Compression and reflection of visually evoked cortical waves

A cortical field theory - dynamics and symmetries

We characterise cortical dynamics using partial differential equations (PDEs), analysing various connectivity patterns within the cortical sheet. This exploration yields diverse dynamics, encompassing wave equations and limit cycle activity. We presume balanced equations between excitatory and inhibitory neuronal units, reflecting the ubiquitous oscillatory patterns observed in electrophysiological measurements. Our derived dynamics comprise lowest-order wave equations (i.e., the Klein-Gordon model), limit cycle waves, higher-order PDE formulations, and transitions between limit cycles and near-zero states. Furthermore, we delve into the symmetries of the models using the Lagrangian formalism, distinguishing between continuous and discontinuous symmetries. These symmetries allow for mathematical expediency in the analysis of the model and could also be useful in studying the effect of symmetrical input from distributed cortical regions. Overall, our ability to derive multiple constraints on the fields - and predictions of the model - stems largely from the underlying assumption that the brain operates at a critical state. This assumption, in turn, drives the dynamics towards oscillatory or semi-conservative behaviour. Within this critical state, we can leverage results from the physics literature, which serve as analogues for neural fields, and implicit construct validity. Comparisons between our model predictions and electrophysiological findings from the literature - such as spectral power distribution across frequencies, wave propagation speed, epileptic seizure generation, and pattern formation over the cortical surface - demonstrate a close match. This study underscores the importance of utilizing symmetry preserving PDE formulations for further mechanistic insights into cortical activity.

Reconciliation of weak pairwise spike-train correlations and highly coherent local field potentials across space

Multi-electrode arrays covering several square millimeters of neural tissue provide simultaneous access to population signals such as extracellular potentials and spiking activity of one hundred or more individual neurons. The interpretation of the recorded data calls for multiscale computational models with corresponding spatial dimensions and signal predictions. Multi-layer spiking neuron network models of local cortical circuits covering about $1\,{\text{mm}^{2}}$ have been developed, integrating experimentally obtained neuron-type-specific connectivity data and reproducing features of observed in-vivo spiking statistics. Local field potentials can be computed from the simulated spiking activity. We here extend a local network and local field potential model to an area of $4\times 4\,{\text{mm}^{2}}$, preserving the neuron density and introducing distance-dependent connection probabilities and conduction delays. We find that the upscaling procedure preserves the overall spiking statistics of the original model and reproduces asynchronous irregular spiking across populations and weak pairwise spike-train correlations in agreement with experimental recordings from sensory cortex. Also compatible with experimental observations, the correlation of local field potential signals is strong and decays over a distance of several hundred micrometers. Enhanced spatial coherence in the low-gamma band around $50\,\text{Hz}$ may explain the recent report of an apparent band-pass filter effect in the spatial reach of the local field potential.

Transformers and cortical waves: encoders for pulling in context across time

The capabilities of transformer networks such as ChatGPT and other large language models (LLMs) have captured the world's attention. The crucial computational mechanism underlying their performance relies on transforming a complete input sequence - for example, all the words in a sentence - into a long 'encoding vector' that allows transformers to learn long-range temporal dependencies in naturalistic sequences. Specifically, 'self-attention' applied to this encoding vector enhances temporal context in transformers by computing associations between pairs of words in the input sequence. We suggest that waves of neural activity traveling across single cortical areas, or multiple regions on the whole-brain scale, could implement a similar encoding principle. By encapsulating recent input history into a single spatial pattern at each moment in time, cortical waves may enable a temporal context to be extracted from sequences of sensory inputs, the same computational principle as that used in transformers.

Spatiotemporal resonance in mouse primary visual cortex

Human primary visual cortex (V1) responds more strongly, or resonates, when exposed to ∼10, ∼15-20, and ∼40-50 Hz rhythmic flickering light. Full-field flicker also evokes the perception of hallucinatory geometric patterns, which mathematical models explain as standing-wave formations emerging from periodic forcing at resonant frequencies of the simulated neural network. However, empirical evidence for such flicker-induced standing waves in the visual cortex was missing. We recorded cortical responses to flicker in awake mice using high-spatial-resolution widefield imaging in combination with high-temporal-resolution glutamate-sensing fluorescent reporter (iGluSnFR). The temporal frequency tuning curves in the mouse V1 were similar to those observed in humans, showing a banded structure with multiple resonance peaks (8, 15, and 33 Hz). Spatially, all flicker frequencies evoked responses in V1 corresponding to retinotopic stimulus location, but some evoked additional peaks. These flicker-induced cortical patterns displayed standing-wave characteristics and matched linear wave equation solutions in an area restricted to the visual cortex. Taken together, the interaction of periodic traveling waves with cortical area boundaries leads to spatiotemporal activity patterns that may affect perception.

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.

Common modular architecture across diverse cortical areas in early development

In order to deal with a complex environment, animals form a diverse range of neural representations that vary across cortical areas, ranging from largely unimodal sensory input to higher-order representations of goals, outcomes, and motivation. The developmental origin of this diversity is currently unclear, as representations could arise through processes that are already area-specific from the earliest developmental stages or alternatively, they could emerge from an initially common functional organization shared across areas. Here, we use spontaneous activity recorded with two-photon and widefield calcium imaging to reveal the functional organization across the early developing cortex in ferrets, a species with a well-characterized columnar organization and modular structure of spontaneous activity in the visual cortex. We find that in animals 7 to 14 d prior to eye-opening and ear canal opening, spontaneous activity in both sensory areas (auditory and somatosensory cortex, A1 and S1, respectively), and association areas (posterior parietal and prefrontal cortex, PPC and PFC, respectively) showed an organized and modular structure that is highly similar to the organization in V1. In all cortical areas, this modular activity was distributed across the cortical surface, forming functional networks that exhibit millimeter-scale correlations. Moreover, this modular structure was evident in highly coherent spontaneous activity at the cellular level, with strong correlations among local populations of neurons apparent in all cortical areas examined. Together, our results demonstrate a common distributed and modular organization across the cortex during early development, suggesting that diverse cortical representations develop initially according to similar design principles.

