Spiral wave dynamics in neocortex

Turbulence control in memristive neural network via adaptive magnetic flux based on DLS-ADMM technique

High-voltage defibrillation for eliminating cardiac spiral waves has significant side effects, necessitating the pursuit of low-energy alternatives for a long time. Adaptive optimization techniques and machine learning methods provide promising solutions for adaptive control of cardiac wave propagation. In this paper, the control of spiral waves and turbulence, as well as 2D and 3D heterogeneity in memristive neural network by using adaptive magnetic flux (AMF) is investigated based on dynamic learning of synchronization - alternating direction method of multipliers (DLS-ADMM). The results show that AMF can achieve global electrical synchronization under multiple complex conditions. There is a trade-off between AMF accuracy and computational speed, lowering the resolution of AMF requires a higher flux of magnetic fields to achieve the network synchronization, resulting in an increase in average Hamiltonian energy, which implies greater energy consumption. The AMF method is more energy efficient than existing DC and AC methods, but it relies on adequate resolution. The ADMM constraints can enhance the synchronization robustness and energy efficiency of DLS techniques, albeit at the cost of increased the computational complexity. The adaptive elimination of spiral waves and turbulence using AMF presented in this paper may provide a novel approach for the low-energy defibrillation studies, and its practical application and performance enhancement deserve further research.

ElectroFluor Voltage-Sensitive Dyes: Comprehensive Analysis of Wavelength-Dependent Sensitivity and Cross-Channel Bleed-Through

New voltage-sensitive ElectroFluor (EF) dyes that emit across the visible and near-infrared spectrum (e.g., 730 nm) were recently developed. We evaluated EF-530, EF-630, and EF-730p-dyes spectrally orthogonal to green fluorescent protein (GFP)-at excitation wavelengths outside the conventional 470 nm range used for GFP-based indicators. Although previously applied in cardiac voltage imaging, their performance in neuronal tissue remains untested. We performed side-by-side comparisons using population voltage imaging in mouse cerebral cortex slices at optimal excitation wavelengths (530, 630, and 730 nm) and assessed cross-channel signal bleed-through across four excitation wavelengths (475, 530, 630, and 730 nm). All dyes produced robust optical signals at their optimal wavelengths, though non-preferred channels exhibited bleed-through with distinct amplitudes, polarities, and photobleaching patterns. These results provide detailed quantifications of EF dye performance for neuronal population imaging.

Effect of concentration gradient on spiral wave dynamics in the Belousov-Zhabotinsky reaction system

The oscillatory Belousov-Zhabotinsky (BZ) reaction is often used for the study of rotating spiral waves that are responsible for life-threatening cardiac arrhythmia. In this work, we explore the influence of a concentration gradient on the dynamics of spiral waves in the BZ-reaction system. Using ion-exchange resin beads, we introduce a gradient of hydrogen ions in a thin layer of BZ gel hosting a spiral wave. By monitoring the drift of the spiral tips from their initial position, we show that a gradient of hydrogen-ions can manoeuvre the position of the spiral. The magnitude of the drift is found to depend on the gradient strength and relative position of the spiral from the resin beads. Our experimental study is supported with numerical simulations carried out on a modified Oregonator model that we have developed from the Field, Körös, Noyes mechanism of the BZ.

Controlling spiral wave dynamics of the BZ system in a modified Oregonator model: From suppression to turbulence

Spirals are a special class of excitable waves that have its significance in the understanding of cardiac arrests and neuronal transduction. In a theoretical model of the chemical Belousov-Zhabotinsky reaction system, we explore the dynamics of the spatiotemporal patterns that emerge out of competing reaction and diffusion phenomena. By modifying the existing mathematical models of the reaction kinetics, we have been able to explore the explicit effect of hydrogen ion concentration in the system, so as to achieve various regimes of wave activity, from stable spirals to oscillation death. In between the two extremes, we show how instability sets in, with anisotropy leading to drifting spirals, core defects resulting in spiral breakup and turbulence, chaotic oscillations, and target patterns, before the system finally reaches a non-oscillating steady state. On varying other stoichiometric parameters, we also illustrate the changes in system dynamics and wave properties.

Transient chaos and periodic structures in a model of neuronal early afterdepolarization

The presence of chaos is ubiquitous in mathematical models of neuroscience. In experimental neural systems, chaos was convincingly demonstrated in membranes, neurons, and small networks. However, its effects on the brain have long been debated. In this work, we use a three-dimensional map-based membrane potential model, the logistic KTz, to study chaos in single and coupled neurons. We first obtain an alternative phase diagram for the model using the interspike interval (ISI), evidencing a region of slow spikes (SS), missing from the original diagram of the KTz model. A large chaotic region is found inside the SS phase. Embedded in chaos are several self-similar periodic structures, such as shrimp-shaped domains and other structures. Sampling the behavior of neurons in this diagram, we detect a novel type of action potential, the neuronal early afterdepolarization (nEAD). EADs are pathological oscillations during the action potential, commonly found in cardiac cells and believed to be chaotic and responsible for generating arrhythmias in the heart. nEAD was found experimentally in neurons in a type of epilepsy. We study two chemically coupled neurons with this behavior. We identify and characterize transient chaos in their interaction. A phase diagram for this system presents a novel type of self-similar periodic structures, where the structures appear "chopped" in pieces.

Stereotyped spatiotemporal dynamics of spontaneous activity in visual cortex prior to eye-opening

Over the course of development, functional sensory representations emerge in the visual cortex. Prior to eye-opening, modular patterns of spontaneous activity form long-range networks that may serve as a precursor for mature network organization. Although the spatial structure of these networks has been well studied, their temporal features, which may contribute to their continued plasticity and development, remain largely uncharacterized. To address this, we imaged hours of spontaneous network activity in the visual cortex of developing ferrets of both sexes utilizing a fast calcium indicator (GCaMP8m) and widefield imaging at high temporal resolution (50Hz), then segmented out spatiotemporal events. The spatial structure of this activity was highly modular, exhibiting spatially segregated active domains consistent with prior work. We found that the vast majority of events showed a clear dynamic component in which modules activated sequentially across the field of view, but only a minority of events were well-fit with a linear traveling wave. We found that spatiotemporal events occur in repeated and stereotyped motifs, reoccurring across hours of imaging. Finally, we found that the most frequently occurring single-frame spatial activity patterns were predictive of future activity patterns over hundreds of milliseconds. Together, our results demonstrate that spontaneous activity in the early developing cortex exhibits a rich spatiotemporal structure, suggesting a potential role in the maturation and refinement of future functional representations.

