Traveling Waves in the Brain

Sequentially activated discrete modules appear as traveling waves in neuronal measurements with limited spatiotemporal sampling

Numerous studies have identified traveling waves in the cortex and suggested they play important roles in brain processing. These waves are most often measured using macroscopic methods that are unable to assess the local spiking activity underlying wave dynamics. Here, we investigated the possibility that waves may not be traveling at the single neuron scale. We first show that sequentially activating two discrete brain areas can appear as traveling waves in EEG simulations. We next reproduce these results using an analytical model of two sequentially activated regions. Using this model, we were able to generate wave-like activity with variable directions, velocities, and spatial patterns, and to map the discriminability limits between traveling waves and modular sequential activations. Finally, we investigated the link between field potentials and single neuron excitability using large-scale measurements from turtle cortex ex vivo. We found that while field potentials exhibit wave-like dynamics, the underlying spiking activity was better described by consecutively activated spatially adjacent groups of neurons. Taken together, this study suggests caution when interpreting phase delay measurements as continuously propagating wavefronts in two different spatial scales. A careful distinction between modular and wave excitability profiles across scales will be critical for understanding the nature of cortical computations.

Complex Dynamics of Propagating Waves in a Two-Dimensional Neural Field

Propagating waves with complex dynamics have been widely observed in neural population activity. To understand their formation mechanisms, we investigate a type of two-dimensional neural field model by systematically varying its recurrent excitatory and inhibitory inputs. We show that the neural field model exhibits a rich repertoire of dynamical activity states when the relevant strength of excitation and inhibition is increased, ranging from localized rotating and traveling waves to global waves. Particularly, near the transition between stable states of rotating and traveling waves, the model exhibits a bistable state; that is, both the rotating and the traveling waves can exist, and the inclusion of noise can induce spontaneous transitions between them. Furthermore, we demonstrate that when there are multiple propagating waves, they exhibit rich collective propagation dynamics with variable propagating speeds and trajectories. We use techniques from time series analysis such detrended fluctuation analysis to characterize the effect of the strength of excitation and inhibition on these collective dynamics, which range from purely random motion to motion with long-range spatiotemporal correlations. These results provide insights into the possible contribution of excitation and inhibition toward a range of previously observed spatiotemporal wave phenomena.

Detection and analysis of spatiotemporal patterns in brain activity

There is growing evidence that population-level brain activity is often organized into propagating waves that are structured in both space and time. Such spatiotemporal patterns have been linked to brain function and observed across multiple recording methodologies and scales. The ability to detect and analyze these patterns is thus essential for understanding the working mechanisms of neural circuits. Here we present a mathematical and computational framework for the identification and analysis of multiple classes of wave patterns in neural population-level recordings. By drawing a conceptual link between spatiotemporal patterns found in the brain and coherent structures such as vortices found in turbulent flows, we introduce velocity vector fields to characterize neural population activity. These vector fields are calculated for both phase and amplitude of oscillatory neural signals by adapting optical flow estimation methods from the field of computer vision. Based on these velocity vector fields, we then introduce order parameters and critical point analysis to detect and characterize a diverse range of propagating wave patterns, including planar waves, sources, sinks, spiral waves, and saddle patterns. We also introduce a novel vector field decomposition method that extracts the dominant spatiotemporal structures in a recording. This enables neural data to be represented by the activity of a small number of independent spatiotemporal modes, providing an alternative to existing dimensionality reduction techniques which separate space and time components. We demonstrate the capabilities of the framework and toolbox with simulated data, local field potentials from marmoset visual cortex and optical voltage recordings from whole mouse cortex, and we show that pattern dynamics are non-random and are modulated by the presence of visual stimuli. These methods are implemented in a MATLAB toolbox, which is freely available under an open-source licensing agreement.

Structured activity such as propagating wave patterns at the level of neural circuits can arise from highly variable firing activity of individual neurons. This property makes the brain, a quintessential example of a complex system, analogous to other complex physical systems such as turbulent fluids, in which structured patterns like vortices similarly emerge from molecules that behave irregularly. In this study, by uniquely adapting techniques for the identification of coherent structures in fluid turbulence, we develop new analytical and computational methods for the reliable detection of a diverse range of propagating wave patterns in large-scale neural recordings, for comprehensive analysis and visualization of these patterns, and for analysis of their dominant spatiotemporal modes. We demonstrate that these methods can be used to uncover the essential spatiotemporal properties of neural population activity recorded by different modalities, thus offering new insights into understanding the working mechanisms of neural systems.

