Mechanisms of cortical electrical activity and emergence of gamma rhythm

Neural field theory of adaptive effects on auditory evoked responses and mismatch negativity in multifrequency stimulus sequences

Physiologically based neural field theory (NFT) of the corticothalamic system, including adaptation, is used to calculate the responses evoked by trains of auditory stimuli that differ in frequency. In oddball paradigms, fully distinguishable frequencies lead to different standard (common stimulus) and deviant (rare stimulus) responses; the signal obtained by subtracting the standard response from the deviant is termed the mismatch negativity (MMN). In this analysis, deviant responses are found to correspond to unadapted cortex, whereas the part of auditory cortex that processes the standard stimuli adapts over several stimulus presentations until the final standard response form is achieved. No higher-order memory processes are invoked. In multifrequency experiments, the deviant response approaches the standard one as the deviant frequency approaches that of the standard and analytic criteria for this effect to be obtained. It is shown that these criteria can also be used to understand adaptation in random tone sequences. A method of probing MMNs and adaptation in random tone sequences is suggested to makes more use of such data.

Neural Field Theory of Evoked Response Sequences and Mismatch Negativity With Adaptation

Physiologically based neural field theory of the corticothalamic system is used to calculate the responses evoked by trains of auditory stimuli that correspond to different cortical locations via the tonotopic map. The results are shown to account for standard and deviant evoked responses to frequent and rare stimuli, respectively, in the auditory oddball paradigms widely used in human cognitive studies, and the so-called mismatch negativity between them. It also reproduces a wide range of other effects and variants, including the mechanism by which a change in standard responses relative to deviants can develop through adaptation, different responses when two deviants are presented in a row or a standard is presented after two deviants, relaxation of standard responses back to deviant form after a stimulus-free period, and more complex sequences. Some cases are identified in which adaptation does not account for the whole difference between standard and deviant responses. The results thus provide a systematic means to determine how much of the response is due to adaptation in the system comprising the primary auditory cortex and medial geniculate nucleus, and how much requires involvement of higher-level processing.

Spectrum of connectivity fluctuations including the effect of activity-dependent feedback

The spatiotemporal spectrum of feedback-driven fluctuations of brain connectivity is investigated using nonlinear neural field theory of the corticothalamic system. Weakly nonlinear dynamics of neural feedbacks are expanded in terms of first order perturbations of neural activity relative to a fixed point. Susceptibilities are used to quantify the change in connectivity per unit change in presynaptic or postsynaptic activity caused by nonlinear feedbacks such as facilitation, depression, sensitization, potentiation, and the effects of discrete eigenmode structure are included for a spherical brain geometry. Spectral signatures such as resonances are identified that allow the presence of particular presynaptic and postsynaptic feedback effects to be inferred. These include additional resonances at high frequencies and shifts of existing spectral peaks, mostly visible in the lowest spatial modes of the response.

NFTsim: Theory and Simulation of Multiscale Neural Field Dynamics

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

Spectral signatures of activity-dependent neural feedback in the corticothalamic system

The modulation of neural quantities by presynaptic and postsynaptic activities via local feedback processes is investigated by incorporating nonlinear phenomena such as relative refractory period, synaptic enhancement, synaptic depression, and habituation. This is done by introducing susceptibilities, which quantify the response in either firing threshold or synaptic strength to unit change in either presynaptic or postsynaptic activity. Effects on the power spectra are then analyzed for a realistic corticothalamic model to determine the spectral signatures of various nonlinear processes and to what extent these are distinct. Depending on the feedback processes, there can be enhancements or reductions in low-frequency and/or alpha power, splitting of the alpha resonance, and/or appearance of new resonances at high frequencies. These features in the power spectra allow processes to be fully distinguished where they are unique, or partly distinguished if they are common to only a subset of feedbacks, and can potentially be used to constrain the types, strengths, and dynamics of feedbacks present.

Unified neural field theory of brain dynamics underlying oscillations in Parkinson's disease and generalized epilepsies

The mechanisms underlying pathologically synchronized neural oscillations in Parkinson's disease (PD) and generalized epilepsies are explored in parallel via a physiologically-based neural field model of the corticothalamic-basal ganglia (CTBG) system. The basal ganglia (BG) are approximated as a single effective population and their roles in the modulation of oscillatory dynamics of the corticothalamic (CT) system and vice versa are analyzed. In addition to normal EEG rhythms, enhanced activity around 4 Hz and 20 Hz exists in the model, consistent with the characteristic frequencies observed in PD. These rhythms result from resonances in loops formed between the BG and CT populations, analogous to those that underlie epileptic oscillations in a previous CT model, and which are still present in the combined CTBG system. Dopamine depletion is argued to weaken the dampening of these loop resonances in PD, and network connections then explain the significant coherence observed between BG, thalamic, and cortical population activity around 4-8 Hz and 20 Hz. Parallels between the afferent and efferent connection sites of the thalamic reticular nucleus (TRN) and BG predict low dopamine to correspond to a reduced likelihood of tonic-clonic (grand mal) seizures, which agrees with experimental findings. Furthermore, the model predicts an increased likelihood of absence (petit mal) seizure resulting from pathologically low dopamine levels in accordance with experimental observations. Suppression of absence seizure activity is demonstrated when afferent and efferent BG connections to the CT system are strengthened, which is consistent with other CTBG modeling studies. The BG are demonstrated to have a suppressive effect on activity of the CTBG system near tonic-clonic seizure states, which provides insight into the reported efficacy of current treatments in BG circuits. Sleep states of the TRN are also found to suppress pathological PD activity in accordance with observations. Overall, the findings demonstrate strong parallels between coherent oscillations in generalized epilepsies and PD, and provide insights into possible comorbidities.

Eliminating Absence Seizures through the Deep Brain Stimulation to Thalamus Reticular Nucleus

Deep brain stimulation (DBS) can play a crucial role in the modulation of absence seizures, yet relevant biophysical mechanisms are not completely established. In this paper, on the basis of a biophysical mean-field model, we investigate a typical absence epilepsy activity by introducing slow kinetics of GABA_B receptors on thalamus reticular nucleus (TRN). We find that the region of spike and slow-wave discharges (SWDs) can be reduced greatly when we add the DBS to TRN. Furthermore, we systematically explore how the corresponding stimulation parameters including frequency, amplitude and positive input duration suppress the SWDs under certain conditions. It is shown that the SWDs can be controlled as key stimulation parameters are suitably chosen. The results in this paper can be helpful for researchers to understand the thalamus stimulation in treating epilepsy patients, and provide theoretical basis for future experimental and clinical studies.

