The organization of the phase of electrical activity in the cortex is critical to inter-site communication, but the balance of this communication across large-scale (>8 cm), macroscopic (>1 cm), and mesoscopic (1 cm to 1 mm) ranges is an open question. The spatial frequencies (i.e. the spatial scales) of cortical waves have been characterized in the gray matter for micro- and mesoscopic scales of cortex and show decreasing spatial power with increasing spatial frequency. This research, however, has been limited by the size of the measurement array, thus excluding large-scale traveling waves. Obversely, poor spatial resolution of extracranial measurements prevents incontrovertible large-scale estimates of spatial power. We estimate the spatial frequency spectrum of phase dynamics in order to quantify the uncertain large-scale range, utilizing stereotactic electroencephalogram to measure local-field potentials within the gray matter. We take advantage of the large extent of spatial coverage of the cortical sheet, and irregular sampling is offset by use of linear algebra techniques. We find the spatial power of the phase is highest at the lowest spatial frequencies (longest wavelengths), consistent with the power spectra ranges for micro- and meso-scale dynamics, but here shown up to the size of the measurement array (up to 8-16 cm). This result arises across a wide range of temporal frequencies, from the delta band (1-3 Hz) through to the high gamma range (60-100 Hz).

Attention facilitates stimulus processing by selecting specific locations (spatial attention) or features (feature-based attention). It can be sustained on a given location or feature or reoriented between locations or between features, enabling attentional exploration. Sustained attention has long been associated with alpha (8-12 Hz) oscillations, whereas exploratory attention has been more recently proposed to rely on theta (4-7 Hz) oscillations. However, whether theta oscillations universally index exploration across spatial and nonspatial dimensions remains unclear as prior evidence stems from disparate paradigms and attentional manipulations. Here, we systematically examined attentional exploration of stimulus dimensions (location/feature) in human participants (male/female) using EEG and a cueing paradigm during the (1) precue-to-stimulus (first attentional orienting) and (2) poststimulus (during stimulus processing) trial periods. In the precue-to-stimulus period, multivariate decoding revealed rhythmic modulations of neural information content: alpha-band rhythms emerged during sustained attention regardless of dimension, whereas theta-band rhythms were observed selectively when attention was sustained on features but required exploration of spatial locations. Poststimulus analyses confirmed this link: theta power increased during invalid trials that required attentional reorienting relative to valid trials, and this effect predicted faster reaction times and higher accuracy. Together, these findings clarify the functional role of neural oscillations in attentional orienting and exploration, highlighting theta as a signature of spatial exploration rather than a domain-general mechanism.

Abstract Brain activity unfolds across space and time, giving rise to spatiotemporal dynamics that can manifest as cortical traveling waves –smooth phase shifts propagating across the cortex. Although traveling waves have been observed across species and measurement scales, their functional role in human cognition remains largely inferred from correlational evidence. In healthy humans, large-scale neural dynamics must be studied non-invasively, which provides limited access to their neural origins. Here, we tested whether global traveling waves causally contribute to inter-areal communication during attention. Using transcranial magnetic stimulation (TMS), we induced long-range traveling waves detectable with electroencephalography and assessed their neural and behavioral consequences during an attentional search task. Double-pulse TMS applied over the right frontal eye field transiently disrupted ongoing global waves and selectively induced direction- and frequency-specific traveling waves propagating toward the occipital visual cortex. These TMS-induced anterior-to-posterior theta traveling waves were rhythmically modulated by stimulation latency relative to search-trial onset. Critically, behavioral performance exhibited the same rhythmic pattern, with improved attentional search performance when TMS-induced traveling waves were more prominent. Together, these findings provide causal evidence that large-scale traveling waves support inter-areal communication during rhythmic visual attention.

