Cortical travelling waves: mechanisms and computational principles

Abstract

Multichannel recording technologies have revealed travelling waves of neural activity in multiple sensory, motor and cognitive systems. These waves can be spontaneously generated by recurrent circuits or evoked by external stimuli. They travel along brain networks at multiple scales, transiently modulating spiking and excitability as they pass. Here, we review recent experimental findings that have found evidence for travelling waves at single-area (mesoscopic) and whole-brain (macroscopic) scales. We place these findings in the context of the current theoretical understanding of wave generation and propagation in recurrent networks. During the large low-frequency rhythms of sleep or the relatively desynchronized state of the awake cortex, travelling waves may serve a variety of functions, from long-term memory consolidation to processing of dynamic visual stimuli. We explore new avenues for experimental and computational understanding of the role of spatiotemporal activity patterns in the cortex.

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Figure 1: Macroscopic waves during human sleep.
Figure 2: Two models for the stimulus-evoked response in the visual cortex.
Figure 3: Mesoscopic waves in the visual cortex.
Figure 4: Two models for the generation of mesoscopic travelling waves.
Figure 5: Patterning of place field firing by hippocampal travelling waves.
Figure 6: Computation with cortical waves.

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Acknowledgements

The authors thank Z. Davis, T. Bartol, G. Pao, A. Destexhe, Y. Frégnac and C. F. Stevens for helpful discussions and J. Ogawa for helpful discussions and help with illustrations. L.M. acknowledges support from the US National Institute of Mental Health (5T32MH020002-17). F.C. acknowledges support from Agence Nationale de la Recherche (ANR) projects BalaV1 (ANR-13-BSV4-0014-02) and Trajectory (ANR-15-CE37-0011-01). J.R. acknowledges support from the Fiona and Sanjay Jha Chair in Neuroscience at the Salk Institute. T.J.S. acknowledges support from Howard Hughes Medical Institute, Swartz Foundation and the Office of Naval Research (N000141210299).

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L.M., F.C., J.R. and T.J.S. researched data for the article, made substantial contributions to discussions of the content, wrote the article and reviewed and/or edited the manuscript before submission.

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Correspondence to Terrence J. Sejnowski.

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PowerPoint slides

Glossary

Phase offsets

The differences in phase (an amplitude-invariant measure of position in an oscillation cycle) between two (or more) oscillations.

Travelling waves

A disturbance that travels through a physical medium that may be water, air or a neural network.

Complex spatiotemporal patterns

Patterns that can result from the summation of many individual waves. Depending on the properties of the medium, the pattern resulting from these interactions can differ greatly.

Mesoscopic

A scale between microscopic and macroscopic. In neuroscience, the mesoscopic scale describes single regions (such as cortical areas or subcortical nuclei) spanning millimetres to centimetres. Cortical networks at this scale can be imaged through recently developed recording technologies.

Macroscopic

The scale of the whole brain; traditionally recorded with extracranial techniques (electroencephalography and magnetoencephalography) and more recently recorded with intracranial methods (electrocorticography).

Electroencephalography

(EEG). A neural recording technique in which electrodes are placed on the scalp, outside the skull (extracranial), that is of great use in studying the sensory and cognitive processes of normal human subjects.

Electrocorticography

(ECoG). A recording technique in which electrodes are placed directly on the cortical surface, offering both high spatial (up to 2 millimetres or greater) and high temporal resolution.

Local field potential

(LFP). The electric potential recorded in the extracellular space of the cortex. The LFP is thought to reflect the synaptic currents from neurons within a few hundred micrometres around the electrode.

Multielectrode arrays

(MEAs). One-dimensional or two-dimensional grids of electrodes, which offer the ability to sample local field potential and spiking activity at the mesoscopic scale.

Voltage-sensitive dyes

(VSDs). Fluorescent dyes applied directly to the surface of the cortex that allow the subthreshold membrane potential of neural populations to be recorded. The resulting signals are linearly related to the average membrane potential of neurons at each point in the cortex. This technique captures neural activity over a large field of view with very high spatial (up to 20 micrometres) and temporal (up to 1 millisecond) resolution.

Slow oscillation

The large, 0.1–1.0 Hz rhythm of deep non-rapid-eye-movement sleep.

Volume conduction

Passive transmission of an electric field through biological tissue. The fields can be created from a single source of neural activity and will appear as identical, highly synchronous waveforms across electrodes; a cause of spatial smoothing (blurring) in scalp electroencephalography.

K-Complex

A brief ( 1 second), biphasic waveform composed of a strong negative potential followed by a positive deflection. K-Complexes occur predominantly during stage 2 non-rapid-eye-movement sleep and are driven by transitions from cortical down to up states.

Sleep spindles

Thalamocortical 11–15 Hz oscillations prevalent in stage 2 non-rapid-eye-movement sleep. These oscillatory periods have long been associated with learning and memory, including sleep-dependent consolidation of long-term memory.

Cell assemblies

A group of interconnected, repeatedly co-activated neurons whose signature spike pattern is thought to collectively represent a specific sensory stimulus or memory.

Coupled oscillator networks

Models of emergent collective behaviour in large ensembles. In these networks, individual units are characterized by a state (or phase) between 0 and 2π. Interactions among units are typically modelled as attractive, such that units with different states tend to synchronize depending on the coupling strength of the interaction.

Irregular asynchronous (IA) state

A state of asynchronous, highly irregular firing in spiking network models. This state exhibits the low-correlated firing that is the hallmark of cortical dynamics under general conditions of excitatory and inhibitory balance.

Stochastic neural field theory

An extension of the neural field model of Wilson and Cowan to include the effects of neural and synaptic noise.

Dorsoventral axis

In rodents, the long axis of the hippocampus, running from a dorsal, medial position to a ventral, lateral position; synonymous with septotemporal axis.

Reaction–diffusion systems

Models of chemical dynamics that take into account local reactions and diffusion across space. These reactions exhibit complex dynamics, including travelling waves and emergent patterns.

Temporal reversibility

A property of a system whose dynamics remain the same when time is reversed. This feature implies important mathematical properties for the system under study.

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Muller, L., Chavane, F., Reynolds, J. et al. Cortical travelling waves: mechanisms and computational principles. Nat Rev Neurosci 19, 255–268 (2018). https://doi.org/10.1038/nrn.2018.20

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