From individual spiking neurons to population behavior: Systematic elimination of short-wavelength spatial modes

Mean-field models of the brain approximate spiking dynamics by assuming that each neuron responds to its neighbors via a naive spatial average that neglects local fluctuations and correlations in firing activity. In this paper we address this issue by introducing a rigorous formalism to enable spatial coarse-graining of spiking dynamics, scaling from the microscopic level of a single type 1 (integrator) neuron to a macroscopic assembly of spiking neurons that are interconnected by chemical synapses and nearest-neighbor gap junctions. Spiking behavior at the single-neuron scale ℓ≈10μm is described by Wilson's two-variable conductance-based equations [H. R. Wilson, J. Theor. Biol. 200, 375 (1999)], driven by fields of incoming neural activity from neighboring neurons. We map these equations to a coarser spatial resolution of grid length Bℓ, with B≫1 being the blocking ratio linking micro and macro scales. Our method systematically eliminates high-frequency (short-wavelength) spatial modes q(->) in favor of low-frequency spatial modes Q(->) using an adiabatic elimination procedure that has been shown to be equivalent to the path-integral coarse graining applied to renormalization group theory of critical phenomena. This bottom-up neural regridding allows us to track the percolation of synaptic and ion-channel noise from the single neuron up to the scale of macroscopic population-average variables. Anticipated applications of neural regridding include extraction of the current-to-firing-rate transfer function, investigation of fluctuation criticality near phase-transition tipping points, determination of spatial scaling laws for avalanche events, and prediction of the spatial extent of self-organized macrocolumnar structures. As a first-order exemplar of the method, we recover nonlinear corrections for a coarse-grained Wilson spiking neuron embedded in a network of identical diffusively coupled neurons whose chemical synapses have been disabled. Intriguingly, we find that reblocking transforms the original type 1 Wilson integrator into a type 2 resonator whose spike-rate transfer function exhibits abrupt spiking onset with near-vertical takeoff and chaotic dynamics just above threshold.

Neural field theory of nonlinear wave-wave and wave-neuron processes

Systematic expansion of neural field theory equations in terms of nonlinear response functions is carried out to enable a wide variety of nonlinear wave-wave and wave-neuron processes to be treated systematically in systems involving multiple neural populations. The results are illustrated by analyzing second-harmonic generation, and they can also be applied to wave-wave coalescence, multiharmonic generation, facilitation, depression, refractoriness, and other nonlinear processes.

Simulations of pattern dynamics for reaction-diffusion systems via SIMULINK

BACKGROUND

Investigation of the nonlinear pattern dynamics of a reaction-diffusion system almost always requires numerical solution of the system's set of defining differential equations. Traditionally, this would be done by selecting an appropriate differential equation solver from a library of such solvers, then writing computer codes (in a programming language such as C or Matlab) to access the selected solver and display the integrated results as a function of space and time. This "code-based" approach is flexible and powerful, but requires a certain level of programming sophistication. A modern alternative is to use a graphical programming interface such as Simulink to construct a data-flow diagram by assembling and linking appropriate code blocks drawn from a library. The result is a visual representation of the inter-relationships between the state variables whose output can be made completely equivalent to the code-based solution.

RESULTS

As a tutorial introduction, we first demonstrate application of the Simulink data-flow technique to the classical van der Pol nonlinear oscillator, and compare Matlab and Simulink coding approaches to solving the van der Pol ordinary differential equations. We then show how to introduce space (in one and two dimensions) by solving numerically the partial differential equations for two different reaction-diffusion systems: the well-known Brusselator chemical reactor, and a continuum model for a two-dimensional sheet of human cortex whose neurons are linked by both chemical and electrical (diffusive) synapses. We compare the relative performances of the Matlab and Simulink implementations.

CONCLUSIONS

The pattern simulations by Simulink are in good agreement with theoretical predictions. Compared with traditional coding approaches, the Simulink block-diagram paradigm reduces the time and programming burden required to implement a solution for reaction-diffusion systems of equations. Construction of the block-diagram does not require high-level programming skills, and the graphical interface lends itself to easy modification and use by non-experts.

Prediction and verification of nonlinear sleep spindle harmonic oscillations

This paper examines nonlinear effects in a neural field model of the corticothalamic system to predict the EEG power spectrum of sleep spindles. Nonlinearity in the thalamic relay nuclei gives rise to a spindle harmonic visible in the cortical EEG. By deriving an analytic expression for nonlinear spectrum, the power in the spindle harmonic is predicted to scale quadratically with the power in the spindle oscillation. By isolating sleep spindles from background sleep in experimental EEG data, the spindle harmonic is directly observed.

Neural masses and fields in dynamic causal modeling

Dynamic causal modeling (DCM) provides a framework for the analysis of effective connectivity among neuronal subpopulations that subtend invasive (electrocorticograms and local field potentials) and non-invasive (electroencephalography and magnetoencephalography) electrophysiological responses. This paper reviews the suite of neuronal population models including neural masses, fields and conductance-based models that are used in DCM. These models are expressed in terms of sets of differential equations that allow one to model the synaptic underpinnings of connectivity. We describe early developments using neural mass models, where convolution-based dynamics are used to generate responses in laminar-specific populations of excitatory and inhibitory cells. We show that these models, though resting on only two simple transforms, can recapitulate the characteristics of both evoked and spectral responses observed empirically. Using an identical neuronal architecture, we show that a set of conductance based models-that consider the dynamics of specific ion-channels-present a richer space of responses; owing to non-linear interactions between conductances and membrane potentials. We propose that conductance-based models may be more appropriate when spectra present with multiple resonances. Finally, we outline a third class of models, where each neuronal subpopulation is treated as a field; in other words, as a manifold on the cortical surface. By explicitly accounting for the spatial propagation of cortical activity through partial differential equations (PDEs), we show that the topology of connectivity-through local lateral interactions among cortical layers-may be inferred, even in the absence of spatially resolved data. We also show that these models allow for a detailed analysis of structure-function relationships in the cortex. Our review highlights the relationship among these models and how the hypothesis asked of empirical data suggests an appropriate model class.

Cortical information flow in Parkinson's disease: a composite network/field model

The basal ganglia play a crucial role in the execution of movements, as demonstrated by the severe motor deficits that accompany Parkinson's disease (PD). Since motor commands originate in the cortex, an important question is how the basal ganglia influence cortical information flow, and how this influence becomes pathological in PD. To explore this, we developed a composite neuronal network/neural field model. The network model consisted of 4950 spiking neurons, divided into 15 excitatory and inhibitory cell populations in the thalamus and cortex. The field model consisted of the cortex, thalamus, striatum, subthalamic nucleus, and globus pallidus. Both models have been separately validated in previous work. Three field models were used: one with basal ganglia parameters based on data from healthy individuals, one based on data from individuals with PD, and one purely thalamocortical model. Spikes generated by these field models were then used to drive the network model. Compared to the network driven by the healthy model, the PD-driven network had lower firing rates, a shift in spectral power toward lower frequencies, and higher probability of bursting; each of these findings is consistent with empirical data on PD. In the healthy model, we found strong Granger causality between cortical layers in the beta and low gamma frequency bands, but this causality was largely absent in the PD model. In particular, the reduction in Granger causality from the main “input” layer of the cortex (layer 4) to the main “output” layer (layer 5) was pronounced. This may account for symptoms of PD that seem to reflect deficits in information flow, such as bradykinesia. In general, these results demonstrate that the brain's large-scale oscillatory environment, represented here by the field model, strongly influences the information processing that occurs within its subnetworks. Hence, it may be preferable to drive spiking network models with physiologically realistic inputs rather than pure white noise.