Sequentially activated discrete modules appear as traveling waves in neuronal measurements with limited spatiotemporal sampling

Numerous studies have identified traveling waves in the cortex and suggested they play important roles in brain processing. These waves are most often measured using macroscopic methods that are unable to assess the local spiking activity underlying wave dynamics. Here, we investigated the possibility that waves may not be traveling at the single neuron scale. We first show that sequentially activating two discrete brain areas can appear as traveling waves in EEG simulations. We next reproduce these results using an analytical model of two sequentially activated regions. Using this model, we were able to generate wave-like activity with variable directions, velocities, and spatial patterns, and to map the discriminability limits between traveling waves and modular sequential activations. Finally, we investigated the link between field potentials and single neuron excitability using large-scale measurements from turtle cortex ex vivo. We found that while field potentials exhibit wave-like dynamics, the underlying spiking activity was better described by consecutively activated spatially adjacent groups of neurons. Taken together, this study suggests caution when interpreting phase delay measurements as continuously propagating wavefronts in two different spatial scales. A careful distinction between modular and wave excitability profiles across scales will be critical for understanding the nature of cortical computations.

Propagating population activity patterns during spontaneous slow waves in the thalamus of rodents

Slow waves (SWs) represent the most prominent electrophysiological events in the thalamocortical system under anesthesia and during deep sleep. Recent studies have revealed that SWs have complex spatiotemporal dynamics and propagate across neocortical regions. However, it is still unclear whether neuronal activity in the thalamus exhibits similar propagation properties during SWs. Here, we report propagating population activity in the thalamus of ketamine/xylazine-anesthetized rats and mice visualized by high-density silicon probe recordings. In both rodent species, propagation of spontaneous thalamic activity during up-states was most frequently observed in dorsal thalamic nuclei such as the higher order posterior (Po), lateral posterior (LP) or laterodorsal (LD) nuclei. The preferred direction of thalamic activity spreading was along the dorsoventral axis, with over half of the up-states exhibiting a gradual propagation in the ventral-to-dorsal direction. Furthermore, simultaneous neocortical and thalamic recordings collected under anesthesia demonstrated that there is a weak but noticeable interrelation between propagation patterns observed during cortical up-states and those displayed by thalamic population activity. In addition, using chronically implanted silicon probes, we detected propagating activity patterns in the thalamus of naturally sleeping rats during slow-wave sleep. However, in comparison to propagating up-states observed under anesthesia, these propagating patterns were characterized by a reduced rate of occurrence and a faster propagation speed. Our findings suggest that the propagation of spontaneous population activity is an intrinsic property of the thalamocortical network during synchronized brain states such as deep sleep or anesthesia. Additionally, our data implies that the neocortex may have partial control over the formation of propagation patterns within the dorsal thalamus under anesthesia.

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.

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.

How far neuroscience is from understanding brains

The cellular biology of brains is relatively well-understood, but neuroscientists have not yet generated a theory explaining how brains work. Explanations of how neurons collectively operate to produce what brains can do are tentative and incomplete. Without prior assumptions about the brain mechanisms, I attempt here to identify major obstacles to progress in neuroscientific understanding of brains and central nervous systems. Most of the obstacles to our understanding are conceptual. Neuroscience lacks concepts and models rooted in experimental results explaining how neurons interact at all scales. The cerebral cortex is thought to control awake activities, which contrasts with recent experimental results. There is ambiguity distinguishing task-related brain activities from spontaneous activities and organized intrinsic activities. Brains are regarded as driven by external and internal stimuli in contrast to their considerable autonomy. Experimental results are explained by sensory inputs, behavior, and psychological concepts. Time and space are regarded as mutually independent variables for spiking, post-synaptic events, and other measured variables, in contrast to experimental results. Dynamical systems theory and models describing evolution of variables with time as the independent variable are insufficient to account for central nervous system activities. Spatial dynamics may be a practical solution. The general hypothesis that measurements of changes in fundamental brain variables, action potentials, transmitter releases, post-synaptic transmembrane currents, etc., propagating in central nervous systems reveal how they work, carries no additional assumptions. Combinations of current techniques could reveal many aspects of spatial dynamics of spiking, post-synaptic processing, and plasticity in insects and rodents to start with. But problems defining baseline and reference conditions hinder interpretations of the results. Furthermore, the facts that pooling and averaging of data destroy their underlying dynamics imply that single-trial designs and statistics are necessary.

