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

Dynamics of neural fields with exponential temporal kernel

We consider the standard neural field equation with an exponential temporal kernel. We analyze the time-independent (static) and time-dependent (dynamic) bifurcations of the equilibrium solution and the emerging spatiotemporal wave patterns. We show that an exponential temporal kernel does not allow static bifurcations such as saddle-node, pitchfork, and in particular, static Turing bifurcations. However, the exponential temporal kernel possesses the important property that it takes into account the finite memory of past activities of neurons, which Green's function does not. Through a dynamic bifurcation analysis, we give explicit bifurcation conditions. Hopf bifurcations lead to temporally non-constant, but spatially constant solutions, but Turing-Hopf bifurcations generate spatially and temporally non-constant solutions, in particular, traveling waves. Bifurcation parameters are the coefficient of the exponential temporal kernel, the transmission speed of neural signals, the time delay rate of synapses, and the ratio of excitatory to inhibitory synaptic weights.

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.

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.

Phase-encoded fMRI tracks down brainstorms of natural language processing with subsecond precision

Natural language processing unfolds information overtime as spatially separated, multimodal, and interconnected neural processes. Existing noninvasive subtraction-based neuroimaging techniques cannot simultaneously achieve the spatial and temporal resolutions required to visualize ongoing information flows across the whole brain. Here we have developed rapid phase-encoded designs to fully exploit the temporal information latent in functional magnetic resonance imaging data, as well as overcoming scanner noise and head-motion challenges during overt language tasks. We captured real-time information flows as coherent hemodynamic waves traveling over the cortical surface during listening, reading aloud, reciting, and oral cross-language interpreting tasks. We were able to observe the timing, location, direction, and surge of traveling waves in all language tasks, which were visualized as "brainstorms" on brain "weather" maps. The paths of hemodynamic traveling waves provide direct evidence for dual-stream models of the visual and auditory systems as well as logistics models for crossmodal and cross-language processing. Specifically, we have tracked down the step-by-step processing of written or spoken sentences first being received and processed by the visual or auditory streams, carried across language and domain-general cognitive regions, and finally delivered as overt speeches monitored through the auditory cortex, which gives a complete picture of information flows across the brain during natural language functioning. PRACTITIONER POINTS: Phase-encoded fMRI enables simultaneous imaging of high spatial and temporal resolution, capturing continuous spatiotemporal dynamics of the entire brain during real-time overt natural language tasks. Spatiotemporal traveling wave patterns provide direct evidence for constructing comprehensive and explicit models of human information processing. This study unlocks the potential of applying rapid phase-encoded fMRI to indirectly track the underlying neural information flows of sequential sensory, motor, and high-order cognitive processes.

A modular and adaptable analysis pipeline to compare slow cerebral rhythms across heterogeneous datasets

Neuroscience is moving toward a more integrative discipline where understanding brain function requires consolidating the accumulated evidence seen across experiments, species, and measurement techniques. A remaining challenge on that path is integrating such heterogeneous data into analysis workflows such that consistent and comparable conclusions can be distilled as an experimental basis for models and theories. Here, we propose a solution in the context of slow-wave activity (<1 Hz), which occurs during unconscious brain states like sleep and general anesthesia and is observed across diverse experimental approaches. We address the issue of integrating and comparing heterogeneous data by conceptualizing a general pipeline design that is adaptable to a variety of inputs and applications. Furthermore, we present the Collaborative Brain Wave Analysis Pipeline (Cobrawap) as a concrete, reusable software implementation to perform broad, detailed, and rigorous comparisons of slow-wave characteristics across multiple, openly available electrocorticography (ECoG) and calcium imaging datasets.

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.

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.

Phase-encoded fMRI tracks down brainstorms of natural language processing with sub-second precision

The human language system interacts with cognitive and sensorimotor regions during natural language processing. However, where, when, and how these processes occur remain unclear. Existing noninvasive subtraction-based neuroimaging techniques cannot simultaneously achieve the spatial and temporal resolutions required to visualize ongoing information flows across the whole brain. Here we have developed phase-encoded designs to fully exploit the temporal information latent in functional magnetic resonance imaging (fMRI) data, as well as overcoming scanner noise and head-motion challenges during overt language tasks. We captured neural information flows as coherent waves traveling over the cortical surface during listening, reciting, and oral cross-language interpreting. The timing, location, direction, and surge of traveling waves, visualized as 'brainstorms' on brain 'weather' maps, reveal the functional and effective connectivity of the brain in action. These maps uncover the functional neuroanatomy of language perception and production and motivate the construction of finer-grained models of human information processing.