Brain states as wave-like motifs

There is ample evidence of wave-like activity in the brain at multiple scales and levels. This emerging literature supports the broader adoption of a wave perspective of brain activity. Specifically, a brain state can be described as a set of recurring, sequential patterns of propagating brain activity, namely a wave. We examine a collective body of experimental work investigating wave-like properties. Based on these works, we consider brain states as waves using a scale-agnostic framework across time and space. Emphasis is placed on the sequentiality and periodicity associated with brain activity. We conclude by discussing the implications, prospects, and experimental opportunities of this framework.

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.

Non-Gaussian anomalous diffusion of optical vortices

Anomalous diffusion of different particlelike entities, the deviation from typical Brownian motion, is ubiquitous in complex physical and biological systems. While optical vortices move randomly in evolving speckle fields, optical vortices have only been observed to exhibit pure Brownian motion in random speckle fields. Here we present direct experimental evidence of the anomalous diffusion of optical vortices in temporally varying speckle patterns from multiple-scattering viscoelastic media. Moreover, we observe two characteristic features, i.e., the self-similarity and the antipersistent correlation of the optical vortex motion, indicating that the mechanism of the observed subdiffusion of optical vortices can only be attributed to fractional Brownian motion (FBM). We further demonstrate that the vortex displacements exhibit a non-Gaussian heavy-tailed distribution. Additionally, we modulate the extent of subdiffusion, such as diffusive scaling exponents, and the non-Gaussianity of optical vortices by altering the viscoelasticity of samples. The discovery of the complex FBM but non-Gaussian subdiffusion of optical vortices may not only offer insight into certain fundamental physics, including the anomalous diffusion of vortices in fluids and the decoupling between Brownianity and Gaussianity, but also suggest a strong potential for utilizing optical vortices as tracers in microrheology instead of the introduced exogenous probe particles in particle tracking microrheology.

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.

Functional Dissection of Ipsilateral and Contralateral Neural Activity Propagation Using Voltage-Sensitive Dye Imaging in Mouse Prefrontal Cortex

Prefrontal cortex (PFC) intrahemispheric activity and the interhemispheric connection have a significant impact on neuropsychiatric disorder pathology. This study aimed to generate a functional map of FC intrahemispheric and interhemispheric connections. Functional dissection of mouse PFCs was performed using the voltage-sensitive dye (VSD) imaging method with high speed (1 ms/frame), high resolution (256 × 256 pixels), and a large field of view (∼10 mm). Acute serial 350 μm slices were prepared from the bregma covering the PFC and numbered 1-5 based on their distance from the bregma (i.e., 1.70, 1.34, 0.98, 0.62, and 0.26 mm) with reference to the Mouse Brain Atlas (Paxinos and Franklin, 2008). The neural response to electrical stimulation was measured at nine sites and then averaged, and a functional map of the propagation patterns was created. Intracortical propagation was observed in slices 3-5, encompassing the anterior cingulate cortex (ACC) and corpus callosum (CC). The activity reached area 33 of the ACC. Direct white matter stimulation activated area 33 in both hemispheres. Similar findings were obtained via DiI staining of the CC. Imaging analysis revealed directional biases in neural signals traveling within the ACC, whereby the signal transmission speed and probability varied based on the signal direction. Specifically, the spread of neural signals from cg2 to cg1 was stronger than that from cingulate cortex area 1(cg1) to cingulate cortex area 2(cg2), which has implications for interhemispheric functional connections. These findings highlight the importance of understanding the PFC functional anatomy in evaluating neuromodulators like serotonin and dopamine, as well as other factors related to neuropsychiatric diseases.

Sleep and vigilance states: Embracing spatiotemporal dynamics

The classic view of sleep and vigilance states is a global stationary perspective driven by the interaction between neuromodulators and thalamocortical systems. However, recent data are challenging this view by demonstrating that vigilance states are highly dynamic and regionally complex. Spatially, sleep- and wake-like states often co-occur across distinct brain regions, as in unihemispheric sleep, local sleep in wakefulness, and during development. Temporally, dynamic switching prevails around state transitions, during extended wakefulness, and in fragmented sleep. This knowledge, together with methods monitoring brain activity across multiple regions simultaneously at millisecond resolution with cell-type specificity, is rapidly shifting how we consider vigilance states. A new perspective incorporating multiple spatial and temporal scales may have important implications for considering the governing neuromodulatory mechanisms, the functional roles of vigilance states, and their behavioral manifestations. A modular and dynamic view highlights novel avenues for finer spatiotemporal interventions to improve sleep function.

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

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

Markov modeling of phase singularity interaction effects in human atrial and ventricular fibrillation

Atrial and ventricular fibrillation (AF/VF) are characterized by the repetitive regeneration of topological defects known as phase singularities (PSs). The effect of PS interactions has not been previously studied in human AF and VF. We hypothesized that PS population size would influence the rate of PS formation and destruction in human AF and VF, due to increased inter-defect interaction. PS population statistics were studied in computational simulations (Aliev-Panfilov), human AF and human VF. The influence of inter-PS interactions was evaluated by comparison between directly modeled discrete-time Markov chain (DTMC) transition matrices of the PS population changes, and M/M/∞ birth-death transition matrices of PS dynamics, which assumes that PS formations and destructions are effectively statistically independent events. Across all systems examined, PS population changes differed from those expected with M/M/∞. In human AF and VF, the formation rates decreased slightly with PS population when modeled with the DTMC, compared with the static formation rate expected through M/M/∞, suggesting new formations were being inhibited. In human AF and VF, the destruction rates increased with PS population for both models, with the DTMC rate increase exceeding the M/M/∞ estimates, indicating that PS were being destroyed faster as the PS population grew. In human AF and VF, the change in PS formation and destruction rates as the population increased differed between the two models. This indicates that the presence of additional PS influenced the likelihood of new PS formation and destruction, consistent with the notion of self-inhibitory inter-PS interactions.