On the dynamics of cortical development: synchrony and synaptic self-organization

We describe a model for cortical development that resolves long-standing difficulties of earlier models. It is proposed that, during embryonic development, synchronous firing of neurons and their competition for limited metabolic resources leads to selection of an array of neurons with ultra-small-world characteristics. Consequently, in the visual cortex, macrocolumns linked by superficial patchy connections emerge in anatomically realistic patterns, with an ante-natal arrangement which projects signals from the surrounding cortex onto each macrocolumn in a form analogous to the projection of a Euclidean plane onto a Möbius strip. This configuration reproduces typical cortical response maps, and simulations of signal flow explain cortical responses to moving lines as functions of stimulus velocity, length, and orientation. With the introduction of direct visual inputs, under the operation of Hebbian learning, development of mature selective response “tuning” to stimuli of given orientation, spatial frequency, and temporal frequency would then take place, overwriting the earlier ante-natal configuration. The model is provisionally extended to hierarchical interactions of the visual cortex with higher centers, and a general principle for cortical processing of spatio-temporal images is sketched.

Cortical gamma oscillations: the functional key is activation, not cognition

Cortical oscillatory synchrony in the gamma range has been attracting increasing attention in cognitive neuroscience ever since being proposed as a solution to the so-called binding problem. This growing literature is critically reviewed in both its basic neuroscience and cognitive aspects. A physiological "default assumption" regarding these oscillations is introduced, according to which they signal a state of physiological activation of cortical tissue, and the associated need to balance excitation with inhibition in particular. As such these oscillations would belong among a variety of generic neural control operations that enable neural tissue to perform its systems level functions, without implementing those functions themselves. Regional control of cerebral blood flow provides an analogy in this regard, and gamma oscillations are tightly correlated with this even more elementary control operation. As correlates of neural activation they will also covary with cognitive activity, and this typically suffices to account for the covariation between gamma activity and cognitive task variables. A number of specific cases of gamma synchrony are examined in this light, including the original impetus for attributing cognitive significance to gamma activity, namely the experiments interpreted as evidence for "binding by synchrony". This examination finds no compelling reasons to assign functional roles to oscillatory synchrony in the gamma range beyond its generic functions at the level of infrastructural neural control.

Stochastic generation of gamma-band activity in primary visual cortex of awake and anesthetized monkeys

Oscillatory neural activity within the gamma band (25-90 Hz) is generally thought to be able to provide a timing signal for harmonizing neural computations across different brain regions. Using time-frequency analyses of the dynamics of gamma-band activity in the local field potentials recorded from monkey primary visual cortex, we found identical temporal characteristics of gamma activity in both awake and anesthetized brain states, including large variability of peak frequency, brief oscillatory epochs (<100 ms on average), and stochastic statistics of the incidence and duration of oscillatory events. These findings indicate that gamma-band activity is temporally unstructured and is inherently a stochastic signal generated by neural networks. This idea was corroborated further by our neural-network simulations. Our results suggest that gamma-band activity is too random to serve as a clock signal for synchronizing neuronal responses in awake as in anesthetized monkeys. Instead, gamma-band activity is more likely to be filtered neuronal network noise. Its mean frequency changes with global state and is reduced under anesthesia.

The laminar cortex model: a new continuum cortex model incorporating laminar architecture

Local field potentials (LFPs) are widely used to study the function of local networks in the brain. They are also closely correlated with the blood-oxygen-level-dependent signal, the predominant contrast mechanism in functional magnetic resonance imaging. We developed a new laminar cortex model (LCM) to simulate the amplitude and frequency of LFPs. Our model combines the laminar architecture of the cerebral cortex and multiple continuum models to simulate the collective activity of cortical neurons. The five cortical layers (layer I, II/III, IV, V, and VI) are simulated as separate continuum models between which there are synaptic connections. The LCM was used to simulate the dynamics of the visual cortex under different conditions of visual stimulation. LFPs are reported for two kinds of visual stimulation: general visual stimulation and intermittent light stimulation. The power spectra of LFPs were calculated and compared with existing empirical data. The LCM was able to produce spontaneous LFPs exhibiting frequency-inverse (1/ƒ) power spectrum behaviour. Laminar profiles of current source density showed similarities to experimental data. General stimulation enhanced the oscillation of LFPs corresponding to gamma frequencies. During simulated intermittent light stimulation, the LCM captured the fundamental as well as high order harmonics as previously reported. The power spectrum expected with a reduction in layer IV neurons, often observed with focal cortical dysplasias associated with epilepsy was also simulated.

Local field potentials (LFPs) are low-frequency fluctuations of the electric fields produced by the brain. They have been widely studied to understand brain function and activity. LFPs reflect the activity of neurons within a few square millimeters of the cerebral cortex, an area containing more than 10,000 neurons. To avoid the complexity of simulating such a large number of individual neurons, the continuum cortex model was devised to simulate the collective activity of groups of neurons generating cortical LFPs. However, the continuum cortex model assumes that the cortex is two-dimensional and does not take into account the laminar architecture of the cerebral cortex. We developed a three-dimensional laminar cortex model (LCM) by combining laminar architecture with the continuum cortex model. This expansion enables the LCM to simulate the detailed three-dimensional distribution of the LFP within the cortex. We used the LCM to simulate LFPs within the visual cortex under different conditions of visual stimulation. The LCM reproduced the key features of LFPs observed in electrophysiological experiments. We conclude that the LCM is a potentially useful tool to investigate the underlying mechanism of LFPs.

A Computational Feedforward Model Predicts Categorization of Masked Emotional Body Language for Longer, but Not for Shorter, Latencies

Given the presence of massive feedback loops in brain networks, it is difficult to disentangle the contribution of feedforward and feedback processing to the recognition of visual stimuli, in this case, of emotional body expressions. The aim of the work presented in this letter is to shed light on how well feedforward processing explains rapid categorization of this important class of stimuli. By means of parametric masking, it may be possible to control the contribution of feedback activity in human participants. A close comparison is presented between human recognition performance and the performance of a computational neural model that exclusively modeled feedforward processing and was engineered to fulfill the computational requirements of recognition. Results show that the longer the stimulus onset asynchrony (SOA), the closer the performance of the human participants was to the values predicted by the model, with an optimum at an SOA of 100 ms. At short SOA latencies, human performance deteriorated, but the categorization of the emotional expressions was still above baseline. The data suggest that, although theoretically, feedback arising from inferotemporal cortex is likely to be blocked when the SOA is 100 ms, human participants still seem to rely on more local visual feedback processing to equal the model's performance.