Computational models for state-dependent traveling waves in hippocampal formation

Hippocampal theta (4-10 Hz) oscillations have been identified as traveling waves in both rodents and humans. In freely foraging rodents, the theta traveling wave is a planar wave propagating from the dorsal to ventral hippocampus along the septotemporal axis. Motivated from experimental findings, we develop a spiking neural network of excitatory and inhibitory neurons to generate state-dependent hippocampal traveling waves to improve current mechanistic understanding of propagating waves. Model simulations demonstrate the necessary conditions for generating wave propagation and characterize the traveling wave properties with respect to model parameters, running speed and brain state of the animal. Networks with long-range inhibitory connections are more suitable than networks with long-range excitatory connections. We further generalize the spiking neural network to model traveling waves in the medial entorhinal cortex (MEC) and predict that traveling theta waves in the hippocampus and entorhinal cortex are in sink.

Development of top-down cortical propagations in youth

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

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.

Complexity of cortical wave patterns of the wake mouse cortex

Rich spatiotemporal dynamics of cortical activity, including complex and diverse wave patterns, have been identified during unconscious and conscious brain states. Yet, how these activity patterns emerge across different levels of wakefulness remain unclear. Here we study the evolution of wave patterns utilizing data from high spatiotemporal resolution optical voltage imaging of mice transitioning from barbiturate-induced anesthesia to wakefulness (N = 5) and awake mice (N = 4). We find that, as the brain transitions into wakefulness, there is a reduction in hemisphere-scale voltage waves, and an increase in local wave events and complexity. A neural mass model recapitulates the essential cellular-level features and shows how the dynamical competition between global and local spatiotemporal patterns and long-range connections can explain the experimental observations. These mechanisms possibly endow the awake cortex with enhanced integrative processing capabilities.

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.

Topological Maps and Brain Computations From Low to High

We first briefly summarize data from microelectrode studies on visual maps in non-human primates and other mammals, and characterize differences among the features of the approximately topological maps in the three main sensory modalities. We then explore the almost 50% of human neocortex that contains straightforward topological visual, auditory, and somatomotor maps by presenting a new parcellation as well as a movie atlas of cortical area maps on the FreeSurfer average surface, fsaverage. Third, we review data on moveable map phenomena as well as a recent study showing that cortical activity during sensorimotor actions may involve spatially locally coherent traveling wave and bump activity. Finally, by analogy with remapping phenomena and sensorimotor activity, we speculate briefly on the testable possibility that coherent localized spatial activity patterns might be able to ‘escape’ from topologically mapped cortex during ‘serial assembly of content’ operations such as scene and language comprehension, to form composite ‘molecular’ patterns that can move across some cortical areas and possibly return to topologically mapped cortex to generate motor output there.

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.

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.

Propagating wave activity in a tangential cortical slice

Propagating neural waves in the cerebral cortex influence the integration of incoming sensory information with ongoing cortical activity. However, the neural circuit elements that support these cortical waves remain to be fully defined. Here, a novel tangential slice preparation was developed that exhibited propagating wave activity across the dorsal cortical sheet, as assessed using autofluorescence imaging following focal electrical stimulation. Analysis of functional connectivity in the slice preparation with laser-scanning photostimulation via glutamate uncaging revealed a lack of short-latency, presumed monosynaptic, long-range connections (>300 μm) in the slice preparation. These results establish a novel slice preparation for assessing cortical dynamics and support the proposition that interactions among local cortical elements are sufficient to enable widespread propagating wave activity.

Optical Analysis of Acute Changes after Peripheral Nerve Injury in Spatio-Temporal Pattern of Neural Response to Forelimb Stimulation in Rat Somatosensory Cortex

Peripheral nerve injury induces functional reorganization of the central nervous system. The mechanisms underlying this reorganization have been widely studied. Our previous study involving multiple-site optical recording reported that a neural excitatory wave induced by somatic stimulation begins in a small area and propagates in the cortex. In the present study, to examine the possible role of this propagation wave in cortical reorganization, we analyzed the early changes in the spatio-temporal pattern of the sensory-evoked wave immediately, and 30 min, after nerve injury. The response to hypothenar stimulation, innervated by the ulnar nerve and adjoining the median nerve area, persisted after injury to either the ulnar or median nerve. Initially, we assessed changes in the response pattern at the focus. The latency increased after ulnar nerve injury, whereas no change was observed after median nerve injury. Similarly, no change was noted in the duration of the response signal with either nerve injury. Second, changes in the propagation wave pattern were analyzed. Ulnar nerve injury decreased the propagation velocity in the medial direction but the median nerve injury induced no changes. These results indicated that the propagation wave pattern is readily altered, even immediately after nerve injury, and suggest that this immediate change in the spatio-temporal pattern is one of the factors contributing to the cortical reorganization.

