 1. While 8.3-Hz oscillations were visible on all channels in this grid, the relative timing of this signal varied systematically, such that the onset time of each oscillation cycle correlated with the electrode’s anterior-posterior position.

(G) Illustration of the average traveling wave on this cluster across trials. Each electrode’s time-averaged waveform is computed as the average signal relative to oscillation troughs triggered from electrode 5.

(F) Circular histogram indicating the distribution across trials of propagation directions for the traveling waves on this cluster.

(E) Analysis of phase-gradient directionality (PGD) for the traveling waves on this cluster. Black line indicates the median PGD for this cluster, computed across trials. Gray bars indicate the distribution of median PGD values expected by chance for this cluster, estimated from shuffled data.

(D) The topography of this traveling wave’s phase at four time points during this trial.

(C) Illustration of the circular-linear model for quantifying single-trial spatial phase gradients and traveling waves. Black dots indicate the relative phase for each electrode in this cluster on this trial; colored surface indicates the fitted phase plane from the circular-linear model; black lines indicate residuals.

(B) Relative phase of this traveling wave on this trial across the 3 × 8 electrode grid. Color indicates the relative phase on each electrode. Arrow indicates direction of wave propagation. Inset shows the normalized power spectrum for each electrode, demonstrating that all the electrodes exhibit narrowband 8.3-Hz oscillations.

(A) Top: raw signals for 4 s of one trial from three selected electrodes. The selected electrodes are ordered from anterior (top) to posterior (bottom). Middle: a 500-ms zoomed version of the signals from the top panel. Bottom: signals filtered at 6–10 Hz.

The widespread presence of oscillation clusters indicates that neuronal oscillations at a single frequency were present across large regions of the human cortex. If the timing of these oscillations were synchronized, it could provide evidence for large-scale oscillatory networks (). Thus, we next characterized the timing of activity across each oscillation cluster to identify patterns of phase synchrony, such as traveling waves ().

The frequencies of oscillation clusters often differed across individuals even for electrodes in the same anatomical region ( Figure S2 ). This suggested to us that oscillation clusters could reflect distinctive cortical networks that were individualized for a given patient. To assess whether there were true intersubject differences in the frequencies of oscillation clusters, we tested for a spatial correlation in the frequencies of narrowband oscillations across electrodes in each subject using Moran’s I statistic (). Here, we computed I for each subject and compared the mean I with the values computed from a shuffling procedure that randomly interchanged electrodes between subjects. This analysis thus tested the hypothesis that the frequencies of oscillations were more correlated between nearby electrodes within a patient compared to electrodes at similar anatomical locations in other patients. The mean within-subject frequency correlation that we observed () was entirely outside the range of values computed from the shuffled data ( Figure S1 G). This result indicated that clusters of ECoG electrodes with narrowband oscillations at the same frequency reflected robust within-subject spatial frequency clustering.

Using this technique, we identified electrodes with narrowband oscillations at various frequencies. Most patients had spatially contiguous clusters of electrodes that showed narrowband oscillations at the same or a similar frequency. We identified these electrode groups using a clustering algorithm (see STAR Methods Figures S1 A–S1F). We refer to a contiguous group of four or more electrodes with oscillations at similar frequencies as an “oscillation cluster.” Across 77 patients, we found a total of 208 oscillation clusters. Oscillation clusters were present at frequencies from 2 to 15 Hz, involved 59% of all electrodes (2,401 of 4,077), and were present in 74 (96%) patients.

One form of a traveling wave that could appear in ECoG signals from one patient is a phase wave, which is a neuronal oscillation that is visible simultaneously on multiple electrodes at the same frequency with a systematic timing (or phase) gradient across space. Owing to the spatial phase gradient, the oscillation appears to propagate across the cortex (). A requirement for this type of traveling wave is that the signals across multiple neighboring electrodes exhibit oscillations at the same frequency. Thus, our first step in identifying human cortical traveling waves was to find clusters of cortex where contiguous electrodes showed oscillations at the same frequency. To identify these patterns, we examined the recording from each electrode individually, identified sites that showed narrowband oscillations, and then measured their frequency. We distinguished these oscillations by using a peak-picking algorithm, which found narrowband oscillatory peaks that were elevated over the backgroundECoG power spectrum ().

To identify traveling waves in the human cortex, we examined direct ECoG brain recordings from neurosurgical patients performing a working memory task (), which was previously shown to elicit large-amplitude oscillations related to memory at various frequencies (). Here, we analyzed these data using a new analytical framework that can identify traveling waves by characterizing the spatiotemporal structure of the oscillations in each patient individually.

Discussion

Klimesch, 1999 Klimesch W. EEG alpha and theta oscillations reflect cognitive and memory performance: a review and analysis. Roux and Uhlhaas, 2014 Roux F.

Uhlhaas P.J. Working memory and neural oscillations: α-γ versus θ-γ codes for distinct WM information?. Lisman and Jensen, 2013 Lisman J.E.

Jensen O. The θ-γ neural code. Our work shows that human cortical traveling waves can be modeled as a network of WCOs. In addition to suggesting a mechanism underlying traveling waves, the WCO model has implications for understanding traveling wave dynamics in behavior. A key part of the WCO model is the link between local oscillation frequency and the direction of wave propagation. Traditionally, the frequency of a brain oscillation has been considered to be important because it indicates the functional role of a given oscillation. For example, oscillations in the neighboring theta and alpha bands have been associated with memory and idling, respectively (). Instead, our results suggest that—at least for the frequencies and regions we examined—the precise frequency of an oscillation could most closely relate to broad physiological factors such as the direction of wave propagation ().

Bastos et al., 2015 Bastos A.M.

Vezoli J.

