Neuronal oscillations of different frequencies can interact in several ways. There has been particular interest in the modulation of the amplitude of high-frequency oscillations by the phase of low-frequency oscillations, since recent evidence suggests a functional role for this type of cross-frequency coupling (CFC). Phase-amplitude coupling has been reported in continuous electrophysiological signals obtained from the brain at both local and macroscopic levels. In the present work, we present a new measure for assessing phase-amplitude CFC. This measure is defined as an adaptation of the Kullback-Leibler distance-a function that is used to infer the distance between two distributions-and calculates how much an empirical amplitude distribution-like function over phase bins deviates from the uniform distribution. We show that a CFC measure defined this way is well suited for assessing the intensity of phase-amplitude coupling. We also review seven other CFC measures; we show that, by some performance benchmarks, our measure is especially attractive for this task. We also discuss some technical aspects related to the measure, such as the length of the epochs used for these analyses and the utility of surrogate control analyses. Finally, we apply the measure and a related CFC tool to actual hippocampal recordings obtained from freely moving rats and show, for the first time, that the CA3 and CA1 regions present different CFC characteristics.

Significance Anesthesiologists reversibly manipulate the brain function of nearly 60,000 patients each day, but brain-state monitoring is not an accepted practice in anesthesia care because markers that reliably track changes in level of consciousness under general anesthesia have yet to be identified. We found specific behavioral and electrophysiological changes that mark the transition between consciousness and unconsciousness induced by propofol, one of the most commonly used anesthetic drugs. Our results provide insights into the mechanisms of propofol-induced unconsciousness and establish EEG signatures of this brain state that could be used to monitor the brain activity of patients receiving general anesthesia.

Phase-amplitude cross-frequency coupling (CFC) between theta (4 -12 Hz) and gamma (30 -100 Hz) oscillations occurs frequently in the hippocampus. However, it still remains unclear whether thetagamma coupling has any functional significance. To address this issue, we studied CFC in local field potential oscillations recorded from the CA3 region of the dorsal hippocampus of rats as they learned to associate items with their spatial context. During the course of learning, the amplitude of the low gamma subband (30 -60 Hz) became more strongly modulated by theta phase in CA3, and higher levels of theta-gamma modulation were maintained throughout overtraining sessions. Furthermore, the strength of theta-gamma coupling was directly correlated with the increase in performance accuracy during learning sessions. These findings suggest a role for hippocampal theta-gamma coupling in memory recall.associative memory ͉ brain rhythms ͉ local field potential B rain oscillations have been classically divided into specific frequency ranges associated with multiple cognitive processes (1, 2). Oscillations in these frequency bands may occur simultaneously and can interact with each other (3, 4), suggesting that this coupling may reflect a higher-order representation (5, 6). In one type of interaction, the phase of low-frequency rhythms modulates the amplitude of higher-frequency oscillations (3). This type of cross-frequency coupling (CFC) is called phase-amplitude modulation, and its best known example occurs in the rodent hippocampus between the theta (4-12 Hz) phase and the amplitude of gamma (30-100 Hz) oscillations (6-9). Based on this finding, theoretical work has suggested that gamma and theta oscillations coordinate in support of a neural code (10-15). According to this view, events are represented by distinct neuronal ensembles, each contained within a distinct gamma cycle, and entire episodes are encoded by a succession of event-specific gamma cycles embedded into each theta cycle (12-15). These theories are elegant and appealing, but there is a paucity of evidence linking the existence of theta-gamma coupling to behavior (but see ref. 16). Therefore, it remains unclear whether the hippocampal theta-gamma coupling possesses any functional role (13).Here, we investigated coupling between theta and gamma rhythms as rats learned which of two stimuli was rewarded depending on the environmental context in which the stimuli were presented. Learning in this type of conditional discrimination task depends on hippocampal function (17, 18). On each trial, a rat initially explored one of two environmental contexts, then the two stimuli were placed into different corners of the environment and the rat was required to choose the correct stimulus for that context to receive a reward (Fig. 1A). In our preliminary studies, we found that the initial context exploration period is essential for learning the context-dependent choice. Therefore, we focused on the prominent theta and gamma activity that is prevalent during this period. We fou...

Oscillatory rhythms in different frequency ranges mark different behavioral states and are thought to provide distinct temporal windows that coherently bind cooperating neuronal assemblies. However, the rhythms in different bands can also interact with each other, suggesting the possibility of higher-order representations of brain states by such rhythmic activity. To explore this possibility, we analyzed local field potential oscillations recorded simultaneously from the striatum and the hippocampus. As rats performed a task requiring active navigation and decision making, the amplitudes of multiple high-frequency oscillations were dynamically modulated in task-dependent patterns by the phase of cooccurring theta-band oscillations both within and across these structures, particularly during decision-making behavioral epochs. Moreover, the modulation patterns uncovered distinctions among both high-and low-frequency subbands. Cross-frequency coupling of multiple neuronal rhythms could be a general mechanism used by the brain to perform networklevel dynamical computations underlying voluntary behavior.amplitude modulation ͉ gamma ͉ theta O scillations in neural population voltage activity are universal phenomena (1). Among brain rhythms, theta oscillations in local field potentials (LFPs) recorded in the hippocampus are prominent during active behaviors (2-5), and these have long been intensively analyzed in the rodent in relation to spatial navigation (6), memory (7), and sleep (8). Theta-band rhythms (4-12 Hz) are now known to occur in other cortical (9-12) and subcortical (12-15) regions, however, including the striatum (14-17), studied here. Gamma oscillations (30-100 Hz) have also received special attention because of their proposed role in functions such as sensory binding (18), selective attention (19-21), transient neuronal assembly formation (22), and information transmission and storage (23-25). The existence of physiologically meaningful neocortical oscillations at even higher frequencies, above the traditional gamma range, has been reported as well (10,(26)(27)(28). In rodents, for example, brief sharp-wave associated ripples (120-200 Hz) appear in the hippocampal formation during slow wave sleep, immobility and consummatory behavior, characteristically in the absence of theta waves (2, 29).The oscillatory activities conventionally assigned to different frequency bands are not completely independent (2-4, 9, 10, 30). In one type of interaction, the phase of low-frequency rhythms modulates the amplitude of higher-frequency oscillations (9, 10, 30). For example, theta phase is known to modulate gamma power in rodent hippocampal and cortical circuits (2-4, 31), and the phase of theta rhythms recorded in the human neocortex can modulate wide-band (60-200 Hz) high-frequency oscillations (10). Such theta-gamma nesting is thought to play a role in sequential memory organization and maintenance of working memory, and more generally in ''phase coding' ' (25, 31). Based on evidence suggesting that theta rhythms i...