Effect of temperature fluctuation on the localized pattern of action potential in cardiac tissue

Based on the improved FitzHugh-Nagumo myocardial model driven by a constant external current, the effect of temperature fluctuation in a network of electrically coupled myocardial cells are investigated through analytical and numerical computations. Through the technique of multiple scale expansion, we successfully reduced the complex nonlinear system of equations to a more tractable and solvable nonlinear amplitude equation on which the analysis of linear stability is performed. Interestingly from this analysis, a plot of critical amplitude of action potential versus wave number revealed the growth rate of modulational instability (MI) is an increasing function of the thermoelectric couplings; [Formula: see text] and [Formula: see text], under fixed conditions of nonlinear electrical couplings. In order to verify our analytical predictions through the study the long-time evolution of the modulated cardiac impulses, numerical computation is finally carried out. Numerical experiment revealed the existence of localized coherent structures with some recognized features of synchronization. Through the mechanism of MI, changes in thermoelectrical couplings promote wave localization and mode transition in electrical activities in the cell lattice. Results could provide new insights in understanding the underlying mechanism of the manifestation of sudden heart disorder subjected to heavily temperature fluctuation.

Direction-selective motion discrimination by traveling waves in visual cortex

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

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

A New Unifying Account of the Roles of Neuronal Entrainment

Rhythms are a fundamental and defining feature of neuronal activity in animals including humans. This rhythmic brain activity interacts in complex ways with rhythms in the internal and external environment through the phenomenon of 'neuronal entrainment', which is attracting increasing attention due to its suggested role in a multitude of sensory and cognitive processes. Some senses, such as touch and vision, sample the environment rhythmically, while others, like audition, are faced with mostly rhythmic inputs. Entrainment couples rhythmic brain activity to external and internal rhythmic events, serving fine-grained routing and modulation of external and internal signals across multiple spatial and temporal hierarchies. This interaction between a brain and its environment can be experimentally investigated and even modified by rhythmic sensory stimuli or invasive and non-invasive neuromodulation techniques. We provide a comprehensive overview of the topic and propose a theoretical framework of how neuronal entrainment dynamically structures information from incoming neuronal, bodily and environmental sources. We discuss the different types of neuronal entrainment, the conceptual advances in the field, and converging evidence for general principles.

Social cognition in context: A naturalistic imaging approach

Social processing occurs within dynamic, complex, and multimodal contexts, but the study of social cognition typically involves static, artificial stimuli. Naturalistic approaches (e.g., movie viewing) can recapture the richness and complexity of real-world interactions. Novel analytic approaches allow for the investigation of functional brain organization in response to contextually embedded and extended events with a complex temporal structure during movie viewing or narrative processing. In addition to these within-brain measures, movies afford between-brain analyses such as inter-subject correlation, which allows for identification of stimulus-specific brain response through the correlation of brain activity between participants' brains. Research using these approaches offers both practical and theoretical advantages in understanding how we navigate our social world. Practically, movies are engaging stimuli that allow for more rapid presentation of multiple event types and improve compliance even in very young populations. Theoretically, studies have validated the use of these measures by demonstrating functional selectivity to contextually embedded stimuli. Naturalistic approaches also allow for novel insights. For example, regions associated with social cognition have longer temporal receptive windows, making them well suited to social-cognitive processes that require integration of information over longer timescales. Furthermore, the similarity in the temporal and spatial brain response between individuals during naturalistic viewing is related to age, predictive of friendships, and reduced in autism spectrum disorder. These findings offer first glimpses into the power of using these naturalistic, dynamic approaches to understand how we perceive, reason about, and interact with others.

