During adolescence, the integration of specialized functional brain networks related to cognitive control continues to increase. Slow frequency oscillations (4–10 Hz) have been shown to support cognitive control processes, especially within prefrontal regions. However, it is unclear how neural oscillations contribute to functional brain network development and improvements in cognitive control during adolescence. To bridge this gap, we employed magnetoencephalography (MEG) to explore changes in oscillatory power and phase coupling across cortical networks in a sample of 68 adolescents and young adults. We found a redistribution of power from lower to higher frequencies throughout adolescence, such that delta band (1–3 Hz) power decreased, whereas beta band power (14–16 and 22–26 Hz) increased. Delta band power decreased with age most strongly in association networks within the frontal lobe and operculum. Conversely, beta band power increased throughout development, most strongly in processing networks and the posterior cingulate cortex, a hub of the default mode (DM) network. In terms of phase, theta band (5–9 Hz) phase-locking robustly decreased with development, following an anterior-to-posterior gradient, with the greatest decoupling occurring between association networks. Additionally, decreased slow frequency phase-locking between frontolimbic regions was related to decreased impulsivity with age. Thus, greater decoupling of slow frequency oscillations may afford functional networks greater flexibility during the resting state to instantiate control when required.

Angular measurements are often modeled as circular random variables, where there are natural circular analogues of moments, including correlation. Because a product of circles is a torus, a d-dimensional vector of circular random variables lies on a d-dimensional torus. For such vectors we present here a class of graphical models, which we call torus graphs, based on the full exponential family with pairwise interactions. The topological distinction between a torus and Euclidean space has several important consequences.Our development was motivated by the problem of identifying phase coupling among oscillatory signals recorded from multiple electrodes in the brain: oscillatory phases across electrodes might tend to advance or recede together, indicating coordination across brain areas. The data analyzed here consisted of 24 phase angles measured repeatedly across 840 experimental trials (replications) during a memory task, where the electrodes were in 4 distinct brain regions, all known to be active while memories are being stored or retrieved. In realistic numerical simulations, we found that a standard pairwise assessment, known as phase locking value, is unable to describe multivariate phase interactions, but that torus graphs can accurately identify conditional associations. Torus graphs generalize several more restrictive approaches that have appeared in various scientific literatures, and produced intuitive results in the data we analyzed. Torus graphs thus unify multivariate analysis of circular data and present fertile territory for future research.

Because local field potentials (LFPs) arise from multiple sources in different spatial locations, they do not easily reveal coordinated activity across neural populations on a trial-to-trial basis. As we show here, however, once disparate source signals are decoupled, their trial-to-trial fluctuations become more accessible, and cross-population correlations become more apparent. To decouple sources we introduce a general framework for estimation of current source densities (CSDs). In this framework, the set of LFPs result from noise being added to the transform of the CSD by a biophysical forward model, while the CSD is considered to be the sum of a zero-mean, stationary, spatiotemporal Gaussian process, having fast and slow components, and a mean function, which is the sum of multiple time-varying functions distributed across space, each varying across trials. We derived biophysical forward models relevant to the data we analyzed. In simulation studies this approach improved identification of source signals compared to existing CSD estimation methods. Using data recorded from primate auditory cortex, we analyzed trial-to-trial fluctuations in both steady-state and task-evoked signals. We found cortical layer-specific phase coupling between two probes and showed that the same analysis applied directly to LFPs did not recover these patterns. We also found task-evoked CSDs to be correlated across probes, at specific cortical depths. Using data from Neuropixels probes in mouse visual areas, we again found evidence for depth-specific phase coupling of primary visual cortex and lateromedial area based on the CSDs.

The problem of identifying functional connectivity from multiple time series data recorded in each of two or more brain areas arises in many neuroscientific investigations. For a single stationary time series in each of two brain areas statistical tools such as cross-correlation and Granger causality may be applied. On the other hand, to examine multivariate interactions at a single time point, canonical correlation, which finds the linear combinations of signals that maximize the correlation, may be used. We report here a new method that produces interpretations much like these standard techniques and, in addition, 1) extends the idea of canonical correlation to 3-way arrays (with dimensionality number of signals by number of time points by number of trials), 2) allows for nonstationarity, 3) also allows for nonlinearity, 4) scales well as the number of signals increases, and 5) captures predictive relationships, as is done with Granger causality. We demonstrate the effectiveness of the method through simulation studies and illustrate by analyzing local field potentials recorded from a behaving primate. NEW & NOTEWORTHY Multiple signals recorded from each of multiple brain regions may contain information about cross-region interactions. This article provides a method for visualizing the complicated interdependencies contained in these signals and assessing them statistically. The method combines signals optimally but allows the resulting measure of dependence to change, both within and between regions, as the responses evolve dynamically across time. We demonstrate the effectiveness of the method through numerical simulations and by uncovering a novel connectivity pattern between hippocampus and prefrontal cortex during a declarative memory task.

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