The inhibitory control of traveling waves in cortical networks

Propagating waves of activity can be evoked and can occur spontaneously in vivo and in vitro in cerebral cortex. These waves are thought to be instrumental in the propagation of information across cortical regions and as a means to modulate the sensitivity of neurons to subsequent stimuli. In normal tissue, the waves are sparse and tightly controlled by inhibition and other negative feedback processes. However, alterations of this balance between excitation and inhibition can lead to pathological behavior such as seizure-type dynamics (with low inhibition) or failure to propagate (with high inhibition). We develop a spiking one-dimensional network of neurons to explore the reliability and control of evoked waves and compare this to a cortical slice preparation where the excitability can be pharmacologically manipulated. We show that the waves enhance sensitivity of the cortical network to stimuli in specific spatial and temporal ways. To gain further insight into the mechanisms of propagation and transitions to pathological behavior, we derive a mean-field model for the synaptic activity. We analyze the mean-field model and a piece-wise constant approximation of it and study the stability of the propagating waves as spatial and temporal properties of the inhibition are altered. We show that that the transition to seizure-like activity is gradual but that the loss of propagation is abrupt and can occur via either the loss of existence of the wave or through a loss of stability leading to complex patterns of propagation.

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.

Multielectrode Cortical Stimulation Selectively Induces Unidirectional Wave Propagation of Excitatory Neuronal Activity in Biophysical Neural Model

Cortical stimulation is emerging as an experimental tool in basic research and a promising therapy for a range of neuropsychiatric conditions. As multielectrode arrays enter clinical practice, the possibility of using spatiotemporal patterns of electrical stimulation to induce desired physiological patterns has become theoretically possible, but in practice can only be implemented by trial-and-error because of a lack of predictive models. Experimental evidence increasingly establishes traveling waves as fundamental to cortical information-processing, but we lack an understanding of how to control wave properties despite rapidly improving technologies. This study uses a hybrid biophysical-anatomical and neural-computational model to predict and understand how a simple pattern of cortical surface stimulation could induce directional traveling waves via asymmetric activation of inhibitory interneurons. We found that pyramidal cells and basket cells are highly activated by the anodal electrode and minimally activated by the cathodal electrodes, while Martinotti cells are moderately activated by both electrodes but exhibit a slight preference for cathodal stimulation. Network model simulations found that this asymmetrical activation results in a traveling wave in superficial excitatory cells that propagates unidirectionally away from the electrode array. Our study reveals how asymmetric electrical stimulation can easily facilitate traveling waves by relying on two distinct types of inhibitory interneuron activity to shape and sustain the spatiotemporal dynamics of endogenous local circuit mechanisms.SIGNIFICANCE STATEMENT Electrical brain stimulation is becoming increasingly useful to probe the workings of brain and to treat a variety of neuropsychiatric disorders. However, stimulation is currently performed in a trial-and-error fashion as there are no methods to predict how different electrode arrangements and stimulation paradigms will affect brain functioning. In this study, we demonstrate a hybrid modeling approach, which makes experimentally testable predictions that bridge the gap between the microscale effects of multielectrode stimulation and the resultant circuit dynamics at the mesoscale. Our results show how custom stimulation paradigms can induce predictable, persistent changes in brain activity, which has the potential to restore normal brain function and become a powerful therapy for neurological and psychiatric conditions.

A deep generative adversarial network capturing complex spiral waves in disinhibited circuits of the cerebral cortex

BACKGROUND

In the cerebral cortex, disinhibited activity is characterized by propagating waves that spread across neural tissue. In this pathological state, a widely reported form of activity are spiral waves that travel in a circular pattern around a fixed spatial locus termed the center of mass. Spiral waves exhibit stereotypical activity and involve broad patterns of co-fluctuations, suggesting that they may be of lower complexity than healthy activity.

RESULTS

To evaluate this hypothesis, we performed dense multi-electrode recordings of cortical networks where disinhibition was induced by perfusing a pro-epileptiform solution containing 4-Aminopyridine as well as increased potassium and decreased magnesium. Spiral waves were identified based on a spatially delimited center of mass and a broad distribution of instantaneous phases across electrodes. Individual waves were decomposed into "snapshots" that captured instantaneous neural activation across the entire network. The complexity of these snapshots was examined using a measure termed the participation ratio. Contrary to our expectations, an eigenspectrum analysis of these snapshots revealed a broad distribution of eigenvalues and an increase in complexity compared to baseline networks. A deep generative adversarial network was trained to generate novel exemplars of snapshots that closely captured cortical spiral waves. These synthetic waves replicated key features of experimental data including a tight center of mass, a broad eigenvalue distribution, spatially-dependent correlations, and a high complexity. By adjusting the input to the model, new samples were generated that deviated in systematic ways from the experimental data, thus allowing the exploration of a broad range of states from healthy to pathologically disinhibited neural networks.

CONCLUSIONS

Together, results show that the complexity of population activity serves as a marker along a continuum from healthy to disinhibited brain states. The proposed generative adversarial network opens avenues for replicating the dynamics of cortical seizures and accelerating the design of optimal neurostimulation aimed at suppressing pathological brain activity.

Propagating spatiotemporal activity patterns across macaque motor cortex carry kinematic information

Propagating spatiotemporal neural patterns are widely evident across sensory, motor, and association cortical areas. However, it remains unclear whether any characteristics of neural propagation carry information about specific behavioral details. Here, we provide the first evidence for a link between the direction of cortical propagation and specific behavioral features of an upcoming movement on a trial-by-trial basis. We recorded local field potentials (LFPs) from multielectrode arrays implanted in the primary motor cortex of two rhesus macaque monkeys while they performed a 2D reach task. Propagating patterns were extracted from the information-rich high-gamma band (200 to 400 Hz) envelopes in the LFP amplitude. We found that the exact direction of propagating patterns varied systematically according to initial movement direction, enabling kinematic predictions. Furthermore, characteristics of these propagation patterns provided additional predictive capability beyond the LFP amplitude themselves, which suggests the value of including mesoscopic spatiotemporal characteristics in refining brain-machine interfaces.