Nonlinear analysis of periodic waves in a neural field model

Various types of brain activity, including motor, visual, and language, are accompanied by the propagation of periodic waves of electric potential in the cortex, possibly providing the synchronization of the epicenters involved in these activities. One example is cortical electrical activity propagating during sleep and described as traveling waves [Massimini et al., J. Neurosci. 24, 6862-6870 (2004)]. These waves modulate cortical excitability as they progress. Clinically related examples include cortical spreading depression in which a wave of depolarization propagates not only in migraine but also in stroke, hemorrhage, or traumatic brain injury [Whalen et al., Sci. Rep. 8, 1-9 (2018)]. Here, we consider the possible role of epicenters and explore a neural field model with two nonlinear integrodifferential equations for the distributions of activating and inhibiting signals. It is studied with symmetric connectivity functions characterizing signal exchange between two populations of neurons, excitatory and inhibitory. Bifurcation analysis is used to investigate the emergence of periodic traveling waves and of standing oscillations from the stationary, spatially homogeneous solutions, and the stability of these solutions. Both types of solutions can be started by local oscillations indicating a possible role of epicenters in the initiation of wave propagation.

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.

Cortical stimulation in aphasia following ischemic stroke: toward model-guided electrical neuromodulation

The aim of this paper is to integrate different bodies of research including brain traveling waves, brain neuromodulation, neural field modeling and post-stroke language disorders in order to explore the opportunity of implementing model-guided, cortical neuromodulation for the treatment of post-stroke aphasia. Worldwide according to WHO, strokes are the second leading cause of death and the third leading cause of disability. In ischemic stroke, there is not enough blood supply to provide enough oxygen and nutrients to parts of the brain, while in hemorrhagic stroke, there is bleeding within the enclosed cranial cavity. The present paper focuses on ischemic stroke. We first review accumulating observations of traveling waves occurring spontaneously or triggered by external stimuli in healthy subjects as well as in patients with brain disorders. We examine the putative functions of these waves and focus on post-stroke aphasia observed when brain language networks become fragmented and/or partly silent, thus perturbing the progression of traveling waves across perilesional areas. Secondly, we focus on a simplified model based on the current literature in the field and describe cortical traveling wave dynamics and their modulation. This model uses a biophysically realistic integro-differential equation describing spatially distributed and synaptically coupled neural networks producing traveling wave solutions. The model is used to calculate wave parameters (speed, amplitude and/or frequency) and to guide the reconstruction of the perturbed wave. A stimulation term is included in the model to restore wave propagation to a reasonably good level. Thirdly, we examine various issues related to the implementation model-guided neuromodulation in the treatment of post-stroke aphasia given that closed-loop invasive brain stimulation studies have recently produced encouraging results. Finally, we suggest that modulating traveling waves by acting selectively and dynamically across space and time to facilitate wave propagation is a promising therapeutic strategy especially at a time when a new generation of closed-loop cortical stimulation systems is about to arrive on the market.

Stress impacts sensory variability through cortical sensory activity motifs

Medically unexplained symptoms in depression are common. These individual-specific complaints are often considered an 'idiom of distress', yet animal studies suggest that cortical sensory representations are flexible and influenced by spontaneous cortical activity. We hypothesized that stress would reveal activity dynamics in somatosensory cortex resulting in greater sensory-evoked response variability. Using millisecond resolution in vivo voltage sensitive dye (VSD) imaging in mouse neocortex, we characterized spontaneous regional depolarizations within limb and barrel regions of somatosensory cortex, or spontaneous sensory motifs, and their influence on sensory variability. Stress revealed an idiosyncratic increase in spontaneous sensory motifs that is normalized by selective serotonin reuptake inhibitor treatment. Spontaneous motif frequency is associated with increased variability in sensory-evoked responses, and we optogenetically demonstrate that regional depolarization in somatosensory cortex increases sensory-evoked variability for seconds. This reveals a putative circuit level target for changes in sensory processing and for unexplained physical complaints in stress-related psychopathology.

Emergence of spatially periodic diffusive waves in small-world neuronal networks

It has been observed in experiment that the anatomical structure of neuronal networks in the brain possesses the feature of small-world networks. Yet how the small-world structure affects network dynamics remains to be fully clarified. Here we study the dynamics of a class of small-world networks consisting of pulse-coupled integrate-and-fire (I&F) neurons. Under stochastic Poisson drive, we find that the activity of the entire network resembles diffusive waves. To understand its underlying mechanism, we analyze the simplified regular-lattice network consisting of firing-rate-based neurons as an approximation to the original I&F small-world network. We demonstrate both analytically and numerically that, with strongly coupled connections, in the absence of noise, the activity of the firing-rate-based regular-lattice network spatially forms a static grating pattern that corresponds to the spatial distribution of the firing rate observed in the I&F small-world neuronal network. We further show that the spatial grating pattern with different phases comprise the continuous attractor of both the I&F small-world and firing-rate-based regular-lattice network dynamics. In the presence of input noise, the activity of both networks is perturbed along the continuous attractor, which gives rise to the diffusive waves. Our numerical simulations and theoretical analysis may potentially provide insights into the understanding of the generation of wave patterns observed in cortical networks.

