A sensorimotor role for traveling waves in primate visual cortex

A Translaminar Spacetime Code Supports Touch-Evoked Traveling Waves

Linking sensory-evoked traveling waves to underlying circuit patterns is critical to understanding the neural basis of sensory perception. To form this link, we performed simultaneous electrophysiology and two-photon calcium imaging through transparent NeuroGrids and mapped touch-evoked cortical traveling waves and their underlying microcircuit dynamics. In awake mice, both passive and active whisker touch elicited traveling waves within and across barrels, with a fast early component followed by a variable late wave that lasted hundreds of milliseconds post-stimulus. Strikingly, late-wave dynamics were modulated by stimulus value and correlated with task performance. Mechanistically, the late wave component was i) modulated by motor feedback, ii) complemented by a sparse ensemble pattern across layer 2/3, which a balanced-state network model reconciled via inhibitory stabilization, and iii) aligned to regenerative Layer-5 apical dendritic Ca 2+ events. Our results reveal a translaminar spacetime pattern organized by cortical feedback in the sensory cortex that supports touch-evoked traveling waves.

GRAPHICAL ABSTRACT AND HIGHLIGHTS

Whisker touch evokes both early- and late-traveling waves in the barrel cortex over 100's of millisecondsReward reinforcement modulates wave dynamics Late wave emergence coincides with network sparsity in L23 and time-locked L5 dendritic Ca 2+ spikes Experimental and computational results link motor feedback to distinct translaminar spacetime patterns.

Representing stimulus motion with waves in adaptive neural fields

Traveling waves of neural activity emerge in cortical networks both spontaneously and in response to stimuli. The spatiotemporal structure of waves can indicate the information they encode and the physiological processes that sustain them. Here, we investigate the stimulus-response relationships of traveling waves emerging in adaptive neural fields as a model of visual motion processing. Neural field equations model the activity of cortical tissue as a continuum excitable medium, and adaptive processes provide negative feedback, generating localized activity patterns. Synaptic connectivity in our model is described by an integral kernel that weakens dynamically due to activity-dependent synaptic depression, leading to marginally stable traveling fronts (with attenuated backs) or pulses of a fixed speed. Our analysis quantifies how weak stimuli shift the relative position of these waves over time, characterized by a wave response function we obtain perturbatively. Persistent and continuously visible stimuli model moving visual objects. Intermittent flashes that hop across visual space can produce the experience of smooth apparent visual motion. Entrainment of waves to both kinds of moving stimuli are well characterized by our theory and numerical simulations, providing a mechanistic description of the perception of visual motion.

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

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.

A Traveling Waves Perspective on Temporal Binding

Brain oscillations are involved in many cognitive processes, and several studies have investigated their role in cognition. In particular, the phase of certain oscillations has been related to temporal binding and integration processes, with some authors arguing that perception could be an inherently rhythmic process. However, previous research on oscillations mostly overlooked their spatial component: how oscillations propagate through the brain as traveling waves, with systematic phase delays between brain regions. Here, we argue that interpreting oscillations as traveling waves is a useful paradigm shift to understand their role in temporal binding and address controversial results. After a brief definition of traveling waves, we propose an original view on temporal integration that considers this new perspective. We first focus on cortical dynamics, then speculate about the role of thalamic nuclei in modulating the waves, and on the possible consequences for rhythmic temporal binding. In conclusion, we highlight the importance of considering oscillations as traveling waves when investigating their role in cognitive functions.

Perceptual Cycles Travel Across Retinotopic Space

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.

Neural population dynamics of human working memory

The activity of neurons in macaque prefrontal cortex (PFC) persists during working memory (WM) delays, providing a mechanism for memory.1,2,3,4,5,6,7,8,9,10,11 Although theory,11,12 including formal network models,13,14 assumes that WM codes are stable over time, PFC neurons exhibit dynamics inconsistent with these assumptions.15,16,17,18,19 Recently, multivariate reanalyses revealed the coexistence of both stable and dynamic WM codes in macaque PFC.20,21,22,23 Human EEG studies also suggest that WM might contain dynamics.24,25 Nonetheless, how WM dynamics vary across the cortical hierarchy and which factors drive dynamics remain unknown. To elucidate WM dynamics in humans, we decoded WM content from fMRI responses across multiple cortical visual field maps.26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48 We found coexisting stable and dynamic neural representations of WM during a memory-guided saccade task. Geometric analyses of neural subspaces revealed that early visual cortex exhibited stronger dynamics than high-level visual and frontoparietal cortex. Leveraging models of population receptive fields, we visualized and made the neural dynamics interpretable. We found that during WM delays, V1 population initially encoded a narrowly tuned bump of activation centered on the peripheral memory target. Remarkably, this bump then spread inward toward foveal locations, forming a vector along the trajectory of the forthcoming memory-guided saccade. In other words, the neural code transformed into an abstraction of the stimulus more proximal to memory-guided behavior. Therefore, theories of WM must consider both sensory features and their task-relevant abstractions because changes in the format of memoranda naturally drive neural dynamics.

Beta traveling waves in monkey frontal and parietal areas encode recent reward history

Brain function depends on neural communication, but the mechanisms of this communication are not well understood. Recent studies suggest that one form of neural communication is through traveling waves (TWs)-patterns of neural oscillations that propagate within and between brain areas. We show that TWs are robust in microarray recordings in frontal and parietal cortex and encode recent reward history. Two adult male monkeys made saccades to obtain probabilistic rewards and were sensitive to the (statistically irrelevant) reward on the previous trial. TWs in frontal and parietal areas were stronger in trials that followed a prior reward versus a lack of reward and, in the frontal lobe, correlated with the monkeys' behavioral sensitivity to the prior reward. The findings suggest that neural communication mediated by TWs within the frontal and parietal lobes contribute to maintaining information about recent reward history and mediating the impact of this history on the monkeys' expectations.

Interacting spiral wave patterns underlie complex brain dynamics and are related to cognitive processing

The large-scale activity of the human brain exhibits rich and complex patterns, but the spatiotemporal dynamics of these patterns and their functional roles in cognition remain unclear. Here by characterizing moment-by-moment fluctuations of human cortical functional magnetic resonance imaging signals, we show that spiral-like, rotational wave patterns (brain spirals) are widespread during both resting and cognitive task states. These brain spirals propagate across the cortex while rotating around their phase singularity centres, giving rise to spatiotemporal activity dynamics with non-stationary features. The properties of these brain spirals, such as their rotational directions and locations, are task relevant and can be used to classify different cognitive tasks. We also demonstrate that multiple, interacting brain spirals are involved in coordinating the correlated activations and de-activations of distributed functional regions; this mechanism enables flexible reconfiguration of task-driven activity flow between bottom-up and top-down directions during cognitive processing. Our findings suggest that brain spirals organize complex spatiotemporal dynamics of the human brain and have functional correlates to cognitive processing.