Bistable nerve conduction

It has been demonstrated experimentally that slow and fast conduction waves with distinct conduction velocities can occur in the same nerve system depending on the strength or the form of the stimulus, which give rise to two modes of nerve functions. However, the mechanisms remain to be elucidated. In this study, we use computer simulations of the cable equation with modified Hodgkin-Huxley kinetics and analytical solutions of a simplified model to show that stimulus-dependent slow and fast waves recapitulating the experimental observations can occur in the cable, which are the two stable conduction states of a bistable conduction behavior. The bistable conduction is caused by a positive feedback loop of the wavefront upstroke speed, mediated by the sodium channel inactivation properties. Although the occurrence of bistable conduction only requires the presence of the sodium current, adding a calcium current to the model further promotes bistable conduction by potentiating the slow wave. We also show that the bistable conduction is robust, occurring for sodium and calcium activation thresholds well within the experimentally determined ones of the known sodium and calcium channel families. Since bistable conduction can occur in the cable equation of Hodgkin-Huxley kinetics with a single inward current, i.e., the sodium current, it can be a generic mechanism applicable to stimulus-dependent fast and slow conduction not only in the nerve systems but also in other electrically excitable systems, such as cardiac muscles.

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.

Horizontal connectivity in V1: Prediction of coherence in contour and motion integration

This study demonstrates the functional importance of the Surround context relayed laterally in V1 by the horizontal connectivity, in controlling the latency and the gain of the cortical response to the feedforward visual drive. We report here four main findings: 1) a centripetal apparent motion sequence results in a shortening of the spiking latency of V1 cells, when the orientation of the local inducer and the global motion axis are both co-aligned with the RF orientation preference; 2) this contextual effects grows with visual flow speed, peaking at 150–250°/s when it matches the propagation speed of horizontal connectivity (0.15–0.25 mm/ms); 3) For this speed range, the axial sensitivity of V1 cells is tilted by 90° to become co-aligned with the orientation preference axis; 4) the strength of modulation by the surround context correlates with the spatiotemporal coherence of the apparent motion flow. Our results suggest an internally-generated binding process, linking local (orientation /position) and global (motion/direction) features as early as V1. This long-range diffusion process constitutes a plausible substrate in V1 of the human psychophysical bias in speed estimation for collinear motion. Since it is demonstrated in the anesthetized cat, this novel form of contextual control of the cortical gain and phase is a built-in property in V1, whose expression does not require behavioral attention and top-down control from higher cortical areas. We propose that horizontal connectivity participates in the propagation of an internal “prediction” wave, shaped by visual experience, which links contour co-alignment and global axial motion at an apparent speed in the range of saccade-like eye movements.

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.

Propofol Anesthesia Alters Cortical Traveling Waves

Oscillatory dynamics in cortex seem to organize into traveling waves that serve a variety of functions. Recent studies show that propofol, a widely used anesthetic, dramatically alters cortical oscillations by increasing slow-delta oscillatory power and coherence. It is not known how this affects traveling waves. We compared traveling waves across the cortex of non-human primates before, during, and after propofol-induced loss of consciousness (LOC). After LOC, traveling waves in the slow-delta (∼1 Hz) range increased, grew more organized, and traveled in different directions relative to the awake state. Higher frequency (8-30 Hz) traveling waves, by contrast, decreased, lost structure, and switched to directions where the slow-delta waves were less frequent. The results suggest that LOC may be due, in part, to increases in the strength and direction of slow-delta traveling waves that, in turn, alter and disrupt traveling waves in the higher frequencies associated with cognition.

Neurons learn by predicting future activity

Understanding how the brain learns may lead to machines with human-like intellectual capacities. It was previously proposed that the brain may operate on the principle of predictive coding. However, it is still not well understood how a predictive system could be implemented in the brain. Here we demonstrate that the ability of a single neuron to predict its future activity may provide an effective learning mechanism. Interestingly, this predictive learning rule can be derived from a metabolic principle, where neurons need to minimize their own synaptic activity (cost), while maximizing their impact on local blood supply by recruiting other neurons. We show how this mathematically derived learning rule can provide a theoretical connection between diverse types of brain-inspired algorithms, thus, offering a step toward development of a general theory of neuronal learning. We tested this predictive learning rule in neural network simulations and in data recorded from awake animals. Our results also suggest that spontaneous brain activity provides “training data” for neurons to learn to predict cortical dynamics. Thus, the ability of a single neuron to minimize surprise: i.e. the difference between actual and expected activity, could be an important missing element to understand computation in the brain.

Improved spatio-temporal measurements of visually evoked fields using optically-pumped magnetometers

Recent developments in performance and practicality of optically-pumped magnetometers (OPMs) have enabled new capabilities in non-invasive brain function mapping through magnetoencephalography. In particular, the lack of cryogenic operating conditions allows for more flexible placement of sensor heads closer to the brain, leading to improved spatial resolution and source localisation capabilities. Through recording visually evoked brain fields (VEFs), we demonstrate that the closer sensor proximity can be exploited to improve temporal resolution. We use OPMs, and superconducting quantum interference devices (SQUIDs) for reference, to measure brain responses to flash and pattern reversal stimuli. We find highly reproducible signals with consistency across multiple participants, stimulus paradigms and sensor modalities. The temporal resolution advantage of OPMs is manifest in a twofold improvement, compared to SQUIDs. The capability for improved spatio-temporal signal tracing is illustrated by simultaneous vector recordings of VEFs in the primary and associative visual cortex, where a time lag on the order of 10–20 ms is consistently found. This paves the way for further spatio-temporal studies of neurophysiological signal tracking in visual stimulus processing, and other brain responses, with potentially far-reaching consequences for time-critical mapping of functionality in healthy and pathological brains.