Next-generation neural mass and field modeling

The Wilson-Cowan population model of neural activity has greatly influenced our understanding of the mechanisms for the generation of brain rhythms and the emergence of structured brain activity. As well as the many insights that have been obtained from its mathematical analysis, it is now widely used in the computational neuroscience community for building large-scale in silico brain networks that can incorporate the increasing amount of knowledge from the Human Connectome Project. Here, we consider a neural population model in the spirit of that originally developed by Wilson and Cowan, albeit with the added advantage that it can account for the phenomena of event-related synchronization and desynchronization. This derived mean-field model provides a dynamic description for the evolution of synchrony, as measured by the Kuramoto order parameter, in a large population of quadratic integrate-and-fire model neurons. As in the original Wilson-Cowan framework, the population firing rate is at the heart of our new model; however, in a significant departure from the sigmoidal firing rate function approach, the population firing rate is now obtained as a real-valued function of the complex-valued population synchrony measure. To highlight the usefulness of this next-generation Wilson-Cowan style model, we deploy it in a number of neurobiological contexts, providing understanding of the changes in power spectra observed in electro- and magnetoencephalography neuroimaging studies of motor cortex during movement, insights into patterns of functional connectivity observed during rest and their disruption by transcranial magnetic stimulation, and to describe wave propagation across cortex.

Peripheral Nerve Ligation Elicits Widespread Alterations in Cortical Sensory Evoked and Spontaneous Activity

Peripheral neuropathies result in adaptation in primary sensory and other regions of cortex, and provide a framework for understanding the localized and widespread adaptations that arise from altered sensation. Mesoscale cortical imaging achieves high temporal resolution of activity using optical sensors of neuronal activity to simultaneously image across a wide expanse of cortex and capture this adaptation using sensory-evoked and spontaneous cortical activity. Saphenous nerve ligation in mouse is an animal model of peripheral neuropathy that produces hyperalgesia circumscribed to the hindlimb. We performed saphenous nerve ligation or sham, followed by mesoscale cortical imaging using voltage sensitive dye (VSD) after ten days. We utilized subcutaneous electrical stimulation at multiple stimulus intensities to characterize sensory responses after ligation or sham, and acquired spontaneous activity to characterize functional connectivity and large scale cortical network reorganization. Relative to sham animals, the primary sensory-evoked response to hindlimb stimulation in ligated animals was unaffected in magnitude at all stimulus intensities. However, we observed a diminished propagating wave of cortical activity at lower stimulus intensities in ligated animals after hindlimb, but not forelimb, sensory stimulation. We simultaneously observed a widespread decrease in cortical functional connectivity, where midline association regions appeared most affected. These results are consistent with localized and broad alterations in intracortical connections in response to a peripheral insult, with implications for novel circuit level understanding and intervention for peripheral neuropathies and other conditions affecting sensation.

Phasic alerting effects on visual processing speed are associated with intrinsic functional connectivity in the cingulo-opercular network

Phasic alertness refers to short-lived increases in the brain's "state of readiness", and thus to optimized performance following warning cues. Parametric modelling of whole report task performance based on the computational theory of visual attention (TVA) has demonstrated that visual processing speed is increased in such cue compared to no-cue conditions. Furthermore, with respect to the underlying neural mechanisms, individual visual processing speed has been related to intrinsic functional connectivity (iFC) within the cingulo-opercular network, suggesting that this network's iFC is relevant for the tonic maintenance of an appropriate readiness or alertness state. In the present study, we asked whether iFC in the cingulo-opercular network is also related to the individual ability to actively profit from warning cues, i.e. to the degree of phasic alerting. We obtained resting-state functional magnetic resonance imaging (rs-fMRI) data from 32 healthy young participants and combined an independent component analysis of rs-fMRI time courses and dual regression approach to determine iFC in the cingulo-opercular network. In a separate behavioural testing session, we parametrically assessed the effects of auditory phasic alerting cues on visual processing speed in a TVA-based whole report paradigm. A voxel-wise multiple regression revealed that higher individual phasic alerting effects on visual processing speed were significantly associated with lower iFC in the cingulo-opercular network, with a peak in the left superior orbital gyrus. As phasic alertness was neither related to iFC in other attention-relevant, auditory, or visual networks nor associated with any inter-network connectivity pattern, the results suggest that the individual profit in visual processing speed gained from phasic alerting is primarily associated with iFC in the cingulo-opercular network.

