Neural oscillation

Neural oscillation

Neural oscillation is rhythmic or repetitive neural activity in the central nervous system. Neural tissue can generate oscillatory activity in many ways, driven either by mechanisms localized within individual neurons or by interactions between neurons. In individual neurons, oscillations can appear either as subthreshold changes in membrane potential or as rhythmic patterns of action potentials, which then produce oscillatory activation of post-synaptic neurons. At the level of neural ensembles, synchronized activity of large numbers of neurons can give rise to macroscopic oscillations, which can be observed in the electroencephalogram (EEG). Oscillatory activity in groups of neurons generally arise from feedback connections between the neurons that result in the synchronization of their firing patterns. The interaction between neurons can give rise to oscillations at a different frequency than the firing frequency of individual neurons. A well-known example of macroscopic neural oscillations is alpha activity.

Neural oscillations were observed by researchers as early as Hans Berger, but their functional role is still not fully understood. The possible roles of neural oscillations include internal clock mechanisms, information transfer mechanisms and the generation of rhythmic motor output. Over the last decades more insight has been gained, especially with advances in brain imaging. A major area of research in neuroscience involves determining how oscillations are generated and what their roles are. Oscillatory activity in the brain is widely observed at different levels of observation and is thought to play a key role in processing neural information. Numerous experimental studies indeed support a functional role of neural oscillations; a unified interpretation, however, is still lacking.

Simulation of neural oscillations at 10 Hz. Upper panel shows spiking of individual neurons (with each dot representing an individual action potential within the population of neurons), and the lower panel the local field potential reflecting their summed activity.



Neural oscillations are characterized by their frequency, amplitude and phase. These signal properties can be extracted from neural recordings using time-frequency analysis. In large-scale oscillations, amplitude changes are considered to result from changes in synchronization within a neural ensemble, also referred to as local synchronization, and have been linked to cognitive functions such as perception and motor control. In addition local synchronization, changes in the synchronization between oscillatory activity of distant neural ensembles have been observed. This type of oscillatory activities might be identified as a neural mechanism for information transfer.[1]

EEG signals oscillate across a range of frequencies. Scientists have defined a set of frequency bands which group specific ranges of frequencies from this spectrum. The first discovered and best-known frequency band is alpha activity (8–12 Hz) that can be detected from the occipital lobe during relaxed wakefulness.[2] Other frequency bands are: delta (1–4 Hz), theta (4–8 Hz), beta (13–30 Hz) and gamma (30–70 Hz) frequency band. Although neural oscillations in human brain activity are mostly investigated using EEG recordings, they are also observed using more invasive recording techniques such as single-unit recordings. Intracellularly, oscillations are observed in subthreshold membrane potential oscillations,[3] whereas extracellularly they are reflected in changes in local field potentials (LFPs). Large-scale oscillations can be measured by the non-invasive method of EEG or MEG and arise from synchronous activity of large numbers of neurons.

The study of neural oscillations belongs to the field of “neurodynamics”, an area of research in the cognitive sciences that places a strong focus upon the dynamic character of neural activity in describing brain function. The term neurodynamics dates back before the 1940s,[4] and is an offshoot of neuro-cybernetics. This approach uses differential equations to describe how neural activity evolves over time patterns and aims to relate cognitive functions to specific dynamic patterns in the brain. Its focus on the dynamics of neural activity contrast with other approaches in cognitive neuroscience that relate cognitive functions to specific areas of the brain.


Oscillatory activity is observed throughout the central nervous system at all levels of organization. Three different levels have been widely recognized: the micro-scale (activity of a single neuron), the meso-scale (activity of a local group of neurons) and the macro-scale (activity of different brain regions).[5]

Tonic firing pattern of single neuron showing rhythmic spiking activity


Neurons generate action potentials resulting from changes in the electric membrane potential. Neurons can generate multiple action potentials in sequence forming so-called spike trains. These spike trains are the basis for neural coding and information transfer in the brain. Spike trains can form all kinds of patterns, such as rhythmic spiking and bursting, and often display oscillatory activity. Oscillatory activity in single neurons can also be observed in sub-threshold fluctuations in membrane potential. These rhythmic changes in membrane potential do not reach the critical threshold and therefore do not result in an action potential. They can result from postsynaptic potentials from synchronous inputs or from intrinsic properties of neurons.