Traveling Waves in Quasi-One-Dimensional Neuronal Minicolumns

Traveling waves of neuronal activity in the cortex have been observed in vivo. These traveling waves have been correlated to various features of observed cortical dynamics, including spike timing variability and correlated fluctuations in neuron membrane potential. Although traveling waves are typically studied as either strictly one-dimensional or two-dimensional excitations, here we investigate the conditions for the existence of quasi-one-dimensional traveling waves that could be sustainable in parts of the brain containing cortical minicolumns. For that, we explore a quasi-one-dimensional network of heterogeneous neurons with a biologically influenced computational model of neuron dynamics and connectivity. We find that background stimulus reliably evokes traveling waves in networks with local connectivity between neurons. We also observe traveling waves in fully connected networks when a model for action potential propagation speed is incorporated. The biological properties of the neurons influence the generation and propagation of the traveling waves. Our quasi-one-dimensional model is not only useful for studying the basic properties of traveling waves in neuronal networks; it also provides a simplified representation of possible wave propagation in columnar or minicolumnar networks found in the cortex.

Visual exposure enhances stimulus encoding and persistence in primary cortex

Experience shapes sensory responses, already at the earliest stages of cortical processing. We provide evidence that, in the primary visual cortex of anesthetized cats, brief repetitive exposure to a set of simple, abstract stimuli expands the range and decreases the variability of neuronal responses that persist after stimulus offset. These refinements increase the stimulus-specific clustering of neuronal population responses and result in a more efficient encoding of both stimulus identity and stimulus structure, thus potentially benefiting simple readouts in higher cortical areas. Similar results can be achieved via local plasticity mechanisms in recurrent networks, through self-organized refinements of internal dynamics that do not require changes in firing amplitudes.

The brain adapts to the sensory environment. For example, simple sensory exposure can modify the response properties of early sensory neurons. How these changes affect the overall encoding and maintenance of stimulus information across neuronal populations remains unclear. We perform parallel recordings in the primary visual cortex of anesthetized cats and find that brief, repetitive exposure to structured visual stimuli enhances stimulus encoding by decreasing the selectivity and increasing the range of the neuronal responses that persist after stimulus presentation. Low-dimensional projection methods and simple classifiers demonstrate that visual exposure increases the segregation of persistent neuronal population responses into stimulus-specific clusters. These observed refinements preserve the representational details required for stimulus reconstruction and are detectable in postexposure spontaneous activity. Assuming response facilitation and recurrent network interactions as the core mechanisms underlying stimulus persistence, we show that the exposure-driven segregation of stimulus responses can arise through strictly local plasticity mechanisms, also in the absence of firing rate changes. Our findings provide evidence for the existence of an automatic, unguided optimization process that enhances the encoding power of neuronal populations in early visual cortex, thus potentially benefiting simple readouts at higher stages of visual processing.

Modulation of the dynamical state in cortical network models

Cortical neural responses can be modulated by various factors, such as stimulus inputs and the behavior state of the animal. Understanding the circuit mechanisms underlying modulations of network dynamics is important to understand the flexibility of circuit computations. Identifying the dynamical state of a network is an important first step to predict network responses to external stimulus and top-down modulatory inputs. Models in stable or unstable dynamical regimes require different analytic tools to estimate the network responses to inputs and the structure of neural variability. In this article, I review recent cortical models of state-dependent responses and their predictions about the underlying modulatory mechanisms.

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.

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.

Dynamic Patterns of Spontaneous Ongoing Activity in the Visual Cortex of Anesthetized and Awake Monkeys are Different

Ongoing internal cortical activity plays a major role in perception and behavior both in animals and humans. Previously we have shown that spontaneous patterns resembling orientation-maps appear over large cortical areas in the primary visual-cortex of anesthetized cats. However, it remains unknown 1) whether spontaneous-activity in the primate also displays similar patterns and 2) whether a significant difference exists between cortical ongoing-activity in the anesthetized and awake primate. We explored these questions by combining voltage-sensitive-dye imaging with multiunit and local-field-potential recordings. Spontaneously emerging orientation and ocular-dominance maps, spanning up to 6 × 6 mm2, were readily observed in anesthetized but not in awake monkeys. Nevertheless, spontaneous correlated-activity involving orientation-domains was observed in awake monkeys. Under both anesthetized and awake conditions, spontaneous correlated-activity coincided with traveling waves. We found that spontaneous activity resembling orientation-maps in awake animals spans smaller cortical areas in each instance, but over time it appears across all of V1. Furthermore, in the awake monkey, our results suggest that the synaptic strength had been completely reorganized including connections between dissimilar elements of the functional architecture. These findings lend support to the notion that ongoing-activity has many more fast switching representations playing an important role in cortical function and behavior.

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.