Waves traveling over a map of visual space can ignite short-term predictions of sensory input

Recent analyses have found waves of neural activity traveling across entire visual cortical areas in awake animals. These traveling waves modulate the excitability of local networks and perceptual sensitivity. The general computational role of these spatiotemporal patterns in the visual system, however, remains unclear. Here, we hypothesize that traveling waves endow the visual system with the capacity to predict complex and naturalistic inputs. We present a network model whose connections can be rapidly and efficiently trained to predict individual natural movies. After training, a few input frames from a movie trigger complex wave patterns that drive accurate predictions many frames into the future solely from the network's connections. When the recurrent connections that drive waves are randomly shuffled, both traveling waves and the ability to predict are eliminated. These results suggest traveling waves may play an essential computational role in the visual system by embedding continuous spatiotemporal structures over spatial maps.

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

The relationship between sensory stimuli and perceptions is brain-state dependent: in wakefulness stimuli evoke perceptions; under anesthesia perceptions are abolished; 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 perception. 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 and 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 elicited by specifically by external visual stimuli.

Near-field potentials index local neural computations more accurately than population spiking

Local field potentials (LFP) are low-frequency extracellular voltage fluctuations thought to primarily arise from synaptic activity. However, unlike highly localized neuronal spiking, LFP is spatially less specific. LFP measured at one location is not entirely generated there due to far-field contributions that are passively conducted across volumes of neural tissue. We sought to quantify how much information within the locally generated, near-field low-frequency activity (nfLFP) is masked by volume-conducted far-field signals. To do so, we measured laminar neural activity in primary visual cortex (V1) of monkeys viewing sequences of multifeatured stimuli. We compared information content of regular LFP and nfLFP that was mathematically stripped of volume-conducted far-field contributions. Information content was estimated by decoding stimulus properties from neural responses via spatiotemporal multivariate pattern analysis. Volume-conducted information differed from locally generated information in two important ways: (1) for stimulus features relevant to V1 processing (orientation and eye-of-origin), nfLFP contained more information. (2) in contrast, the volume-conducted signal was more informative regarding temporal context (relative stimulus position in a sequence), a signal likely to be coming from elsewhere. Moreover, LFP and nfLFP differed both spectrally as well as spatially, urging caution regarding the interpretations of individual frequency bands and/or laminar patterns of LFP. Most importantly, we found that population spiking of local neurons was less informative than either the LFP or nfLFP, with nfLFP containing most of the relevant information regarding local stimulus processing. These findings suggest that the optimal way to read out local computational processing from neural activity is to decode the local contributions to LFP, with significant information loss hampering both regular LFP and local spiking.

Author’s Contributions

Conceptualization, D.A.T., J.A.W, and A.M.; Data Collection, J.A.W., M.A.C., K.D.; Formal Analysis, D.A.T. and J.A.W.; Data Visualization, D.A.T. and J.A.W.; Original Draft, D.A.T., J.A.W., and A.M.; Revisions and Final Draft, D.A.T., J.A.W., M.A.C., K.D., M.T.W., A.M.B., and A.M.

Competing Interests

The authors declare no conflicts of interest.

Coherent noise enables probabilistic sequence replay in spiking neuronal networks

Animals rely on different decision strategies when faced with ambiguous or uncertain cues. Depending on the context, decisions may be biased towards events that were most frequently experienced in the past, or be more explorative. A particular type of decision making central to cognition is sequential memory recall in response to ambiguous cues. A previously developed spiking neuronal network implementation of sequence prediction and recall learns complex, high-order sequences in an unsupervised manner by local, biologically inspired plasticity rules. In response to an ambiguous cue, the model deterministically recalls the sequence shown most frequently during training. Here, we present an extension of the model enabling a range of different decision strategies. In this model, explorative behavior is generated by supplying neurons with noise. As the model relies on population encoding, uncorrelated noise averages out, and the recall dynamics remain effectively deterministic. In the presence of locally correlated noise, the averaging effect is avoided without impairing the model performance, and without the need for large noise amplitudes. We investigate two forms of correlated noise occurring in nature: shared synaptic background inputs, and random locking of the stimulus to spatiotemporal oscillations in the network activity. Depending on the noise characteristics, the network adopts various recall strategies. This study thereby provides potential mechanisms explaining how the statistics of learned sequences affect decision making, and how decision strategies can be adjusted after learning.

Development of top-down cortical propagations in youth

Hierarchical processing requires activity propagating between higher- and lower-order cortical areas. However, functional neuroimaging studies have chiefly quantified fluctuations within regions over time rather than propagations occurring over space. Here, we leverage advances in neuroimaging and computer vision to track cortical activity propagations in a large sample of youth (n = 388). We delineate cortical propagations that systematically ascend and descend a cortical hierarchy in all individuals in our developmental cohort, as well as in an independent dataset of densely sampled adults. Further, we demonstrate that top-down, descending hierarchical propagations become more prevalent with greater demands for cognitive control as well as with development in youth. These findings emphasize that hierarchical processing is reflected in the directionality of propagating cortical activity and suggest top-down propagations as a potential mechanism of neurocognitive maturation in youth.

Saccadic modulation of neural excitability in auditory areas of the neocortex

In natural "active" vision, humans and other primates use eye movements (saccades) to sample bits of information from visual scenes. In the visual cortex, non-retinal signals linked to saccades shift visual cortical neurons into a high excitability state as each saccade ends. The extent of this saccadic modulation outside of the visual system is unknown. Here, we show that during natural viewing, saccades modulate excitability in numerous auditory cortical areas with a temporal pattern complementary to that seen in visual areas. Control somatosensory cortical recordings indicate that the temporal pattern is unique to auditory areas. Bidirectional functional connectivity patterns suggest that these effects may arise from regions involved in saccade generation. We propose that by using saccadic signals to yoke excitability states in auditory areas to those in visual areas, the brain can improve information processing in complex natural settings.