CORTICAL PHASE TRANSITIONS: PROPERTIES DEMONSTRATED IN CONTINUUM SIMULATIONS AT MESOSCOPIC AND MACROSCOPIC SCALES

Continuum simulations of cortical dynamics permit consistent simulations to be performed at different spatial scales, using scale-adjusted parameter values. Properties of the simulations described here accord with Freeman's experimental and theoretical findings on gamma synchrony, phase transition, phase cones, and null spikes. State equations include effects of retrograde action potential propagation into dendritic trees, and kinetics of AMPA, GABA, and NMDA receptors. Realistic field potentials and pulse rates, gamma resonance and oscillation, and 1/f2 background activity are obtained. Zero-lag synchrony and traveling waves occur as complementary aspects of cortical transmission, and lead/lag relations between excitatory and inhibitory cell populations vary systematically around transition to autonomous gamma oscillation. Autonomous gamma is initiated by focal excitation of excitatory cells and suppressed by laterally spreading trans-cortical excitation. By implication, patches of cortex excited to gamma oscillation can mutually synchronize into larger fields, self-organized into sequences by mutual negative feedback relations, while the sequence of synchronous fields is regulated both by cortical/subcortical interactions and by traveling waves in the cortex — the latter observable as phase cones. At a critical level of cortical excitation, just before transition to autonomous gamma, patches of cortex exhibit selective sensitivity to action potential pulse trains modulated in the gamma band, while autonomous gamma releases pulse trains modulated in the same band, implying coupling of input and output modes. Transition between input and output modes may be heralded by phase slips and null spikes. Synaptic segregation by retrograde action potential propagation implies state-specific synaptic information storage.

Synchronous chaos and broad band gamma rhythm in a minimal multi-layer model of primary visual cortex

Visually induced neuronal activity in V1 displays a marked gamma-band component which is modulated by stimulus properties. It has been argued that synchronized oscillations contribute to these gamma-band activity. However, analysis of Local Field Potentials (LFPs) across different experiments reveals considerable diversity in the degree of oscillatory behavior of this induced activity. Contrast-dependent power enhancements can indeed occur over a broad band in the gamma frequency range and spectral peaks may not arise at all. Furthermore, even when oscillations are observed, they undergo temporal decorrelation over very few cycles. This is not easily accounted for in previous network modeling of gamma oscillations. We argue here that interactions between cortical layers can be responsible for this fast decorrelation. We study a model of a V1 hypercolumn, embedding a simplified description of the multi-layered structure of the cortex. When the stimulus contrast is low, the induced activity is only weakly synchronous and the network resonates transiently without developing collective oscillations. When the contrast is high, on the other hand, the induced activity undergoes synchronous oscillations with an irregular spatiotemporal structure expressing a synchronous chaotic state. As a consequence the population activity undergoes fast temporal decorrelation, with concomitant rapid damping of the oscillations in LFPs autocorrelograms and peak broadening in LFPs power spectra. We show that the strength of the inter-layer coupling crucially affects this spatiotemporal structure. We predict that layer VI inactivation should induce global changes in the spectral properties of induced LFPs, reflecting their slower temporal decorrelation in the absence of inter-layer feedback. Finally, we argue that the mechanism underlying the emergence of synchronous chaos in our model is in fact very general. It stems from the fact that gamma oscillations induced by local delayed inhibition tend to develop chaos when coupled by sufficiently strong excitation.

Visual stimulation elicits neuronal responses in visual cortex. When the contrast of the used stimuli increases, the power of this induced activity is boosted over a broad frequency range (30–100 Hz), called the “gamma band.” It would be tempting to hypothesize that this phenomenon is due to the emergence of oscillations in which many neurons fire collectively in a rhythmic way. However, previous models trying to explain contrast-related power enhancements using synchronous oscillations failed to reproduce the observed spectra because they originated unrealistically sharp spectral peaks. The aim of our study is to reconcile synchronous oscillations with broad-band power spectra. We argue here that, thanks to the interaction between neuronal populations at different depths in the cortical tissue, the induced oscillatory responses are synchronous, but, at the same time, chaotic. The chaotic nature of the dynamics makes it possible to have broad-band power spectra together with synchrony. Our modeling study allows us formulating qualitative experimental predictions that provide a potential test for our theory. We predict that if the interactions between cortical layers are suppressed, for instance by inactivating neurons in deep layers, the induced responses might become more regular and narrow isolated peaks might develop in their power spectra.

Brain rhythms reveal a hierarchical network organization

Recordings of ongoing neural activity with EEG and MEG exhibit oscillations of specific frequencies over a non-oscillatory background. The oscillations appear in the power spectrum as a collection of frequency bands that are evenly spaced on a logarithmic scale, thereby preventing mutual entrainment and cross-talk. Over the last few years, experimental, computational and theoretical studies have made substantial progress on our understanding of the biophysical mechanisms underlying the generation of network oscillations and their interactions, with emphasis on the role of neuronal synchronization. In this paper we ask a very different question. Rather than investigating how brain rhythms emerge, or whether they are necessary for neural function, we focus on what they tell us about functional brain connectivity. We hypothesized that if we were able to construct abstract networks, or "virtual brains", whose dynamics were similar to EEG/MEG recordings, those networks would share structural features among themselves, and also with real brains. Applying mathematical techniques for inverse problems, we have reverse-engineered network architectures that generate characteristic dynamics of actual brains, including spindles and sharp waves, which appear in the power spectrum as frequency bands superimposed on a non-oscillatory background dominated by low frequencies. We show that all reconstructed networks display similar topological features (e.g. structural motifs) and dynamics. We have also reverse-engineered putative diseased brains (epileptic and schizophrenic), in which the oscillatory activity is altered in different ways, as reported in clinical studies. These reconstructed networks show consistent alterations of functional connectivity and dynamics. In particular, we show that the complexity of the network, quantified as proposed by Tononi, Sporns and Edelman, is a good indicator of brain fitness, since virtual brains modeling diseased states display lower complexity than virtual brains modeling normal neural function. We finally discuss the implications of our results for the neurobiology of health and disease.

Is gamma-band activity in the local field potential of V1 cortex a "clock" or filtered noise?