Characterization of spatiotemporal dynamics in EEG data during picture naming with optical flow patterns

In this study, we investigate the spatiotemporal dynamics of the neural oscillations by analyzing the electric potential that arises from neural activity. We identify two types of dynamics based on the frequency and phase of oscillations: standing waves or as out-of-phase and modulated waves, which represent a combination of standing and moving waves. To characterize these dynamics, we use optical flow patterns such as sources, sinks, spirals and saddles. We compare analytical and numerical solutions with real EEG data acquired during a picture-naming task. Analytical approximation of standing waves helps us to establish some properties of pattern location and number. Specifically, sources and sinks are mainly located in the same location, while saddles are positioned between them. The number of saddles correlates with the sum of all the other patterns. These properties are confirmed in both the simulated and real EEG data. In particular, source and sink clusters in the EEG data overlap with each other with median percentages around 60%, and hence have high spatial correlation, while source/sink clusters overlap with saddle clusters in less than 1%, and have different locations. Our statistical analysis showed that saddles account for about 45% of all patterns, while the remaining patterns are present in similar proportions.

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.

Controlling periodic long-range signalling to drive a morphogenetic transition

Cells use signal relay to transmit information across tissue scales. However, the production of information carried by signal relay remains poorly characterised. To determine how the coding features of signal relay are generated, we used the classic system for long-range signalling: the periodic cAMP waves that drive Dictyostelium collective migration. Combining imaging and optogenetic perturbation of cell signalling states, we find that migration is triggered by an increase in wave frequency generated at the signalling centre. Wave frequency is regulated by cAMP wave circulation, which organises the long-range signal. To determine the mechanisms modulating wave circulation, we combined mathematical modelling, the general theory of excitable media, and mechanical perturbations to test competing models. Models in which cell density and spatial patterning modulate the wave frequency cannot explain the temporal evolution of signalling waves. Instead, our evidence leads to a model where wave circulation increases the ability for cells to relay the signal, causing further increase in the circulation rate. This positive feedback between cell state and signalling pattern regulates the long-range signal coding that drives morphogenesis.

A discrete Huber-Braun neuron model: from nodal properties to network performance

Many of the well-known neuron models are continuous time systems with complex mathematical definitions. Literatures have shown that a discrete mathematical model can effectively replicate the complete dynamical behaviour of a neuron with much reduced complexity. Hence, we propose a new discrete neuron model derived from the Huber-Braun neuron with two additional slow and subthreshold currents alongside the ion channel currents. We have also introduced temperature dependent ion channels to study its effects on the firing pattern of the neuron. With bifurcation and Lyapunov exponents we showed the chaotic and periodic regions of the discrete model. Further to study the complexity of the neuron model, we have used the sample entropy algorithm. Though the individual neuron analysis gives us an idea about the dynamical properties, it's the collective behaviour which decides the overall behavioural pattern of the neuron. Hence, we investigate the spatiotemporal behaviour of the discrete neuron model in single- and two-layer network. We have considered obstacle as an important factor which changes the excitability of the neurons in the network. Literatures have shown that spiral waves can play a positive role in breaking through quiescent areas of the brain as a pacemaker by creating a coherence resonance behaviour. Hence, we are interested in studying the induced spiral waves in the network. In this condition when an obstacle is introduced the wave propagation is disturbed and we could see multiple wave re-entry and spiral waves. In a two-layer network when the obstacle is considered only in one layer and stimulus applied to the layer having the obstacle, the wave re-entry is seen in both the layer though the other layer is not exposed to obstacle. But when both the layers are inserted with an obstacle and stimuli also applied to the layers, they behave like independent layers with no coupling effect. In a two-layer network, stimulus play an important role in spatiotemporal dynamics of the network.

Supplementary Information

The online version contains supplementary material available at 10.1007/s11571-022-09806-1.

Spatiotemporal patterns and collective dynamics of bi-layer coupled Izhikevich neural networks with multi-area channels

The firing behavior and bifurcation of different types of Izhikevich neurons are analyzed firstly through numerical simulation. Then, a bi-layer neural network driven by random boundary is constructed by means of system simulation, in which each layer is a matrix network composed of 200 × 200 Izhikevich neurons, and the bi-layer neural network is connected by multi-area channels. Finally, the emergence and disappearance of spiral wave in matrix neural network are investigated, and the synchronization property of neural network is discussed. Obtained results show that random boundary can induce spiral waves under appropriate conditions, and it is clear that the emergence and disappearance of spiral wave can be observed only when the matrix neural network is constructed by regular spiking Izhikevich neurons, while it cannot be observed in neural networks constructed by other modes such as fast spiking, chattering and intrinsically bursting. Further research shows that the variation of synchronization factor with coupling strength between adjacent neurons shows an inverse bell-like curve in the form of "inverse stochastic resonance", but the variation of synchronization factor with coupling strength of inter-layer channels is a curve that is approximately monotonically decreasing. More importantly, it is found that lower synchronicity is helpful to develop spatiotemporal patterns. These results enable people to further understand the collective dynamics of neural networks under random conditions.

Three-dimensional chiral morphodynamics of chemomechanical active shells

Morphogenesis of active shells such as cells is a fundamental chemomechanical process that often exhibits three-dimensional (3D) large deformations and chemical pattern dynamics simultaneously. Here, we establish a chemomechanical active shell theory accounting for mechanical feedback and biochemical regulation to investigate the symmetry-breaking and 3D chiral morphodynamics emerging in the cell cortex. The active bending and stretching of the elastic shells are regulated by biochemical signals like actomyosin and RhoA, which, in turn, exert mechanical feedback on the biochemical events via deformation-dependent diffusion and inhibition. We show that active deformations can trigger chemomechanical bifurcations, yielding pulse spiral waves and global oscillations, which, with increasing mechanical feedback, give way to traveling or standing waves subsequently. Mechanical feedback is also found to contribute to stabilizing the polarity of emerging patterns, thus ensuring robust morphogenesis. Our results reproduce and unravel the experimentally observed solitary and multiple spiral patterns, which initiate asymmetric cleavage in Xenopus and starfish embryogenesis. This study underscores the crucial roles of mechanical feedback in cell development and also suggests a chemomechanical framework allowing for 3D large deformation and chemical signaling to explore complex morphogenesis in living shell-like structures.