Rhythmic attentional scanning

Sensory processing, short-term memory, and decision-making often deal with multiple items, or options, simultaneously. I review evidence suggesting that the brain handles such multiple items by "rhythmic attentional scanning (RAS)": each item is processed in a separate cycle of the theta rhythm, involving several gamma cycles, to reach an internally consistent representation in the form of a gamma-synchronized neuronal group. Within each theta cycle, items that are extended in representational space are scanned by traveling waves. Such scanning might go across small numbers of simple items linked into a chunk.

Synaptic propagation in neuronal networks with finite-support space-dependent coupling

Traveling waves of electrical activity are ubiquitous in biological neuronal networks. Traveling waves in the brain are associated with sensory processing, phase coding, and sleep. The neuron and network parameters that determine traveling waves' evolution are the synaptic space constant, synaptic conductance, membrane time constant, and synaptic decay time constant. We used an abstract neuron model in a one-dimensional network to investigate the propagation characteristics of traveling wave activity. We formulate a set of evolution equations based on the network connectivity parameters. Using a combination of numerical and analytical approaches, we show that these traveling waves are stable to a series of perturbations with biological relevance.

High resolution, wide field optical imaging of macaque visual cortex with a curved detector

Objective. Cortical activity can be recorded using a variety of tools, ranging in scale from the single neuron (microscopic) to the whole brain (macroscopic). There is usually a trade-off between scale and resolution; optical imaging techniques, with their high spatio-temporal resolution and wide field of view, are best suited to study brain activity at the mesoscale. Optical imaging of cortical areas is however in practice limited by the curvature of the brain, which causes the image quality to deteriorate significantly away from the center of the image.Approach. To address this issue and harness the full potential of optical cortical imaging techniques, we developed a new wide-field optical imaging system adapted to the macaque brain. Our system is composed of a curved detector, an aspherical lens and a ring composed of light emitting diodes providing uniform illumination at wavelengths relevant for the different optical imaging methods, including intrinsic and fluorescence imaging.Main results. The system was characterized and compared with the standard macroscope used for cortical imaging, and a three-fold increase of the area in focus was measured as well as a four-fold increase in the evenness of the optical qualityin vivo.Significance. This new instrument, which is to the best of our knowledge the first use of a curved detector for cortical imaging, should facilitate the observation of wide mesoscale phenomena such as dynamic propagating waves within and between cortical maps, which are otherwise difficult to observe due to technical limitations of the currently available recording tools.

V1-bypassing suppression leads to direction-specific microsaccade modulation in visual coding and perception

Microsaccades play a critical role in refreshing visual information and have been shown to have direction-specific influences on human perception. However, the neural mechanisms underlying such direction-specific effects remains unknown. Here, we report the emergence of direction-specific microsaccade modulation in the middle layer of V2 but not in V1: responses of V2 neurons after microsaccades moved toward their receptive fields were stronger than those when microsaccades moved away. The decreased responses from V1 to V2, which are correlated with the amplitude of microsaccades away from receptive fields, suggest topographically location-specific suppression from an oculomotor source. Consistent with directional effects in V2, microsaccades function as a guide for monkeys' behavior in a peripheral detection task; both can be explained by a dynamic neural network. Our findings suggest a V1-bypassing suppressive circuit for direction-specific microsaccade modulation in V2 and its functional influence on visual sensitivity, which highlights the optimal sampling nature of microsaccades.

Visual evoked feedforward-feedback traveling waves organize neural activity across the cortical hierarchy in mice

Sensory processing is distributed among many brain regions that interact via feedforward and feedback signaling. Neuronal oscillations have been shown to mediate intercortical feedforward and feedback interactions. Yet, the macroscopic structure of the multitude of such oscillations remains unclear. Here, we show that simple visual stimuli reliably evoke two traveling waves with spatial wavelengths that cover much of the cerebral hemisphere in awake mice. 30-50 Hz feedforward waves arise in primary visual cortex (V1) and propagate rostrally, while 3-6 Hz feedback waves originate in the association cortex and flow caudally. The phase of the feedback wave modulates the amplitude of the feedforward wave and synchronizes firing between V1 and parietal cortex. Altogether, these results provide direct experimental evidence that visual evoked traveling waves percolate through the cerebral cortex and coordinate neuronal activity across broadly distributed networks mediating visual processing.

Spatiotemporal patterns of spontaneous brain activity: a mini-review

The brain exists in a state of constant activity in the absence of any external sensory input. The spatiotemporal patterns of this spontaneous brain activity have been studied using various recording and imaging techniques. This has enabled considerable progress to be made in elucidating the cellular and network mechanisms that are involved in the observed spatiotemporal dynamics. This mini-review outlines different spatiotemporal dynamic patterns that have been identified in four commonly used modalities: electrophysiological recordings, optical imaging, functional magnetic resonance imaging, and electroencephalography. Signal sources for each modality, possible sources of the observed dynamics, and future directions are also discussed.

Long-range cortical synchronization supports abrupt visual learning

Visual plasticity declines sharply after the critical period, yet we easily learn to recognize new faces and places, even as adults. Such learning is often characterized by a "moment of insight," an abrupt and dramatic improvement in recognition. The mechanisms that support abrupt learning are unknown, but one hypothesis is that they involve changes in synchronization between brain regions. To test this hypothesis, we used a behavioral task in which non-human primates rapidly learned to recognize novel images and to associate them with specific responses. Simultaneous recordings from inferotemporal and prefrontal cortices revealed a transient synchronization of neural activity between these areas that peaked around the moment of insight. Synchronization was strongest between inferotemporal sites that encoded images and reward-sensitive prefrontal sites. Moreover, its magnitude intensified gradually over image exposures, suggesting that abrupt learning is the culmination of a search for informative signals within a circuit linking sensory information to task demands.

Spontaneous neuronal oscillations in the human insula are hierarchically organized traveling waves

The insula plays a fundamental role in a wide range of adaptive human behaviors, but its electrophysiological dynamics are poorly understood. Here, we used human intracranial electroencephalographic recordings to investigate the electrophysiological properties and hierarchical organization of spontaneous neuronal oscillations within the insula. We analyzed the neuronal oscillations of the insula directly and found that rhythms in the theta and beta frequency oscillations are widespread and spontaneously present. These oscillations are largely organized along the anterior–posterior (AP) axis of the insula. Both the left and right insula showed anterior-­to-posterior decreasing gradients for the power of oscillations in the beta frequency band. The left insula also showed a posterior-to-anterior decreasing frequency gradient and an anterior-to-posterior decreasing power gradient in the theta frequency band. In addition to measuring the power of these oscillations, we also examined the phase of these signals across simultaneous recording channels and found that the insula oscillations in the theta and beta bands are traveling waves. The strength of the traveling waves in each frequency was positively correlated with the amplitude of each oscillation. However, the theta and beta traveling waves were uncoupled to each other in terms of phase and amplitude, which suggested that insular traveling waves in the theta and beta bands operate independently. Our findings provide new insights into the spatiotemporal dynamics and hierarchical organization of neuronal oscillations within the insula, which, given its rich connectivity with widespread cortical regions, indicates that oscillations and traveling waves have an important role in intrainsular and interinsular communications.

