Markers of criticality in phase synchronization

Abstract

The concept of the brain as a critical dynamical system is very attractive because systems close to criticality are thought to maximize their dynamic range of information processing and communication. To date, there have been two key experimental observations in support of this hypothesis: (i) neuronal avalanches with power law distribution of size and (ii) long-range temporal correlations (LRTCs) in the amplitude of neural oscillations. The case for how these maximize dynamic range of information processing and communication is still being made and because a significant substrate for information coding and transmission is neural synchrony it is of interest to link synchronization measures with those of criticality. We propose a framework for characterizing criticality in synchronization based on an analysis of the moment-to-moment fluctuations of phase synchrony in terms of the presence of LRTCs. This framework relies on an estimation of the rate of change of phase difference and a set of methods we have developed to detect LRTCs. We test this framework against two classical models of criticality (Ising and Kuramoto) and recently described variants of these models aimed to more closely represent human brain dynamics. From these simulations we determine the parameters at which these systems show evidence of LRTCs in phase synchronization. We demonstrate proof of principle by analysing pairs of human simultaneous EEG and EMG time series, suggesting that LRTCs of corticomuscular phase synchronization can be detected in the resting state and experimentally manipulated. The existence of LRTCs in fluctuations of phase synchronization suggests that these fluctuations are governed by non-local behavior, with all scales contributing to system behavior. This has important implications regarding the conditions under which one should expect to see LRTCs in phase synchronization. Specifically, brain resting states may exhibit LRTCs reflecting a state of readiness facilitating rapid task-dependent shifts toward and away from synchronous states that abolish LRTCs.

Generalized CNS arousal: An elementary force within the vertebrate nervous system

“…In order to be functionally effective, the brain, in low GA, must be poised in the vicinity of the transition to higher GA; that is, at a critical point between two states (Botcharova et al, 2014; Alonso et al, 2014)…”

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.…”

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

“…It has been proposed that synchronization in the brain is delicately poised at a transition between completely ordered and disordered interactions (Kitzbichler et al, 2009; Botcharova et al, 2014), a feature that may arise more generally from brain dynamics that are self-organized at the edge of stability (Beggs, 2008; Shew et al, 2009; Chialvo, 2010). The so called metastable dynamics that arise at this transition, are hypothesized to facilitate optimal information transfer (Barnett et al, 2013), maximize dynamic range and adaptability (Kinouchi and Copelli, 2006; Shew et al, 2009) as well as increase the network's capacity for information storage (Shew et al, 2011).…”