Rotational synchronization of pinned spiral waves

Coupled rotors can spontaneously synchronize, giving rise to a plethora of intriguing dynamics. We present here a pair of spiral waves as two synchronizing rotors, coupled by diffusion. The spirals are pinned to unexcitable obstacles, which enables us to modify their frequencies and restrain their drift. In experiments with the Belousov-Zhabotinsky reaction, we show that two counterrotating spiral rotors, pinned to circular heterogeneities, can synchronize in frequency and phase. The nature of the phase synchronization varies depending on the difference in their characteristic frequencies. We observe in-phase and out-of-phase synchronization, lag synchronization, and phase resetting across the experiments. The time required for the two spirals to synchronize is found to depend upon the relative size of their pinning obstacles and the distance separating them. This distance can also modify the phase lag of the two rotors upon synchronization. Our experimental observations are reproduced and explained further on the basis of numerical simulations of an excitable reaction-diffusion model.

Transient brain-wide coactivations and structured transitions revealed in hemodynamic imaging data

Brain-wide patterns in resting human brains, as either structured functional connectivity (FC) or recurring brain states, have been widely studied in the neuroimaging literature. In particular, resting-state FCs estimated over windowed timeframe neuroimaging data from sub-minutes to minutes using correlation or blind source separation techniques have reported many brain-wide patterns of significant behavioral and disease correlates. The present pilot study utilized a novel whole-head cap-based high-density diffuse optical tomography (DOT) technology, together with data-driven analysis methods, to investigate recurring transient brain-wide patterns in spontaneous fluctuations of hemodynamic signals at the resolution of single timeframes from thirteen healthy adults in resting conditions. Our results report that a small number, i.e., six, of brain-wide coactivation patterns (CAPs) describe major spatiotemporal dynamics of spontaneous hemodynamic signals recorded by DOT. These CAPs represent recurring brain states, showing spatial topographies of hemispheric symmetry, and exhibit highly anticorrelated pairs. Moreover, a structured transition pattern among the six brain states is identified, where two CAPs with anterior-posterior spatial patterns are significantly involved in transitions among all brain states. Our results further elucidate two brain states of global positive and negative patterns, indicating transient neuronal coactivations and co-deactivations, respectively, over the entire cortex. We demonstrate that these two brain states are responsible for the generation of a subset of peaks and troughs in global signals (GS), supporting the recent reports on neuronal relevance of hemodynamic GS. Collectively, our results suggest that transient neuronal events (i.e., CAPs), global brain activity, and brain-wide structured transitions co-exist in humans and these phenomena are closely related, which extend the observations of similar neuronal events recently reported in animal hemodynamic data. Future studies on the quantitative relationship among these transient events and their relationships to windowed FCs along with larger sample size are needed to understand their changes with behaviors and diseased conditions.

Brain-wide neural co-activations in resting human

Spontaneous neural activity in human as assessed with resting-state functional magnetic resonance imaging (fMRI) exhibits brain-wide coordinated patterns in the frequency of < 0.1 Hz. However, understanding of fast brain-wide networks at the timescales of neuronal events (milliseconds to sub-seconds) and their spatial, spectral, and transitional characteristics remain limited due to the temporal constraints of hemodynamic signals. With milli-second resolution and whole-head coverage, scalp-based electroencephalography (EEG) provides a unique window into brain-wide networks with neuronal-timescale dynamics, shedding light on the organizing principles of brain functions. Using the state-of-the-art signal processing techniques, we reconstructed cortical neural tomography from resting-state EEG and extracted component-based co-activation patterns (cCAPs). These cCAPs revealed brain-wide intrinsic networks and their dynamics, indicating the configuration/reconfiguration of resting human brains into recurring and transitional functional states, which are featured with the prominent spatial phenomena of global patterns and anti-state pairs of co-(de)activations. Rich oscillational structures across a wide frequency band (i.e., 0.6 Hz, 5 Hz, and 10 Hz) were embedded in the nonstationary dynamics of these functional states. We further identified a superstructure that regulated between-state immediate and long-range transitions involving the entire set of identified cCAPs and governed a significant aspect of brain-wide network dynamics. These findings demonstrated how resting-state EEG data can be functionally decomposed using cCAPs to reveal rich dynamic structures of brain-wide human neural activations.

Rotor Localization and Phase Mapping of Cardiac Excitation Waves Using Deep Neural Networks

The analysis of electrical impulse phenomena in cardiac muscle tissue is important for the diagnosis of heart rhythm disorders and other cardiac pathophysiology. Cardiac mapping techniques acquire local temporal measurements and combine them to visualize the spread of electrophysiological wave phenomena across the heart surface. However, low spatial resolution, sparse measurement locations, noise and other artifacts make it challenging to accurately visualize spatio-temporal activity. For instance, electro-anatomical catheter mapping is severely limited by the sparsity of the measurements, and optical mapping is prone to noise and motion artifacts. In the past, several approaches have been proposed to create more reliable maps from noisy or sparse mapping data. Here, we demonstrate that deep learning can be used to compute phase maps and detect phase singularities in optical mapping videos of ventricular fibrillation, as well as in very noisy, low-resolution and extremely sparse simulated data of reentrant wave chaos mimicking catheter mapping data. The self-supervised deep learning approach is fundamentally different from classical phase mapping techniques. Rather than encoding a phase signal from time-series data, a deep neural network instead learns to directly associate phase maps and the positions of phase singularities with short spatio-temporal sequences of electrical data. We tested several neural network architectures, based on a convolutional neural network (CNN) with an encoding and decoding structure, to predict phase maps or rotor core positions either directly or indirectly via the prediction of phase maps and a subsequent classical calculation of phase singularities. Predictions can be performed across different data, with models being trained on one species and then successfully applied to another, or being trained solely on simulated data and then applied to experimental data. Neural networks provide a promising alternative to conventional phase mapping and rotor core localization methods. Future uses may include the analysis of optical mapping studies in basic cardiovascular research, as well as the mapping of atrial fibrillation in the clinical setting.