Neuronal spiking can be classified by their activity patterns. The excitability of neurons can be subdivided in Class I and II. Class I neurons can generate action potentials with arbitrarily low frequency depending on the input strength, whereas Class II neurons generate action potentials in a certain frequency band, which is relatively insensitive to changes in input strength.[6] Class II neurons are also more prone to display sub-threshold oscillations in membrane potential.


A group of neurons can also generate oscillatory activity. Through synaptic interactions, the firing patterns of different neurons may become synchronized and the rhythmic changes in electric potential caused by their action potentials will add up (constructive interference). This gives rise to oscillations in local field potential with much larger amplitude and can therefore also be measured outside the scalp using electroencephalography and magnetoencephalography. The frequency of large-scale oscillations does not necessarily match the firing rate of individual neurons. Instead of the synchronization of individual spikes, the firing rate of different neurons may be modulated at a common (lower) frequency.


Common modulations in firing rate give also rise to oscillations in their summed activity. Many brain waves, such as the delta wave and theta rhythm, are considered the result of slow modulatory activity. Because of their lower frequencies and the more extended spatial extend, this type of neural activity is generally referred to as large-scale oscillations.


Intrinsic properties

Scientists have identified some intrinsic neuronal properties that play an important role in generating membrane potential oscillations. In particular, voltage-gated ion channels are critical in the generation of action potentials. The dynamics of these ion channels have been captured in the well-established Hodgkin-Huxley model that describes how action potentials are initiated and propagated by means of a set of differential equations. Using bifurcation analysis, different oscillatory regimes of these neuronal models can be determined, allowing for the classification of types of neuronal responses. The oscillatory dynamics of neuronal spiking as identified in the Hodgkin-Huxley model closely agree with empirical findings. In addition to periodic spiking, subthreshold membrane potential oscillations, i.e. fluctuations that do not result in action potentials, may also contribute to oscillatory activity by facilitating synchronous activity of neighboring neurons.[7][8]

Network properties

Apart from intrinsic properties of neurons, network properties are also an important source of oscillatory activity. Neurons communicate with one another via synapses and affect the timing of spike trains in the post-synaptic neurons. Depending on the properties of the connection, such as the coupling strength, time delay and whether coupling is excitatory or inhibitory, the spike trains of the interacting neurons may become synchronized.[9] Neurons are locally connected, forming small clusters that are called neural ensembles. Certain network structures promote oscillatory activity at specific frequencies. For example, neuronal activity generated by two populations of interconnected inhibitory and excitatory cells can show spontaneous oscillations that are described by the Wilson-Cowan model.

If a group of neurons engages in synchronized oscillatory activity, the neural ensemble can be mathematically represented as a single oscillator.[5] Different neural ensembles are again coupled through long-range connections and form a network of weakly coupled oscillators at the next spatial scale. Weakly coupled oscillators can generate a range of dynamics including oscillatory activity.[10] Long-range connections between different brain structures, such as the thalamus and the cortex, involve time-delays due to the finite conduction velocity of axons. Because most connections are reciprocal, they form feed-back loops that support oscillatory activity. Oscillations recorded from multiple cortical areas can become synchronized and form a large-scale network, whose dynamics and functional connectivity can be studied by means of spectral analysis and Granger causality measures.[11] Coherent activity of large-scale brain activity may form dynamic links between brain areas required for the integration of distributed information.[12]

Certain neurotransmitters are known to regulate the amount of oscillatory activity. GABA concentration has been shown to be positively correlated with frequency of oscillations in induced stimuli. The exact relationship, however, can only be resolved with further pharmacological research on how GABA concentrations affect oscillatory dynamics of single neurons and local field potentials of ensembles of neurons.[13]

