Botcharova, M; (2014) Modelling and analysis of amplitude, phase and synchrony in human brain activity patterns. Doctoral thesis , UCL (University College London).

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Abstract

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.

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