The inspection paradox: An important consideration in the evaluation of rotor lifetimes in cardiac fibrillation

Background and Objective: Renewal theory is a statistical approach to model the formation and destruction of phase singularities (PS), which occur at the pivots of spiral waves. A common issue arising during observation of renewal processes is an inspection paradox, due to oversampling of longer events. The objective of this study was to characterise the effect of a potential inspection paradox on the perception of PS lifetimes in cardiac fibrillation. Methods: A multisystem, multi-modality study was performed, examining computational simulations (Aliev-Panfilov (APV) model, Courtmanche-Nattel model), experimentally acquired optical mapping Atrial and Ventricular Fibrillation (AF/VF) data, and clinically acquired human AF and VF. Distributions of all PS lifetimes across full epochs of AF, VF, or computational simulations, were compared with distributions formed from lifetimes of PS existing at 10,000 simulated commencement timepoints. Results: In all systems, an inspection paradox led towards oversampling of PS with longer lifetimes. In APV computational simulations there was a mean PS lifetime shift of +84.9% (95% CI, ± 0.3%) (p < 0.001 for observed vs overall), in Courtmanche-Nattel simulations of AF +692.9% (95% CI, ±57.7%) (p < 0.001), in optically mapped rat AF +374.6% (95% CI, ± 88.5%) (p = 0.052), in human AF mapped with basket catheters +129.2% (95% CI, ±4.1%) (p < 0.05), human AF-HD grid catheters 150.8% (95% CI, ± 9.0%) (p < 0.001), in optically mapped rat VF +171.3% (95% CI, ±15.6%) (p < 0.001), in human epicardial VF 153.5% (95% CI, ±15.7%) (p < 0.001). Conclusion: Visual inspection of phase movies has the potential to systematically oversample longer lasting PS, due to an inspection paradox. An inspection paradox is minimised by consideration of the overall distribution of PS lifetimes.

Studying Synaptically Evoked Cortical Responses ex vivo With Combination of a Single Neuron Recording (Whole-Cell) and Population Voltage Imaging (Genetically Encoded Voltage Indicator)

In a typical electrophysiology experiment, synaptic stimulus is delivered in a cortical layer (1-6) and neuronal responses are recorded intracellularly in individual neurons. We recreated this standard electrophysiological paradigm in brain slices of mice expressing genetically encoded voltage indicators (GEVIs). This allowed us to monitor membrane voltages in the target pyramidal neurons (whole-cell), and population voltages in the surrounding neuropil (optical imaging), simultaneously. Pyramidal neurons have complex dendritic trees that span multiple cortical layers. GEVI imaging revealed areas of the brain slice that experienced the strongest depolarization on a specific synaptic stimulus (location and intensity), thus identifying cortical layers that contribute the most afferent activity to the recorded somatic voltage waveform. By combining whole-cell with GEVI imaging, we obtained a crude distribution of activated synaptic afferents in respect to the dendritic tree of a pyramidal cell. Synaptically evoked voltage waves propagating through the cortical neuropil (dendrites and axons) were not static but rather they changed on a millisecond scale. Voltage imaging can identify areas of brain slices in which the neuropil was in a sustained depolarization (plateau), long after the stimulus onset. Upon a barrage of synaptic inputs, a cortical pyramidal neuron experiences: (a) weak temporal summation of evoked voltage transients (EPSPs); and (b) afterhyperpolarization (intracellular recording), which are not represented in the GEVI population imaging signal (optical signal). To explain these findings [(a) and (b)], we used four voltage indicators (ArcLightD, chi-VSFP, Archon1, and di-4-ANEPPS) with different optical sensitivity, optical response speed, labeling strategy, and a target neuron type. All four imaging methods were used in an identical experimental paradigm: layer 1 (L1) synaptic stimulation, to allow direct comparisons. The population voltage signal showed paired-pulse facilitation, caused in part by additional recruitment of new neurons and dendrites. "Synaptic stimulation" delivered in L1 depolarizes almost an entire cortical column to some degree.

Spatiotemporal characteristics in systems of diffusively coupled excitable slow-fast FitzHugh-Rinzel dynamical neurons

In this paper, we study an excitable, biophysical system that supports wave propagation of nerve impulses. We consider a slow-fast, FitzHugh-Rinzel neuron model where only the membrane voltage interacts diffusively, giving rise to the formation of spatiotemporal patterns. We focus on local, nonlinear excitations and diverse neural responses in an excitable one- and two-dimensional configuration of diffusively coupled FitzHugh-Rinzel neurons. The study of the emerging spatiotemporal patterns is essential in understanding the working mechanism in different brain areas. We derive analytically the coefficients of the amplitude equations in the vicinity of Hopf bifurcations and characterize various patterns, including spirals exhibiting complex geometric substructures. Furthermore, we derive analytically the condition for the development of antispirals in the neighborhood of the bifurcation point. The emergence of broken target waves can be observed to form spiral-like profiles. The spatial dynamics of the excitable system exhibits two- and multi-arm spirals for small diffusive couplings. Our results reveal a multitude of neural excitabilities and possible conditions for the emergence of spiral-wave formation. Finally, we show that the coupled excitable systems with different firing characteristics participate in a collective behavior that may contribute significantly to irregular neural dynamics.