Spatially distributed computation in cortical circuits

The traditional view of neural computation in the cerebral cortex holds that sensory neurons are specialized, i.e., selective for certain dimensions of sensory stimuli. This view was challenged by evidence of contextual interactions between stimulus dimensions in which a neuron's response to one dimension strongly depends on other dimensions. Here, we use methods of mathematical modeling, psychophysics, and electrophysiology to address shortcomings of the traditional view. Using a model of a generic cortical circuit, we begin with the simple demonstration that cortical responses are always distributed among neurons, forming characteristic waveforms, which we call neural waves. When stimulated by patterned stimuli, circuit responses arise by interference of neural waves. Results of this process depend on interaction between stimulus dimensions. Comparison of modeled responses with responses of biological vision makes it clear that the framework of neural wave interference provides a useful alternative to the standard concept of neural computation.

Spatiotopic and retinotopic memory in the context of natural images

Neural responses throughout the visual cortex encode stimulus location in a retinotopic (i.e., eye-centered) reference frame, and memory for stimulus position is most precise in retinal coordinates. Yet visual perception is spatiotopic: objects are perceived as stationary, even though eye movements cause frequent displacement of their location on the retina. Previous studies found that, after a single saccade, memory of retinotopic locations is more accurate than memory of spatiotopic locations. However, it is not known whether various aspects of natural viewing affect the retinotopic reference frame advantage. We found that the retinotopic advantage may in part depend on a retinal afterimage, which can be effectively nullified through backwards masking. Moreover, in the presence of natural scenes, spatiotopic memory is more accurate than retinotopic memory, but only when subjects are provided sufficient time to process the scene before the eye movement. Our results demonstrate that retinotopic memory is not always more accurate than spatiotopic memory and that the fidelity of memory traces in both reference frames are sensitive to the presence of contextual cues.

Spontaneous traveling waves naturally emerge from horizontal fiber time delays and travel through locally asynchronous-irregular states

Studies of sensory-evoked neuronal responses often focus on mean spike rates, with fluctuations treated as internally-generated noise. However, fluctuations of spontaneous activity, often organized as traveling waves, shape stimulus-evoked responses and perceptual sensitivity. The mechanisms underlying these waves are unknown. Further, it is unclear whether waves are consistent with the low rate and weakly correlated “asynchronous-irregular” dynamics observed in cortical recordings. Here, we describe a large-scale computational model with topographically-organized connectivity and conduction delays relevant to biological scales. We find that spontaneous traveling waves are a general property of these networks. The traveling waves that occur in the model are sparse, with only a small fraction of neurons participating in any individual wave. Consequently, they do not induce measurable spike correlations and remain consistent with locally asynchronous irregular states. Further, by modulating local network state, they can shape responses to incoming inputs as observed in vivo.

Spontaneous traveling cortical waves shape neural responses. Using a large-scale computational model, the authors show that transmission delays shape locally asynchronous spiking dynamics into traveling waves without inducing correlations and boost responses to external input, as observed in vivo.

Neural activity in the human anterior thalamus during natural vision

In natural vision humans and other primates explore environment by active sensing, using saccadic eye movements to relocate the fovea and sample different bits of information multiple times per second. Saccades induce a phase reset of ongoing neuronal oscillations in primary and higher-order visual cortices and in the medial temporal lobe. As a result, neuron ensembles are shifted to a common state at the time visual input propagates through the system (i.e., just after fixation). The extent of the brain’s circuitry that is modulated by saccades is not yet known. Here, we evaluate the possibility that saccadic phase reset impacts the anterior nuclei of the thalamus (ANT). Using recordings in the human thalamus of three surgical patients during natural vision, we found that saccades and visual stimulus onset both modulate neural activity, but with distinct field potential morphologies. Specifically, we found that fixation-locked field potentials had a component that preceded saccade onset. It was followed by an early negativity around 50 ms after fixation onset which is significantly faster than any response to visual stimulus presentation. The timing of these events suggests that the ANT is predictively modulated before the saccadic eye movement. We also found oscillatory phase concentration, peaking at 3–4 Hz, coincident with suppression of Broadband High-frequency Activity (BHA; 80–180 Hz), both locked to fixation onset supporting the idea that neural oscillations in these nuclei are reorganized to a low excitability state right after fixation onset. These findings show that during real-world natural visual exploration neural dynamics in the human ANT is influenced by visual and oculomotor events, which supports the idea that ANT, apart from their contribution to episodic memory, also play a role in natural vision.

Go with the FLOW: visualizing spatiotemporal dynamics in optical widefield calcium imaging

Widefield calcium imaging has recently emerged as a powerful experimental technique to record coordinated large-scale brain activity. These measurements present a unique opportunity to characterize spatiotemporally coherent structures that underlie neural activity across many regions of the brain. In this work, we leverage analytic techniques from fluid dynamics to develop a visualization framework that highlights features of flow across the cortex, mapping wavefronts that may be correlated with behavioural events. First, we transform the time series of widefield calcium images into time-varying vector fields using optic flow. Next, we extract concise diagrams summarizing the dynamics, which we refer to as FLOW (flow lines in optical widefield imaging) portraits. These FLOW portraits provide an intuitive map of dynamic calcium activity, including regions of initiation and termination, as well as the direction and extent of activity spread. To extract these structures, we use the finite-time Lyapunov exponent technique developed to analyse time-varying manifolds in unsteady fluids. Importantly, our approach captures coherent structures that are poorly represented by traditional modal decomposition techniques. We demonstrate the application of FLOW portraits on three simple synthetic datasets and two widefield calcium imaging datasets, including cortical waves in the developing mouse and spontaneous cortical activity in an adult mouse.