Mathematical description

Oscillations can often be described and analyzed using mathematics. Mathematicians have identified several dynamical mechanisms that generate rhythmicity. Among the most important are harmonic (linear) oscillators, limit-cycle oscillators, and delayed-feedback oscillators.[14] Harmonic oscillations appear very frequently in nature—examples are sound waves, the motion of a pendulum, and vibrations of every sort. They generally arise when a physical system is perturbed by a small degree from a minimum-energy state, and are well-understood mathematically. Noise-driven harmonic oscillators realistically simulate alpha rhythm in the waking EEG as well as slow waves and spindles in the sleep EEG. Successful EEG analysis algorithms were based on such models. Several other EEG components are better described by limit-cycle or delayed-feedback oscillations. Limit-cycle oscillations arise from physical systems that show large deviations from equilibrium, whereas delayed-feedback oscillations arise when components of a system affect each other after significant time delays. Limit-cycle oscillations can be complex but there are powerful mathematical tools for analyzing them; the mathematics of delayed-feedback oscillations is primitive in comparison. Linear oscillators and limit-cycle oscillators qualitatively differ in terms of how they respond to fluctuations in input. In a linear oscillator, the frequency is more or less constant but the amplitude can vary greatly. In a limit-cycle oscillator, the amplitude tends to be more or less constant but the frequency can vary greatly. A heartbeat is an example of a limit-cycle oscillation in that the frequency of beats varies widely, while each individual beat continues to pump about the same amount of blood.

Computational models adopt a variety of abstractions in order to describe complex oscillatory dynamics observed in brain activity. Many models are used in the field, each defined at a different level of abstraction and trying to model different aspects of neural systems. They range from models of the short-term behaviour of individual neurons, through models of how the dynamics of neural circuitry arise from interactions between individual neurons, to models of how behaviour can arise from abstract neural modules that represent complete subsystems.

Single neuron model

Simulation of a Hindmarsh-Rose neuron showing typical bursting behavior: a fast rhythm generated by individual spikes and a slower rhythm generated by the bursts.

A model of a biological neuron is a mathematical description of the properties of nerve cells, or neurons, that is designed to accurately describe and predict its biological processes. The most successful and widely-used model of neurons, the Hodgkin-Huxley model, is based on data from the squid giant axon. It is a set of nonlinear ordinary differential equations that approximates the electrical characteristics of a neuron, in particular the generation and propagation of action potentials. The model is very accurate and detailed and Hodgkin and Huxley received the 1963 Nobel Prize in physiology or medicine for this work.

The mathematics of the Hodgkin-Huxley model are quite complicated and several simplifications have been proposed, such as the FitzHugh-Nagumo model and the Hindmarsh-Rose model. Such models only capture the basic neuronal dynamics, such as rhythmic spiking and bursting, but are more computationally efficient. This allows the stimulation of a large number of interconnected neurons that form a neural network.

Spiking model

A biological neural network describes a population of physically interconnected neurons or a group of disparate neurons whose inputs or signalling targets define a recognizable circuit. These models aim to describe how the dynamics of neural circuitry arise from interactions between individual neurons. Local interactions between neurons can result in the synchronization of spiking activity and form the basis of oscillatory activity. In particular, the interplay between pyramidal cells and inhibitory interneurons can give rise to brain rhythms such as gamma activity.[15]

Neural mass model

Simulation of a neural mass model showing network spiking during the onset of a seizure.[16] As the gain A is increased the network starts to oscillate at 3Hz.

Neural field models is another important tool in studying neural oscillations and is a mathematical framework describing the spatio-temporal evolution of variables such as mean firing rate. In modeling the activity of large numbers of neurons, the central idea is to take the density of neurons to the continuum limit, resulting in spatially continuous neural networks. Instead of modelling individual neurons, this approach approximates a group of neurons by its average properties and interactions. It is based on the mean field approach, an area of statistical physics that deals with large-scale systems. Models based on these principles have been used to provide mathematical descriptions of neural oscillations and EEG rhythms. They have been used to investigate visual hallucinations,[17] and mechanisms for short-term memory and motion perception.

