Propagating waves of activity in the neocortex: what they are, what they do

Layer III neurons control synchronized waves in the immature cerebral cortex

Correlated spiking activity prevails in immature cortical networks and is believed to contribute to neuronal circuit maturation; however, its spatiotemporal organization is not fully understood. Using wide-field calcium imaging from acute whole-brain slices of rat pups on postnatal days 1-6, we found that correlated spikes were initiated in the anterior part of the lateral entorhinal cortex and propagated anteriorly to the frontal cortex and posteriorly to the medial entorhinal cortex, forming traveling waves that engaged almost the entire cortex. The waves were blocked by ionotropic glutamatergic receptor antagonists but not by GABAergic receptor antagonists. During wave events, glutamatergic and GABAergic synaptic inputs were balanced and induced UP state-like depolarization. Magnified monitoring with cellular resolution revealed that the layer III neurons were first activated when the waves were initiated. Consistent with this finding, layer III contained a larger number of neurons that were autonomously active, even under a blockade of synaptic transmission. During wave propagation, the layer III neurons constituted a leading front of the wave. The waves did not enter the parasubiculum; however, in some cases, they were reflected at the parasubicular border and propagated back in the opposite direction. During this reflection process, the layer III neurons in the medial entorhinal cortex maintained persistent activity. Thus, our data emphasize the role of layer III in early network behaviors and provide insight into the circuit mechanisms through which cerebral cortical networks maturate.

Traveling waves in visual cortex

Electrode recordings and imaging studies have revealed that localized visual stimuli elicit waves of activity that travel across primary visual cortex. Traveling waves are present also during spontaneous activity, but they can be greatly reduced by widespread and intensive visual stimulation. In this Review, we summarize the evidence in favor of these traveling waves. We suggest that their substrate may lie in long-range horizontal connections and that their functional role may involve the integration of information over large regions of space.

A computational role for bistability and traveling waves in motor cortex

Adaptive changes in behavior require rapid changes in brain states yet the brain must also remain stable. We investigated two neural mechanisms for evoking rapid transitions between spatiotemporal synchronization patterns of beta oscillations (13–30 Hz) in motor cortex. Cortex was modeled as a sheet of neural oscillators that were spatially coupled using a center-surround connection topology. Manipulating the inhibitory surround was found to evoke reliable transitions between synchronous oscillation patterns and traveling waves. These transitions modulated the simulated local field potential in agreement with physiological observations in humans. Intermediate levels of surround inhibition were also found to produce bistable coupling topologies that supported both waves and synchrony. State-dependent perturbation between bistable states produced very rapid transitions but were less reliable. We surmise that motor cortex may thus employ state-dependent computation to achieve very rapid changes between bistable motor states when the demand for speed exceeds the demand for accuracy.

Spontaneous high-gamma band activity reflects functional organization of auditory cortex in the awake macaque

In the absence of sensory stimuli, spontaneous activity in the brain has been shown to exhibit organization at multiple spatiotemporal scales. In the macaque auditory cortex, responses to acoustic stimuli are tonotopically organized within multiple, adjacent frequency maps aligned in a caudorostral direction on the supratemporal plane (STP) of the lateral sulcus. Here, we used chronic microelectrocorticography to investigate the correspondence between sensory maps and spontaneous neural fluctuations in the auditory cortex. We first mapped tonotopic organization across 96 electrodes spanning approximately two centimeters along the primary and higher auditory cortex. In separate sessions, we then observed that spontaneous activity at the same sites exhibited spatial covariation that reflected the tonotopic map of the STP. This observation demonstrates a close relationship between functional organization and spontaneous neural activity in the sensory cortex of the awake monkey.

Genetically engineered fluorescent voltage reporters

Fluorescent membrane voltage indicators that enable optical imaging of neuronal circuit operations in the living mammalian brain are powerful tools for biology and particularly neuroscience. Classical voltage-sensitive dyes, typically low molecular-weight organic compounds, have been in widespread use for decades but are limited by issues related to optical noise, the lack of generally applicable procedures that enable staining of specific cell populations, and difficulties in performing imaging experiments over days and weeks. Genetically encoded voltage indicators (GEVIs) represent a newer alternative that overcomes several of the limitations inherent to classical voltage-sensitive dyes. We critically review the fundamental concepts of this approach, the variety of available probes and their state of development.

