A dynamical systems approach for estimating phase interactions between rhythms of different frequencies from experimental data

Synchronization of neural oscillations as a mechanism of brain function is attracting increasing attention. Neural oscillation is a rhythmic neural activity that can be easily observed by noninvasive electroencephalography (EEG). Neural oscillations show the same frequency and cross-frequency synchronization for various cognitive and perceptual functions. However, it is unclear how this neural synchronization is achieved by a dynamical system. If neural oscillations are weakly coupled oscillators, the dynamics of neural synchronization can be described theoretically using a phase oscillator model. We propose an estimation method to identify the phase oscillator model from real data of cross-frequency synchronized activities. The proposed method can estimate the coupling function governing the properties of synchronization. Furthermore, we examine the reliability of the proposed method using time-series data obtained from numerical simulation and an electronic circuit experiment, and show that our method can estimate the coupling function correctly. Finally, we estimate the coupling function between EEG oscillation and the speech sound envelope, and discuss the validity of these results.Author summary: In this paper, we propose an estimation method to identify a dynamical system from rhythmic time-series data. Rhythmic activities have been observed frequently and are synchronized in various fields, and synchronization is an important topic in nonlinear science. It is well known that such synchronization can be described theoretically by a phase oscillator model under the condition that the rhythmic activities can be considered weakly coupled limit-cycle oscillators. Based on this theory, we propose a method to identify the interaction between rhythmic activities as a network of phase oscillators. A practical advantage of the proposed method is that, without detailed modeling, we can extract the phase oscillator model directly from time-series data. For the above theoretical and practical reasons, this method can be applied to rhythmic data from a wide range of fields. In this study, we have focused on human brain activities in which electroencephalography (EEG) signals are often synchronized with each other and with external periodic stimuli. We demonstrate that the proposed method can successfully estimate the interaction between EEG activity and speech rhythm. Consequently, the proposed method can reveal the role of neural synchronization.