Global Neuromagnetic Cortical Fields Have Non-Zero Velocity

Globally coherent patterns of phase can be obscured by analysis techniques that aggregate brain activity measures across-trials, whether prior to source localization or for estimating inter-areal coherence. We analyzed, at single-trial level, whole head MEG recorded during an observer-triggered apparent motion task. Episodes of globally coherent activity occurred in the delta, theta, alpha and beta bands of the signal in the form of large-scale waves, which propagated with a variety of velocities. Their mean speed at each frequency band was proportional to temporal frequency, giving a range of 0.06 to 4.0 m/s, from delta to beta. The wave peaks moved over the entire measurement array, during both ongoing activity and task-relevant intervals; direction of motion was more predictable during the latter. A large proportion of the cortical signal, measurable at the scalp, exists as large-scale coherent motion. We argue that the distribution of observable phase velocities in MEG is dominated by spatial filtering considerations in combination with group velocity of cortical activity. Traveling waves may index processes involved in global coordination of cortical activity.

Human cortical traveling waves: dynamical properties and correlations with responses

The spatiotemporal behavior of human EEG oscillations is investigated. Traveling waves in the alpha and theta ranges are found to be common in both prestimulus and poststimulus EEG activity. The dynamical properties of these waves, including their speeds, directions, and durations, are systematically characterized for the first time, and the results show that there are significant changes of prestimulus spontaneous waves in the presence of an external stimulus. Furthermore, the functional relevance of these waves is examined by studying how they are correlated with reaction times on a single trial basis; prestimulus alpha waves traveling in the frontal-to-occipital direction are found to be most correlated to reaction speeds. These findings suggest that propagating waves of brain oscillations might be involved in mediating long-range interactions between widely distributed parts of human cortex.

Computing the center of mass for traveling alpha waves in the human brain

The phenomenon of traveling waves of the brain is an intriguing area of research, and its mechanisms and neurobiological bases have been unknown since the 1950s. The present study offers a new method to compute traveling alpha waves using the center of mass algorithm. Electroencephalographic alpha waves are oscillations with a characteristic frequency range and reactivity to closed eyes. Several lines of evidence derived from qualitative observations suggest that the alpha waves represent a spreading wave process with specific trajectories in the human brain. We found that during a certain alpha wave peak recorded with 30 electrodes the trajectory starts and ends in distinct regions of the brain, mostly frontal-occipital, frontal-frontal, or occipital-frontal, but the position of the trajectory at the time in which the maximal positivity of the alpha wave occurs has a definite position near the central regions. Thus we observed that the trajectory always crossed around the central zones, traveling from one region to another region of the brain. A similar trajectory pattern was observed for different alpha wave peaks in one alpha burst, and in different subjects, with a mean velocity of 2.1+/-0.29 m/s. We found that all our results were clear and reproducible in all of the subjects. To our knowledge, the present method documents the first explicit description of a spreading wave process with a singular pattern in the human brain in terms of the center of mass algorithm.

Visual illusions and travelling alpha waves produced by flicker at alpha frequency

The aim of the study was to obtain some experimental evidence of the 'scanning hypothesis' that links electroencephalogram (EEG) alpha-activity with rhythmically spreading waves in the visual cortex. The hypothesis was tested in experiments with 29 healthy adults. Under flicker stimulation through closed lids with the frequency of the individual alpha-rhythm, all subjects perceived illusory visual objects (a ring or a circle, a spiral or a spiral spring, or a grid). Most frequently noted was the perception of a ring or a circle; less frequently, a three-dimensional spiral; and even less frequently, a curved grid. It was found that the optimal stimulation frequency for this effect was tightly connected with the dominant alpha-rhythm frequency, with a correlation coefficient of 0.86. The probability of observing the ring and spiral illusion was highest at this frequency, while that for the grid illusion occurred at frequencies that differed by +/- 1-2 Hz. We observed 10 typical trajectories of travelling EEG alpha-waves on the scalp, and a significant interrelation between the occipital-frontal trajectory and illusions of the ring and spiral. The link between these effects and the propagation of the wave process through the visual cortex, as reflected by the EEG alpha-rhythm, is discussed. The data support the hypothesis of (Pitts, W. McCulloch, W.S., 1947), which proposes the scanning of the visual cortex by a spreading wave process operating at the frequency of the alpha-rhythm, which reads information from the visual cortex.

Steady-state visual evoked potentials and travelling waves

OBJECTIVE

The amplitude and phase of the steady-state visual evoked potential (SSVEP) is sensitive to cognition and attention but the underlying mechanism is not well understood. This study examines stimulus evoked changes in the SSVEP phase topography and the putative role of travelling waves.

