Review
Brain Oscillations and the Importance of Waveform Shape

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The properties of neural oscillations are commonly correlated to disease or behavior states. These measures are mostly derived using traditional spectral analysis techniques that assume a sinusoidal basis.

Electrical recordings from many brain regions, at multiple spatial scales, exhibit neural oscillations that are nonsinusoidal.

New methods have been developed to quantify the nonsinusoidal features of oscillations and account for these features when using traditional spectral analysis.

Features of oscillatory waveform shape have been related to physiological processes and behaviors.

Manipulating the features of stimulation waveforms changes the effects of rhythmic electrical stimulation.

Oscillations are a prevalent feature of brain recordings. They are believed to play key roles in neural communication and computation. Current analysis methods for studying neural oscillations often implicitly assume that the oscillations are sinusoidal. While these approaches have proven fruitful, we show here that there are numerous instances in which neural oscillations are nonsinusoidal. We highlight approaches to characterize nonsinusoidal features and account for them in traditional spectral analysis. Instead of being a nuisance, we discuss how these nonsinusoidal features may provide crucial and so far overlooked physiological information related to neural communication, computation, and cognition.

Section snippets

Neural Oscillation Characterization

Rhythms in neural activity are observed across various temporal and spatial scales and are often referred to as oscillations (see Glossary) [1]. Traditionally, neural oscillations have been clustered into canonical frequency bands, including delta (1–4 Hz), theta (4–8 Hz), alpha (8–12 Hz), beta (15–30 Hz), gamma (30–90 Hz), and high gamma (>50 Hz). These bands roughly correspond to frequency ranges commonly observed in human electroencephalography (EEG) studies. Although they have been observed for

Nonsinusoidal Waveforms Are Stereotyped

One strong indication that the waveform shape of neural oscillations contains physiological information is that features of these waveforms are stereotyped across recordings. This consistency indicates that the waveform shape reflects something specific about the physiology of the recorded brain region. We review here several examples of this phenomenon.

In human electrophysiology, oscillations with stereotyped nonsinusoidal shapes include the sensorimotor ‘mu rhythm’, motor cortical beta

Methods for Characterizing Nonsinusoidal Oscillations

Given the numerous examples of stereotyped oscillatory waveforms described above, metrics have been developed to quantify the features of the waveform shape, although they are underutilized. We recently quantified the sharpness of peaks and troughs by calculating the short-term voltage change around each extrema in the raw trace [11]. The ratio between peak and trough sharpness was shown to differentiate neural activity between neurological treatment conditions in Parkinson's disease (PD). In

Distinguishing between Different Oscillatory Processes by Waveform Shape

The aforementioned methods for quantifying the features of oscillatory waveforms can be used to distinguish between oscillatory phenomena that appear at similar spatial locations, and at the same frequency, but have different physiological origins. Because distinct neural processes can coexist in the same frequency band, applying a narrow bandpass filter may make multiple distinct oscillatory processes indistinguishable from one another. For example, in the rat gustatory cortex there are three

Oscillation Waveform Shape Relates to Physiology

Robust differences in the waveform shapes of the oscillations mentioned above can be assumed to represent differences in the properties of their underlying generators. For example, the sharp transients that occur in spike-wave discharges, as well as in an alpha rhythm in the gustatory cortex, correspond to synchronous local spiking 62, 63, 64, 65. By contrast, the smooth ‘wave’ component of the spike-wave discharge coincided with a slow depolarization of layer 5/6 neurons [66]. The ‘spike’

Oscillatory Waveform Shape Relates to Disease and Behavior States

Two recent studies have compared the shape of neural oscillations between disease states. In anesthetized rats, the relative duration of up- and down-states were measured in parietal cortical slow oscillations [28]. There was no difference in slow oscillation frequency between rats developing epilepsy compared to control animals. However, the rats developing epilepsy had relatively longer up-states. Recently we used electrocorticography (ECoG) to analyze primary motor cortex of patients with PD

Concluding Remarks

We have reviewed a broad literature showing that oscillations have diverse waveform shapes. These nonsinusoidal features likely relate to physiology, making it theoretically possible to infer physiology from waveform shape. Importantly, this idea has been hinted at or directly mentioned in several earlier reports 12, 23, 36, 38, 43, 49, 51, 84, 85; however, such reports of waveform shape have been brief and sparse in the literature of neural oscillations. While relatively novel in neuroscience,

Acknowledgments

We thank Richard Gao, Tammy Tran, and Roemer van der Meij for comments on the manuscript, and Erik Peterson, Tom Donoghue, Colin Hoy, Chris Holdgraf, Nicole Swann, and Brad Postle for invaluable discussion. S.R.C. is supported by the National Science Foundation Graduate Research Fellowship Program. B.V. is supported by the University of California, San Diego, the Qualcomm Institute, California Institute for Telecommunications and Information Technology, Strategic Research Opportunities Program,

Glossary

Amplitude
the magnitude of an oscillation in a signal, measured in volts.
Arch
a periodic waveform in which one extremum is consistently sharper than the opposite.
Cross-frequency coupling (CFC)
a biophysical interaction between two oscillators with different fundamental frequencies.
Multiplex
multiple streams of information encoded in a single signal.
Nonsinusoidal
an oscillatory waveform shape that deviates from a sine wave.
Oscillation
a periodic component of a time series, such that the phase at one

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