Non-identical smoothing operators for estimating time-frequency interdependence in electrophysiological recordings

Synchronization of neural activity from distant parts of the brain is crucial for the coordination of cognitive activities. Because neural synchronization varies both in time and frequency, time–frequency (T-F) coherence is commonly employed to assess interdependences in electrophysiological recordings. T-F coherence entails smoothing the cross and power spectra to ensure statistical consistency of the estimate, which reduces its T-F resolution. This trade-off has been described in detail when the cross and power spectra are smoothed using identical smoothing operators, which may yield spurious coherent frequencies. In this article, we examine the use of non-identical smoothing operators for the estimation of T-F interdependence, i.e., phase synchronization is characterized by phase locking between signals captured by the cross spectrum and we may hence improve the trade-off by selectively smoothing the auto spectra. We first show that the frequency marginal density of the present estimate is bound within [0,1] when using non-identical smoothing operators. An analytic calculation of the bias and variance of present estimators is performed and compared with the bias and variance of standard T-F coherence using Monte Carlo simulations. We then test the use of non-identical smoothing operators on simulated data, whose T-F properties are known through construction. Finally, we analyze empirical data from eyes-closed surface electroencephalography recorded in human subjects to investigate alpha-band synchronization. These analyses show that selectively smoothing the auto spectra reduces the bias of the estimator and may improve the detection of T-F interdependence in electrophysiological data at high temporal resolution

Investigating large-scale brain dynamics using field potential recordings: Analysis and interpretation

New technologies to record electrical activity from the brain on a massive scale offer tremendous opportunities for discovery. Electrical measurements of large-scale brain dynamics, termed field potentials, are especially important to understanding and treating the human brain. Here, our goal is to provide best practices on how field potential recordings (EEG, MEG, ECoG and LFP) can be analyzed to identify large-scale brain dynamics, and to highlight critical issues and limitations of interpretation in current work. We focus our discussion of analyses around the broad themes of activation, correlation, communication and coding. We provide best-practice recommendations for the analyses and interpretations using a forward model and an inverse model. The forward model describes how field potentials are generated by the activity of populations of neurons. The inverse model describes how to infer the activity of populations of neurons from field potential recordings. A recurring theme is the challenge of understanding how field potentials reflect neuronal population activity given the complexity of the underlying brain systems