Kuramoto model

Simulation of Kuramoto model showing neural synchronization and oscillations in the mean field

The Kuramoto model of coupled phase oscillators[18] is one of the most abstract and fundamental model used to investigate neural oscillations and sychronization. It captures the activity of a local system (e.g., neuron or cortical area) by its circular phase alone and hence ignores the amplitude of oscillations.[19] Interactions amongst these oscillators are introduced by a simple algebraic form (such as a sin function) and collectively generate a dynamical pattern at the global scale. The Kuramoto model is widely used to study oscillatory brain activity and several extensions have been proposed that increase its neurobiological plausibility, for instance by incorporating topological properties of local cortical connectivity.[20] In particular, it describes how the activity of a group of interaction neurons can become synchronized and generate large-scale oscillations. Simulations using the Kuramoto model with realistic long-range cortical connectivity and time-delayed interactions reveal the emergence of slow patterned fluctuations that reproduce resting-state BOLD functional maps.[21]

Activity patterns

Both single and groups of neurons can generate oscillatory activity spontaneously. In addition, they may show oscillatory responses to perceptual input or motor output. Some types of neurons will rhythmically in absence of any synaptic input. Likewise, brain wide activity reveals oscillatory activity while subjects do not engage in any activity, so-called resting-state activity. These ongoing rhythms can change in different ways in response to perceptual input or motor output. Oscillatory activity may respond by increasing or decreasing in frequency and amplitude or show a temporary interruption, which is referred to as phase resetting. Finally, external activity may not interact with ongoing activity at all, resulting in an additive response.

Oscillatory responses
The frequency of ongoing oscillatory activity is increased between t1 and t2.  
The amplitude of ongoing oscillatory activity is increased between t1 and t2.  
The phase of ongoing oscillatory activity is reset at t1.  
Activity is linearly added to ongoing oscillatory activity between t1 and t2.  

Ongoing activity

Spontaneous activity is brain activity in the absence of an explicit task, such as sensory input or motor output, and hence also referred to as resting-state activity. It is opposed to induced activity, i.e. brain activity that is induced by sensory stimuli or motor responses. The term ongoing brain activity is used in electroencephalography and magnetoencephalography for those signal components that are not associated with the processing of a stimulus or the occurrence of specific other events, such as moving a body part, i.e. that do not form evoked potentials/evoked fields, or induced activity. Spontaneous activity is usually considered to be noise if one is interested in stimulus processing. However, spontaneous activity is considered to play a crucial role during brain development, such as in network formation and synaptogenesis. Spontaneous activity may be informative regarding the current mental state of the person (e.g. wakefulness, alertness) and is often used in sleep research. Certain types of oscillatory activity, such as alpha waves, are part of spontaneous activity. Statistical analysis of power fluctuations of alpha activity reveals a bimodal distribution, i.e. a high- and low-amplitude mode, and hence shows that resting-state activity does not just reflect a noise process.[22] In case of fMRI, spontaneous fluctuations in the blood oxygen level dependent (BOLD) signal reveal correlation patterns that are linked to resting states networks, such as the default network.[23] These distributed patterns of fMRI activity also show correlations with fluctuations of oscillatory EEG activity in different frequency bands.[24]

Ongoing brain activity may also have an important role in perception, as it may interact with activity related to incoming stimuli. Indeed, EEG studies suggest that visual perception is dependent on both the phase and amplitude of cortical oscillations.[25][26][27]

Frequency response

In response to input a neuron or neuronal ensemble may change the frequency at which it oscillations. This is very common in single neurons where the firing rate varies proportionally with the summed activity it receives. This is referred to as rate coding. Frequency changes are also commonly observed in central pattern generators and directly relate to the speed of motor activities, such as step frequency in walking. In oscillatory activity involving different brain areas changes in frequency are not so common, as the frequency of oscillatory activity is often related to the time-delays between brain areas.

Amplitude response

Next to evoked activity, neural activity related to stimulus processing may result in induced activity. Induced activity refers to changes in ongoing brain activity induced by processing of stimuli or movement preparation. A well-studied type of induced activity is amplitude change in oscillatory activity. For instance, gamma activity often increases during increased mental activity such as during object representation.[28] Because induced responses may have different phases across measurements and therefore would cancel out during averaging, they can only be obtained using time-frequency analysis. Induced activity generally reflects the activity of numerous neurons: amplitude changes in oscillatory activity are thought to arise from the synchronization of neural activity, for instance by synchronization of spike timing or membrane potential fluctuations of individual neurons. Increases and decreases in oscillatory activity are therefore often referred to as event-related synchronization and desynchronization.[29]

