Uncovering the synchronization dynamics from correlated neuronal activity quantifies assembly formation

EEG Synchronization-Parameters in Patients With Subcortical Arteriosclerotic Encephalopathy and Gait Disorder

PURPOSE

Subcortical arteriosclerotic encephalopathy (SAE) is characterized by extensive white matter lesions in the MRI. Clinical symptoms are cognitive impairment, ranging from mild deficits to vascular dementia, impaired executive functioning, and gait disorders. In the EEG of SAE patients with vascular dementia, the lower frequencies are increased. However, it is unclear whether EEG changes also exist in SAE patients with gait disorders but without vascular dementia.

METHODS

The authors analyzed the EEGs of 50 nondemented patients with SAE and gait disorders and 50 healthy controls applying pointwise transinformation as a measure of synchronization.

RESULTS

Hundred seconds of waking EEG that appeared unaltered in visual analysis were sufficient to prove changes in synchronization. The authors found a decrease in the mean level of synchronization, combined with an elongation of synchronization time in all examined brain areas. These effects correlated slightly with the extent of subcortical lesions.

CONCLUSIONS

Changes in EEG synchronization in patients with SAE and gait disorders seem to occur independently of cognitive function. The causal relationship of the changes in EEG synchronization and gait disorders remains to be clarified. The results of this study might point to a decrease in coupling efficiency in these patients, with the increase in synchronization duration as a possible compensatory mechanism. Because a time-efficient signal transmission particularly during gait execution is crucial, reduced efficiency might contribute to an impairment of postural stabilization. The study results might indicate a neuronal network for planning and execution of motor activity and particularly gait, extending from the frontal over the central to the parietal cortex.

Attractor-state itinerancy in neural circuits with synaptic depression

Neural populations with strong excitatory recurrent connections can support bistable states in their mean firing rates. Multiple fixed points in a network of such bistable units can be used to model memory retrieval and pattern separation. The stability of fixed points may change on a slower timescale than that of the dynamics due to short-term synaptic depression, leading to transitions between quasi-stable point attractor states in a sequence that depends on the history of stimuli. To better understand these behaviors, we study a minimal model, which characterizes multiple fixed points and transitions between them in response to stimuli with diverse time- and amplitude-dependencies. The interplay between the fast dynamics of firing rate and synaptic responses and the slower timescale of synaptic depression makes the neural activity sensitive to the amplitude and duration of square-pulse stimuli in a nontrivial, history-dependent manner. Weak cross-couplings further deform the basins of attraction for different fixed points into intricate shapes. We find that while short-term synaptic depression can reduce the total number of stable fixed points in a network, it tends to strongly increase the number of fixed points visited upon repetitions of fixed stimuli. Our analysis provides a natural explanation for the system's rich responses to stimuli of different durations and amplitudes while demonstrating the encoding capability of bistable neural populations for dynamical features of incoming stimuli.

Uncovering temporal structure in hippocampal output patterns

Place cell activity of hippocampal pyramidal cells has been described as the cognitive substrate of spatial memory. Replay is observed during hippocampal sharp-wave-ripple-associated population burst events (PBEs) and is critical for consolidation and recall-guided behaviors. PBE activity has historically been analyzed as a phenomenon subordinate to the place code. Here, we use hidden Markov models to study PBEs observed in rats during exploration of both linear mazes and open fields. We demonstrate that estimated models are consistent with a spatial map of the environment, and can even decode animals’ positions during behavior. Moreover, we demonstrate the model can be used to identify hippocampal replay without recourse to the place code, using only PBE model congruence. These results suggest that downstream regions may rely on PBEs to provide a substrate for memory. Additionally, by forming models independent of animal behavior, we lay the groundwork for studies of non-spatial memory.

