Resting state MEG oscillations show long-range temporal correlations of phase synchrony that break down during finger movement

Abstract

The capacity of the human brain to interpret and respond to multiple temporal scales in its surroundings suggests that its internal interactions must also be able to operate over a broad temporal range. In this paper, we utilize a recently introduced method for characterizing the rate of change of the phase difference between MEG signals and use it to study the temporal structure of the phase interactions between MEG recordings from the left and right motor cortices during rest and during a finger-tapping task. We use the Hilbert transform to estimate moment-to-moment fluctuations of the phase difference between signals. After confirming the presence of scale-invariance we estimate the Hurst exponent using detrended fluctuation analysis (DFA). An exponent of >0.5 is indicative of long-range temporal correlations (LRTCs) in the signal. We find that LRTCs are present in the α/μ and β frequency bands of resting state MEG data. We demonstrate that finger movement disrupts LRTCs correlations, producing a phase relationship with a structure similar to that of Gaussian white noise. The results are validated by applying the same analysis to data with Gaussian white noise phase difference, recordings from an empty scanner and phase-shuffled time series. We interpret the findings through comparison of the results with those we obtained from an earlier study during which we adopted this method to characterize phase relationships within a Kuramoto model of oscillators in its sub-critical, critical, and super-critical synchronization states. We find that the resting state MEG from left and right motor cortices shows moment-to-moment fluctuations of phase difference with a similar temporal structure to that of a system of Kuramoto oscillators just prior to its critical level of coupling, and that finger tapping moves the system away from this pre-critical state toward a more random state.

The Parkinsonian Subthalamic Network: Measures of Power, Linear, and Non-linear Synchronization and their Relationship to L-DOPA Treatment and OFF State Motor Severity

“…i.e., temporal order within the fluctuation rates of change of phase difference (See Botcharova et al, 2014). Exponents values in the alpha-theta (0.55 ± 0.04, ON, intra -) and low beta (0.58 ± 0.03, ON intra -) bands are in the range that is in agreement with those previously reported in the motor cortex during a movement task (Botcharova et al, 2015). …”

“…Such a regime would ultimately reduce the effective transfer entropy via phase (see (Barnett et al, 2013) for more details), reducing the encoding space available to the network by a recruitment of highly coherent yet informationally redundant neuronal units in the disease state (Hanslmayr et al, 2012). Previous use of DFA-PS in analyzing changes during movement at the level of the left and right motor cortices show that compared to the resting state, movement is associated with a decrease in exponent value (Botcharova et al, 2015). This would suggest that an increase in the degree of LRTCs present in the derivative of the phase difference between two signals is associated with an anti-kinetic state.…”

“…Filter orders were chosen to include three cycles of the slowest component frequency. This approach has been used in previously studies (e.g., Linkenkaer-Hansen et al, 2001; Botcharova et al, 2015). The band passed signal is given by:…”

The Kuramoto model in complex networks

“…Temporal and spatial synchronization patterns from fMRI were also reproduced for low frequencies between 0.01-0.13Hz [396], a range for which the time delays between the oscillators can be neglected, since the delay time scale in the cortex area is much faster than the periods of the oscillators [397]. Furthermore, the variant of the Kuramoto model (346) proved itself to be relevant in the study of criticality in brain dynamics [398], besides also reproducing moment-to-moment fluctuations of phase differences of resting states in magnetoencephalography (MEG) oscillations recorded during finger movement experiments [399]. Other aspects of dynamical criticality in human brain functional networks were studied in [400] by comparing times series generated with the Kuramoto model and fMRI data recorded from normal subjects under resting conditions.…”

Model selection for identifying power-law scaling

“…frequency bands: delta (2-4 Hz), theta (4-8 Hz), alpha(8)(9)(10)(11)(12), beta (20-30 Hz) and gamma. We selected a range of interval sizes n = [N/500 N/5], with N = 7.3 · 10 4292 seconds corresponding to the number of samples in 535 the shortest time series available.…”