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.

Dynamical patterns underlying response properties of cortical circuits

Recent experimental studies show cortical circuit responses to external stimuli display varied dynamical properties. These include stimulus strength-dependent population response patterns, a shift from synchronous to asynchronous states and a decline in neural variability. To elucidate the mechanisms underlying these response properties and explore how they are mechanistically related, we develop a neural circuit model that incorporates two essential features widely observed in the cerebral cortex. The first feature is a balance between excitatory and inhibitory inputs to individual neurons; the second feature is distance-dependent connectivity. We show that applying a weak external stimulus to the model evokes a wave pattern propagating along lateral connections, but a strong external stimulus triggers a localized pattern; these stimulus strength-dependent population response patterns are quantitatively comparable with those measured in experimental studies. We identify network mechanisms underlying this population response, and demonstrate that the dynamics of population-level response patterns can explain a range of prominent features in neural responses, including changes to the dynamics of neurons' membrane potentials and synaptic inputs that characterize the shift of cortical states, and the stimulus-evoked decline in neuron response variability. Our study provides a unified population activity pattern-based view of diverse cortical response properties, thus shedding new insights into cortical processing.

Electric field dynamics in the brain during multi-electrode transcranial electric stimulation

Neural oscillations play a crucial role in communication between remote brain areas. Transcranial electric stimulation with alternating currents (TACS) can manipulate these brain oscillations in a non-invasive manner. Recently, TACS using multiple electrodes with phase shifted stimulation currents were developed to alter long-range connectivity. Typically, an increase in coordination between two areas is assumed when they experience an in-phase stimulation and a disorganization through an anti-phase stimulation. However, the underlying biophysics of multi-electrode TACS has not been studied in detail. Here, we leverage direct invasive recordings from two non-human primates during multi-electrode TACS to characterize electric field magnitude and phase as a function of the phase of stimulation currents. Further, we report a novel "traveling wave" stimulation where the location of the electric field maximum changes over the stimulation cycle. Our results provide a mechanistic understanding of the biophysics of multi-electrode TACS and enable future developments of novel stimulation protocols.

Analysis of Propagation of Slow Rhythmic Activity Induced in Ex Vivo Rat Brain Slices

Slow wave oscillation is a synchronous oscillatory mechanism that is a characteristic wave type of the cerebral cortex during physiological deep sleep or anesthesia. It may play an important role in cortical analysis of sensory input. Our goal was (1) to develop optimal conditions for the induction of this slow rhythmic activity in adult rat cortical slices, (2) to identify connections through which the activity propagates between coupled cortical regions, and (3) to study the pattern of horizontal and vertical flow of activity developed spontaneously in cortical slices. Experiments were performed on intact or differently incised rat cortical slices. According to our results, spontaneous cortical activity develops reliably in slightly modified artificial cerebrospinal fluid, first in the entorhinal cortical region of horizontally cut slices and then it spreads directly to the perirhinal (PRh) cortex. The activity readily generated in layer 2/3 of the entorhinal cortex then quickly spreads vertically to upper layer 2-3 in the same area and to the neighboring regions, that is, to the PRh cortex. Synchronization of activity in neighboring cortical areas occurs through both callosal connections and layer 2-3 intrinsic network, which are important in the propagation of spontaneous, inherent cortical slow wave activity.

Metastable brain waves

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

Unraveling the spatiotemporal brain dynamics during a simulated reach-to-eat task

The reach-to-eat task involves a sequence of action components including looking, reaching, grasping, and feeding. While cortical representations of individual action components have been mapped in human functional magnetic resonance imaging (fMRI) studies, little is known about the continuous spatiotemporal dynamics among these representations during the reach-to-eat task. In a periodic event-related fMRI experiment, subjects were scanned while they reached toward a food image, grasped the virtual food, and brought it to their mouth within each 16-s cycle. Fourier-based analysis of fMRI time series revealed periodic signals and noise distributed across the brain. Independent component analysis was used to remove periodic or aperiodic motion artifacts. Time-frequency analysis was used to analyze the temporal characteristics of periodic signals in each voxel. Circular statistics was then used to estimate mean phase angles of periodic signals and select voxels based on the distribution of phase angles. By sorting mean phase angles across regions, we were able to show the real-time spatiotemporal brain dynamics as continuous traveling waves over the cortical surface. The activation sequence consisted of approximately the following stages: (1) stimulus related activations in occipital and temporal cortices; (2) movement planning related activations in dorsal premotor and superior parietal cortices; (3) reaching related activations in primary sensorimotor cortex and supplementary motor area; (4) grasping related activations in postcentral gyrus and sulcus; (5) feeding related activations in orofacial areas. These results suggest that phase-encoded design and analysis can be used to unravel sequential activations among brain regions during a simulated reach-to-eat task.