Stimulus-entrained oscillatory activity propagates as waves from area 18 to 17 in cat visual cortex

Previous studies in cat visual cortex reported that area 18 can actively drive neurons in area 17 through cortico-cortical projections. However, the dynamics of such cortico-cortical interaction remains unclear. Here we used multielectrode arrays to examine the spatiotemporal pattern of neuronal activity in cat visual cortex across the 17/18 border. We found that full-field contrast reversal gratings evoked oscillatory wave activity propagating from area 18 to 17. The wave direction was independent of the grating orientation, and could not be accounted for by the spatial distribution of receptive field latencies, suggesting that the waves are largely mediated by intrinsic connections in the cortex. Different from the evoked waves, spontaneous waves propagated along both directions across the 17/18 border. Together, our results suggest that visual stimulation may enhance the flow of information from area 18 to 17.

Imaging neural circuit dynamics with a voltage-sensitive fluorescent protein

Population signals from neuronal ensembles in cortex during behavior are commonly measured with EEG, local field potential (LFP), and voltage-sensitive dyes. A genetically encoded voltage indicator would be useful for detection of such signals in specific cell types. Here we describe how this goal can be achieved with Butterfly, a voltage-sensitive fluorescent protein (VSFP) with a subthreshold detection range and enhancements designed for voltage imaging from single neurons to brain in vivo. VSFP-Butterfly showed reliable membrane targeting, maximum response gain around standard neuronal resting membrane potential, fast kinetics for single-cell synaptic responses, and a high signal-to-noise ratio. Butterfly reports excitatory postsynaptic potentials (EPSPs) in cortical neurons, whisker-evoked responses in barrel cortex, 25-Hz gamma oscillations in hippocampal slices, and 2- to 12-Hz slow waves during brain state modulation in vivo. Our findings demonstrate that cell class-specific voltage imaging is practical with VSFP-Butterfly, and expand the genetic toolbox for the detection of neuronal population dynamics.

Genetically encoded probes for optical imaging of brain electrical activity

The combination of optical imaging methods with targeted expression of protein-based fluorescent probes constitutes a powerful approach for functional analysis of selected cell populations within intact neuronal circuitries. Herein, we lay out the conceptual motivation for optogenetic recording of brain electrical activity using genetically encoded voltage-sensitive fluorescent proteins (VSFPs), describe how the current generation of VSFPs has evolved, and demonstrate how VSFPs report membrane voltage signals in isolated cells, brain slices, and living animals. We conclude with a critical appraisal of VSFPs for voltage recording and highlight promising applications of this emerging methodology for bridging cellular and intact systems biology.

Interactions between two propagating waves in rat visual cortex

Sensory-evoked propagating waves are frequently observed in sensory cortex. However, it is largely unknown how an evoked propagating wave affects the activity evoked by subsequent sensory inputs, or how two propagating waves interact when evoked by simultaneous sensory inputs. Using voltage-sensitive dye imaging, we investigated the interactions between two evoked waves in rat visual cortex, and the spatiotemporal patterns of depolarization in the neuronal population due to wave-to-wave interactions. We have found that visually-evoked propagating waves have a refractory period of about 300 ms, within which the response to a subsequent visual stimulus is suppressed. Simultaneous presentation of two visual stimuli at different locations can evoke two waves propagating toward each other, and these two waves fuse. Fusion significantly shortens the latency and half-width of the response, leading to changes in the spatial profile of evoked population activity. The visually-evoked propagating wave may also be suppressed by a preceding spontaneous wave. The refractory period following a propagating wave and the fusion between two waves may contribute to visual sensory processing by modifying the spatiotemporal profile of population neuronal activity evoked by sensory events.

Robustness of traveling waves in ongoing activity of visual cortex

Numerous studies have revealed traveling waves of activity in sensory cortex, both following sensory stimulation and during ongoing activity. We contributed to this body of work by measuring the spike-triggered average of the local field potential (stLFP) at multiple concurrent locations (Nauhaus et al., 2009) in the visual cortex of anesthetized cats and macaques. We found the stLFP to be progressively delayed at increasing distances from the site of the triggering spikes, and interpreted this as a traveling wave of depolarization originating from that site. Our results were criticized, however, on two grounds. First, a study using the same recording techniques in the visual cortex of awake macaques reported an apparent lack of traveling waves, and proposed that traveling waves could arise artifactually from excessive filtering of the field potentials (Ray and Maunsell, 2011). Second, the interpretability of the stLFP was questioned (Kenneth Miller, personal communication), as the stLFP must reflect not only interactions between spike trains and field potentials, but also correlations within and across the spike trains. Here, we show that our data and interpretation are not imperiled by these criticisms. We reanalyzed our field potentials to remove any possible artifact due to filtering and to discount the effects of correlations within and across the triggering spike trains. In both cases, we found that the traveling waves were still present. In fact, closer inspection of Ray and Maunsell's (2011) data from awake cortex shows that they do agree with ours, as they contain clear evidence for traveling waves.