Probing the Functional and Structural Connectivity Underlying EEG Traveling Waves

Neural oscillations play an important role in the maintenance of brain function by regulating multi-scale neural activity. Characterizing the traveling properties of EEG is helpful for understanding the spatiotemporal dynamics of neural oscillations. However, traveling EEG based on non-invasive approach has little been investigated, and the relationship with brain intrinsic connectivity is not well known. In this study, traveling EEG of different frequency bands on the scalp in terms of the center of mass (EEG-CM) was examined. Then, two quantitative indexes describing the spatiotemporal features of EEG-CM were proposed, i.e., the traveling lateralization and velocity of EEG-CM. Further, based on simultaneous EEG-MRI approach, the relationship between traveling EEG-CM and the resting-state functional networks, as well as the microstructural connectivity of white matter was investigated. The results showed that there was similar spatial distribution of EEG-CM under different frequency bands, while the velocity of rhythmic EEG-CM increased in higher frequency bands. The lateralization of EEG-CM in low frequency bands (< 30 Hz) demonstrated negative relationship with the basal ganglia network (BGN). In addition, the velocity of the traveling EEG-CM was associated with the fractional anisotropy (FA) in corpus callosum and corona radiate. These results provided valid quantitative EEG index for understanding the spatiotemporal characteristics of the scalp EEG, and implied that the EEG dynamics were representations of functional and structural organization of cortical and subcortical structures.

Mean-Field Models for EEG/MEG: From Oscillations to Waves

Neural mass models have been used since the 1970s to model the coarse-grained activity of large populations of neurons. They have proven especially fruitful for understanding brain rhythms. However, although motivated by neurobiological considerations they are phenomenological in nature, and cannot hope to recreate some of the rich repertoire of responses seen in real neuronal tissue. Here we consider a simple spiking neuron network model that has recently been shown to admit an exact mean-field description for both synaptic and gap-junction interactions. The mean-field model takes a similar form to a standard neural mass model, with an additional dynamical equation to describe the evolution of within-population synchrony. As well as reviewing the origins of this next generation mass model we discuss its extension to describe an idealised spatially extended planar cortex. To emphasise the usefulness of this model for EEG/MEG modelling we show how it can be used to uncover the role of local gap-junction coupling in shaping large scale synaptic waves.

Cortex-Wide Dynamics of Intrinsic Electrical Activities: Propagating Waves and Their Interactions

Cortical circuits generate patterned activities that reflect intrinsic brain dynamics that lay the foundation for any, including stimuli-evoked, cognition and behavior. However, the spatiotemporal organization properties and principles of this intrinsic activity have only been partially elucidated because of previous poor resolution of experimental data and limited analysis methods. Here we investigated continuous wave patterns in the 0.5-4 Hz (delta band) frequency range on data from high-spatiotemporal resolution optical voltage imaging of the upper cortical layers in anesthetized mice. Waves of population activities propagate in heterogeneous directions to coordinate neuronal activities between different brain regions. The complex wave patterns show characteristics of both stereotypy and variety. The location and type of wave patterns determine the dynamical evolution when different waves interact with each other. Local wave patterns of source, sink, or saddle emerge at preferred spatial locations. Specifically, "source" patterns are predominantly found in cortical regions with low multimodal hierarchy such as the primary somatosensory cortex. Our findings reveal principles that govern the spatiotemporal dynamics of spontaneous cortical activities and associate them with the structural architecture across the cortex.SIGNIFICANCE STATEMENT Intrinsic brain activities, as opposed to external stimulus-evoked responses, have increasingly gained attention, but it remains unclear how these intrinsic activities are spatiotemporally organized at the cortex-wide scale. By taking advantage of the high spatiotemporal resolution of optical voltage imaging, we identified five wave pattern types, and revealed the organization properties of different wave patterns and the dynamical mechanisms when they interact with each other. Moreover, we found a relationship between the emergence probability of local wave patterns and the multimodal structure hierarchy across cortical areas. Our findings reveal the principles of spatiotemporal wave dynamics of spontaneous activities and associate them with the underlying hierarchical architecture across the cortex.

Spontaneous travelling cortical waves gate perception in behaving primates

Perceptual sensitivity varies from moment to moment. One potential source of variability is spontaneous fluctuations in cortical activity that can travel as a wave¹. Spontaneous traveling waves have been reported during anesthesia^2–7, but it is not known whether spontaneous traveling waves play a role during waking perception. Using newly developed analytic techniques to characterize the moment-to-moment dynamics of noisy multielectrode data, we find spontaneous waves of activity in extrastriate visual cortex of awake, behaving marmosets (Callithrix jacchus). In monkeys trained to detect faint visual targets, the timing and position of spontaneous traveling waves, prior to target onset, predict the magnitude of target-evoked activity and the likelihood of target detection. In contrast, spatially disorganized fluctuations of neural activity are much less predictive. These results reveal an important role for spontaneous traveling waves in sensory processing through modulating neural and perceptual sensitivity.

A methodological framework for inverse-modeling of propagating cortical activity using MEG/EEG

The prevailing view on the dynamics of large-scale electrical activity in the human cortex is that it constitutes a functional network of discrete and localized circuits. Within this view, a natural way to analyse magnetoencephalographic (MEG) and electroencephalographic (EEG) data is by adopting methods from network theory. Invasive recordings, however, demonstrate that cortical activity is spatially continuous, rather than discrete, and exhibits propagation behavior. Furthermore, human cortical activity is known to propagate under a variety of conditions such as non-REM sleep, general anesthesia, and coma. Although several MEG/EEG studies have investigated propagating cortical activity, not much is known about the conditions under which such activity can be successfully reconstructed from MEG/EEG sensor-data. This study provides a methodological framework for inverse-modeling of propagating cortical activity. Within this framework, cortical activity is represented in the spatial frequency domain, which is more natural than the dipole domain when dealing with spatially continuous activity. We define angular power spectra, which show how the power of cortical activity is distributed across spatial frequencies, angular gain/phase spectra, which characterize the spatial filtering properties of linear inverse operators, and angular resolution matrices, which summarize how linear inverse operators leak signal within and across spatial frequencies. We adopt the framework to provide insight into the performance of several linear inverse operators in reconstructing propagating cortical activity from MEG/EEG sensor-data. We also describe how prior spatial frequency information can be incorporated into the inverse-modeling to obtain better reconstructions.