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.

High-Density Porous Graphene Arrays Enable Detection and Analysis of Propagating Cortical Waves and Spirals

Cortical propagating waves have recently attracted significant attention by the neuroscience community. These travelling waves have been suggested to coordinate different brain areas and play roles in assisting neural plasticity and learning. However, it is extremely challenging to record them with very fine spatial scales over large areas to investigate their effect on neural dynamics or network connectivity changes. In this work, we employ high-density porous graphene microelectrode arrays fabricated using laser pyrolysis on flexible substrates to study the functional network connectivity during cortical propagating waves. The low-impedance porous graphene arrays are used to record cortical potentials during theta oscillations and drug-induced seizures in vivo. Spatiotemporal analysis on the neural recordings reveal that theta oscillations and epileptiform activities have distinct characteristics in terms of both synchronization and resulting propagating wave patterns. To investigate the network connectivity during the propagating waves, we perform network analysis. The results show that the propagating waves are consistent with the functional connectivity changes in the neural circuits, suggesting that the underlying network states are reflected by the cortical potential propagation patterns.

Nonlinear reactions of limbic structure electrical activity in response to rhythmical photostimulation in guinea pigs

Photostimulation of the visual analyzer with a periodic signal is widely used in research and clinical practice, as well as in brain-computer interface technologies. In most studies of rhythmic photostimulation in structures of visual system at all its levels, the nonlinear nature of the response reactions is noted. However, the mechanism of formation of the induced electrophysiological reactions remains unclear. In addition, there is no literature data on the nature of response reactions of "non-visual" brain structures. The goal of the present study was to investigate the peculiarities and dynamics of the electrophysiological response of the limbic system to rhythmic photostimulation and analize the dynamics of harmonic components in the response spectra. We investigated the electrical activity of the guinea pig limbic system in response to photostimulation with a 10 Hz sinusoidal signal. Local field potentials were recorded simultaneously from the hippocampus, entorhinal cortex, medial septum and amygdala. Similar to the visual system structures, we have shown that response reactions in the limbic system had a pronounced nonlinear character, consisting in the presence of the stimulation frequency harmonics in the local field potential spectra. The correlation analysis of the dynamics of the harmonics' amplitudes did not reveal reliable relationships between them. The dynamics of the phase difference between the stimulus and individual harmonics varied in time, following different logic. Based on the results of the present work, we propose that the harmonics reveal independent processes having a different functional purpose and the nervous system operates with these harmonics independently.

Infant brain responses to felt and observed touch of hands and feet: an MEG study

There is growing interest concerning the ways in which the human body, both one's own and that of others, is represented in the developing human brain. In two experiments with 7-month-old infants, we employed advances in infant magnetoencephalography (MEG) brain imaging to address novel questions concerning body representations in early development. Experiment 1 evaluated the spatiotemporal organization of infants' brain responses to being touched. A punctate touch to infants' hands and feet produced significant activation in the hand and foot areas of contralateral primary somatosensory cortex as well as in other parietal and frontal areas. Experiment 2 explored infant brain responses to visually perceiving another person's hand or foot being touched. Results showed significant activation in early visual regions and also in regions thought to be involved in multisensory body and self-other processing. Furthermore, observed touch of the hand and foot activated the infant's own primary somatosensory cortex, although less consistently than felt touch. These findings shed light on aspects of early social cognition, including action imitation, which may build, at least in part, on infant neural representations that map equivalences between the bodies of self and other.

Sensory-evoked propagating waves of activity in the primary sensory cortices: poorly understood, yet ubiquitous

Any sensory stimulus evokes a propagating wave of activity in the corresponding sensory cortex that exceeds its topographical boundaries within the primary sensory map. Hama and colleagues (Hama N, Kawai M, Ito S-I, Hirota A. J Neurophysiol 119: 1934–1946, 2018) provided a first study, in the tactile modality, of the interactions between two successively evoked waves. We argue that the difficulty in finding a simple rule to account for all the various observed interactions calls for an effort to clarify the mechanisms and substrates of the propagating waves and their role in sensory processing.