Itinerancy between attractor states in neural systems

Converging evidence from neural, perceptual and simulated data suggests that discrete attractor states form within neural circuits through learning and development. External stimuli may bias neural activity to one attractor state or cause activity to transition between several discrete states. Evidence for such transitions, whose timing can vary across trials, is best accrued through analyses that avoid any trial-averaging of data. One such method, hidden Markov modeling, has been effective in this context, revealing state transitions in many neural circuits during many tasks. Concurrently, modeling efforts have revealed computational benefits of stimulus processing via transitions between attractor states. This review describes the current state of the field, with comments on how its perceived limitations have been addressed.

A Recurrent Increase of Synchronization in the EEG Continues from Waking throughout NREM and REM Sleep

Pointwise transinformation (PTI) provides a quantitative nonlinear approach to spatiotemporal synchronization patterns of the rhythms of coupled cortical oscillators. We applied PTI to the waking and sleep EEGs of 21 healthy sleepers; we calculated the mean levels and distances of synchronized episodes and estimated the dominant frequency shift from unsynchronized to synchronized EEG segments by spectral analysis. Recurrent EEG synchronization appeared and ceased abruptly in the anterior, central, and temporal derivations; in the posterior derivations it appeared more fluctuating. This temporal dynamics of synchronization remained stable throughout all states of vigilance, while the dominant frequencies of synchronized phases changed markedly. Mean synchronization had high frontal and occipital levels and low central and midtemporal levels. Thus, a fundamental coupling pattern with recurrent increases of synchronization in the EEG (“RISE”) seems to exist during the brain's resting state. The generators of RISE could be coupled corticocortical neuronal assemblies which might be modulated by subcortical structures. RISE designates the recurrence of transiently synchronized cortical microstates that are independent of specific EEG waves, the spectral content of the EEG, and especially the current state of vigilance. Therefore, it might be suited for EEG analysis in clinical situations without stable vigilance.

Rates and rhythms: a synergistic view of frequency and temporal coding in neuronal networks

In the CNS, activity of individual neurons has a small but quantifiable relationship to sensory representations and motor outputs. Coactivation of a few 10s to 100s of neurons can code sensory inputs and behavioral task performance within psychophysical limits. However, in a sea of sensory inputs and demand for complex motor outputs how is the activity of such small subpopulations of neurons organized? Two theories dominate in this respect: increases in spike rate (rate coding) and sharpening of the coincidence of spiking in active neurons (temporal coding). Both have computational advantages and are far from mutually exclusive. Here, we review evidence for a bias in neuronal circuits toward temporal coding and the coexistence of rate and temporal coding during population rhythm generation. The coincident expression of multiple types of gamma rhythm in sensory cortex suggests a mechanistic substrate for combining rate and temporal codes on the basis of stimulus strength.

Pointwise transinformation distinguishes a recurrent increase of synchronization in the rapid eye movement sleep electroencephalogram

The analysis of electroencephalogram (EEG) coupling patterns is essential for understanding how interrelations between cortical sites change with the wake-sleep cycle. Waking and sleep EEGs of 12 normal sleepers were analyzed by pointwise transinformation (PTI). Stage-dependent differences of PTI were assessed, and a spectral analysis of synchronized events was performed. A pattern of recurrent EEG synchronization was distinguished in all rapid eye movement (REM) sleep phases. The mean coupling of EEG leads differed regionally, with high coupling levels of frontal and occipital derivations and lower midtemporal and central coupling levels. Mean coupling levels were comparable in stages R, W, and N1 but were lower than in N2 and N3. An REM-specific pattern of low EEG synchronization was identified for F7-F8 and T3-T4, with lowest coupling levels during tonic REM sleep. Also, maximal intervals of uncoupled EEG were longer during tonic REM sleep. Because of these results, a new descriptive entity is proposed: the recurrent increase of synchronization in the EEG (RISE). This seems to reflect the dynamic aspects of spatiotemporal EEG synchronization on small time scales. A possibly specific low coupling pattern of the temporal leads may distinguish REM sleep from other states with a "desynchronized" EEG and, to some extent, tonic from phasic REM sleep.