Direction-selective motion discrimination by traveling waves in visual cortex

The majority of neurons in primary visual cortex respond selectively to bars of light that have a specific orientation and move in a specific direction. The spatial and temporal responses of such neurons are non-separable. How neurons accomplish that computational feat without resort to explicit time delays is unknown. We propose a novel neural mechanism whereby visual cortex computes non-separable responses by generating endogenous traveling waves of neural activity that resonate with the space-time signature of the visual stimulus. The spatiotemporal characteristics of the response are defined by the local topology of excitatory and inhibitory lateral connections in the cortex. We simulated the interaction between endogenous traveling waves and the visual stimulus using spatially distributed populations of excitatory and inhibitory neurons with Wilson-Cowan dynamics and inhibitory-surround coupling. Our model reliably detected visual gratings that moved with a given speed and direction provided that we incorporated neural competition to suppress false motion signals in the opposite direction. The findings suggest that endogenous traveling waves in visual cortex can impart direction-selectivity on neural responses without resort to explicit time delays. They also suggest a functional role for motion opponency in eliminating false motion signals.

It is well established that the so-called ‘simple cells’ of the primary visual cortex respond preferentially to oriented bars of light that move across the visual field with a particular speed and direction. The spatiotemporal responses of such neurons are said to be non-separable because they cannot be constructed from independent spatial and temporal neural mechanisms. Contemporary theories of how neurons compute non-separable responses typically rely on finely tuned transmission delays between signals from disparate regions of the visual field. However the existence of such delays is controversial. We propose an alternative neural mechanism for computing non-separable responses that does not require transmission delays. It instead relies on the predisposition of the cortical tissue to spontaneously generate spatiotemporal waves of neural activity that travel with a particular speed and direction. We propose that the endogenous wave activity resonates with the visual stimulus to elicit direction-selective neural responses to visual motion. We demonstrate the principle in computer models and show that competition between opposing neurons robustly enhances their ability to discriminate between visual gratings that move in opposite directions.

Perisaccadic remapping: What? How? Why?

About 25 years ago, the discovery of receptive field (RF) remapping in the parietal cortex of nonhuman primates revealed that visual RFs, widely assumed to have a fixed retinotopic organization, can change position before every saccade. Measuring such changes can be deceptively difficult. As a result, studies that followed have generated a fascinating but somewhat confusing picture of the phenomenon. In this review, we describe how observations of RF remapping depend on the spatial and temporal sampling of visual RFs and saccade directions. Further, we summarize some of the theories of how remapping might occur in neural circuitry. Finally, based on neurophysiological and psychophysical observations, we discuss the ways in which remapping information might facilitate computations in downstream brain areas.

Dynamic Modulation of Cortical Excitability during Visual Active Sensing

Visual physiology is traditionally investigated by presenting stimuli with gaze held constant. However, during active viewing of a scene, information is actively acquired using systematic patterns of fixations and saccades. Prior studies suggest that during such active viewing, both nonretinal, saccade-related signals and “extra-classical” receptive field inputs modulate visual processing. This study used a set of active viewing tasks that allowed us to compare visual responses with and without direct foveal input, thus isolating the contextual eye movement-related influences. Studying nonhuman primates, we find strong contextual modulation in primary visual cortex (V1): excitability and response amplification immediately after fixation onset, transiting to suppression leading up to the next saccade. Time-frequency decomposition suggests that this amplification and suppression cycle stems from a phase reset of ongoing neuronal oscillatory activity. The impact of saccade-related contextual modulation on stimulus processing makes active visual sensing fundamentally different from the more passive processes investigated in traditional paradigms.

By isolating contextual eye movement-related influences during active vision, Barczak et al. show that eye movements affect excitability in V1 such that responses are amplified immediately after fixation onset and suppressed as the next saccade approaches. This amplification and suppression cycle stems from a phase reset of ambient oscillatory activity in V1.

Machine classification of spatiotemporal patterns: automated parameter search in a rebounding spiking network

Various patterns of electrical activities, including travelling waves, have been observed in cortical experimental data from animal models as well as humans. By applying machine learning techniques, we investigate the spatiotemporal patterns, found in a spiking neuronal network with inhibition-induced firing (rebounding). Our cortical sheet model produces a wide variety of network activities including synchrony, target waves, and travelling wavelets. Pattern formation is controlled by modifying a Gaussian derivative coupling kernel through varying the level of inhibition, coupling strength, and kernel geometry. We have designed a computationally efficient machine classifier, based on statistical, textural, and temporal features, to identify the parameter regimes associated with different spatiotemporal patterns. Our results reveal that switching between synchrony and travelling waves can occur transiently and spontaneously without a stimulus, in a noise-dependent fashion, or in the presence of stimulus when the coupling strength and level of inhibition are at moderate values. They also demonstrate that when a target wave is formed, its wave speed is most sensitive to perturbations in the coupling strength between model neurons. This study provides an automated method to characterize activities produced by a novel spiking network that phenomenologically models large scale dynamics in the cortex.

Low-Dimensional Spatiotemporal Dynamics Underlie Cortex-wide Neural Activity

Cognition arises from the dynamic flow of neural activity through the brain. To capture these dynamics, we used mesoscale calcium imaging to record neural activity across the dorsal cortex of awake mice. We found that the large majority of variance in cortex-wide activity (∼75%) could be explained by a limited set of ∼14 "motifs" of neural activity. Each motif captured a unique spatiotemporal pattern of neural activity across the cortex. These motifs generalized across animals and were seen in multiple behavioral environments. Motif expression differed across behavioral states, and specific motifs were engaged by sensory processing, suggesting the motifs reflect core cortical computations. Together, our results show that cortex-wide neural activity is highly dynamic but that these dynamics are restricted to a low-dimensional set of motifs, potentially allowing for efficient control of behavior.

The Neural Basis for Response Latency in a Sensory-Motor Behavior

We seek a neural circuit explanation for sensory-motor reaction times. In the smooth eye movement region of the frontal eye fields (FEFSEM), the latencies of pairs of neurons show trial-by-trial correlations that cause trial-by-trial correlations in neural and behavioral latency. These correlations can account for two-third of the observed variation in behavioral latency. The amplitude of preparatory activity also could contribute, but the responses of many FEFSEM neurons fail to support predictions of the traditional "ramp-to-threshold" model. As a correlate of neural processing that determines reaction time, the local field potential in FEFSEM includes a brief wave in the 5-15-Hz frequency range that precedes pursuit initiation and whose phase is correlated with the latency of pursuit in individual trials. We suggest that the latency of the incoming visual motion signals combines with the state of preparatory activity to determine the latency of the transient response that controls eye movement.

