Cross frequency coupling (CFC) is emerging as a fundamental feature of brain activity, correlated with brain function and dysfunction. Many different types of CFC have been identified through application of numerous data analysis methods, each developed to characterize a specific CFC type. Choosing an inappropriate method weakens statistical power and introduces opportunities for confounding effects. To address this, we propose a statistical modeling framework to estimate high frequency amplitude as a function of both the low frequency amplitude and low frequency phase; the result is a measure of phase-amplitude coupling that accounts for changes in the low frequency amplitude. We show in simulations that the proposed method successfully detects CFC between the low frequency phase or amplitude and the high frequency amplitude, and outperforms an existing method in biologically-motivated examples. Applying the method to in vivo data, we illustrate examples of CFC during a seizure and in response to electrical stimuli.

Neural oscillations enable communication between brain regions. Closed-loop brain stimulation attempts to modify this activity by stimulation locked to the phase of concurrent neural oscillations. If successful, this may be a major step forward for clinical brain stimulation therapies. The challenge for effective phase-locked systems is accurately calculating the phase of a source oscillation in real time. The basic operations of filtering the source signal to a frequency band of interest and extracting its phase cannot be performed in real time without distortion. We present a method for continuously estimating phase that reduces this distortion by using an autoregressive model to predict the future of a filtered signal before passing it though the Hilbert transform. This method outperforms published approaches on real data and is available as a reusable open-source module. We also examine the challenge of compensating for the filter phase response and outline promising directions of future study.

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Closing the loop between brain activity and behavior is one of the most active areas of development in neuroscience. There is particular interest in developing closed-loop control of neural oscillations. Many studies report correlations between oscillations and functional processes. Oscillation-informed closed-loop experiments might determine whether these relationships are causal and would provide important mechanistic insights which may lead to new therapeutic tools. These closed-loop perturbations require accurate estimates of oscillatory phase and amplitude, which are challenging to compute in real time. We developed an easy to implement, fast and accurate Toolkit for Oscillatory Real-time Tracking and Estimation (TORTE). TORTE operates with the open-source Open Ephys GUI (OEGUI) system, making it immediately compatible with a wide range of acquisition systems and experimental preparations. TORTE efficiently extracts oscillatory phase and amplitude from a target signal and includes a variety of options to trigger closed-loop perturbations. Implementing these tools into existing experiments is easy and adds minimal latency to existing protocols. Most labs use in-house lab-specific approaches, limiting replication and extension of their experiments by other groups. Accuracy of the extracted analytic signal and accuracy of oscillation-informed perturbations with TORTE match presented results by these groups. However, TORTE provides access to these tools in a flexible, easy to use toolkit without requiring proprietary software. We hope that the availability of a high-quality, open-source, and broadly applicable toolkit will increase the number of labs able to perform oscillatory closed-loop experiments, and will improve the replicability of protocols and data across labs.