β-Adrenergic modulation of spontaneous spatiotemporal activity patterns and synchrony in hyperexcitable hippocampal circuits

A description of healthy and pathological brain dynamics requires an understanding of spatiotemporal patterns of neural activity and characteristics of its propagation between interconnected circuits. However, the structure and modulation of the neural activation maps underlying these patterns and their propagation remain elusive. We investigated effects of β-adrenergic receptor (β-AR) stimulation on the spatiotemporal characteristics of emergent activity in rat hippocampal circuits. Synchronized epileptiform-like activity, such as interictal bursts (IBs) and ictal-like events (ILEs), were evoked by 4-aminopyridine (4-AP), and their dynamics were studied using a combination of electrophysiology and fast voltage-sensitive dye imaging. Dynamic characterization of the spontaneous IBs showed that they originated in dentate gyrus/CA3 border and propagated toward CA1. To determine how β-AR modulates spatiotemporal characteristics of the emergent IBs, we used the β-AR agonist isoproterenol (ISO). ISO significantly reduced the spatiotemporal extent and propagation velocity of the IBs and significantly altered network activity in the 1- to 20-Hz range. Dual whole cell recordings of the IBs in CA3/CA1 pyramidal cells and optical analysis of those regions showed that ISO application reduced interpyramidal and interregional synchrony during the IBs. In addition, ISO significantly reduced duration not only of the shorter duration IBs but also the prolonged ILEs in 4-AP. To test whether the decrease in ILE duration was model dependent, we used a different hyperexcitability model, zero magnesium (0 Mg(2+)). Prolonged ILEs were readily formed in 0 Mg(2+), and addition of ISO significantly reduced their durations. Taken together, these novel results provide evidence that β-AR activation dynamically reshapes the spatiotemporal activity patterns in hyperexcitable circuits by altering network rhythmogenesis, propagation velocity, and intercellular/regional synchronization.

Neural information processing with feedback modulations

Descending feedback connections, together with ascending feedforward ones, are the indispensable parts of the sensory pathways in the central nervous system. This study investigates the potential roles of feedback interactions in neural information processing. We consider a two-layer continuous attractor neural network (CANN), in which neurons in the first layer receive feedback inputs from those in the second one. By utilizing the intrinsic property of a CANN, we use a projection method to reduce the dimensionality of the network dynamics significantly. The simplified dynamics allows us to elucidate the effects of feedback modulation analytically. We find that positive feedback enhances the stability of the network state, leading to an improved population decoding performance, whereas negative feedback increases the mobility of the network state, inducing spontaneously moving bumps. For strong, negative feedback interaction, the network response to a moving stimulus can lead the actual stimulus position, achieving an anticipative behavior. The biological implications of these findings are discussed. The simulation results agree well with our theoretical analysis.

In vivo Large-Scale Cortical Mapping Using Channelrhodopsin-2 Stimulation in Transgenic Mice Reveals Asymmetric and Reciprocal Relationships between Cortical Areas

We have mapped intracortical activity in vivo independent of sensory input using arbitrary point channelrhodopsin-2 (ChR2) stimulation and regional voltage sensitive dye imaging in B6.Cg-Tg (Thy1-COP4/EYFP)18Gfng/J transgenic mice. Photostimulation of subsets of deep layer pyramidal neurons within forelimb, barrel, or visual primary sensory cortex led to downstream cortical maps that were dependent on synaptic transmission and were similar to peripheral sensory stimulation. ChR2-evoked maps confirmed homotopic connections between hemispheres and intracortical sensory and motor cortex connections. This ability of optogentically activated subpopulations of neurons to drive appropriate downstream maps suggests that mechanisms exist to allow prototypical cortical maps to self-assemble from the stimulation of neuronal subsets. Using this principle of map self-assembly, we employed ChR2 point stimulation to map connections between cortical areas that are not selectively activated by peripheral sensory stimulation or behavior. Representing the functional cortical regions as network nodes, we identified asymmetrical connection weights in individual nodes and identified the parietal association area as a network hub. Furthermore, we found that the strength of reciprocal intracortical connections between primary and secondary sensory areas are unequal, with connections from primary to secondary sensory areas being stronger than the reciprocal.