Modeling carbachol-induced hippocampal network synchronization using hidden Markov models

In this work we studied the neural state transitions undergone by the hippocampal neural network using a hidden Markov model (HMM) framework. We first employed a measure based on the Lempel-Ziv (LZ) estimator to characterize the changes in the hippocampal oscillation patterns in terms of their complexity. These oscillations correspond to different modes of hippocampal network synchronization induced by the cholinergic agonist carbachol in the CA1 region of mice hippocampus. HMMs are then used to model the dynamics of the LZ-derived complexity signals as first-order Markov chains. Consequently, the signals corresponding to our oscillation recordings can be segmented into a sequence of statistically discriminated hidden states. The segmentation is used for detecting transitions in neural synchronization modes in data recorded from wild-type and triple transgenic mice models (3xTG) of Alzheimer's disease (AD). Our data suggest that transition from low-frequency (delta range) continuous oscillation mode into high-frequency (theta range) oscillation, exhibiting repeated burst-type patterns, occurs always through a mode resembling a mixture of the two patterns, continuous with burst. The relatively random patterns of oscillation during this mode may reflect the fact that the neuronal network undergoes re-organization. Further insight into the time durations of these modes (retrieved via the HMM segmentation of the LZ-derived signals) reveals that the mixed mode lasts significantly longer (p < 10(-4)) in 3xTG AD mice. These findings, coupled with the documented cholinergic neurotransmission deficits in the 3xTG mice model, may be highly relevant for the case of AD.

Detecting neural-state transitions using hidden Markov models for motor cortical prostheses

Neural prosthetic interfaces use neural activity related to the planning and perimovement epochs of arm reaching to afford brain-directed control of external devices. Previous research has primarily centered on accurately decoding movement intention from either plan or perimovement activity, but has assumed that temporal boundaries between these epochs are known to the decoding system. In this work, we develop a technique to automatically differentiate between baseline, plan, and perimovement epochs of neural activity. Specifically, we use a generative model of neural activity to capture how neural activity varies between these three epochs. Our approach is based on a hidden Markov model (HMM), in which the latent variable (state) corresponds to the epoch of neural activity, coupled with a state-dependent Poisson firing model. Using an HMM, we demonstrate that the time of transition from baseline to plan epochs, a transition in neural activity that is not accompanied by any external behavior changes, can be detected using a threshold on the a posteriori HMM state probabilities. Following detection of the plan epoch, we show that the intended target of a center-out movement can be detected about as accurately as that by a maximum-likelihood estimator using a window of known plan activity. In addition, we demonstrate that our HMM can detect transitions in neural activity corresponding to targets not found in training data. Thus the HMM technique for automatically detecting transitions between epochs of neural activity enables prosthetic interfaces that can operate autonomously.

Messages of Oscillatory Correlograms: A Spike Train Model

Oscillatory correlograms are widely used to study neuronal activity that shows a joint periodic rhythm. In most cases, the statistical analysis of cross-correlation histograms (CCH) features is based on the null model of independent processes, and the resulting conclusions about the underlying processes remain qualitative. Therefore, we propose a spike train model for synchronous oscillatory firing activity that directly links characteristics of the CCH to parameters of the underlying processes. The model focuses particularly on asymmetric central peaks, which differ in slope and width on the two sides. Asymmetric peaks can be associated with phase offsets in the (sub-) millisecond range. These spatiotemporal firing patterns can be highly consistent across units yet invisible in the underlying processes. The proposed model includes a single temporal parameter that accounts for this peak asymmetry.

The model provides approaches for the analysis of oscillatory correlograms, taking into account dependencies and nonstationarities in the underlying processes. In particular, the auto- and the cross-correlogram can be investigated in a joint analysis because they depend on the same spike train parameters. Particular temporal interactions such as the degree to which different units synchronize in a common oscillatory rhythm can also be investigated. The analysis is demonstrated by application to a simulated data set.