Slow Waves in Cortical Slices: How Spontaneous Activity is Shaped by Laminar Structure

Cortical slow oscillations (SO) of neural activity spontaneously emerge and propagate during deep sleep and anesthesia and are also expressed in isolated brain slices and cortical slabs. We lack full understanding of how SO integrate the different structural levels underlying local excitability of cell assemblies and their mutual interaction. Here, we focus on ongoing slow waves (SWs) in cortical slices reconstructed from a 16-electrode array designed to probe the neuronal activity at multiple spatial scales. In spite of the variable propagation patterns observed, we reproducibly found a smooth strip of loci leading the SW fronts, overlapping cortical layers 4 and 5, along which Up states were the longest and displayed the highest firing rate. Propagation modes were uncorrelated in time, signaling a memoryless generation of SWs. All these features could be modeled by a multimodular large-scale network of spiking neurons with a specific balance between local and intermodular connectivity. Modules work as relaxation oscillators with a weakly stable Down state and a peak of local excitability to model layers 4 and 5. These conditions allow for both optimal sensitivity to the network structure and richness of propagation modes, both of which are potential substrates for dynamic flexibility in more general contexts.

Global vs. Network-Specific Regulations as the Source of Intrinsic Coactivations in Resting-State Networks

Spontaneous neural activities are endowed with specific patterning characterized by synchronizations within functionally relevant distant regions that are termed as resting-state networks (RSNs). Although the mechanisms that organize the large-scale neural systems are still largely unknown, recent studies have proposed a hypothesis that network-specific coactivations indeed emerge as the result of globally propagating neural activities with specific paths of transmission. However, the extent to which such a centralized global regulation, rather than network-specific control, contributes to the RSN synchronization remains unknown. In the present study, we investigated the contribution from each mechanism by directly identifying the global as well as local component of resting-state functional MRI (fMRI) data provided by human connectome project, using temporal independent component analysis (ICA). Based on the spatial distribution pattern, each ICA component was classified as global or local. Time lag mapping of each IC revealed several paths of global or semi-global propagations that are partially overlapping yet spatially distinct to each other. Consistent with previous studies, the time lag of global oscillation, although being less spatially homogenous than what was assumed to be, contributed to the RSN synchronization. However, an equivalent contribution was also shown on the part of the more locally confined activities that are independent to each other. While allowing the view that network-specific coactivation occurs as part of the sequences of global neural activities, these results further confirm an equally important role of the network-specific regulation for its coactivation, regardless of whether vascular artifacts contaminate the global component in fMRI measures.

Large-scale cortical travelling waves predict localized future cortical signals

Predicting future brain signal is highly sought-after, yet difficult to achieve. To predict the future phase of cortical activity at localized ECoG and MEG recording sites, we exploit its predominant, large-scale, spatiotemporal dynamics. The dynamics are extracted from the brain signal through Fourier analysis and principal components analysis (PCA) only, and cast in a data model that predicts future signal at each site and frequency of interest. The dominant eigenvectors of the PCA that map the large-scale patterns of past cortical phase to future ones take the form of smoothly propagating waves over the entire measurement array. In ECoG data from 3 subjects and MEG data from 20 subjects collected during a self-initiated motor task, mean phase prediction errors were as low as 0.5 radians at local sites, surpassing state-of-the-art methods of within-time-series or event-related models. Prediction accuracy was highest in delta to beta bands, depending on the subject, was more accurate during episodes of high global power, but was not strongly dependent on the time-course of the task. Prediction results did not require past data from the to-be-predicted site. Rather, best accuracy depended on the availability in the model of long wavelength information. The utility of large-scale, low spatial frequency traveling waves in predicting future phase activity at local sites allows estimation of the error introduced by failing to account for irreducible trajectories in the activity dynamics.

Prediction is an important step in scientific progress, often leading to real-world applications. Prediction of future brain activity could lead to improvements in detecting driver and pilot error or real-time brain testing using transcranial magnetic stimulation. Previous studies have either supposed that the ‘noise’ level in the cortex is high, setting the prediction bar rather low; or used localized measurements to predict future activity, with modest success. A long-held but controversial hypothesis is that the cortex is best characterized as a multi-scale dynamic structure, in which the flow of activity at one scale, say, the area responsible for motor control, is inextricably tied to activity at smaller and larger scales, for example within a cortical column and the whole cortex. We test this hypothesis by analyzing large-scale traveling waves of cortical activity. Like waves arriving on a beach, the ongoing wave motion allows better prediction of future activity compared to monitoring the local rise and fall; in the best cases the future wave cycle is predicted with as low as 20° average error angle. The prediction techniques developed for the present research rely on mathematics related to quantifying large-scale weather patterns or analysis of fluid dynamics.

A System for Accurate Tracking and Video Recordings of Rodent Eye Movements using Convolutional Neural Networks for Biomedical Image Segmentation

Research in neuroscience and vision science relies heavily on careful measurements of animal subject's gaze direction. Rodents are the most widely studied animal subjects for such research because of their economic advantage and hardiness. Recently, video based eye trackers that use image processing techniques have become a popular option for gaze tracking because they are easy to use and are completely noninvasive. Although significant progress has been made in improving the accuracy and robustness of eye tracking algorithms, unfortunately, almost all of the techniques have focused on human eyes, which does not account for the unique characteristics of the rodent eye images, e.g., variability in eye parameters, abundance of surrounding hair, and their small size. To overcome these unique challenges, this work presents a flexible, robust, and highly accurate model for pupil and corneal reflection identification in rodent gaze determination that can be incrementally trained to account for variability in eye parameters encountered in the field. To the best of our knowledge, this is the first paper that demonstrates a highly accurate and practical biomedical image segmentation based convolutional neural network architecture for pupil and corneal reflection identification in eye images. This new method, in conjunction with our automated infrared videobased eye recording system, offers the state of the art technology in eye tracking for neuroscience and vision science research for rodents.