Response of traveling waves to transient inputs in neural fields

We analyze the effects of transient stimulation on traveling waves in neural field equations. Neural fields are modeled as integro-differential equations whose convolution term represents the synaptic connections of a spatially extended neuronal network. The adjoint of the linearized wave equation can be used to identify how a particular input will shift the location of a traveling wave. This wave response function is analogous to the phase response curve of limit cycle oscillators. For traveling fronts in an excitatory network, the sign of the shift depends solely on the sign of the transient input. A complementary estimate of the effective shift is derived using an equation for the time-dependent speed of the perturbed front. Traveling pulses are analyzed in an asymmetric lateral inhibitory network and they can be advanced or delayed, depending on the position of spatially localized transient inputs. We also develop bounds on the amplitude of transient input necessary to terminate traveling pulses, based on the global bifurcation structure of the neural field.

Dynamical synapses enhance neural information processing: gracefulness, accuracy, and mobility

Experimental data have revealed that neuronal connection efficacy exhibits two forms of short-term plasticity: short-term depression (STD) and short-term facilitation (STF). They have time constants residing between fast neural signaling and rapid learning and may serve as substrates for neural systems manipulating temporal information on relevant timescales. This study investigates the impact of STD and STF on the dynamics of continuous attractor neural networks and their potential roles in neural information processing. We find that STD endows the network with slow-decaying plateau behaviors: the network that is initially being stimulated to an active state decays to a silent state very slowly on the timescale of STD rather than on that of neuralsignaling. This provides a mechanism for neural systems to hold sensory memory easily and shut off persistent activities gracefully. With STF, we find that the network can hold a memory trace of external inputs in the facilitated neuronal interactions, which provides a way to stabilize the network response to noisy inputs, leading to improved accuracy in population decoding. Furthermore, we find that STD increases the mobility of the network states. The increased mobility enhances the tracking performance of the network in response to time-varying stimuli, leading to anticipative neural responses. In general, we find that STD and STP tend to have opposite effects on network dynamics and complementary computational advantages, suggesting that the brain may employ a strategy of weighting them differentially depending on the computational purpose.

Evoked traveling alpha waves predict visual-semantic categorization-speed

In the present study we have tested the hypothesis that evoked traveling alpha waves are behaviorally significant. The results of a visual-semantic categorization task show that three early ERP components including the P1-N1 complex had a dominant frequency characteristic in the alpha range and behaved like traveling waves do. They exhibited a traveling direction from midline occipital to right lateral parietal sites. Phase analyses revealed that this traveling behavior of ERP components could be explained by phase-delays in the alpha but not theta and beta frequency range. Most importantly, we found that the speed of the traveling alpha wave was significantly and negatively correlated with reaction time indicating that slow traveling speed was associated with fast picture-categorization. We conclude that evoked alpha oscillations are functionally associated with early access to visual-semantic information and generate--or at least modulate--the early waveforms of the visual ERP.

Ongoing physiological processes in the cerebral cortex

Functional magnetic resonance imaging (fMRI) has revealed that the human brain undergoes prominent, regional hemodynamic fluctuations when a subject is at rest. These ongoing fluctuations exhibit distinct patterns of spatiotemporal synchronization that have been dubbed "resting state functional connectivity", and which currently serve as a principal tool to investigate neural networks in the normal and pathological human brain. Despite the wide application of this approach in human neuroscience, the neural mechanisms that give rise to spontaneous fMRI correlations are largely unknown. Here we review results of recent electrophysiological studies in the cerebral cortex of humans and nonhuman primates that link neural activity to ongoing fMRI fluctuations. We begin by describing results obtained with simultaneous fMRI and electrophysiological measurements that allow for the identification of direct neural correlates of resting state functional connectivity. We next highlight experiments that investigate the correlational structure of spontaneous neural signals, including the spatial variation of signal coherence over the cortical surface, across cortical laminae, and between the two hemispheres. In the final section we speculate on the origins and potential consequences of ongoing signals for normal brain function, and point out inherent limitations of the fMRI correlation approach.

Towards a model-based integration of co-registered electroencephalography/functional magnetic resonance imaging data with realistic neural population meshes

Brain activity can be measured with several non-invasive neuroimaging modalities, but each modality has inherent limitations with respect to resolution, contrast and interpretability. It is hoped that multimodal integration will address these limitations by using the complementary features of already available data. However, purely statistical integration can prove problematic owing to the disparate signal sources. As an alternative, we propose here an advanced neural population model implemented on an anatomically sound cortical mesh with freely adjustable connectivity, which features proper signal expression through a realistic head model for the electroencephalogram (EEG), as well as a haemodynamic model for functional magnetic resonance imaging based on blood oxygen level dependent contrast (fMRI BOLD). It hence allows simultaneous and realistic predictions of EEG and fMRI BOLD from the same underlying model of neural activity. As proof of principle, we investigate here the influence on simulated brain activity of strengthening visual connectivity. In the future we plan to fit multimodal data with this neural population model. This promises novel, model-based insights into the brain's activity in sleep, rest and task conditions.