Gamma-band (25-90 Hz) peaks in local field potential (LFP) power spectra are present throughout the cerebral cortex and have been related to perception, attention, memory, and disorders (e.g., schizophrenia and autism). It has been theorized that gamma oscillations provide a "clock" for precise temporal encoding and "binding" of signals about stimulus features across brain regions. For gamma to function as a clock, it must be autocoherent: phase and frequency conserved over a period of time. We computed phase and frequency trajectories of gamma-band bursts, using time-frequency analysis of LFPs recorded in macaque primary visual cortex (V1) during visual stimulation. The data were compared with simulations of random networks and clock signals in noise. Gamma-band bursts in LFP data were statistically indistinguishable from those found in filtered broadband noise. Therefore, V1 LFP data did not contain clock-like gamma-band signals. We consider possible functions for stochastic gamma-band activity, such as a synchronizing pulse signal.

Dynamic causal modeling with neural fields

The aim of this paper is twofold: first, to introduce a neural field model motivated by a well-known neural mass model; second, to show how one can estimate model parameters pertaining to spatial (anatomical) properties of neuronal sources based on EEG or LFP spectra using Bayesian inference. Specifically, we consider neural field models of cortical activity as generative models in the context of dynamic causal modeling (DCM). This paper considers the simplest case of a single cortical source modeled by the spatiotemporal dynamics of hidden neuronal states on a bounded cortical surface or manifold. We build this model using multiple layers, corresponding to cortical lamina in the real cortical manifold. These layers correspond to the populations considered in classical (Jansen and Rit) neural mass models. This allows us to formulate a neural field model that can be reduced to a neural mass model using appropriate constraints on its spatial parameters. In turn, this enables one to compare and contrast the predicted responses from equivalent neural field and mass models respectively. We pursue this using empirical LFP data from a single electrode to show that the parameters controlling the spatial dynamics of cortical activity can be recovered, using DCM, even in the absence of explicit spatial information in observed data.

A data-driven framework for neural field modeling

This paper presents a framework for creating neural field models from electrophysiological data. The Wilson and Cowan or Amari style neural field equations are used to form a parametric model, where the parameters are estimated from data. To illustrate the estimation framework, data is generated using the neural field equations incorporating modeled sensors enabling a comparison between the estimated and true parameters. To facilitate state and parameter estimation, we introduce a method to reduce the continuum neural field model using a basis function decomposition to form a finite-dimensional state-space model. Spatial frequency analysis methods are introduced that systematically specify the basis function configuration required to capture the dominant characteristics of the neural field. The estimation procedure consists of a two-stage iterative algorithm incorporating the unscented Rauch-Tung-Striebel smoother for state estimation and a least squares algorithm for parameter estimation. The results show that it is theoretically possible to reconstruct the neural field and estimate intracortical connectivity structure and synaptic dynamics with the proposed framework.

LFP spectral peaks in V1 cortex: network resonance and cortico-cortical feedback

This paper is about how cortical recurrent interactions in primary visual cortex (V1) together with feedback from extrastriate cortex can account for spectral peaks in the V1 local field potential (LFP). Recent studies showed that visual stimulation enhances the γ-band (25-90 Hz) of the LFP power spectrum in macaque V1. The height and location of the γ-band peak in the LFP spectrum were correlated with visual stimulus size. Extensive spatial summation, possibly mediated by feedback connections from extrastriate cortex and long-range horizontal connections in V1, must play a crucial role in the size dependence of the LFP. To analyze stimulus-effects on the LFP of V1 cortex, we propose a network model for the visual cortex that includes two populations of V1 neurons, excitatory and inhibitory, and also includes feedback to V1 from extrastriate cortex. The neural network model for V1 was a resonant system. The model's resonance frequency (ResF) was in the γ-band and varied up or down in frequency depending on cortical feedback. The model's ResF shifted downward with stimulus size, as in the real cortex, because increased size recruited more activity in extrastriate cortex and V1 thereby causing stronger feedback. The model needed to have strong local recurrent inhibition within V1 to obtain ResFs that agree with cortical data. Network resonance as a consequence of recurrent excitation and inhibition appears to be a likely explanation for γ-band peaks in the LFP power spectrum of the primary visual cortex.

Comparisons of the dynamics of local field potential and multiunit activity signals in macaque visual cortex

The local field potential (LFP) and multiunit activity (MUA) are extracellularly recorded signals that describe local neuronal network dynamics. In our experiments, the LFP and MUA, recorded from the same electrode in macaque primary visual cortex V1 in response to drifting grating visual stimuli, were evaluated on coarse timescales (∼1-5 s) and fine timescales (<0.1 s). On coarse timescales, MUA and the LFP both produced sustained visual responses to optimal and non-optimal oriented visual stimuli. The sustainedness of the two signals across the population of recording sites was correlated (correlation coefficient, ∼0.4). At most recording sites, the MUA was at least as sustained as the LFP and significantly more sustained for optimal orientations. In previous literature, the blood oxygen level-dependent (BOLD) signal of functional magnetic resonance imaging studies was found to be more strongly correlated with the LFP than with the MUA as a result of the lack of sustained response in the MUA signal. Because we found that MUA was as sustained as the LFP, MUA may also be correlated with BOLD. On fine timescales, we computed the coherence between the LFP and MUA over the frequency range 10-150 Hz. The LFP and MUA were weakly but significantly coherent (∼0.14) in the gamma band (20-90 Hz). The amount of gamma-band coherence was correlated with the power in the gamma band of the LFP. The data were consistent with the proposal that the LFP and MUA are generated in a noisy, resonant cortical network.

Attractor dynamics and thermodynamic analogies in the cerebral cortex: synchronous oscillation, the background EEG, and the regulation of attention

Ongoing changes in attention and cognition depend upon cortical/subcortical interactions, which select sequences of different spatial patterns of activation in the cortex. It is proposed that each pattern of cortical activation permits evolution of electrocortical wave activity toward statistically stationary states, analogous to thermodynamic equilibrium. In each steady-state, neurons fire with an intrinsic Poisson spike probability and also with a bursting pattern related to network oscillations. Excitatory cell dendrites act as a regenerative reservoir in which pulse generation is balanced against dissipations. Equilibria exhibit contrasting limits. One limit, at high cortical activation, generates widespread zero-lag synchrony among excitatory cells, with partial suppression of noise. Excitatory and inhibitory cells approach zero-lag local correlation, with 1/4 cycle lag-correlation at greater distances of separation. The high-activation limit defines a correlated system of attractor basins, capable of co-ordinating synaptic modifications and intracortical signal generation. Suppression of noise would enhance convergence about attractor basins in the manner of simulated annealing, while, conversely, the persistence of some noise prevents network paralysis by phase locking. At the opposite limit-that of low activation-spikes and waves have low cross- and auto-correlation, but have wide-spectrum sensitivity to inputs. It is hypothesised that cortical regions, transiently at equilibrium near these extremes, engage in interaction with each other and with subcortical systems, to generate ongoing sequences of attention and cognition. This account is compatible with classical and recently observed experimental phenomena. The principle features inferred from a simplified linear mathematical account are reproduced in a more physiologically realistic and non-linear numerical simulation.