Moving spiral wave chimeras

We consider a two-dimensional array of heterogeneous nonlocally coupled phase oscillators on a flat torus and study the bound states of two counter-rotating spiral chimeras, shortly two-core spiral chimeras, observed in this system. In contrast to other known spiral chimeras with motionless incoherent cores, the two-core spiral chimeras typically show a drift motion. Due to this drift, their incoherent cores become spatially modulated and develop specific fingerprint patterns of varying synchrony levels. In the continuum limit of infinitely many oscillators, the two-core spiral chimeras can be studied using the Ott-Antonsen equation. Numerical analysis of this equation allows us to reveal the stability region of different spiral chimeras, which we group into three main classes-symmetric, asymmetric, and meandering spiral chimeras.

Cross Laminar Traveling Components of Field Potentials due to Volume Conduction of Non-Traveling Neuronal Activity in Macaque Sensory Cortices

Field potentials (FPs) reflect neuronal activities in the brain, and often exhibit traveling peaks across recording sites. While traveling FPs are interpreted as propagation of neuronal activity, not all studies directly reveal such propagating patterns of neuronal activation. Neuronal activity is associated with transmembrane currents that form dipoles and produce negative and positive fields. Thereby, FP components reverse polarity between those fields and have minimal amplitudes at the center of dipoles. Although their amplitudes could be smaller, FPs are never flat even around these reversals. What occurs around the reversal has not been addressed explicitly, although those are rationally in the middle of active neurons. We show that sensory FPs around the reversal appeared with peaks traveling across cortical laminae in macaque sensory cortices. Interestingly, analyses of current source density did not depict traveling patterns but lamina-delimited current sinks and sources. We simulated FPs produced by volume conduction of a simplified 2 dipoles' model mimicking sensory cortical laminar current source density components. While FPs generated by single dipoles followed the temporal patterns of the dipole moments without traveling peaks, FPs generated by concurrently active dipole moments appeared with traveling components in the vicinity of dipoles by superimposition of individually non-traveling FPs generated by single dipoles. These results indicate that not all traveling FP are generated by traveling neuronal activity, and that recording positions need to be taken into account to describe FP peak components around active neuronal populations.SIGNIFICANCE STATEMENT Field potentials (FPs) generated by neuronal activity in the brain occur with fields of opposite polarity. Likewise, in the cerebral cortices, they have mirror-imaged waveforms in upper and lower layers. We show that FPs appear like traveling across the cortical layers. Interestingly, the traveling FPs occur without traveling components of current source density, which represents transmembrane currents associated with neuronal activity. These seemingly odd findings are explained using current source density models of multiple dipoles. Concurrently active, non-traveling dipoles produce FPs as mixtures of FPs produced by individual dipoles, and result in traveling FP waveforms as the mixing ratio depends on the distances from those dipoles. The results suggest that not all traveling FP components are associated with propagating neuronal activity.

Topological braiding and virtual particles on the cell membrane

Braiding of topological structures in complex matter fields provides a robust framework for encoding and processing information, and it has been extensively studied in the context of topological quantum computation. In living systems, topological defects are crucial for the localization and organization of biochemical signaling waves, but their braiding dynamics remain unexplored. Here, we show that the spiral wave cores, which organize the Rho-GTP protein signaling dynamics and force generation on the membrane of starfish egg cells, undergo spontaneous braiding dynamics. Experimentally measured world line braiding exponents and topological entropy correlate with cellular activity and agree with predictions from a generic field theory. Our analysis further reveals the creation and annihilation of virtual quasi-particle excitations during defect scattering events, suggesting phenomenological parallels between quantum and living matter.

Noise induced suppression of spiral waves in a hybrid FitzHugh-Nagumo neuron with discontinuous resetting

A modified FitzHugh-Nagumo neuron model with sigmoid function-based recovery variable is considered with electromagnetic flux coupling. The dynamical properties of the proposed neuron model are investigated, and as the excitation current becomes larger, the number of fixed points decreases to one. The bifurcation plots are investigated to show the chaotic and periodic regimes for various values of excitation current and parameters. A N×N network of the neuron model is constructed to study the wave propagation and wave re-entry phenomena. Investigations are conducted to show that for larger flux coupling values, the spiral waves are suppressed, but for such values of the flux coupling, the individual nodes are driven into periodic regimes. By introducing Gaussian noise as an additional current term, we showed that when noise is introduced for the entire simulation time, the dynamics of the nodes are largely altered while the noise exposure for 200-time units will not alter the dynamics of the nodes completely.

Attractor competition enriches cortical dynamics during awakening from anesthesia

Slow oscillations (≲ 1 Hz), a hallmark of slow-wave sleep and deep anesthesia across species, arise from spatiotemporal patterns of activity whose complexity increases as wakefulness is approached and cognitive functions emerge. The arousal process constitutes an open window to the unknown mechanisms underlying the emergence of such dynamical richness in awake cortical networks. Here, we investigate the changes in network dynamics as anesthesia fades out in the rat visual cortex. Starting from deep anesthesia, slow oscillations gradually increase their frequency, eventually expressing maximum regularity. This stage is followed by the abrupt onset of an infra-slow (~0.2 Hz) alternation between sleep-like oscillations and activated states. A population rate model reproduces this transition driven by an increased excitability that brings it to periodically cross a critical point. Based on our model, dynamical richness emerges as a competition between two metastable attractor states, a conclusion strongly supported by the data.

Cortical propagation tracks functional recovery after stroke

Stroke is a debilitating condition affecting millions of people worldwide. The development of improved rehabilitation therapies rests on finding biomarkers suitable for tracking functional damage and recovery. To achieve this goal, we perform a spatiotemporal analysis of cortical activity obtained by wide-field calcium images in mice before and after stroke. We compare spontaneous recovery with three different post-stroke rehabilitation paradigms, motor training alone, pharmacological contralesional inactivation and both combined. We identify three novel indicators that are able to track how movement-evoked global activation patterns are impaired by stroke and evolve during rehabilitation: the duration, the smoothness, and the angle of individual propagation events. Results show that, compared to pre-stroke conditions, propagation of cortical activity in the subacute phase right after stroke is slowed down and more irregular. When comparing rehabilitation paradigms, we find that mice treated with both motor training and pharmacological intervention, the only group associated with generalized recovery, manifest new propagation patterns, that are even faster and smoother than before the stroke. In conclusion, our new spatiotemporal propagation indicators could represent promising biomarkers that are able to uncover neural correlates not only of motor deficits caused by stroke but also of functional recovery during rehabilitation. In turn, these insights could pave the way towards more targeted post-stroke therapies.