Stereotypical spatiotemporal activity patterns during slow-wave activity in the neocortex

Alternating epochs of activity and silence are a characteristic feature of neocortical networks during certain sleep cycles and deep states of anesthesia. The mechanism and functional role of these slow oscillations (<1 Hz) have not yet been fully characterized. Experimental and theoretical studies show that slow-wave oscillations can be generated autonomously by neocortical tissue but become more regular through a thalamo-cortical feedback loop. Evidence for a functional role of slow-wave activity comes from EEG recordings in humans during sleep, which show that activity travels as stereotypical waves over the entire brain, thought to play a role in memory consolidation. We used an animal model to investigate activity wave propagation on a smaller scale, namely within the rat somatosensory cortex. Signals from multiple extracellular microelectrodes in combination with one intracellular recording in the anesthetized animal in vivo were utilized to monitor the spreading of activity. We found that activity propagation in most animals showed a clear preferred direction, suggesting that it often originated from a similar location in the cortex. In addition, the breakdown of active states followed a similar pattern with slightly weaker direction preference but a clear correlation to the direction of activity spreading, supporting the notion of a wave-like phenomenon similar to that observed after strong sensory stimulation in sensory areas. Taken together, our findings support the idea that activity waves during slow-wave sleep do not occur spontaneously at random locations within the network, as was suggested previously, but follow preferred synaptic pathways on a small spatial scale.

Flow detection of propagating waves with temporospatial correlation of activity

Voltage-sensitive dye imaging (VSDI) allows population patterns of cortical activity to be recorded with high temporal resolution, and recent findings ascribe potential significance to these spatial propagation patterns--both for normal cortical processing and in pathologies such as epilepsy. However, analysis of these spatiotemporal patterns has been mostly qualitative to date. In this report, we describe an algorithm to quantify fast local flow patterns of cortical population activation, as measured with VSDI. The algorithm uses correlation of temporal features across space, and therefore differs from conventional optical flow algorithms which use correlation of spatial features over time. This alternative approach allows us to take advantage of the characteristics of fast optical imaging data, which have very high temporal resolution but less spatial resolution. We verify the method both on artificial and biological data, and demonstrate its use.

Spatial learning and action planning in a prefrontal cortical network model

The interplay between hippocampus and prefrontal cortex (PFC) is fundamental to spatial cognition. Complementing hippocampal place coding, prefrontal representations provide more abstract and hierarchically organized memories suitable for decision making. We model a prefrontal network mediating distributed information processing for spatial learning and action planning. Specific connectivity and synaptic adaptation principles shape the recurrent dynamics of the network arranged in cortical minicolumns. We show how the PFC columnar organization is suitable for learning sparse topological-metrical representations from redundant hippocampal inputs. The recurrent nature of the network supports multilevel spatial processing, allowing structural features of the environment to be encoded. An activation diffusion mechanism spreads the neural activity through the column population leading to trajectory planning. The model provides a functional framework for interpreting the activity of PFC neurons recorded during navigation tasks. We illustrate the link from single unit activity to behavioral responses. The results suggest plausible neural mechanisms subserving the cognitive “insight” capability originally attributed to rodents by Tolman & Honzik. Our time course analysis of neural responses shows how the interaction between hippocampus and PFC can yield the encoding of manifold information pertinent to spatial planning, including prospective coding and distance-to-goal correlates.

We study spatial cognition, a high-level brain function based upon the ability to elaborate mental representations of the environment supporting goal-oriented navigation. Spatial cognition involves parallel information processing across a distributed network of interrelated brain regions. Depending on the complexity of the spatial navigation task, different neural circuits may be primarily involved, corresponding to different behavioral strategies. Navigation planning, one of the most flexible strategies, is based on the ability to prospectively evaluate alternative sequences of actions in order to infer optimal trajectories to a goal. The hippocampal formation and the prefrontal cortex are two neural substrates likely involved in navigation planning. We adopt a computational modeling approach to show how the interactions between these two brain areas may lead to learning of topological representations suitable to mediate action planning. Our model suggests plausible neural mechanisms subserving the cognitive spatial capabilities attributed to rodents. We provide a functional framework for interpreting the activity of prefrontal and hippocampal neurons recorded during navigation tasks. Akin to integrative neuroscience approaches, we illustrate the link from single unit activity to behavioral responses while solving spatial learning tasks.