A mechanism for ultra-slow oscillations in the cortical default network

When the brain is in its noncognitive "idling" state, functional MRI measurements reveal the activation of default cortical networks whose activity is suppressed during cognitive processing. This default or background mode is characterized by ultra-slow BOLD oscillations (∼0.05 Hz), signaling extremely slow cycling in cortical metabolic demand across distinct cortical regions. Here we describe a model of the cortex which predicts that slow cycling of cortical activity can arise naturally as a result of nonlinear interactions between temporal (Hopf) and spatial (Turing) instabilities. The Hopf instability is triggered by delays in the inhibitory postsynaptic response, while the Turing instability is precipitated by increases in the strength of the gap-junction coupling between interneurons. We comment on possible implications for slow dendritic computation and information processing.

Neural population modes capture biologically realistic large scale network dynamics

Large scale brain networks are understood nowadays to underlie the emergence of cognitive functions, though the detailed mechanisms are hitherto unknown. The challenges in the study of large scale brain networks are amongst others their high dimensionality requiring significant computational efforts, the complex connectivity across brain areas and the associated transmission delays, as well as the stochastic nature of neuronal processes. To decrease the computational effort, neurons are clustered into neural masses, which then are approximated by reduced descriptions of population dynamics. Here, we implement a neural population mode approach (Assisi et al. in Phys. Rev. Lett. 94(1):018106, 2005; Stefanescu and Jirsa in PLoS Comput. Biol. 4(11):e1000219, 2008), which parsimoniously captures various types of population behavior. We numerically demonstrate that the reduced population mode system favorably captures the high-dimensional dynamics of neuron networks with an architecture involving homogeneous local connectivity and a large-scale, fiber-like connection with time delay.

Searching for autocoherence in the cortical network with a time-frequency analysis of the local field potential

Gamma-band peaks in the power spectrum of local field potentials (LFP) are found in multiple brain regions. It has been theorized that gamma oscillations may serve as a 'clock' signal for the purposes of precise temporal encoding of information and 'binding' of stimulus features across regions of the brain. Neurons in model networks may exhibit periodic spike firing or synchronized membrane potentials that give rise to a gamma-band oscillation that could operate as a 'clock'. The phase of the oscillation in such models is conserved over the length of the stimulus. We define these types of oscillations to be 'autocoherent'. We investigated the hypothesis that autocoherent oscillations are the basis of the experimentally observed gamma-band peaks: the autocoherent oscillator (ACO) hypothesis. To test the ACO hypothesis, we developed a new technique to analyze the autocoherence of a time-varying signal. This analysis used the continuous Gabor transform to examine the time evolution of the phase of each frequency component in the power spectrum. Using this analysis method, we formulated a statistical test to compare the ACO hypothesis with measurements of the LFP in macaque primary visual cortex, V1. The experimental data were not consistent with the ACO hypothesis. Gamma-band activity recorded in V1 did not have the properties of a 'clock' signal during visual stimulation. We propose instead that the source of the gamma-band spectral peak is the resonant V1 network driven by random inputs.

Axonal velocity distributions in neural field equations

By modelling the average activity of large neuronal populations, continuum mean field models (MFMs) have become an increasingly important theoretical tool for understanding the emergent activity of cortical tissue. In order to be computationally tractable, long-range propagation of activity in MFMs is often approximated with partial differential equations (PDEs). However, PDE approximations in current use correspond to underlying axonal velocity distributions incompatible with experimental measurements. In order to rectify this deficiency, we here introduce novel propagation PDEs that give rise to smooth unimodal distributions of axonal conduction velocities. We also argue that velocities estimated from fibre diameters in slice and from latency measurements, respectively, relate quite differently to such distributions, a significant point for any phenomenological description. Our PDEs are then successfully fit to fibre diameter data from human corpus callosum and rat subcortical white matter. This allows for the first time to simulate long-range conduction in the mammalian brain with realistic, convenient PDEs. Furthermore, the obtained results suggest that the propagation of activity in rat and human differs significantly beyond mere scaling. The dynamical consequences of our new formulation are investigated in the context of a well known neural field model. On the basis of Turing instability analyses, we conclude that pattern formation is more easily initiated using our more realistic propagator. By increasing characteristic conduction velocities, a smooth transition can occur from self-sustaining bulk oscillations to travelling waves of various wavelengths, which may influence axonal growth during development. Our analytic results are also corroborated numerically using simulations on a large spatial grid. Thus we provide here a comprehensive analysis of empirically constrained activity propagation in the context of MFMs, which will allow more realistic studies of mammalian brain activity in the future.

The generation of rhythms within a cortical region: analysis of a neural mass model

Rhythms in brain electrical activity are assumed to play a significant role in many cognitive and perceptual processes. It is thus of great value to analyze these rhythms and their mutual relationships in large scale models of cortical regions. In the present work, we modified the neural mass model by Wendling et al. (Eur. J. Neurosci. 15 (2002) 1499-1508) by including a new inhibitory self-loop among GABAA,fast interneurons. A theoretical analysis was performed to demonstrate that, thanks to this loop, GABAA,fast interneurons can produce a gamma rhythm in the power spectral density (PSD) even without the participation of the other neural populations. Then, the model of a whole cortical region, built upon four interconnected neural populations (pyramidal cells, excitatory, GABAA,slow and GABAA,fast interneurons) was investigated by changing the internal connectivity parameters. Results show that different rhythm combinations (beta and gamma, alpha and gamma, or a wide spectrum) can be obtained within the same region by simply altering connectivity values, without the need to change synaptic kinetics. Finally, two or three cortical regions were connected by using different topologies of long range connections. Results show that long-range connections directed from pyramidal neurons to GABAA,fast interneurons are the most efficient to transmit rhythms from one region to another. In this way, PSD with three or four peaks can be obtained using simple connectivity patterns. The model can be of value to gain a deeper insight into the mechanisms involved in the generation of gamma rhythms and provide a better understanding of cortical EEG spectra.

Neurophysiological changes with age probed by inverse modeling of EEG spectra

OBJECTIVE

To investigate age-associated changes in physiologically-based EEG spectral parameters in the healthy population.

METHODS

Eyes-closed EEG spectra of 1498 healthy subjects aged 6-86 years were fitted to a mean-field model of thalamocortical dynamics in a cross-sectional study. Parameters were synaptodendritic rates, cortical wave decay rates, connection strengths (gains), axonal delays for thalamocortical loops, and power normalizations. Age trends were approximated using smooth asymptotically linear functions with a single turning point. We also considered sex differences and relationships between model parameters and traditional quantitative EEG measures.

RESULTS

The cross-sectional data suggest that changes tend to be most rapid in childhood, generally leveling off at age 15-20 years. Most gains decrease in magnitude with age, as does power normalization. Axonal and dendritic delays decrease in childhood and then increase. Axonal delays and gains show small but significant sex differences.