Bosman C.A.

Schoffelen J.-M.

Oostenveld R.

Dowdall J.R.

De Weerd P.

Kennedy H.

Fries P. Visual areas exert feedforward and feedback influences through distinct frequency channels. Going forward, it will be important to test the functional relevance of traveling waves in more detail. One key issue is characterizing the potential importance of the direction of wave propagation. Although most traveling waves propagated in a posterior-to-anterior direction, some subjects reliably showed traveling waves with the opposite direction of propagation. Given this variability, an important issue is whether traveling waves with different directions support distinct functional or physiological processes. In visual perception, there is evidence that oscillations with anterior and posterior directions support feedforward and feedback processing, respectively (). Likewise, it will be interesting to test whether human traveling theta and alpha waves move in different directions to support distinct physiological processes. An alternate possibility is that human traveling theta and alpha waves consistently support a single functional process and that the variation in propagation directions we observed reflect intersubject differences in the anatomy or frequency gradients.

Kjelstrup et al., 2008 Kjelstrup K.B.

Solstad T.

Brun V.H.

Hafting T.

Leutgeb S.

Witter M.P.

Moser E.I.

Moser M.B. Finite scale of spatial representation in the hippocampus. Lubenov and Siapas, 2009 Lubenov E.V.

Siapas A.G. Hippocampal theta oscillations are travelling waves. Badre and D’Esposito, 2009 Badre D.

D’Esposito M. Is the rostro-caudal axis of the frontal lobe hierarchical?. Harry et al., 2016 Harry B.B.

Umla-Runge K.

Lawrence A.D.

Graham K.S.

Downing P.E. Evidence for integrated visual face and body representations in the anterior temporal lobes. Finally, a different potential role for traveling waves is that they could relate to detailed features of neural coding. It is notable that several known neural coding schemes also exhibit posterior-to-anterior spatial gradients, such as the representation of spatial and temporal information in the hippocampus (), of task rules in the frontal lobe (), and of object abstractness in the visual system (). Traveling waves that follow the structure of these networks could be important for these computational processes.

Patten et al., 2012 Patten T.M.

Rennie C.J.

Robinson P.A.

Gong P. Human cortical traveling waves: dynamical properties and correlations with responses. Bahramisharif et al., 2013 Bahramisharif A.

van Gerven M.A.

Aarnoutse E.J.

Mercier M.R.

Schwartz T.H.

Foxe J.J.

Ramsey N.F.

Jensen O. Propagating neocortical gamma bursts are coordinated by traveling alpha waves. Alexander et al., 2013 Alexander D.M.

Jurica P.

Trengove C.

Nikolaev A.R.

Gepshtein S.

Zvyagintsev M.

Mathiak K.

Schulze-Bonhage A.

Ruescher J.

Ball T.

van Leeuwen C. Traveling waves and trial averaging: the nature of single-trial and averaged brain responses in large-scale cortical signals. Elements of the traveling theta and alpha waves we observed were noted in previous studies that used different types of methods to examine spatial characteristics of human brain signals (e.g.,, among many others). A differentiating feature of our approach was that we identified traveling waves across multiple regions, directions, and frequencies directly in individual subjects at the single-trial level. Because different subjects exhibited widely varying types of traveling waves even in the same anatomical region, it suggests that there are substantial intersubject differences in the spatial and temporal structure of brain oscillations and traveling waves. These patterns may not be adequately appreciated because they are difficult to capture with typical group-average analyses.

Freeman, 1975 Freeman W. Mass Action in the Nervous System. Freeman, 2003 Freeman W.J. The wave packet: an action potential for the 21st century. Michel et al., 2004 Michel C.M.

Murray M.M.

Lantz G.

Gonzalez S.

Spinelli L.

Grave de Peralta R. EEG source imaging. Alexander et al., 2013 Alexander D.M.

Jurica P.

Trengove C.

Nikolaev A.R.

Gepshtein S.

Zvyagintsev M.

Mathiak K.

Schulze-Bonhage A.

Ruescher J.

Ball T.

van Leeuwen C. Traveling waves and trial averaging: the nature of single-trial and averaged brain responses in large-scale cortical signals. More broadly, because our results show that neuronal oscillations can be synchronized across large regions of cortex, researchers and clinicians examining noninvasive brain recordings should consider that aspects of their findings may result from large neural masses () rather than precisely localizable point sources (). Furthermore, whereas many electrical signals from the brain are commonly interpreted as event-related potentials or as task-induced power changes from local oscillators, instead it is possible that these signals could result from traveling waves that become transiently organized at a particular time point and phase across a cortical region (). Thus, single-trial analysis of traveling waves could be an intriguing new direction for scalp electroencephalography and magnetoencephalography.

Ezzyat et al., 2017 Ezzyat Y.

Kragel J.E.

Burke J.F.

Levy D.F.

Lyalenko A.

Wanda P.

O’Sullivan L.

Hurley K.B.

Busygin S.

Pedisich I.

et al. Direct brain stimulation modulates encoding states and memory performance in humans. In addition to demonstrating a new fundamental feature of human brain activity, our findings could have significant practical implications. The potential for non-invasively measuring traveling waves on a single-trial basis may be useful for the development of brain-computer interfaces (BCI). However, for traveling waves to be useful for BCIs, given the intersubject differences we observed, it seems important to characterize these patterns individually for each subject rather than averaging across individuals. Our results suggest a way to predict the mean direction of traveling wave propagation at the individual subject level, by measuring the spatial gradient of a subject’s intrinsic oscillatory frequencies. Measuring traveling waves’ instantaneous properties may provide a new tool for neural interfacing, by tracking a subject’s attention or cognitive state for timing stimulus presentation or neuromodulation ().