Spike correlations in a songbird agree with a simple markov population model

The relationships between neural activity at the single-cell and the population levels are of central importance for understanding neural codes. In many sensory systems, collective behaviors in large cell groups can be described by pairwise spike correlations. Here, we test whether in a highly specialized premotor system of songbirds, pairwise spike correlations themselves can be seen as a simple corollary of an underlying random process. We test hypotheses on connectivity and network dynamics in the motor pathway of zebra finches using a high-level population model that is independent of detailed single-neuron properties. We assume that neural population activity evolves along a finite set of states during singing, and that during sleep population activity randomly switches back and forth between song states and a single resting state. Individual spike trains are generated by associating with each of the population states a particular firing mode, such as bursting or tonic firing. With an overall modification of one or two simple control parameters, the Markov model is able to reproduce observed firing statistics and spike correlations in different neuron types and behavioral states. Our results suggest that song- and sleep-related firing patterns are identical on short time scales and result from random sampling of a unique underlying theme. The efficiency of our population model may apply also to other neural systems in which population hypotheses can be tested on recordings from small neuron groups.

To deal with the vast complexity of the brain and its many degrees of freedom, many reductionist methods have been designed that can be used to simplify neural interactions to just a few key underlying macroscopic variables. Despite these theoretical advances, even today relatively few population models have been subjected to stringent experimental tests. We explore whether second-order spike correlations measured in songbirds can be explained by single-neuron statistics and population dynamics, both reflecting hypotheses on network connectivity. We formulate a Markov population model with essentially two degrees of freedom and associated with different behavioral states of birds such as waking, singing, or sleeping. Excellent agreement between spike-train data and model is achieved, given a few connectivity assumptions that strengthen the view of a hierarchical organization of songbird motor networks. This work is an important demonstration that a broad range of neural activity patterns can be compatible at the population level with few underlying degrees of freedom.

Techniques for extracting single-trial activity patterns from large-scale neural recordings

Large, chronically implanted arrays of microelectrodes are an increasingly common tool for recording from primate cortex and can provide extracellular recordings from many (order of 100) neurons. While the desire for cortically based motor prostheses has helped drive their development, such arrays also offer great potential to advance basic neuroscience research. Here we discuss the utility of array recording for the study of neural dynamics. Neural activity often has dynamics beyond that driven directly by the stimulus. While governed by those dynamics, neural responses may nevertheless unfold differently for nominally identical trials, rendering many traditional analysis methods ineffective. We review recent studies - some employing simultaneous recording, some not - indicating that such variability is indeed present both during movement generation and during the preceding premotor computations. In such cases, large-scale simultaneous recordings have the potential to provide an unprecedented view of neural dynamics at the level of single trials. However, this enterprise will depend not only on techniques for simultaneous recording but also on the use and further development of analysis techniques that can appropriately reduce the dimensionality of the data, and allow visualization of single-trial neural behavior.

Natural stimuli evoke dynamic sequences of states in sensory cortical ensembles

Although temporal coding is a frequent topic of neurophysiology research, trial-to-trial variability in temporal codes is typically dismissed as noise and thought to play no role in sensory function. Here, we show that much of this supposed "noise" faithfully reflects stimulus-related processes carried out in coherent neural networks. Cortical neurons responded to sensory stimuli by progressing through sequences of states, identifiable only in examinations of simultaneously recorded ensembles. The specific times at which ensembles transitioned from state to state varied from trial to trial, but the state sequences were reliable and stimulus-specific. Thus, the characterization of ensemble responses in terms of state sequences captured facets of sensory processing that are missing from, and obscured in, other analyses. This work provides evidence that sensory neurons act as parts of a systems-level dynamic process, the nature of which can best be appreciated through observation of distributed ensembles.