IMPACT STATEMENT

The motor cortex for smooth pursuit eye movements contributes to sensory-motor reaction time through the amplitude of preparatory activity and the latency of transient, visually driven responses.

Propagating Motor Cortical Dynamics Facilitate Movement Initiation

Voluntary movement initiation involves the modulations of large groups of neurons in the primary motor cortex (M1). Yet similar modulations occur during movement planning when no movement occurs. Here, we show that a sequential spatiotemporal pattern of excitability propagates across M1 prior to the movement initiation in one of two oppositely oriented directions along the rostro-caudal axis. Using spatiotemporal patterns of intracortical microstimulation, we find that reaction time increases significantly when stimulation is delivered against, but not with, the natural propagation direction. Functional connections among M1 units emerge at movement that are oriented along the same rostro-caudal axis but not during movement planning. Finally, we show that beta amplitude profiles can more accurately decode muscle activity when they conform to the natural propagating patterns. These findings provide the first causal evidence that large-scale, propagating patterns of cortical excitability are behaviorally relevant and may be a necessary component of movement initiation.

Spatial resolution of local field potential signals in macaque V4

OBJECTIVE

An important challenge for the development of cortical visual prostheses is to generate spatially localized percepts of light, using artificial stimulation. Such percepts are called phosphenes, and the goal of prosthetic applications is to generate a pattern of phosphenes that matches the structure of the retinal image. A preliminary step in this process is to understand how the spatial positions of phosphene-like visual stimuli are encoded in the distributed activity of cortical neurons. The spatial resolution with which the distributed responses discriminate positions puts a limit on the capability of visual prosthesis devices to induce phosphenes at multiple positions. While most previous prosthetic devices have targeted the primary visual cortex, the extrastriate cortex has the advantage of covering a large part of the visual field with a smaller amount of cortical tissue, providing the possibility of a more compact implant. Here, we studied how well ensembles of Local Field Potentials (LFPs) and Multiunit activity (MUA) responses from extrastriate cortical visual area V4 of a behaving macaque monkey can discriminate between two-dimensional spatial positions.

APPROACH

We used support vector machines (SVM) to determine the capabilities of LFPs and MUA to discriminate responses to phosphene-like stimuli (probes) at different spatial separations. We proposed a selection strategy based on the combined responses of multiple electrodes and used the linear learning weights to find the minimum number of electrodes for fine and coarse discriminations. We also measured the contribution of correlated trial-to-trial variability in the responses to the discrimination performance for MUA and LFP.

MAIN RESULTS

We found that despite the large receptive field sizes in V4, the combined responses from multiple sites, whether MUA or LFP, are capable of fine and coarse discrimination of positions. Our electrode selection procedure significantly increased discrimination performance while reducing the required number of electrodes. Analysis of noise correlations in MUA and LFP responses showed that noise correlations in LFPs carry more information about spatial positions.

SIGNIFICANCE

This study determined the coding strategy for fine discrimination, suggesting that spatial positions could be well localized with patterned stimulation in extrastriate area V4. It also provides a novel approach to build a compact prosthesis with relatively few electrodes, which has the potential advantage of reducing tissue damage in real applications.

Recording and Decoding of Vagal Neural Signals Related to Changes in Physiological Parameters and Biomarkers of Disease

Our bodies have built-in neural reflexes that continuously monitor organ function and maintain physiological homeostasis. Whereas the field of bioelectronic medicine has mainly focused on the stimulation of neural circuits to treat various conditions, recent studies have started to investigate the possibility of leveraging the sensory arm of these reflexes to diagnose disease states. To accomplish this, neural signals emanating from the body's built-in biosensors and propagating through peripheral nerves must be recorded and decoded to identify the presence or levels of relevant biomarkers of disease. The process of acquiring these signals poses several technical challenges related to the neural interfaces, surgical techniques, and data-processing framework needed to record and analyze them. However, these challenges can be addressed with a rigorous experimental approach and new advances in implantable electrodes, signal processing, and machine learning methods. Outlined in this review are studies decoding vagus nerve activity as it related to inflammatory, metabolic, and cardiopulmonary biomarkers. Successfully decoding peripheral nerve activity related to disease states will not only enable the development of real-time diagnostic devices, but also help advancing truly closed-loop neuromodulation technologies.

Neuronal Representation of the Saccadic Timing Signals in Macaque Lateral Intraparietal Area

Primates frequently make saccades direct fovea on interesting objects to receive acute visual information. However, saccade displaces the images on retina and disrupts the visual constancy. One possible mechanism to retain visual constancy is by integrating the presaccadic and postsaccadic visual information right at the time of saccade, which makes the timing of saccade crucial. So far, the saccadic timing signals have been found only in the subcortical regions, for example, the cerebellum and superior colliculus, but not in the neocortex. Here we report 2 types of saccadic timing signals in macaque lateral intraparietal area (LIP). First, many presaccadic response neurons started to decline activity either right around the start (saccade-on-decay) or the end (saccade-off-decay) of saccades. Notably, the time difference between saccade-off-decay and saccade-on-decay was highly correlated with the mean duration of saccades but not with the individual ones, and both saccade-off-decay and saccade-on-decay were better aligned with saccade end than saccade start-reflecting prediction. Second, the peak activity plateau of a group of postsaccadic response neurons was highly correlated with the actual duration of saccade-reflecting reality. While the predicted timing signals might facilitate the integration of visual information across saccades in LIP, the actual duration signals might calibrate the prediction errors.

Curved surface geometry-induced topological change of an excitable planar wavefront

On the curved surfaces of living and nonliving materials, planar excitable wavefronts frequently exhibit a directional change and subsequently undergo a discontinuous (topological) change; i.e., a series of wavefront dynamics from collision, annihilation to splitting. Theoretical studies have shown that excitable planar stable waves change their topology significantly depending on the initial conditions on flat surfaces, whereas the directional change of the waves occurs based on the geometry of curved surfaces. However, it is not clear if the geometry of curved surfaces induces this topological change. In this study, we first demonstrated that the curved surface geometry induces bending, collision, and splitting of a planar stable wavefront by numerically solving an excitable reaction-diffusion equation on a bell-shaped surface. We determined two necessary conditions for inducing the topological change: the characteristic length of the curved surface (i.e., the height of the bell-shaped structure) should be greater than the width of the wave, and the ratio of the height to the width of the bell shape should be greater than a threshold. As for the geometrical mechanism of the latter, we found that a bifurcation of the geodesics on the curved surface provides the alternative minimal paths of the wavefront, which circumvent the surface region with a high local curvature, thereby resulting in the topological change. These conditions imply that the topological change of the wavefront can be predicted on the basis of the curved surfaces, whose structures are larger than the wave width.