Traveling Bumps and Their Collisions in a Two-Dimensional Neural Field

A neural field is a continuous version of a neural network model accounting for dynamical pattern forming from populational firing activities in neural tissues. These patterns include standing bumps, moving bumps, traveling waves, target waves, breathers, and spiral waves, many of them observed in various brain areas. They can be categorized into two types: a wave-like activity spreading over the field and a particle-like localized activity. We show through numerical experiments that localized traveling excitation patterns (traveling bumps), which behave like particles, exist in a two-dimensional neural field with excitation and inhibition mechanisms. The traveling bumps do not require any geometric restriction (boundary) to prevent them from propagating away, a fact that might shed light on how neurons in the brain are functionally organized. Collisions of traveling bumps exhibit rich phenomena; they might reveal the manner of information processing in the cortex and be useful in various applications. The trajectories of traveling bumps can be controlled by external inputs.

Spiral wave dynamics in neocortex

Although spiral waves are ubiquitous features of nature and have been observed in many biological systems, their existence and potential function in mammalian cerebral cortex remain uncertain. Using voltage-sensitive dye imaging, we found that spiral waves occur frequently in the neocortex in vivo, both during pharmacologically induced oscillations and during sleep-like states. While their life span is limited, spiral waves can modify ongoing cortical activity by influencing oscillation frequencies and spatial coherence and by reducing amplitude in the area surrounding the spiral phase singularity. During sleep-like states, the rate of occurrence of spiral waves varies greatly depending on brain states. These results support the hypothesis that spiral waves, as an emergent activity pattern, can organize and modulate cortical population activity on the mesoscopic scale and may contribute to both normal cortical processing and to pathological patterns of activity such as those found in epilepsy.

Bifurcations of lurching waves in a thalamic neuronal network

We consider a two-layer, one-dimensional lattice of neurons; one layer consists of excitatory thalamocortical neurons, while the other is comprised of inhibitory reticular thalamic neurons. Such networks are known to support "lurching" waves, for which propagation does not appear smooth, but rather progresses in a saltatory fashion; these waves can be characterized by different spatial widths (different numbers of neurons active at the same time). We show that these lurching waves are fixed points of appropriately defined Poincaré maps, and follow these fixed points as parameters are varied. In this way, we are able to explain observed transitions in behavior, and, in particular, to show how branches with different spatial widths are linked with each other. Our computer-assisted analysis is quite general and could be applied to other spatially extended systems which exhibit this non-trivial form of wave propagation.

Generative models of cortical oscillations: neurobiological implications of the kuramoto model

Understanding the fundamental mechanisms governing fluctuating oscillations in large-scale cortical circuits is a crucial prelude to a proper knowledge of their role in both adaptive and pathological cortical processes. Neuroscience research in this area has much to gain from understanding the Kuramoto model, a mathematical model that speaks to the very nature of coupled oscillating processes, and which has elucidated the core mechanisms of a range of biological and physical phenomena. In this paper, we provide a brief introduction to the Kuramoto model in its original, rather abstract, form and then focus on modifications that increase its neurobiological plausibility by incorporating topological properties of local cortical connectivity. The extended model elicits elaborate spatial patterns of synchronous oscillations that exhibit persistent dynamical instabilities reminiscent of cortical activity. We review how the Kuramoto model may be recast from an ordinary differential equation to a population level description using the nonlinear Fokker–Planck equation. We argue that such formulations are able to provide a mechanistic and unifying explanation of oscillatory phenomena in the human cortex, such as fluctuating beta oscillations, and their relationship to basic computational processes including multistability, criticality, and information capacity.

Neurophysiological and computational principles of cortical rhythms in cognition

Synchronous rhythms represent a core mechanism for sculpting temporal coordination of neural activity in the brain-wide network. This review focuses on oscillations in the cerebral cortex that occur during cognition, in alert behaving conditions. Over the last two decades, experimental and modeling work has made great strides in elucidating the detailed cellular and circuit basis of these rhythms, particularly gamma and theta rhythms. The underlying physiological mechanisms are diverse (ranging from resonance and pacemaker properties of single cells to multiple scenarios for population synchronization and wave propagation), but also exhibit unifying principles. A major conceptual advance was the realization that synaptic inhibition plays a fundamental role in rhythmogenesis, either in an interneuronal network or in a reciprocal excitatory-inhibitory loop. Computational functions of synchronous oscillations in cognition are still a matter of debate among systems neuroscientists, in part because the notion of regular oscillation seems to contradict the common observation that spiking discharges of individual neurons in the cortex are highly stochastic and far from being clocklike. However, recent findings have led to a framework that goes beyond the conventional theory of coupled oscillators and reconciles the apparent dichotomy between irregular single neuron activity and field potential oscillations. From this perspective, a plethora of studies will be reviewed on the involvement of long-distance neuronal coherence in cognitive functions such as multisensory integration, working memory, and selective attention. Finally, implications of abnormal neural synchronization are discussed as they relate to mental disorders like schizophrenia and autism.