Detection of activation phases and quantification of coupling in NREM sleep EEG by pointwise transinformation

BACKGROUND

The coupling dynamics of two time series can be assessed by pointwise transinformation (PTI). Due to its high temporal resolution, this algorithm is ideal for analysis of sleep microstructure. Different types of electroencephalographic (EEG) activation phases, like single K-complexes, K-complexes associated with spindle or alpha activity, K-complexes mixed with delta waves, and arousals, can be detected and changes in EEG coupling can be quantified.

METHODS

Nine hundred ninety-one one-minute EEG segments (C3-A2/C4-A1) containing the described types of activation phases were selected from the sleep EEGs of 12 healthy persons. PTI was calculated with 250 Hz resolution and an embedding dimension of 20. An averaged PTI curve was assessed for single K-complexes and K-complexes followed by spindle and alpha activity, respectively.

RESULTS

During background activity, PTI was nearly 0. With the onset of a K-complex, PTI increased significantly in a sequence of distinct phases (rising - peak - decay). For single K-complexes, the PTI curve had a nearly symmetric dome-shaped form. The decay phase was prolonged by subsequent spindle or alpha activity. In K-complexes mixed with delta activity and in arousals, repetitive maxima of PTI were obtained. The durations of arousals and their coupling phases were correlated (r=0.83).

CONCLUSIONS

PTI displays the coupling dynamics of the sleep EEG with high resolution. It detects phases of activation represented by single K-complexes and various types of arousals. These induce a specific run of the PTI curve clearly distinguishable from background activity. PTI might, therefore, prove useful in the analysis of sleep microstructure.

Extracting the dynamics of perceptual switching from 'noisy' behaviour: an application of hidden Markov modelling to pecking data from pigeons

When studying animal perception, one normally has the chance of localizing perceptual events in time, that is via behavioural responses time-locked to the stimuli. With multistable stimuli, however, perceptual changes occur despite stationary stimulation. Here, the challenge is to infer these not directly observable perceptual states indirectly from the behavioural data. This estimation is complicated by the fact that an animal's performance is contaminated by errors. We propose a two-step approach to overcome this difficulty: First, one sets up a generative, stochastic model of the behavioural time series based on the relevant parameters, including the probability of errors. Second, one performs a model-based maximum-likelihood estimation on the data in order to extract the non-observable perceptual state transitions. We illustrate this methodology for data from experiments on perception of bistable apparent motion in pigeons. The observed behavioural time series is analysed and explained by a combination of a Markovian perceptual dynamics with a renewal process that governs the motor response. We propose a hidden Markov model in which non-observable states represent both the perceptual states and the states of the renewal process of the motor dynamics, while the observable states account for overt pecking performance. Showing that this constitutes an appropriate phenomenological model of the time series of observable pecking events, we use it subsequently to obtain an estimate of the internal (and thus covert) perceptual reversals. These may directly correspond to changes in the activity of mutually inhibitory populations of motion selective neurones tuned to orthogonal directions.

The time distribution of linked spike activity of rabbit sensorimotor cortex neurons in the presence of a rhythmic motor dominant

The existence of a cryptic stationary focus of excitation induced in the cortex by rhythmic electrical stimulation of the paw was detected using sound test stimuli which were previously indifferent to the experimental animals. Neuron activity was recorded in the sensorimotor cortex of rabbits. Neuron pairs were identified which operated in a correlated fashion in the dominant focus. Analysis of linked spike activity in such neuron pairs demonstrated the predominant appearance of linked spikes with intervals of about 2 sec when the focus was created by stimulation with a 2-sec rhythm; intervals were at or about 3 sec when the focus was created by stimulation with a 3-sec rhythm. The studies demonstrated that long-term persistence of the rhythmic nature of the dominant focus occurred at the level of interneuron interactions, i.e., it was a system process. The assimilated rhythm in linked cell activity was observed not only at the point of summation, when output was sent to an effector-i.e., when the dominant was realized as a movement response-but also in the intervals between test stimuli.

