Modelling and analysis of amplitude, phase and synchrony in human brain activity patterns

The critical brain hypothesis provides a framework for viewing the human brain as a critical system, which may transmit information, reorganise itself and react to external stimuli efficiently. A critical system incorporates structures at a range of spatial and temporal scales, and may be associated with power law distributions of neuronal avalanches and power law scaling functions. In the temporal domain, the critical brain hypothesis is supported by a power law decay of the autocorrelation function of neurophysiological signals, which indicates the presence of long-range temporal correlations (LRTCs). LRTCs have been found to exist in the amplitude envelope of neurophysiological signals such as EEG, EMG and MEG, which reveal patterns of local synchronisation within neuronal pools. Synchronisation is an important tool for communication in the nervous system and can also exist between disparate regions of the nervous system. In this thesis, inter-regional synchronisation is characterised by the rate of change of phase difference between neurophysiological time series at different neuronal regions and investigated using the novel phase synchrony analysis method. The phase synchrony analysis method is shown to recover the DFA exponents in time series where these are known. The method indicates that LRTCs are present in the rate of change of phase difference between time series derived from classical models of criticality at critical parameters, and in particular the Ising model of ferromagnetism and the Kuramoto model of coupled oscillators. The method is also applied to the Cabral model, in which Kuramoto oscillators with natural frequencies close to those of cortical rhythms are embedded in a network based on brain connectivity. It is shown that LRTCs in the rate of change of phase difference are disrupted when the network properties of the system are reorganised. The presence of LRTCs is assessed using detrended fluctuation analysis (DFA), which assumes the linearity of a log-log plot of detrended fluctuation magnitude. In this thesis it is demonstrated that this assumption does not always hold, and a novel heuristic technique, ML-DFA, is introduced for validating DFA results. Finally, the phase synchrony analysis method is applied to EEG, EMG and MEG time series. The presence of LRTCs in the rate of change of phase difference between time series recorded from the left and right motor cortices are shown to exist during resting state, but to be disrupted by a finger tapping task. The findings of this thesis are interpreted in the light of the critical brain hypothesis, and shown to provide motivation for future research in this area

A power-law distribution of phase-locking intervals does not imply critical interaction

Neural synchronisation plays a critical role in information processing, storage and transmission. Characterising the pattern of synchronisation is therefore of great interest. It has recently been suggested that the brain displays broadband criticality based on two measures of synchronisation - phase locking intervals and global lability of synchronisation - showing power law statistics at the critical threshold in a classical model of synchronisation. In this paper, we provide evidence that, within the limits of the model selection approach used to ascertain the presence of power law statistics, the pooling of pairwise phase-locking intervals from a non-critically interacting system can produce a distribution that is similarly assessed as being power law. In contrast, the global lability of synchronisation measure is shown to better discriminate critical from non critical interaction.Comment: (v3) Fixed error in Figure 1; (v2) Added references. Minor edits throughout. Clarified relationship between theoretical critical coupling for infinite size system and 'effective' critical coupling system for finite size system. Improved presentation and discussion of results; results unchanged. Revised Figure 1 to include error bars on r and N; results unchanged; (v1) 11 pages, 7 figure

Complexity of multi-dimensional spontaneous EEG decreases during propofol induced general anaesthesia

Emerging neural theories of consciousness suggest a correlation between a specific type of neural dynamical complexity and the level of consciousness: When awake and aware, causal interactions between brain regions are both integrated (all regions are to a certain extent connected) and differentiated (there is inhomogeneity and variety in the interactions). In support of this, recent work by Casali et al (2013) has shown that Lempel-Ziv complexity correlates strongly with conscious level, when computed on the EEG response to transcranial magnetic stimulation. Here we investigated complexity of spontaneous high-density EEG data during propofol-induced general anaesthesia. We consider three distinct measures: (i) Lempel-Ziv complexity, which is derived from how compressible the data are; (ii) amplitude coalition entropy, which measures the variability in the constitution of the set of active channels; and (iii) the novel synchrony coalition entropy (SCE), which measures the variability in the constitution of the set of synchronous channels. After some simulations on Kuramoto oscillator models which demonstrate that these measures capture distinct ‘flavours’ of complexity, we show that there is a robustly measurable decrease in the complexity of spontaneous EEG during general anaesthesia