Cortical traveling waves have been proposed as a fundamental mechanism for neural communication and computation. Methodological uncertainties currently limit the interpretability of noninvasive, extracranial traveling wave data, sparking debates about their cortical origin. Studies using EEG or MEG typically report waves that cover large portions of the sensor array which are often interpreted as reflecting long range cortical waves. Meanwhile, invasive, intracranial recordings in humans and animals routinely find both local, mesoscopic waves and large-scale, macroscopic waves in cortex. Whether the global sensor array waves found with EEG/MEG necessarily correspond to macroscopic cortical waves or whether they are merely projections of local dynamics remains unclear. In this study, we made use of the well-established retinotopic organization of early visual cortex to generate traveling waves with known properties in human participants (N = 19, 10 female, 9 male) via targeted visual stimulation, while simultaneously recording MEG and EEG. The inducer stimuli were designed to elicit waves whose traveling direction in mesoscopic retinotopic visual areas depends on stimulus direction, while leaving macroscopic activation patterns along the visual hierarchy largely unchanged. We observed that the preferred direction of traveling waves across the sensor array was influenced by that of the visual stimulus, but only at the stimulation frequency. Comparison between single-trial and trial-averaged responses further showed considerable temporal variation in traveling wave patterns across trials. Our results highlight that under tight experimental control, noninvasive, extracranial recordings can recover mesoscopic traveling wave activity, thus making them viable tools for the investigation of spatially constrained wave dynamics.

Brain rhythms seem central to understanding the neurophysiological basis of human cognition. Yet, despite significant advances, key questions remain unresolved. In this comprehensive position paper, we review the current state of the art on oscillatory mechanisms and their cognitive relevance. The paper critically examines physiological underpinnings, from phase-related dynamics like cyclic excitability, to amplitude-based phenomena, such as gating by inhibition, and their interactions, such as phase-amplitude coupling, as well as frequency dynamics, like sampling mechanisms. We also critically evaluate future research directions, including travelling waves and brain-body interactions. We then provide an in-depth analysis of the role of brain rhythms across cognitive domains, including perception, attention, memory, and communication, emphasising ongoing debates and open questions in each area. By summarising current theories and highlighting gaps, this position paper offers a roadmap for future research, aimed at facilitating a unified framework of rhythmic brain function underlying cognition.

Brain oscillations might be traveling waves propagating in cortex. Studying their propagation within single cortical areas has mostly been restricted to invasive measurements. Their investigation in healthy humans, however, requires non-invasive recordings, such as MEG or EEG. Identifying traveling waves with these techniques is challenging because source summation, volume conduction, and low signal-to-noise ratios make it difficult to localize cortical activity from sensor responses. The difficulty is compounded by the lack of a known ground truth in traveling wave experiments. Rather than source-localizing cortical responses from sensor activity, we developed a two-part model-based neuroimaging approach: (1) The putative neural sources of a propagating oscillation were modeled within primary visual cortex (V1) via retinotopic mapping from functional MRI recordings (encoding model); and (2) the modeled sources were projected onto MEG and EEG sensors to predict the resulting signal using a biophysical head model. We tested our model by comparing its predictions against the MEG-EEG signal obtained when participants viewed visual stimuli designed to elicit either fovea-to-periphery or periphery-to-fovea traveling waves or standing waves in V1, in which ground truth cortical waves could be reasonably assumed. Correlations on within-sensor phase and amplitude relations between predicted and measured data revealed good model performance. Crucially, the model predicted sensor data more accurately when the input to the model was a traveling wave going in the stimulus direction compared to when the input was a standing wave, or a traveling wave in a different direction. Furthermore, model accuracy peaked at the spatial and temporal frequency parameters of the visual stimulation. Together, our model successfully recovers traveling wave properties in cortex when they are induced by traveling waves in stimuli. This provides a sound basis for using MEG-EEG to study endogenous traveling waves in cortex and test hypotheses related with their role in cognition.