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.

Ubiquitous Neocortical Decoding of Tactile Input Patterns

Whereas functional localization historically has been a key concept in neuroscience, direct neuronal recordings show that input of a particular modality can be recorded well outside its primary receiving areas in the neocortex. Here, we wanted to explore if such spatially unbounded inputs potentially contain any information about the quality of the input received. We utilized a recently introduced approach to study the neuronal decoding capacity at a high resolution by delivering a set of electrical, highly reproducible spatiotemporal tactile afferent activation patterns to the skin of the contralateral second digit of the forepaw of the anesthetized rat. Surprisingly, we found that neurons in all areas recorded from, across all cortical depths tested, could decode the tactile input patterns, including neurons of the primary visual cortex. Within both somatosensory and visual cortical areas, the combined decoding accuracy of a population of neurons was higher than for the best performing single neuron within the respective area. Such cooperative decoding indicates that not only did individual neurons decode the input, they also did so by generating responses with different temporal profiles compared to other neurons, which suggests that each neuron could have unique contributions to the tactile information processing. These findings suggest that tactile processing in principle could be globally distributed in the neocortex, possibly for comparison with internal expectations and disambiguation processes relying on other modalities.

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.

NFTsim: Theory and Simulation of Multiscale Neural Field Dynamics

A user ready, portable, documented software package, NFTsim, is presented to facilitate numerical simulations of a wide range of brain systems using continuum neural field modeling. NFTsim enables users to simulate key aspects of brain activity at multiple scales. At the microscopic scale, it incorporates characteristics of local interactions between cells, neurotransmitter effects, synaptodendritic delays and feedbacks. At the mesoscopic scale, it incorporates information about medium to large scale axonal ranges of fibers, which are essential to model dissipative wave transmission and to produce synchronous oscillations and associated cross-correlation patterns as observed in local field potential recordings of active tissue. At the scale of the whole brain, NFTsim allows for the inclusion of long range pathways, such as thalamocortical projections, when generating macroscopic activity fields. The multiscale nature of the neural activity produced by NFTsim has the potential to enable the modeling of resulting quantities measurable via various neuroimaging techniques. In this work, we give a comprehensive description of the design and implementation of the software. Due to its modularity and flexibility, NFTsim enables the systematic study of an unlimited number of neural systems with multiple neural populations under a unified framework and allows for direct comparison with analytic and experimental predictions. The code is written in C++ and bundled with Matlab routines for a rapid quantitative analysis and visualization of the outputs. The output of NFTsim is stored in plain text file enabling users to select from a broad range of tools for offline analysis. This software enables a wide and convenient use of powerful physiologically-based neural field approaches to brain modeling. NFTsim is distributed under the Apache 2.0 license.

Classification of Spatiotemporal Neural Activity Patterns in Brain Imaging Data

Various patterns of neural activity are observed in dynamic cortical imaging data. Such patterns may reflect how neurons communicate using the underlying circuitry to perform appropriate functions; thus it is crucial to investigate the spatiotemporal characteristics of the observed neural activity patterns. In general, however, neural activities are highly nonlinear and complex, so it is a demanding job to analyze them quantitatively or to classify the patterns of observed activities in various types of imaging data. Here, we present our implementation of a novel method that successfully addresses the above issues for precise comparison and classification of neural activity patterns. Based on two-dimensional representations of the geometric structure and temporal evolution of activity patterns, our method successfully classified a number of computer-generated sample patterns created from combinations of various spatial and temporal patterns. In addition, we validated our method with voltage-sensitive dye imaging data of Alzheimer's disease (AD) model mice. Our analysis algorithm successfully distinguished the activity data of AD mice from that of wild type with significantly higher performance than previously suggested methods. Our result provides a pragmatic solution for precise analysis of spatiotemporal patterns of neural imaging data.

LFP beta amplitude is linked to mesoscopic spatio-temporal phase patterns

Beta oscillations observed in motor cortical local field potentials (LFPs) recorded on separate electrodes of a multi-electrode array have been shown to exhibit non-zero phase shifts that organize into planar waves. Here, we generalize this concept to additional classes of salient patterns that fully describe the spatial organization of beta oscillations. During a delayed reach-to-grasp task we distinguish planar, synchronized, random, circular, and radial phase patterns in monkey primary motor and dorsal premotor cortices. We observe that patterns correlate with the beta amplitude (envelope): Coherent planar/radial wave propagation accelerates with growing amplitude, and synchronized patterns are observed at largest amplitudes. In contrast, incoherent random or circular patterns are observed almost exclusively when beta is strongly attenuated. The occurrence probability of a particular pattern modulates with behavioral epochs in the same way as beta amplitude: Coherent patterns are more present during movement preparation where amplitudes are large, while incoherent phase patterns are dominant during movement execution where amplitudes are small. Thus, we uncover a trigonal link between the spatial arrangement of beta phases, beta amplitude, and behavior. Together with previous findings, we discuss predictions on the spatio-temporal organization of precisely coordinated spiking on the mesoscopic scale as a function of beta power.

Cortical travelling waves: mechanisms and computational principles

Multichannel recording technologies have revealed travelling waves of neural activity in multiple sensory, motor and cognitive systems. These waves can be spontaneously generated by recurrent circuits or evoked by external stimuli. They travel along brain networks at multiple scales, transiently modulating spiking and excitability as they pass. Here, we review recent experimental findings that have found evidence for travelling waves at single-area (mesoscopic) and whole-brain (macroscopic) scales. We place these findings in the context of the current theoretical understanding of wave generation and propagation in recurrent networks. During the large low-frequency rhythms of sleep or the relatively desynchronized state of the awake cortex, travelling waves may serve a variety of functions, from long-term memory consolidation to processing of dynamic visual stimuli. We explore new avenues for experimental and computational understanding of the role of spatiotemporal activity patterns in the cortex.