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

BACKGROUND

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

NEW METHOD

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

RESULTS

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

COMPARISON WITH EXISTING METHOD(S)

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

CONCLUSIONS

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

Phase reorganization leads to transient β-LFP spatial wave patterns in motor cortex during steady-state movement preparation

Previous studies on the origin and properties of spatial patterns in motor cortex β-local field potential (β-LFP) oscillations have focused on planar traveling waves. However, it is unclear 1) whether β-LFP waves are limited to plane waves, or even 2) whether they are propagating waves of excito-excitatory activity, i.e., primarily traveling waves in excitable media; they could reflect, instead, reorganization in the relative phases of transient oscillations at different spatial sites. We addressed these two problems in β-LFPs recorded via microelectrode arrays implanted in three adjacent motor cortex areas of nonhuman primates during steady-state movement preparation. Our findings are fourfold: 1) β-LFP wave patterns emerged as transient events, despite stable firing rates of single neurons concurrently recorded during the same periods. 2) β-LFP waves showed a richer variety of spatial dynamics, including rotating and complex waves. 3) β-LFP wave patterns showed no characteristic wavelength, presenting instead a range of scales with global zero-lag phase synchrony as a limiting case, features surprising for purely excito-excitatory waves but consistent with waves in coupled oscillator systems. 4) Furthermore, excito-excitatory traveling waves induced by optogenetic stimulation in motor cortex showed, in contrast, a characteristic wavelength and reduced phase synchrony. Overall, β-LFP wave statistics differed from those of induced traveling waves in excitable media recorded under the same microelectrode array setup. Our findings suggest phase reorganization in neural coupled oscillators contribute significantly to the origin of transient β-LFP spatial dynamics during preparatory steady states and outline important constraints for spatially extended models of β-LFP dynamics in motor cortex. NEW & NOTEWORTHY We show that a rich variety of transient β-local field potential (β-LFP) wave patterns emerge in motor cortex during preparatory steady states, despite stable neuronal firing rates. Furthermore, unlike optogenetically induced traveling waves, β-LFP waves showed no characteristic wavelength, presenting instead a range of scales with global phase synchrony as a limiting case. Overall, our statistical analyses suggest that transient phase reorganization in neural coupled oscillators, beyond purely excito-excitatory traveling waves, contribute significantly to the origin of motor cortex β-LFP wave patterns.

Optical study of interactions among propagation waves of neural excitation in the rat somatosensory cortex evoked by forelimb and hindlimb stimuli

Multisite optical recording has revealed that the neural excitation wave induced by a sensory stimulation begins at a focus and propagates in the cortex. This wave is considered to be important for computation in the sensory cortex, particularly the integration of sensory information; however, the nature of this wave remains largely unknown. In the present study, we examined the interaction between two waves in the rat sensory cortex induced by hindlimb and forelimb stimuli with different interstimulus intervals. We classified the resultant patterns as follows: 1) the collision of two waves, 2) the hindlimb response being evoked while the forelimb-induced wave is passing the hindlimb focus, and 3) the hindlimb response being evoked after the forelimb-induced wave has passed the hindlimb focus. In pattern 1, the two waves fused into a single wave, but the propagation pattern differed from that predicted by the superimposition of two singly induced propagation courses. In pattern 2, the state of the interaction between the two waves varied depending on the phase of optical signals constituting the forelimb-induced wave around the hindlimb focus. Although no hindlimb-induced wave was observed in the rising phase, the propagating velocity of the forelimb-induced wave increased. At the peak, neither the hindlimb-induced response nor a modulatory effect on the forelimb-induced wave was detected. In pattern 3, the hindlimb-induced wave showed a reduced amplitude and spatial extent. These results indicate that the state of the interaction between waves was strongly influenced by the relative timing of sensory inputs.

NEW & NOTEWORTHY Sensory stimulation-induced cortical excitation propagates as a wave and spreads over a wide area of the sensory cortex. To elucidate the characteristics of this relatively unknown phenomenon, we examined the interaction between two individually induced waves in the somatosensory cortex. Either the waves collided or the preceding wave affected the emergence of the following one. Our results indicate that the state of the interaction was strongly influenced by the relative timing of sensory inputs.

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.