Phase resetting

Another possibility is that input to a neuron or neuronal ensemble resets the phase of ongoing oscillations.[30] Phase resetting is very common in single neurons where spike timing is adjusted to neuronal input. For instance, a neuron may start to spike at a fixed delay in response to periodic input, which is referred to as phase locking.[6] Phase resetting may also occur at the level of neuronal ensembles when the phases of multiple neurons are adjusted simultaneously. Phase resetting of ongoing ensemble oscillations gives an alternative explanation for event-related potentials obtained by averaging multiple EEG trials with respect to the onset of a stimulus or event.[31] That is, if the phase of ongoing oscillations is reset to a fixed phase over multiple trials, oscillations will no longer average out but add up to give rise to an event-related potential. Moreover, phase resetting or phase locking is also fundamental for the synchronization of different neurons or different brain regions.[10][12] In this case the timing of spikes becomes phase locked to the activity of other neurons instead of to external input.

Additive response

The term evoked activity is used in electroencephalography and magnetoencephalography for certain types of stimulus-related activity. Evoked potentials and event-related potentials are obtained from the electroencephalogram by stimulus-locked averaging. As a consequence, those signal components that are the same in each single measurement are conserved and all others, i.e. ongoing or spontaneous activity, are averaged out. That is, event-related potentials only reflect oscillations in brain activity that are phase-locked to the stimulus or event. Evoked activity is often considered to be independent from ongoing brain activity although this is an ongoing debate.[32]


Neural synchronization can be modulated by task constraints, such as attention, and is thought to play a role in feature binding,[33] neuronal communication,[1] and motor coordination.[34] Neuronal oscillations became a hot topic in neuroscience in the 1990s when the studies of the visual system of the brain by Gray, Singer and others appeared to support the neural binding hypothesis.[35] According to this idea, synchronous oscillations in neuronal ensembles bind neurons representing different features of an object. For example, when a person looks at a tree, visual cortex neurons representing the tree trunk and those representing the branches of the same tree would oscillate in synchrony to form a single representation of the tree. This phenomenon is best seen in local field potentials which reflect the synchronous activity of local groups of neurons, but has also been shown EEG and MEG recordings providing increasing evidence for a close relation between synchronous oscillatory activity and a variety of cognitive functions such as perceptual grouping.[33]


Cells in the sinoatrial node, located in the right atrium of the heart, spontaneously depolarize approximately 100 times per minute. Although all of the heart's cells have the ability to generate action potentials that trigger cardiac contraction, the sinoatrial node normally initiates it, simply because it generates impulses slightly faster than the other areas. Hence, these cells generate the normal sinus rhythm and are called pacemaker cells as they directly control the heart rate. In the absence of extrinsic neural and hormonal control, cells in the SA node will rhythmically discharge. The sinoatrial node is richly innervated by the autonomic nervous system, which up or down regulates the spontaneous firing frequency of the pacemaker cells.

Central pattern generator

Synchronized firing of neurons also form the basis of periodic motor commands for rhythmic movements such as locomotion. These rhythmic outputs are produced by a group of interacting neurons that form a network, called a central pattern generator. The defining characteristic of a central pattern generator is that they generate rhythmic output in absence of any periodic or rhythmic input. Most evidence for central pattern generators comes from lower animals, such as the lamprey, but there is also evidence for spinal central pattern generators in humans.[36]

Information processing

Neuronal spiking is generally considered the basis for information transfer in the brain. For such a transfer, information needs to be coded in a spiking pattern. Different types of coding schemes have been proposed, such as rate coding and temporal coding.


Synchronization of neuronal firing may serve as a means to group spatially segregated neurons that respond to the same stimulus in order to bind these responses for further joint processing, i.e. to exploit temporal synchrony to encode relations. Purely theoretical formulations of the binding-by-synchrony hypothesis were proposed first,[37] but subsequently extensive experimental evidence has been reported supporting the potential role of synchrony as a relational code.[38]

Visual perception

The functional role of synchronized oscillatory activity in the brain was mainly established in experiments performed on awake behaving kittens with multiple electrodes implanted in the visual cortex. These experiments showed that groups of spatially segregated neurons engaged in synchronous oscillatory activity when activated by visual stimuli consisting of drifting square wave gratings. The frequency of these oscillations was in the range of 40 Hz and differed from the periodic activation induced by the grating, suggesting that the oscillations and their synchronization were due to internal neuronal interactions.[38] Similar findings were shown in parallel by the group of Eckhorn providing further evidence for the functional role of neural synchronization in feature binding.[39] Since then numerous studies have replicated these findings and extended them to different modalities such as EEG, providing extensive evidence of the functional role of gamma oscillations in visual perception.