Visual Motion Discrimination by Propagating Patterns in Primate Cerebral Cortex

Visual stimuli can evoke waves of neural activity that propagate across the surface of visual cortical areas. The relevance of these waves for visual processing is unknown. Here, we measured the phase and amplitude of local field potentials (LFPs) in electrode array recordings from the motion-processing medial temporal (MT) area of anesthetized male marmosets. Animals viewed grating or dot-field stimuli drifting in different directions. We found that, on individual trials, the direction of LFP wave propagation is sensitive to the direction of stimulus motion. Propagating LFP patterns are also detectable in trial-averaged activity, but the trial-averaged patterns exhibit different dynamics and behaviors from those in single trials and are similar across motion directions. We show that this difference arises because stimulus-sensitive propagating patterns are present in the phase of single-trial oscillations, whereas the trial-averaged signal is dominated by additive amplitude effects. Our results demonstrate that propagating LFP patterns can represent sensory inputs at timescales relevant to visually guided behaviors and raise the possibility that propagating activity patterns serve neural information processing in area MT and other cortical areas.SIGNIFICANCE STATEMENT Propagating wave patterns are widely observed in the cortex, but their functional relevance remains unknown. We show here that visual stimuli generate propagating wave patterns in local field potentials (LFPs) in a movement-sensitive area of the primate cortex and that the propagation direction of these patterns is sensitive to stimulus motion direction. We also show that averaging LFP signals across multiple stimulus presentations (trial averaging) yields propagating patterns that capture different dynamic properties of the LFP response and show negligible direction sensitivity. Our results demonstrate that sensory stimuli can modulate propagating wave patterns reliably in the cortex. The relevant dynamics are normally masked by trial averaging, which is a conventional step in LFP signal processing.

Catching the voltage gradient-asymmetric boost of cortical spread generates motion signals across visual cortex: a brief review with special thanks to Amiram Grinvald

Wide-field voltage imaging is unique in its capability to capture snapshots of activity-across the full gradient of average changes in membrane potentials from subthreshold to suprathreshold levels-of hundreds of thousands of superficial cortical neurons that are simultaneously active. Here, I highlight two examples where voltage-sensitive dye imaging (VSDI) was exploited to track gradual space-time changes of activity within milliseconds across several millimeters of cortex at submillimeter resolution: the line-motion condition, measured in Amiram Grinvald's Laboratory more than 10 years ago and-coming full circle running VSDI in my laboratory-another motion-inducing condition, in which two neighboring stimuli counterchange luminance simultaneously. In both examples, cortical spread is asymmetrically boosted, creating suprathreshold activity drawn out over primary visual cortex. These rapidly propagating waves may integrate brain signals that encode motion independent of direction-selective circuits.

'Blue' voltage-sensitive dyes for studying spatiotemporal dynamics in the brain: visualizing cortical waves

Among many distinct contributions made by Amiram Grinvald's group, the "Blue dyes" is a special gift for visualizing cortical population neuronal activity. The excitation wavelength of blue dyes has minimal overlap with the absorption of hemoglobin, and hence has minimal pulsation artifacts. This advantage leads to high signal-to-noise ratio optical recordings of cortical activity, with sensitivity as good as that of local field potential recordings. High sensitivity imaging allows for recording of spontaneous and evoked activity in single trials without spatial or temporal averaging, and has benefitted many scientists in their research projects. Single trial recording is particularly important for studying the cortex, because spontaneous and ongoing activities interact with sensory evoked events, creating rich dynamics in the wave patterns. Signal averaging in space and time would diminish the dynamic components in the patterns. Here, we discuss how the blue dyes help to achieve high-sensitivity voltage-sensitive dye imaging of spontaneous and evoked cortical activities. Spontaneous cortical activity has a constantly changing spatial pattern and temporal frequency, making it impossible to average in space and time. Amiran Grinvald's invention of blue dyes made it possible to examine the spatiotemporal patterns of cortical dynamics, about 15 years before the first useful genetically coded voltage proteins became available.

Improving voltage-sensitive dye imaging: with a little help from computational approaches

Voltage-sensitive dye imaging (VSDI) is a key neurophysiological recording tool because it reaches brain scales that remain inaccessible to other techniques. The development of this technique from in vitro to the behaving nonhuman primate has only been made possible thanks to the long-lasting, visionary work of Amiram Grinvald. This work has opened new scientific perspectives to the great benefit to the neuroscience community. However, this unprecedented technique remains largely under-utilized, and many future possibilities await for VSDI to reveal new functional operations. One reason why this tool has not been used extensively is the inherent complexity of the signal. For instance, the signal reflects mainly the subthreshold neuronal population response and is not linked to spiking activity in a straightforward manner. Second, VSDI gives access to intracortical recurrent dynamics that are intrinsically complex and therefore nontrivial to process. Computational approaches are thus necessary to promote our understanding and optimal use of this powerful technique. Here, we review such approaches, from computational models to dissect the mechanisms and origin of the recorded signal, to advanced signal processing methods to unravel new neuronal interactions at mesoscopic scale. Only a stronger development of interdisciplinary approaches can bridge micro- to macroscales.