Time-limited self-sustaining rhythms and state transitions in brain networks

Resting-state networks usually show time-limited self-sustaining oscillatory patterns (TLSOPs) with the characteristic features of multiscaled rhythms and frequent switching between different rhythms, but the underlying mechanisms remain unclear. To reveal the mechanisms of multiscaled rhythms, we present a simplified reaction-diffusion model of activation propagation to reproduce TLSOPs in real brain networks. We find that the reproduced TLSOPs do show multiscaled rhythms, depending on the activating threshold and initially chosen activating nodes. To understand the frequent switching between different rhythms, we present an approach of dominant activation paths and find that the multiscaled rhythms can be separated into individual rhythms denoted by different core networks, and the switching between them can be implemented by a time-dependent activating threshold. Further, based on the microstates of TLSOPs, we introduce the concept of a return loop to study the distribution of the return times of microstates in TLSOPs and find that it satisfies the Weibull distribution. Then, to check it for real data, we present a method of a shifting window to transform a continuous time series into a discrete two-state time series and interestingly find that the Weibull distribution also exists in resting-state EEG and fMRI data. Finally, we show that the TLSOP lifetime depends exponentially on the core network size and can be explained by a theory of the complete graphs.