Millions of people worldwide suffer from long-lasting motor deficits caused by stroke. Very recently, the two basic therapeutic approaches, motor training and pharmacological intervention, have been combined in order to achieve a more efficient functional recovery. In this study, we analyze the neurophysiological activity in the brain of mice observed with in vivo calcium imaging before and after the induction of a stroke. We use a newly developed universal approach based on the temporal sequence of local activation in different brain regions to quantify three properties of global propagation patterns: duration, smoothness and angle. These innovative spatiotemporal propagation indicators allow us to track damage and functional recovery following stroke and to quantify the relative success of motor training, pharmacological inactivation, and a combination of both, compared to spontaneous recovery. We show that all three treatments reverse the alterations observed during the subacute phase right after stroke. We also find that combining motor training and pharmacological intervention does not restore pre-stroke features but rather leads to the emergence of new propagation patterns that, surprisingly, are even faster and smoother than the pre-stroke patterns.

Size matters: Effects of the size of heterogeneity on the wave re-entry and spiral wave formation in an excitable media

Network performance of neurons plays a vital role in determining the behavior of many physiological systems. In this paper, we discuss the wave propagation phenomenon in a network of neurons considering obstacles in the network. Numerous studies have shown the disastrous effects caused by the heterogeneity induced by the obstacles, but these studies have been mainly discussing the orientation effects. Hence, we are interested in investigating the effects of both the size and orientation of the obstacles in the wave re-entry and spiral wave formation in the network. For this analysis, we have considered two types of neuron models and a pancreatic beta cell model. In the first neuron model, we use the well-known differential equation-based neuron models, and in the second type, we used the hybrid neuron models with the resetting phenomenon. We have shown that the size of the obstacle decides the spiral wave formation in the network and horizontally placed obstacles will have a lesser impact on the wave re-entry than the vertically placed obstacles.

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.

Asymmetric synchronization in lattices of pinned spiral waves

Networks of coupled oscillators show a wealth of fascinating dynamics and are capable of storing and processing information. In biological and social networks, the coupling is often asymmetric. We use the chirality of rotating spiral waves to introduce this asymmetry in an excitable reaction-diffusion model. The individual vortices are pinned to unexcitable disks and arranged at a constant spacing L along straight lines or simple geometric patterns. In the case of periodic boundaries or pinning disks arranged along the edge of a closed shape, small L values lead to synchronization via repeated wave collisions. The rate of synchronization as a function of L shows a single maximum and is determined by the dispersion behavior of a continuous wave train traveling along the system boundary. For finite systems, spirals are affected by their upstream neighbor, and a single dominant spiral exists along each chain. Specific initial conditions can decouple neighboring vortices even for small L values. We also present a time-delay differential equation that reproduces the phase dynamics in periodic systems.

Pairwise maximum entropy model explains the role of white matter structure in shaping emergent co-activation states

A major challenge in neuroscience is determining a quantitative relationship between the brain's white matter structural connectivity and emergent activity. We seek to uncover the intrinsic relationship among brain regions fundamental to their functional activity by constructing a pairwise maximum entropy model (MEM) of the inter-ictal activation patterns of five patients with medically refractory epilepsy over an average of ~14 hours of band-passed intracranial EEG (iEEG) recordings per patient. We find that the pairwise MEM accurately predicts iEEG electrodes' activation patterns' probability and their pairwise correlations. We demonstrate that the estimated pairwise MEM's interaction weights predict structural connectivity and its strength over several frequencies significantly beyond what is expected based solely on sampled regions' distance in most patients. Together, the pairwise MEM offers a framework for explaining iEEG functional connectivity and provides insight into how the brain's structural connectome gives rise to large-scale activation patterns by promoting co-activation between connected structures.

Traveling waves in non-local pulse-coupled networks

Traveling phase waves are commonly observed in recordings of the cerebral cortex and are believed to organize behavior across different areas of the brain. We use this as motivation to analyze a one-dimensional network of phase oscillators that are nonlocally coupled via the phase response curve (PRC) and the Dirac delta function. Existence of waves is proven and the dispersion relation is computed. Using the theory of distributions enables us to write and solve an associated stability problem. First and second order perturbation theory is applied to get analytic insight and we show that long waves are stable while short waves are unstable. We apply the results to PRCs that come from mitral neurons. We extend the results to smooth pulse-like coupling by reducing the nonlocal equation to a local one and solving the associated boundary value problem.

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.

Synchronization, Stochasticity, and Phase Waves in Neuronal Networks With Spatially-Structured Connectivity

Oscillations in the beta/low gamma range (10–45 Hz) are recorded in diverse neural structures. They have successfully been modeled as sparsely synchronized oscillations arising from reciprocal interactions between randomly connected excitatory (E) pyramidal cells and local interneurons (I). The synchronization of spatially distant oscillatory spiking E–I modules has been well-studied in the rate model framework but less so for modules of spiking neurons. Here, we first show that previously proposed modifications of rate models provide a quantitative description of spiking E–I modules of Exponential Integrate-and-Fire (EIF) neurons. This allows us to analyze the dynamical regimes of sparsely synchronized oscillatory E–I modules connected by long-range excitatory interactions, for two modules, as well as for a chain of such modules. For modules with a large number of neurons (> 10⁵), we obtain results similar to previously obtained ones based on the classic deterministic Wilson-Cowan rate model, with the added bonus that the results quantitatively describe simulations of spiking EIF neurons. However, for modules with a moderate (~ 10⁴) number of neurons, stochastic variations in the spike emission of neurons are important and need to be taken into account. On the one hand, they modify the oscillations in a way that tends to promote synchronization between different modules. On the other hand, independent fluctuations on different modules tend to disrupt synchronization. The correlations between distant oscillatory modules can be described by stochastic equations for the oscillator phases that have been intensely studied in other contexts. On shorter distances, we develop a description that also takes into account amplitude modes and that quantitatively accounts for our simulation data. Stochastic dephasing of neighboring modules produces transient phase gradients and the transient appearance of phase waves. We propose that these stochastically-induced phase waves provide an explanative framework for the observations of traveling waves in the cortex during beta oscillations.