Odor perception

Gilles Laurent and colleagues that showed oscillatory synchronization has an important functional role in odor perception. Perceiving different odors leads to different subsets of neurons firing on different sets of oscillatory cycles.[40] These oscillations can be disrupted by GABA blocker picrotoxin.[41] The disruption of the oscillatory synchronization leads to impairment of behavioral discrimination of chemically similar odorants in bees[42] and to more similar responses across odors in downstream β-lobe neurons.[43]

Sense of time

Neural oscillations are also thought be involved in the sense of time[44] and in somatosensory perception.[45] However, recent findings argue against a clock-like function of cortical gamma oscillations.[46]

Motor coordination

Oscillations have been commonly reported in the motor system. Pfurtscheller and colleagues found a reduction in alpha (8–12 Hz) and beta (13–30 Hz) oscillations in EEG activity when subjects made a movement.[29][47] Using intra-cortical recordings, similar changes in oscillatory activity were found in motor cortex when the monkeys performed motor acts that required significant attention.[48][49] In addition, oscillations at spinal level become synchronised to beta oscillations in motor cortex during constant muscle activation, as determined by MEG/EEG-EMG coherence.[50][51][52] Recently it was found that cortical oscillations propagate as waves across the surface of the motor cortex along dominant spatial axes characteristic of the local circuitry of the motor cortex.[53]

Oscillatory rhythms at 10 Hz have been recorded in inferior olive and may be central in motor timing.[3] These oscillations are also observed in motor output of physiological tremor[54] and when performing slow finger movements.[55] These findings may indicate that the human brain controls continuous movements intermittently. In support, it was shown these movement discontinuities are directly correlated to oscillatory activity in a cerebello-thalamo-cortical loop, which may represent a neural mechanism for the intermittent motor control.[56]


Neural oscillations are extensively linked to memory function, in particular theta activity. Theta rhythms are very strong in rodent hippocampi and entorhinal cortex during learning and memory retrieval, and are believed to be vital to the induction of long-term potentiation, a potential cellular mechanism of learning and memory. The coupling between theta and gamma activity is thought to be vital for memory functions.[57] The tight coordination of spike timing of single neurons with the local theta oscillations is linked to successful memory formation in humans, as more stereotyped spiking predicts better memory.[58]


Specific types of neural oscillations may also appear in pathological situations, such as Parkinson's disease or epilepsy. Interestingly, these pathological oscillations often consist of an aberrant version of a normal oscillation. For example, one of the best known types is the spike and wave oscillation, which is typical of generalized or absence epileptic seizures, and which resembles normal sleep spindle oscillations.


Handwriting of a person affected by Parkinson's disease showing rhythmic tremor activity in the strokes.

A tremor is an involuntary, somewhat rhythmic, muscle contraction and relaxation involving to-and-fro movements of one or more body parts. It is the most common of all involuntary movements and can affect the hands, arms, eyes, face, head, vocal cords, trunk, and legs. Most tremors occur in the hands. In some people, tremor is a symptom of another neurological disorder. Many different forms of tremor have been identified, such as essential tremor or Parkinsonian tremor. It is argued that tremors are likely to be multifactorial in origin, with contributions from neural oscillations in the central nervous systems, but also from peripheral mechanisms such as reflex loop resonances.[59]


Epilepsy is a common chronic neurological disorder characterized by seizures. These seizures are transient signs and/or symptoms of abnormal, excessive or hypersynchronous neuronal activity in the brain.



Brain-computer interface

Neural oscillations have been considered for use as a control signal for various brain-computer interfaces.[60]

See also


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Further reading

  • Buzsáki, György (2006). Rhythms of the Brain. Oxford University Press. ISBN 978-0-19-530106-9. 

External links

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