CONCLUSIONS

Mean-field brain modeling allows interpretation of age-associated EEG trends in terms of physiological processes, including the growth and regression of white matter, influencing axonal delays, and the establishment and pruning of synaptic connections, influencing gains.

SIGNIFICANCE

This study demonstrates the feasibility of inverse modeling of EEG spectra as a noninvasive method for investigating large-scale corticothalamic dynamics, and provides a basis for future comparisons.

Spike-timing-dependent plasticity leads to gamma band responses in a neural network

Early gamma band responses of the human electroencephalogram have been identified as an early interface linking top-down and bottom-up processing. This was based on findings that observed strong sensitivity of this signal to stimulus size and at the same time, to processes of attention and memory. Here, we simulate these findings in a simple random network of biologically plausible spiking neurons. During a learning phase, different stimuli were presented to the network and the synaptic connections were modified according to a spike-timing-dependent plasticity learning rule. In a subsequent test phase, we stimulated the network with (i) patterns of different sizes to simulate bottom-up effects and (ii) with patterns that were or were not presented during the learning phase. The network displayed qualitatively similar behavior as early gamma band responses measured from the scalp of human subjects: there was a general increase in response strength with increasing stimulus size and stronger responses for learned stimuli. We demonstrated that within one neural architecture early gamma band responses can be modulated both by bottom-up factors and by basal learning mechanisms mediated via spike-timing-dependent plasticity.

Mean-field modeling of the basal ganglia-thalamocortical system. I Firing rates in healthy and parkinsonian states

Parkinsonism leads to various electrophysiological changes in the basal ganglia-thalamocortical system (BGTCS), often including elevated discharge rates of the subthalamic nucleus (STN) and the output nuclei, and reduced activity of the globus pallidus external (GPe) segment. These rate changes have been explained qualitatively in terms of the direct/indirect pathway model, involving projections of distinct striatal populations to the output nuclei and GPe. Although these populations partly overlap, evidence suggests dopamine depletion differentially affects cortico-striato-pallidal connection strengths to the two pallidal segments. Dopamine loss may also decrease the striatal signal-to-noise ratio, reducing both corticostriatal coupling and striatal firing thresholds. Additionally, nigrostriatal degeneration may cause secondary changes including weakened lateral inhibition in the GPe, and mesocortical dopamine loss may decrease intracortical excitation and especially inhibition. Here a mean-field model of the BGTCS is presented with structure and parameter estimates closely based on physiology and anatomy. Changes in model rates due to the possible effects of dopamine loss listed above are compared with experiment. Our results suggest that a stronger indirect pathway, possibly combined with a weakened direct pathway, is compatible with empirical evidence. However, altered corticostriatal connection strengths are probably not solely responsible for substantially increased STN activity often found. A lower STN firing threshold, weaker intracortical inhibition, and stronger striato-GPe inhibition help explain the relatively large increase in STN rate. Reduced GPe-GPe inhibition and a lower GPe firing threshold can account for the comparatively small decrease in GPe rate frequently observed. Changes in cortex, GPe, and STN help normalize the cortical rate, also in accord with experiments. The model integrates the basal ganglia into a unified framework along with an existing thalamocortical model that already accounts for a wide range of electrophysiological phenomena. A companion paper discusses the dynamics and oscillations of this combined system.

Mean-field modeling of the basal ganglia-thalamocortical system. II Dynamics of parkinsonian oscillations

Neuronal correlates of Parkinson's disease (PD) include a shift to lower frequencies in the electroencephalogram (EEG) and enhanced synchronized oscillations at 3-7 and 7-30 Hz in the basal ganglia, thalamus, and cortex. This study describes the dynamics of a recent physiologically based mean-field model of the basal ganglia-thalamocortical system, and shows how it accounts for many key electrophysiological correlates of PD. Its detailed functional connectivity comprises partially segregated direct and indirect pathways through two populations of striatal neurons, a hyperdirect pathway involving a corticosubthalamic projection, thalamostriatal feedback, and local inhibition in striatum and external pallidum (GPe). In a companion paper, realistic steady-state firing rates were obtained for the healthy state, and after dopamine loss modeled by weaker direct and stronger indirect pathways, reduced intrapallidal inhibition, lower firing thresholds of the GPe and subthalamic nucleus (STN), a stronger projection from striatum to GPe, and weaker cortical interactions. Here it is shown that oscillations around 5 and 20 Hz can arise with a strong indirect pathway, which also causes increased synchronization throughout the basal ganglia. Furthermore, increased theta power with progressive nigrostriatal degeneration is correlated with reduced alpha power and peak frequency, in agreement with empirical results. Unlike the hyperdirect pathway, the indirect pathway sustains oscillations with phase relationships that coincide with those found experimentally. Alterations in the responses of basal ganglia to transient stimuli accord with experimental observations. Reduced cortical gains due to both nigrostriatal and mesocortical dopamine loss lead to slower changes in cortical activity and may be related to bradykinesia. Finally, increased EEG power found in some studies may be partly explained by a lower effective GPe firing threshold, reduced GPe-GPe inhibition, and/or weaker intracortical connections in parkinsonian patients. Strict separation of the direct and indirect pathways is not necessary to obtain these results.

Modeling brain activation patterns for the default and cognitive states

We argue that spatial patterns of cortical activation observed with EEG, MEG and fMRI might arise from spontaneous self-organisation of interacting populations of excitatory and inhibitory neurons. We examine the dynamical behavior of a mean-field cortical model that includes chemical and electrical (gap-junction) synapses, focusing on two limiting cases: the "slow-soma" limit with slow voltage feedback from soma to dendrite, and the "fast-soma" limit in which the feedback action of soma voltage onto dendrite reversal potentials is instantaneous. For slow soma-dendrite feedback, we find a low-frequency (approximately 1 Hz) dynamic Hopf instability, and a stationary Turing instability that catalyzes formation of patterned distributions of cortical firing-rate activity with pattern wavelength approximately 2 cm. Turing instability can only be triggered when gap-junction diffusion between inhibitory neurons is strong, but patterning is destroyed if the tonic level of subcortical excitation is raised sufficiently. Interaction between the Hopf and Turing instabilities may describe the non-cognitive background or "default" state of the brain, as observed by BOLD imaging. In the fast-soma limit, the model predicts a high-frequency Hopf (approximately 35 Hz) instability, and a traveling-wave gamma-band instability that manifests as a 2-D standing-wave pattern oscillating in place at approximately 30 Hz. Small levels of inhibitory diffusion enhance and broaden the definition of the gamma antinodal regions by suppressing higher-frequency spatial modes, but gamma emergence is not contingent on the presence of inhibitory gap junctions; higher levels of diffusion suppress gamma activity. Fast-soma instabilities are enhanced by increased subcortical stimulation. Prompt soma-dendrite feedback may be an essential component of the genesis and large-scale cortical synchrony of gamma activity observed at the point of cognition.