Complex Dynamics of Propagating Waves in a Two-Dimensional Neural Field

Propagating waves with complex dynamics have been widely observed in neural population activity. To understand their formation mechanisms, we investigate a type of two-dimensional neural field model by systematically varying its recurrent excitatory and inhibitory inputs. We show that the neural field model exhibits a rich repertoire of dynamical activity states when the relevant strength of excitation and inhibition is increased, ranging from localized rotating and traveling waves to global waves. Particularly, near the transition between stable states of rotating and traveling waves, the model exhibits a bistable state; that is, both the rotating and the traveling waves can exist, and the inclusion of noise can induce spontaneous transitions between them. Furthermore, we demonstrate that when there are multiple propagating waves, they exhibit rich collective propagation dynamics with variable propagating speeds and trajectories. We use techniques from time series analysis such detrended fluctuation analysis to characterize the effect of the strength of excitation and inhibition on these collective dynamics, which range from purely random motion to motion with long-range spatiotemporal correlations. These results provide insights into the possible contribution of excitation and inhibition toward a range of previously observed spatiotemporal wave phenomena.

Metastable brain waves

Traveling patterns of neuronal activity-brain waves-have been observed across a breadth of neuronal recordings, states of awareness, and species, but their emergence in the human brain lacks a firm understanding. Here we analyze the complex nonlinear dynamics that emerge from modeling large-scale spontaneous neural activity on a whole-brain network derived from human tractography. We find a rich array of three-dimensional wave patterns, including traveling waves, spiral waves, sources, and sinks. These patterns are metastable, such that multiple spatiotemporal wave patterns are visited in sequence. Transitions between states correspond to reconfigurations of underlying phase flows, characterized by nonlinear instabilities. These metastable dynamics accord with empirical data from multiple imaging modalities, including electrical waves in cortical tissue, sequential spatiotemporal patterns in resting-state MEG data, and large-scale waves in human electrocorticography. By moving the study of functional networks from a spatially static to an inherently dynamic (wave-like) frame, our work unifies apparently diverse phenomena across functional neuroimaging modalities and makes specific predictions for further experimentation.

Detection and analysis of spatiotemporal patterns in brain activity

There is growing evidence that population-level brain activity is often organized into propagating waves that are structured in both space and time. Such spatiotemporal patterns have been linked to brain function and observed across multiple recording methodologies and scales. The ability to detect and analyze these patterns is thus essential for understanding the working mechanisms of neural circuits. Here we present a mathematical and computational framework for the identification and analysis of multiple classes of wave patterns in neural population-level recordings. By drawing a conceptual link between spatiotemporal patterns found in the brain and coherent structures such as vortices found in turbulent flows, we introduce velocity vector fields to characterize neural population activity. These vector fields are calculated for both phase and amplitude of oscillatory neural signals by adapting optical flow estimation methods from the field of computer vision. Based on these velocity vector fields, we then introduce order parameters and critical point analysis to detect and characterize a diverse range of propagating wave patterns, including planar waves, sources, sinks, spiral waves, and saddle patterns. We also introduce a novel vector field decomposition method that extracts the dominant spatiotemporal structures in a recording. This enables neural data to be represented by the activity of a small number of independent spatiotemporal modes, providing an alternative to existing dimensionality reduction techniques which separate space and time components. We demonstrate the capabilities of the framework and toolbox with simulated data, local field potentials from marmoset visual cortex and optical voltage recordings from whole mouse cortex, and we show that pattern dynamics are non-random and are modulated by the presence of visual stimuli. These methods are implemented in a MATLAB toolbox, which is freely available under an open-source licensing agreement.

Structured activity such as propagating wave patterns at the level of neural circuits can arise from highly variable firing activity of individual neurons. This property makes the brain, a quintessential example of a complex system, analogous to other complex physical systems such as turbulent fluids, in which structured patterns like vortices similarly emerge from molecules that behave irregularly. In this study, by uniquely adapting techniques for the identification of coherent structures in fluid turbulence, we develop new analytical and computational methods for the reliable detection of a diverse range of propagating wave patterns in large-scale neural recordings, for comprehensive analysis and visualization of these patterns, and for analysis of their dominant spatiotemporal modes. We demonstrate that these methods can be used to uncover the essential spatiotemporal properties of neural population activity recorded by different modalities, thus offering new insights into understanding the working mechanisms of neural systems.

waveCSD: A method for estimating transmembrane currents originated from propagating neuronal activity in the neocortex: Application to study cortical spreading depression

BACKGROUND

Recent years have witnessed an upsurge in the development of methods for estimating current source densities (CSDs) in the neocortical tissue from their recorded local field potential (LFP) reflections using microelectrode arrays. Among these, methods utilizing linear arrays work under the assumption that CSDs vary as a function of cortical depth; whereas they are constant in the tangential direction, infinitely or in a confined cylinder. This assumption is violated in the analysis of neuronal activity propagating along the neocortical sheet, e.g. propagation of alpha waves or cortical spreading depression.

NEW METHOD

Here, we developed a novel mathematical method (waveCSD) for CSD analysis of LFPs associated with a planar wave of neocortical neuronal activity propagating at a constant velocity towards a linear probe.

RESULTS

Results show that the algorithm is robust to the presence of noise in LFP data and uncertainties in knowledge of propagation velocity. Also, results show high level of accuracy of the method in a wide range of electrode resolutions. Using in vivo experimental recordings from the rat neocortex, we employed waveCSD to characterize transmembrane currents associated with cortical spreading depressions.

COMPARISON WITH EXISTING METHOD(S)

Simulation results indicate that waveCSD has a significantly higher reconstruction accuracy compared to the widely-used inverse CSD method (iCSD), and the regularized kernel CSD method (kCSD), in the analysis of CSDs originating from propagating neuronal activity.

CONCLUSIONS

The waveCSD method provides a theoretical platform for estimation of transmembrane currents from their LFPs in experimental paradigms involving wave propagation.

Theta and Alpha Oscillations Are Traveling Waves in the Human Neocortex

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.