An increasingly large body of data exists which demonstrates that oscillations of frequency 12᎐80 Hz are a consequence of, or are inextricably linked to, the behaviour of inhibitory interneurons in the central nervous system. Ž . Ž . Ž . This frequency range covers the EEG bands beta 1 12᎐20 Hz , beta 2 20᎐30 Hz and gamma 30᎐80 Hz . The pharmacological profile of both spontaneous and sensory-evoked EEG potentials reveals a very strong influence on Ž these rhythms by drugs which have direct effects on GABA receptor-mediated synaptic transmission general A .Ž . anaesthetics, sedativerhypnotics or indirect effects on inhibitory neuronal function opiates, ketamine . In addition, a number of experimental models of, in particular, gamma-frequency oscillations, have revealed both common denominators for oscillation generation and function, and subtle differences in network dynamics between the different frequency ranges. Powerful computer and mathematical modelling techniques based around both clinical and experimental observations have recently provided invaluable insight into the behaviour of large networks of interconnected neurons. In particular, the mechanistic profile of oscillations generated as an emergent property of such networks, and the mathematical derivation of this complex phenomenon have much to contribute to our understanding of how and why neurons oscillate. This review will provide the reader with a brief outline of the basic properties of inhibition-based oscillations in the CNS by combining research from laboratory models, large-scale neuronal network simulations, and mathematical analysis. ᮊ 2000 Elsevier Science B.V. All rights reserved.

Experimental and modeling efforts suggest that rhythms in the CA1 region of the hippocampus that are in the beta range (12-29 Hz) have a different dynamical structure than that of gamma (30 -70 Hz). We use a simplified model to show that the different rhythms employ different dynamical mechanisms to synchronize, based on different ionic currents. The beta frequency is able to synchronize over long conduction delays (corresponding to signals traveling a significant distance in the brain) that apparently cannot be tolerated by gamma rhythms. The synchronization properties are consistent with data suggesting that gamma rhythms are used for relatively local computations whereas beta rhythms are used for higher level interactions involving more distant structures. Rhythms in the gamma range (30-80 Hz) and the beta range (12-30 Hz) are found in many parts of the nervous system and are associated with attention, perception, and cognition (1-3). It has been noted in electroencephalogram (EEG) signals that rhythms of different frequencies are found simultaneously (4). Beta oscillations are readily observable immediately after evoked gamma oscillations in sensory evoked potential recordings (5). This beta activity has been correlated with the long-range synchronous activity of neocortical regions during visuomotor reflex activation (6).This paper concerns the correlation between the frequency band of coherent oscillations and conduction delays between the sites participating in the coherent rhythm. It has been noted (7) in human EEG subjects that gamma rhythms are prevalent in local visual response synchronization, but more distant coherence occurring during multimodal integration between parietal and temporal cortices uses rhythms at frequencies of 12-20Hz (the so-called beta 1 range).We shall use data from the CA1 region of the hippocampus (8-10) as a paradigm to address the questions of how long-distance synchrony is achieved and why there is a correlation between oscillation frequency and the temporal distances between participating sites. The data available from the rat hippocampus slice preparation give clues about details of dynamics that are important to the synchronization process.The work builds on earlier work (11-12) describing and analyzing the role of doublet spikes in interneurons in producing synchrony when there are significant conduction delays. Earlier work (13) using rate models showed, via simulations, that longer conduction delays could be tolerated and still produce synchrony if the carrier rhythm had lower frequencies. However, a rate model is not consistent with the situation in which excitatory cells fire at most one spike per cycle, and with high precision in phase. An alternative solution was suggested by data and large-scale models of the gamma rhythm in the hippocampus (8, 9). In both data and models, the ability to synchronize happened in those parameter regimes in which interneurons produced a spike doublet in many of the cycles. This mechanism was analyzed by Ermentrout and Kopell (11), wh...

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In model networks of E-cells and I-cells (excitatory and inhibitory neurons, respectively), synchronous rhythmic spiking often comes about from the interplay between the two cell groups: the E-cells synchronize the I-cells and vice versa. Under ideal conditions-homogeneity in relevant network parameters and all-to-all connectivity, for instance-this mechanism can yield perfect synchronization. We find that approximate, imperfect synchronization is possible even with very sparse, random connectivity. The crucial quantity is the expected number of inputs per cell. As long as it is large enough (more precisely, as long as the variance of the total number of synaptic inputs per cell is small enough), tight synchronization is possible. The desynchronizing effect of random connectivity can be reduced by strengthening the E --> I synapses. More surprising, it cannot be reduced by strengthening the I --> E synapses. However, the decay time constant of inhibition plays an important role. Faster decay yields tighter synchrony. In particular, in models in which the inhibitory synapses are assumed to be instantaneous, the effects of sparse, random connectivity cannot be seen.