METHODS

Eighteen subjects viewed a central-field checkerboard and full-field flicker stimulus temporally modulated at the peak alpha rhythm frequency. EEG was recorded from 10 midline scalp sites and the bipolar SSVEP obtained from differences between adjacent electrodes.

RESULTS

The SSVEP phase comprised either progressive variations consistent with travelling waves or a phase reversal consistent with standing waves. The checkerboard pattern elicited travelling wave patterns in 14 subjects with estimated phase velocities ranging from 7 to 11 m/s after correcting for folded cortex. The flicker stimulus elicited phase reversals in 9 subjects, suggesting standing waves. Six subjects demonstrated a phase topography specific to the stimulus with travelling wave patterns associated with the checkerboard and standing wave patterns associated with the flicker.

CONCLUSIONS

These differences suggest the emergence of travelling and standing waves under different spatial configurations of visual input to the cortex and that wave phenomena contribute to the spatiotemporal dynamics of the SSVEP.

Characteristics of travelling waves under various conditions

In this mapping study, the goal was to investigate in 10 subjects the phenomenon of the travelling waves (TW), especially of alpha activity, under conditions of (1) rest, (2) calculations, (3) emotional experience and (4) pain. The TW during wakefulness usually arose from the areas with the highest amplitude of alpha, called major peaks, for both positive (pos.) and negative (neg.) polarities. These areas were Pz (pos. and neg.) at rest, O2 (pos.) and Pz (neg.) during calculation, O1 (pos.) and O2 (neg.) during emotion and T6 (pos.) and O1 (neg.) during pain. When differences were determined between the latter 3 conditions and the resting state, a focal event-related desynchronization (ERD) became evident on T5 during math, on Pz during emotion and on both CP areas during pain. Surrounding the areas of ERD were areas of event-related synchronization (ERS). The TW were related to phase differences between the different electrode locations, seen more frequently with the pos. polarity, and more often with emotion or calculation. The direction of the TW was most often toward the midline during rest, from the right to midline (calculation), from the left to midline (emotion) and from the midline to the left (pain). Changes on one side of the head were often associated with opposite types of changes on the other side. Sleep spindles were also analyzed showing the major peaks on Fz and F4 with pos. polarities often seen anteriorly and neg. polarities posteriorly. TW were also seen with spindles, more often with the positive polarity. The direction was usually from the midline for the positive polarity and toward the midline for the neg. phase. The phenomenon of the TW is discussed, especially its possible neurophysiological significance as a means of transmitting information throughout the brain.

The phenomenon of travelling waves: a review

As early as 1934 evidence appeared in animals that waves of activity do not always remain stationary but can actually spread over the whole cortex. In the next year some of the earliest studies on the EEG of man showed phase changes of alpha activity that could account for the TW, which later was described when apparatus was built to better view it, especially in the 1950s. The TW has been described mainly as alpha activity that appears to travel both in abnormal and also normal conditions, including the resting state. The phenomenon seems to be enhanced with either external stimuli or endogenous emotional states, which increase phase changes on different brain areas. The travel has been described in all directions from the frontal to the occipital pole, and early work suggests that the posterior-anterior direction may be more often found in abnormal mental states. The speed of travelling over the scalp has varied usually from 1-20 m/sec, but generally has been reported around 5 m/sec. Most investigators have reported that the positive phase is the one which most clearly travels. In exploring the phenomenon of the travelling wave, it is clear that maximal positivity and negativity of the alpha is not always on the occipital regions, as many clinical studies would imply; instead, the fronto-central areas in particular are often the focus of maximal alpha.(ABSTRACT TRUNCATED AT 250 WORDS)

The relationship of head size to alpha frequency with implications to a brain wave model

Analogies between brain waves and waves in physical systems suggest that EEG frequency may be partly determined by cortical surface area. Since a number of other physiological and anatomical parameters probably influence EEG frequency, only a weak correlation is to be expected. A study was made of 159 subjects, some of whom had either very large or very small heads. A single number representing head size was determined as the cube root of three linear measurements. Several characteristic EEG frequencies were determined for each subject by means of Fourier analysis. The data indicate that alpha frequency is significantly correlated with head size: larger heads tend to produce slower alpha rhythms. It was also shown that alpha frequency tends to be lower in all subjects above roughly age 60. Subjects above produced significantly less alpha rhythm than the younger group. It is suggested that analogies between brain waves and physical waves may explain a number of phenomena which are typical of EEG.