Effects of urethane anaesthesia on sensory processing in the rat barrel cortex revealed by combined optical imaging and electrophysiology

The spatiotemporal dynamics of neuronal assemblies evoked by sensory stimuli have not yet been fully characterised, especially the extent to which they are modulated by prevailing brain states. In order to examine this issue, we induced different levels of anaesthesia, distinguished by specific electroencephalographic indices, and compared somatosensory-evoked potentials (SEPs) with voltage-sensitive dye imaging (VSDI) responses in the rat barrel cortex evoked by whisker deflection. At deeper levels of anaesthesia, all responses were reduced in amplitude but, surprisingly, only VSDI responses exhibited prolonged activation resulting in a delayed return to baseline. Further analysis of the optical signal demonstrated that the reduction in response amplitude was constant across the area of activation, resulting in a global down-scaling of the population response. The manner in which the optical signal relates to the various neuronal generators that produce the SEP signal is also discussed. These data provide information regarding the impact of anaesthetic agents on the brain, and show the value of combining spatial analyses from neuroimaging approaches with more traditional electrophysiological techniques.

Neuronal avalanches in spontaneous activity in vivo

Many complex systems give rise to events that are clustered in space and time, thereby establishing a correlation structure that is governed by power law statistics. In the cortex, such clusters of activity, called "neuronal avalanches," were recently found in local field potentials (LFPs) of spontaneous activity in acute cortex slices, slice cultures, the developing cortex of the anesthetized rat, and premotor and motor cortex of awake monkeys. At present, it is unclear whether neuronal avalanches also exist in the spontaneous LFPs and spike activity in vivo in sensory areas of the mature brain. To address this question, we recorded spontaneous LFPs and extracellular spiking activity with multiple 4 × 4 microelectrode arrays (Michigan Probes) in area 17 of adult cats under anesthesia. A cluster of events was defined as a consecutive sequence of time bins Δt (1-32 ms), each containing at least one LFP event or spike anywhere on the array. LFP cluster sizes consistently distributed according to a power law with a slope largely above -1.5. In two thirds of the corresponding experiments, spike clusters also displayed a power law that displayed a slightly steeper slope of -1.8 and was destroyed by subsampling operations. The power law in spike clusters was accompanied with stronger temporal correlations between spiking activities of neurons that spanned longer time periods compared with spike clusters lacking power law statistics. The results suggest that spontaneous activity of the visual cortex under anesthesia has the properties of neuronal avalanches.

Connecting mean field models of neural activity to EEG and fMRI data

Progress in functional neuroimaging of the brain increasingly relies on the integration of data from complementary imaging modalities in order to improve spatiotemporal resolution and interpretability. However, the usefulness of merely statistical combinations is limited, since neural signal sources differ between modalities and are related non-trivially. We demonstrate here that a mean field model of brain activity can simultaneously predict EEG and fMRI BOLD with proper signal generation and expression. Simulations are shown using a realistic head model based on structural MRI, which includes both dense short-range background connectivity and long-range specific connectivity between brain regions. The distribution of modeled neural masses is comparable to the spatial resolution of fMRI BOLD, and the temporal resolution of the modeled dynamics, importantly including activity conduction, matches the fastest known EEG phenomena. The creation of a cortical mean field model with anatomically sound geometry, extensive connectivity, and proper signal expression is an important first step towards the model-based integration of multimodal neuroimages.

Statistically optimal perception and learning: from behavior to neural representations

Human perception has recently been characterized as statistical inference based on noisy and ambiguous sensory inputs. Moreover, suitable neural representations of uncertainty have been identified that could underlie such probabilistic computations. In this review, we argue that learning an internal model of the sensory environment is another key aspect of the same statistical inference procedure and thus perception and learning need to be treated jointly. We review evidence for statistically optimal learning in humans and animals, and re-evaluate possible neural representations of uncertainty based on their potential to support statistically optimal learning. We propose that spontaneous activity can have a functional role in such representations leading to a new, sampling-based, framework of how the cortex represents information and uncertainty.

