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.
Highlights
The concept of the brain as a dynamical system close to a critical regime is attractive because systems close to criticality are thought to maximize their dynamic range of information processing and communication, show efficiency in transmitting information and a readiness to respond to change (Linkenkaer-Hansen et al, 2001, 2004; Beggs and Plenz, 2003; Stam and de Bruin, 2004; Kinouchi and Copelli, 2006; Sornette, 2006; Shew et al, 2009; Werner, 2009; Chialvo, 2010; Beggs and Timme, 2012; Meisel et al, 2012; Shew and Plenz, 2013)
The aim of this paper is to introduce a new methodology for eliciting a marker of criticality in neuronal synchronization
The presence of long-range temporal correlations (LRTCs) in this quantity is proposed as marker of criticality and is assessed using detrended fluctuation analysis (DFA) in combination with the recently proposed ML-DFA, a heuristic technique for validating the output of DFA
Summary
The concept of the brain as a dynamical system close to a critical regime is attractive because systems close to criticality are thought to maximize their dynamic range of information processing and communication, show efficiency in transmitting information and a readiness to respond to change (Linkenkaer-Hansen et al, 2001, 2004; Beggs and Plenz, 2003; Stam and de Bruin, 2004; Kinouchi and Copelli, 2006; Sornette, 2006; Shew et al, 2009; Werner, 2009; Chialvo, 2010; Beggs and Timme, 2012; Meisel et al, 2012; Shew and Plenz, 2013).A number of modeling studies have shed important light on the behavior of neurally inspired systems close to their critical dynamical range (Kitzbichler et al, 2009; Shew et al, 2009; Breakspear et al, 2010; Daffertshofer and van Wijk, 2011; Poil et al, 2012). To date there have been two significant experimental observations suggesting that the brain may operate at, or near, criticality These are: (i) the discovery that the spatio-temporal distribution of spontaneous neural firing statistics can be characterized as neuronal avalanches with a power law distribution of avalanche size (Beggs and Plenz, 2003) and (ii) the presence of long-range temporal correlations (LRTCs) in the amplitude fluctuations of neural oscillations, typically bandpassed MEG or EEG (Linkenkaer-Hansen et al, 2001; Hardstone et al, 2012). The mechanisms by which avalanches and LRTCs of oscillation amplitude may maximize the dynamic range of information processing and communication are still to be fully understood and experimental and computational neuroscience data linking the two phenomena are only just beginning to emerge (Plenz and Chialvo, 2009; Poil et al, 2012).
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