Generation and control of cortical gamma: findings from simulation at two scales

A continuum model of electrocortical activity was applied separately at centimetric and macrocolumnar scales, permitting analysis of interaction between scales. State equations included effects of retrograde action potential propagation in dendritic trees, and kinetics of AMPA, GABA and NMDA receptors. Parameter values were provided from independent physiological and anatomical estimates. Realistic field potentials and pulse rates were obtained, including resonances in the alpha/theta and gamma ranges, 1/f(2) background activity, and autonomous gamma activity. Zero-lag synchrony and travelling waves occurred as complementary aspects of cortical transmission, and lead/lag relations between excitatory and inhibitory cell populations varied systematically around transition to autonomous gamma oscillation. Properties of the simulations can account for generation and control of gamma activity. All factors acting on excitatory/inhibitory balance controlled the onset and offset of gamma oscillation. Autonomous gamma was initiated by focal excitation of excitatory cells, and suppressed by laterally spreading trans-cortical excitation, which acted on both excitatory and inhibitory cell populations. Consequently, although spatially extensive non-specific reticular activation tended to suppress autonomous gamma, spatial variation of reticular activation could preferentially select fields of synchrony.

Mean field model of acetylcholine mediated dynamics in the thalamocortical system

A recent continuum model of the large scale electrical activity of the thalamocortical system is generalized to include cholinergic modulation. The model is examined analytically and numerically to determine the effect of acetylcholine (ACh) on its steady states, linear stability, spectrum, and temporal responses. Changing the ACh concentration moves the system between zones of one, three, and five steady states, showing that neuromodulation of synaptic strength is a possible mechanism by which multiple steady states emerge in the brain. The lowest firing rate steady state is always stable, and subsequent fixed points alternate between stable and unstable. Increasing ACh concentration changes the form of the spectrum. Increasing the tonic level of ACh concentration increases the magnitudes of the N100 and P200 in the evoked response potential (ERP), without changing the timing of these peaks. Driving the system with a pulse of cholinergic activity results in a transient increase in the firing rate of cortical neurons that lasts over 10s. Step-like increases in cortical ACh concentration cause increases in the firing rate of cortical neurons, with rapid responses due to fast acting nicotinic receptors and slower responses due to muscarinic receptor suppression of intracortical connections.

Characteristics of temporal fluctuations in the hyperpolarized state of the cortical slow oscillation

We present evidence for the hypothesis that transitions between the low- and high-firing states of the cortical slow oscillation correspond to neuronal phase transitions. By analyzing intracellular recordings of the membrane potential during the cortical slow oscillation in rats, we quantify the temporal fluctuations in power and the frequency centroid of the power spectrum in the period of time before "down" to "up" transitions. By taking appropriate averages over such events, we present these statistics as a function of time before transition. The results demonstrate an increase in fluctuation power and time scale broadly consistent with the slowing of systems close to phase transitions. The analysis is complicated and limited by the difficulty in identifying when transitions begin, and removing dc trends in membrane potential.

Anticipation of natural stimuli modulates EEG dynamics: physiology and simulation

In everyday life we often encounter situations in which we can expect a visual stimulus before we actually see it. Here, we study the impact of such stimulus anticipation on the actual response to a visual stimulus. Participants were to indicate the sex of deer and cattle on photographs of the respective animals. On some trials, participants were cued on the species of the upcoming animal whereas on other trials this was not the case. Time frequency analysis of the simultaneously recorded EEG revealed modulations by this cue stimulus in two time windows. Early [Formula: see text] spectral responses [Formula: see text] displayed strongest stimulus-locking for stimuli that were preceded by a cue if they were sufficiently large. Late [Formula: see text] responses displayed enhanced amplitudes in response to large stimuli and to stimuli that were preceded by a cue. For late responses, however, no interaction between cue and stimulus size was observed. We were able to explain these results in a simulation by prestimulus gain modulations (early response) and by decreased response thresholds (late response). Thus, it seems plausible, that stimulus anticipation results in a pretuning of local neural populations.

Mean field model of acetylcholine mediated dynamics in the cerebral cortex

A recent continuum model of the large scale electrical activity of the cerebral cortex is generalized to include cholinergic modulation. In this model, dynamic modulation of synaptic strength acts over the time scales of nicotinic and muscarinic receptor action. The cortical model is analyzed to determine the effect of acetylcholine (ACh) on its steady states, linear stability, spectrum, and temporal responses to changes in subcortical input. ACh increases the firing rate in steady states of the system. Changing ACh concentration does not introduce oscillatory behavior into the system, but increases the overall spectral power. Model responses to pulses in subcortical input are affected by the tonic level of ACh concentration, with higher levels of ACh increasing the magnitude firing rate response of excitatory cortical neurons to pulses of subcortical input. Numerical simulations are used to explore the temporal dynamics of the model in response to changes in ACh concentration. Evidence is seen of a transition from a state in which intracortical inputs are emphasized to a state where thalamic afferents have enhanced influence. Perturbations in ACh concentration cause changes in the firing rate of cortical neurons, with rapid responses due to fast acting facilitatory effects of nicotinic receptors on subcortical afferents, and slower responses due to muscarinic suppression of intracortical connections. Together, these numerical simulations demonstrate that the actions of ACh could be a significant factor modulating early components of evoked response potentials.

Visual gamma oscillations: waves, correlations, and other phenomena, including comparison with experimental data

Mean-field theory of brain dynamics is applied to explain the properties of gamma (> or approximately 30 Hz) oscillations of cortical activity often seen during vision experiments. It is shown that mm-scale patchy connections in the primary visual cortex can support collective gamma oscillations with the correct frequencies and spatial structure, even when driven by uncorrelated inputs. This occurs via resonances associated with the the periodic modulation of the network connections, rather than being due to single-cell properties alone. Near-resonant gamma waves are shown to obey the Schrödinger equation, which enables techniques and insights from quantum theory to be used in exploring these classical oscillations. Resulting predictions for gamma responses to stimuli account in a unified way for a wide range of experimental results, including why oscillations and zero-lag synchrony are associated, and variations in correlation functions with time delay, intercellular distance, and stimulus features. They also imply that gamma oscillations may enable a form of frequency multiplexing of neural signals. Most importantly, it is shown that correlations reproduce experimental results that show maximal correlations between cells that respond to related features, but little correlation with other cells, an effect that has been argued to be associated with segmentation of a scene into separate objects. Consistency with infill of missing contours and increase in response with length of bar-shaped stimuli are discussed. Background correlations expected in the absence of stimulation are also calculated and shown to be consistent in form with experimental measurements and similar to stimulus-induced correlations in structure. Finally, possible links of gamma instabilities to certain classes of photically induced seizures and visual hallucinations are discussed.