EEG microstate periodicity explained by rotating phase patterns of resting-state alpha oscillations

Spatio-temporal patterns in electroencephalography (EEG) can be described by microstate analysis, a discrete approximation of the continuous electric field patterns produced by the cerebral cortex. Resting-state EEG microstates are largely determined by alpha frequencies (8-12 Hz) and we recently demonstrated that microstates occur periodically with twice the alpha frequency. To understand the origin of microstate periodicity, we analyzed the analytic amplitude and the analytic phase of resting-state alpha oscillations independently. In continuous EEG data we found rotating phase patterns organized around a small number of phase singularities which varied in number and location. The spatial rotation of phase patterns occurred with the underlying alpha frequency. Phase rotors coincided with periodic microstate motifs involving the four canonical microstate maps. The analytic amplitude showed no oscillatory behaviour and was almost static across time intervals of 1-2 alpha cycles, resulting in the global pattern of a standing wave. In n=23 healthy adults, time-lagged mutual information analysis of microstate sequences derived from amplitude and phase signals of awake eyes-closed EEG records showed that only the phase component contributed to the periodicity of microstate sequences. Phase sequences showed mutual information peaks at multiples of 50 ms and the group average had a main peak at 100 ms (10 Hz), whereas amplitude sequences had a slow and monotonous information decay. This result was confirmed by an independent approach combining temporal principal component analysis (tPCA) and autocorrelation analysis. We reproduced our observations in a generic model of EEG oscillations composed of coupled non-linear oscillators (Stuart-Landau model). Phase-amplitude dynamics similar to experimental EEG occurred when the oscillators underwent a supercritical Hopf bifurcation, a common feature of many computational models of the alpha rhythm. These findings explain our previous description of periodic microstate recurrence and its relation to the time scale of alpha oscillations. Moreover, our results corroborate the predictions of computational models and connect experimentally observed EEG patterns to properties of critical oscillator networks.

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.

Control of brain network dynamics across diverse scales of space and time

The human brain is composed of distinct regions that are each associated with particular functions and distinct propensities for the control of neural dynamics. However, the relation between these functions and control profiles is poorly understood, as is the variation in this relation across diverse scales of space and time. Here we probe the relation between control and dynamics in brain networks constructed from diffusion tensor imaging data in a large community sample of young adults. Specifically, we probe the control properties of each brain region and investigate their relationship with dynamics across various spatial scales using the Laplacian eigenspectrum. In addition, through analysis of regional modal controllability and partitioning of modes, we determine whether the associated dynamics are fast or slow, as well as whether they are alternating or monotone. We find that brain regions that facilitate the control of energetically easy transitions are associated with activity on short length scales and slow timescales. Conversely, brain regions that facilitate control of difficult transitions are associated with activity on long length scales and fast timescales. Built on linear dynamical models, our results offer parsimonious explanations for the activity propagation and network control profiles supported by regions of differing neuroanatomical structure.

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

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

A model for focal seizure onset, propagation, evolution, and progression

We developed a neural network model that can account for major elements common to human focal seizures. These include the tonic-clonic transition, slow advance of clinical semiology and corresponding seizure territory expansion, widespread EEG synchronization, and slowing of the ictal rhythm as the seizure approaches termination. These were reproduced by incorporating usage-dependent exhaustion of inhibition in an adaptive neural network that receives global feedback inhibition in addition to local recurrent projections. Our model proposes mechanisms that may underline common EEG seizure onset patterns and status epilepticus, and postulates a role for synaptic plasticity in the emergence of epileptic foci. Complex patterns of seizure activity and bi-stable seizure end-points arise when stochastic noise is included. With the rapid advancement of clinical and experimental tools, we believe that this model can provide a roadmap and potentially an in silico testbed for future explorations of seizure mechanisms and clinical therapies.

Interneuron Desynchronization Precedes Seizures in a Mouse Model of Dravet Syndrome

Recurrent seizures, which define epilepsy, are transient abnormalities in the electrical activity of the brain. The mechanistic basis of seizure initiation, and the contribution of defined neuronal subtypes to seizure pathophysiology, remains poorly understood. We performed in vivo two-photon calcium imaging in neocortex during temperature-induced seizures in male and female Dravet syndrome (Scn1a+/-) mice, a neurodevelopmental disorder with prominent temperature-sensitive epilepsy. Mean activity of both putative principal cells and parvalbumin-positive interneurons (PV-INs) was higher in Scn1a+/- relative to wild-type controls during quiet wakefulness at baseline and at elevated core body temperature. However, wild-type PV-INs showed a progressive synchronization in response to temperature elevation that was absent in PV-INs from Scn1a+/- mice. Hence, PV-IN activity remains intact interictally in Scn1a+/- mice, yet exhibits decreased synchrony immediately before seizure onset. We suggest that impaired PV-IN synchronization may contribute to the transition to the ictal state during temperature-induced seizures in Dravet syndrome.SIGNIFICANCE STATEMENT Epilepsy is a common neurological disorder defined by recurrent, unprovoked seizures. However, basic mechanisms of seizure initiation and propagation remain poorly understood. We performed in vivo two-photon calcium imaging in an experimental model of Dravet syndrome (Scn1a+/- mice)-a severe neurodevelopmental disorder defined by temperature-sensitive, treatment-resistant epilepsy-and record activity of putative excitatory neurons and parvalbumin-positive GABAergic neocortical interneurons (PV-INs) during naturalistic seizures induced by increased core body temperature. PV-IN activity was higher in Scn1a+/- relative to wild-type controls during quiet wakefulness. However, wild-type PV-INs showed progressive synchronization in response to temperature elevation that was absent in PV-INs from Scn1a+/- mice before seizure onset. Hence, impaired PV-IN synchronization may contribute to transition to seizure in Dravet syndrome.