Large-scale neural dynamics: simple and complex

We review the use of neural field models for modelling the brain at the large scales necessary for interpreting EEG, fMRI, MEG and optical imaging data. Albeit a framework that is limited to coarse-grained or mean-field activity, neural field models provide a framework for unifying data from different imaging modalities. Starting with a description of neural mass models, we build to spatially extend cortical models of layered two-dimensional sheets with long range axonal connections mediating synaptic interactions. Reformulations of the fundamental non-local mathematical model in terms of more familiar local differential (brain wave) equations are described. Techniques for the analysis of such models, including how to determine the onset of spatio-temporal pattern forming instabilities, are reviewed. Extensions of the basic formalism to treat refractoriness, adaptive feedback and inhomogeneous connectivity are described along with open challenges for the development of multi-scale models that can integrate macroscopic models at large spatial scales with models at the microscopic scale.

Coherence potentials: loss-less, all-or-none network events in the cortex

Transient associations among neurons are thought to underlie memory and behavior. However, little is known about how such associations occur or how they can be identified. Here we recorded ongoing local field potential (LFP) activity at multiple sites within the cortex of awake monkeys and organotypic cultures of cortex. We show that when the composite activity of a local neuronal group exceeds a threshold, its activity pattern, as reflected in the LFP, occurs without distortion at other cortex sites via fast synaptic transmission. These large-amplitude LFPs, which we call coherence potentials, extend up to hundreds of milliseconds and mark periods of loss-less spread of temporal and amplitude information much like action potentials at the single-cell level. However, coherence potentials have an additional degree of freedom in the diversity of their waveforms, which provides a high-dimensional parameter for encoding information and allows identification of particular associations. Such nonlinear behavior is analogous to the spread of ideas and behaviors in social networks.

Functional interactions within the parahippocampal region revealed by voltage-sensitive dye imaging in the isolated guinea pig brain

The massive transfer of information from the neocortex to the entorhinal cortex (and vice versa) is hindered by a powerful inhibitory control generated in the perirhinal cortex. In vivo and in vitro experiments performed in rodents and cats support this conclusion, further extended in the present study to the analysis of the interaction between the entorhinal cortex and other parahippocampal areas, such as the postrhinal and the retrosplenial cortices. The experiments were performed in the in vitro isolated guinea pig brain by a combined approach based on electrophysiological recordings and fast imaging of optical signals generated by voltage-sensitive dyes applied to the entire brain by arterial perfusion. Local stimuli delivered in different portions of the perirhinal, postrhinal, and retrosplenial cortex evoked local responses that did not propagate to the entorhinal cortex. Neither high- and low-frequency-patterned stimulation nor paired associative stimuli facilitated the propagation of activity to the entorhinal region. Similar stimulations performed during cholinergic neuromodulation with carbachol were also ineffective in overcoming the inhibitory network that controls propagation to the entorhinal cortex. The pharmacological inactivation of GABAergic transmission by local application of bicuculline (1 mM) in area 36 of the perirhinal cortex facilitated the longitudinal (rostrocaudal) propagation of activity into the perirhinal/postrhinal cortices but did not cause propagation into the entorhinal cortex. Bicuculline injection in both area 35 and medial entorhinal cortex released the inhibitory control and allowed the propagation of the neural activity to the entorhinal cortex. These results demonstrate that, as for the perirhinal-entorhinal reciprocal interactions, also the connections between the postrhinal/retrosplenial cortices and the entorhinal region are subject to a powerful inhibitory control.

Voltage-sensitive-dye imaging of microstimulation-evoked neural activity through intracortical horizontal and callosal connections in cat visual cortex

Recently, intrinsic signal optical imaging has been widely used as a routine procedure for visualizing cortical functional maps. We do not, however, have a well-established imaging method for visualizing cortical functional connectivity indicating spatio-temporal patterns of activity propagation in the cerebral cortex. In the present study, we developed a novel experimental setup for investigating the propagation of neural activities combining the intracortical microstimulation (ICMS) technique with voltage sensitive dye (VSD) imaging, and demonstrated the feasibility of this setup applying to the measurement of time-dependent intra- and inter-hemispheric spread of ICMS-evoked excitation in the cat visual cortices, areas 17 and 18. A microelectrode array for the ICMS was inserted with a specially designed easy-to-detach electrode holder around the 17/18 transition zones (TZs), where the left and right hemispheres were interconnected via the corpus callosum. The microelectrode array was stably anchored in agarose without any holder, which enabled us to visualize evoked activities even in the vicinity of penetration sites as well as in a wide recording region that covered a part of both hemispheres. The VSD imaging could successfully visualize ICMS-evoked excitation and subsequent propagation in the visual cortices contralateral as well as ipsilateral to the ICMS. Using the orientation maps as positional references, we showed that the activity propagation patterns were consistent with previously reported anatomical patterns of intracortical and interhemispheric connections. This finding indicates that our experimental system can serve for the investigation of cortical functional connectivity.