Attention is key to perception and human behavior, and evidence shows that it periodically samples sensory information (<20Hz). However, this view has been recently challenged due to methodological concerns and gaps in our understanding of the function and mechanism of rhythmic attention. Here we used an intensive ∼22-hour psychophysical protocol combined with reverse correlation analyses to infer the neural representation underlying these rhythms. Participants (male/female) performed a task in which covert spatial (sustained and exploratory) attention was manipulated, and then probed at various delays. Our results show that sustained and exploratory attention periodically modulate perception via different neural computations. While sustained attention suppresses distracting stimulus features at the alpha (∼12Hz) frequency, exploratory attention increases the gain around task-relevant stimulus feature at the theta (∼6Hz) frequency. These findings reveal that both modes of rhythmic attention differentially shape sensory tuning, expanding the current understanding of the rhythmic sampling theory of attention.Significance statementFor the past decade, low-frequency rhythms have been observed in attentional performance. Here, we go beyond description and assess the underlying neural computations in the sensory system. We used an intensive psychophysical protocol combined with reverse correlation analysis to infer the system’s sensitivity to and selectivity for stimulus feature (orientation) across time, and for two attention modes, i.e., sustained and exploratory attention. Our results reveal that sustained and exploratory attention modes differentially shape the sensory tuning to stimulus features: respectively altering either noise suppression or signal enhancement rhythmically, leading to alternating periods of performance enhancement and decrement.

Cortical traveling waves-smooth changes of phase over time across the cortical surface-have been proposed to modulate perception periodically as they travel through retinotopic cortex, yet little is known about the underlying computational principles. Here, we make use of binocular rivalry, a perceptual phenomenon in which perceptual (illusory) waves are perceived when a shift in dominance occurs between two rival images. First, we assessed these perceptual waves using psychophysics. Participants viewed a stimulus restricted to an annulus around fixation, with orthogonal orientations presented to each eye. The stimulus presented to one eye was of greater contrast, thus generating perceptual dominance. When a patch of greater contrast was flashed briefly at one position in the other eye, it created a change in dominance that started at that location of the flash and expanded progressively, like a wave, as the previously suppressed stimulus became dominant. We found that the duration of the perceptual propagation increased with both distance traveled and eccentricity of the annulus. Diverting attention away from the annulus reduced drastically the occurrence and the speed of the wave. Second, we developed a computational model of traveling waves in which competition between the neural representations of the two stimuli is driven by both attentional modulation and mutual inhibition. We found that the model captured the key features of wave propagation dynamics. Together, these findings provide new insights into the functional relevance of cortical traveling waves and offer a framework for further experimental investigation into their role in perception.

Rhythmic light stimulation offers solutions to innumerable cognitive and neurological disorders. However, like any neuromodulatory technique, responses to rhythmic light stimulation are highly variable, producing challenges in replicating lab-based studies and translating findings to the clinic. Across three MEG/EEG experiments, we show that this variability can, in part, be attributed to rhythmic light stimulation eliciting multiple, coexisting neural responses which have separable impacts on cognition. Specifically, we find that rhythmic light stimulation produces distinct neural responses at the fundamental ( f ) and second harmonic ( 2f ) frequencies, and that these responses are differentially shaped by endogenous oscillatory dynamics that vary across participants. Importantly, these responses separably contribute to perception, with harmonic gamma-band responses supporting the representation of stimulus-specific information, and the phase of harmonic alpha-band responses causally contributing to near-threshold visual perception. We reproduce these effects across datasets, paradigms, and oscillatory bands, suggesting that the multiplex oscillatory responses elicited by rhythmic light stimulation are a robust and pervasive phenomenon. We propose that the complexity of neural responses to rhythmic stimulation can explain why there is substantial variability between studies using these techniques, and that understanding these complex responses may help advance neuromodulatory technologies for both fundamental and clinical neuroscience. Supplementary Material All supplementary material can be found at the end of this document. ### Competing Interest Statement The authors have declared no competing interest. Leverhulme Trust, ECF-2021-628