Neuronal assembly dynamics in the rat auditory cortex during reorganization induced by intracortical microstimulation

Single neurons, acting alone, cannot account for the complex and rapid computations that are routinely accomplished by the behaving nervous system. Recent studies with separable multineuron recordings are showing that neuronal assemblies can indeed be detected and that their organization is very dynamic, depending on variables such as time, physical stimulus, and context. Here we explore both single-neuron and assembly properties in the rat's auditory cortex. Acoustic stimuli are used as a normal, physiological input, and weak electrical intracortical microstimulation (ICMS) as a perturbation that forces a rapid cortical reorganization. In this setting, various aspects of neuronal interactions are changed by the ICMS. We found that cortical neurons exhibited highly synchronous oscillatory firing patterns that were enhanced by ICMS. Cross-correlation studies between two spike trains showed that statistically significant correlations depended on the anatomical distance between the two neurons. ICMS changed the strength and the local number of such correlations. Joint petristimulus analysis and gravity analysis showed that the correlation between neuronal activities varied dynamically at several time scales. We have identified neuronal assemblies in two ways, defined through similarity of receptive field properties and defined through correlated firing. Close anatomical spacing between neurons was conducive to, but not sufficient for membership in, the same assembly with either definition. ICMS changed cortical organization by altering assembly membership. Our data show that neuronal assemblies in the rat auditory cortex can be established transiently in time and that their membership is dynamic.

Temporal coding in vision: coding by the spike arrival times leads to oscillations in the case of moving targets

The 'oscillations' which have been observed in the visual cortex of cats and monkeys in the case of moving targets are discussed in relation to a temporal coding based on the arrival times of spikes or bursts. A decoding process for this temporal coding is proposed in which neurons work in a correlator mode. In the case of motion analysis, periodic resetting is needed to avoid information jamming. This resetting is proposed to be responsible for the 'oscillations'. Good initial synchronization is required for the decoding process to be performed efficiently. A diffusive process based on interdendritic ionic currents is proposed and shown to operate efficiently, without any loss of spatial and temporal resolving powers.

Cortical activity flips among quasi-stationary states

Parallel recordings of spike trains of several single cortical neurons in behaving monkeys were analyzed as a hidden Markov process. The parallel spike trains were considered as a multivariate Poisson process whose vector firing rates change with time. As a consequence of this approach, the complete recording can be segmented into a sequence of a few statistically discriminated hidden states, whose dynamics are modeled as a first-order Markov chain. The biological validity and benefits of this approach were examined in several independent ways: (i) the statistical consistency of the segmentation and its correspondence to the behavior of the animals; (ii) direct measurement of the collective flips of activity, obtained by the model; and (iii) the relation between the segmentation and the pair-wise short-term cross-correlations between the recorded spike trains. Comparison with surrogate data was also carried out for each of the above examinations to assure their significance. Our results indicated the existence of well-separated states of activity, within which the firing rates were approximately stationary. With our present data we could reliably discriminate six to eight such states. The transitions between states were fast and were associated with concomitant changes of firing rates of several neurons. Different behavioral modes and stimuli were consistently reflected by different states of neural activity. Moreover, the pair-wise correlations between neurons varied considerably between the different states, supporting the hypothesis that these distinct states were brought about by the cooperative action of many neurons.

Correlated firing in sensory-motor systems

Traditionally, synchronous firing of neurons has been considered to be an epiphenomenon of neuronal networks, reflecting particular properties of circuitry, but having no functional relevance. In the past few years, an alternative view has been advocated, which suggests that temporal correlations serve a role in information processing by expressing relations among the responses of distributed neurons. This hypothesis has received experimental support from recent in vivo studies performed on the sensory systems of a variety of species. These results support earlier proposals that correlated activity might have an important function in sensory-motor integration and memory.