AbstractThe organization of the phase of electrical activity in the cortex is critical to inter-site communication, but the balance of this communication across macroscopic (>15cm), mesoscopic (1 to 15cm) and microscopic (<1cm) ranges is an open question. Traveling waves in the cortex are spatial phase gradients, such that phase values change smoothly through the cortical sheet over time. Macroscopic cortical traveling waves have been understudied compared to micro- or mesoscopic waves. The spatial frequencies (i.e., the characteristic scales) of cortical waves have been characterized in the grey-matter for micro- and mesoscopic scales of cortex and show decreasing spatial power with increasing spatial frequency. This research, however, has been limited by the size of the measurement array, thus excluding macroscopic traveling waves. Obversely, poor spatial resolution of extra-cranial measurements prevents incontrovertible macroscopic estimates of spatial power via electroencephalogram and magnetoencephalogram. We apply a novel method to estimate the spatial frequency spectrum of phase dynamics in order to quantify the uncertain macroscopic scale. Stereotactic electroencephalogram is utilized to leverage measurements of local-field potentials within the grey matter, while also taking advantage of the sometimes large extent of spatial coverage. Irregular sampling of the cortical sheet is offset by use of linear algebra techniques to empirically estimate the spatial frequency spectrum. We find the spatial power of the phase is highest at the lowest spatial frequencies (longest wavelengths), consistent with the power spectra ranges for micro- and meso-scale dynamics, but here shown up to the size of the measurement array (15-25cm), i.e., approaching the entire extent of cortex. Low spatial frequencies dominate the cortical phase dynamics. This has important functional implications as it means that the phase measured at a single contact in the grey-matter is more strongly a function of global phase organization than local. This result arises across a wide range of temporal frequencies, from the delta band (2Hz) through to the high gamma range (100Hz).

Visual perception waxes and wanes periodically over time at low frequencies (theta: 4-7 Hz; alpha: 8-13 Hz), creating "perceptual cycles." These perceptual cycles can be induced when stimulating the brain with a flickering visual stimulus at the theta or alpha frequency. Here, we took advantage of the well-known organization of the visual system into retinotopic maps (topographic correspondence between visual and cortical spaces) to assess the spatial organization of induced perceptual cycles. Specifically, we tested the hypothesis that they can propagate across the retinotopic space. A disk oscillating in luminance (inducer) at 4, 6, 8, or 10 Hz was presented in the periphery of the visual field to induce perceptual cycles at specific frequencies. EEG recordings verified that the brain responded at the corresponding inducer frequencies and their first harmonics. Perceptual cycles were assessed with a concurrent detection task-target stimuli were displayed at threshold contrast (50% detection) at random times during the inducer. Behavioral results confirmed that perceptual performance was modulated periodically by the inducer at each frequency. We additionally manipulated the distance between the target and the inducer (three possible positions) and showed that the optimal phase, that is, moment of highest target detection, shifted across target distance to the inducer, specifically when its flicker frequency was in the alpha range (8 and 10 Hz). These results demonstrate that induced alpha perceptual cycles travel across the retinotopic space in humans at a propagation speed of 0.3-0.5 m/sec, consistent with the speed of unmyelinated horizontal connections in the visual cortex.

The role of brain oscillations in various cognitive functions including visual perception is extensively studied. However, their spatial organization is rarely scrutinized. Recent studies suggest that brain oscillations can travel across the cortex. Mesoscopic waves, traveling within cortical areas, are mainly observed with invasive measurements (e.g., electrocorticography), which limits their investigation. Measuring traveling waves non-invasively in human, such as with magneto- and electro-encephalography (MEG, EEG), is particularly challenging due to technical and biophysical constrains (e.g., source summation, volume conduction). To address these issues, we developed a novel model-based neuroimaging approach. First, in a two-stage computational model, (1) the putative neural sources of a propagating 5Hz-oscillation were modeled within the early visual region (V1) using individual retinotopic mapping from functional MRI recordings (encoding model); and (2) the modeled sources were projected onto the MEG-EEG sensor space to predict the resulting MEG-EEG signal (forward biophysical head model). Second, we tested our model by comparing its predictions against the MEG-EEG signal obtained when participants viewed a radial visual stimulus consisting of a black-and-white sinusoidal wave oscillating at 5Hz and propagating from the center to the periphery of the screen. This "traveling" stimulus was used to elicit a 5Hz-neural oscillation traveling across the retinotopic space. A "standing" stimulus, oscillating at the same frequency with the same phase across the visual field, was used as control. Correlations on amplitude and phase between predicted and measured data revealed a good performance of the model. Crucially, the model was able to distinguish MEG-EEG recordings while participants viewed a traveling stimulus compared to a standing stimulus. Our model aims at bridging the gap between mesoscopic (neuronal populations) and macroscopic (full brain recordings) scales, to facilitate a better understanding of the functional role of brain oscillations for cognition.