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
... omputed 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. coherent whole (integration)     . A number of different measures of neural dynamical complexity have been proposed based on information sharing and transfer [2, 4,        . Properties of these measures have been explored on simple models, for instance neural network activity of artificial agents [9, 15] . However, these measures, based on information sharing and transfer, rely on restrictive assumptions, such as stationarity and linearity, that limit the conclusions that can be drawn when applied to real brain data [16, 17] . A series of recent studies take a more pragmatic approach to investigating the relationship between consciousness and complexity      . These studies have investigated, for subjects in diverse states of consciousness (e.g. wakeful rest, deep sleep, general anaesthesia), the electroencephalographic (EEG) response to transcranial magnetic stimulation (TMS). It has been found that, when subjects are unconscious, the response is stereotypical across electrodes and remains local to the site of stimulation, whereas when subjects are conscious, the response differs between electrodes and spreads across the whole cortex. In this way, the extent of both differentiation and integration is greater when the subject is conscious. A simple measure of complexity based on the (lack of) compressibility of the EEG response, as quantified by the Lempel-Ziv algorithm  , was developed for these data: the Perturbational Complexity Index (PCI)  . The PCI reflects simultaneous integration and differentiation since the EEG response is least compressible when it is both widespread and inhomogeneous. In a first application of this method, the PCI values obtained for conscious subjects were consistently higher than for unconscious subjects, to the extent that a single classifier threshold could be applied: when the PCI value was above the threshold the subject was always conscious and when the PCI value was below the threshold the subject was always unconscious  . On spontaneous steady-state EEG data, several indices labelled as measures of complexity have been computed on single time-series, reflecting local signal diversity over time rather than differentiation and/or integration across a network. These measures include various forms of spectral entropy [24-26] and again Lempel-Ziv complexity          and all of them have a tendency to decrease during general anaesthesia. Recently these measures have also been applied to auditory evoked potentials in disorders of consciousness patients  , and values were found to correlate with behaviourally-diagnosed level of consciousness, although there was no single cross-subject threshold for classifying subjects as conscious or unconscious. Here we investigated three simple measures of complexity on multi-dimensional spontaneous steady-state EEG data from subjects undergoing propofol-induced general anaesthesia. The first of these is the aforementioned Lempel-Ziv complexity. On spontaneous data Lempel-Ziv complexity strictly only reflects differentiation (and not integration); it computes diversity in patterns of activity in both space and time. The other two measures are amplitude and synchrony coalition entropy (respectively ACE and SCE). ACE is a variant of a measure introduced by Shanahan in  , and reflects the entropy over time of the constitution of the set of most active channels, while the novel SCE reflects the entropy over time of the constitution of the set of synchronous channels. ACE is similar to Lempel-Ziv complexity, in the sense that it quantifies variability in space and time of the activity. By contrast, SCE is conceptually different because it quantifies variability in the relationships between pairs of channels. We computed Lempel-Ziv complexity and the coalition entropy measures for sets of equally spaced channels across the whole scalp and also for sets of channels restricted respectively to the frontal, parietal, temporal and occipital lobes, on full broadband signals and on frequencyrestricted signals, in each case comparing results for data from wakeful rest, mild sedation and general anaesthesia. We contrasted these measures' ability to indicate conscious level on these data, with that of control measures not based on signal complexity, including normalized delta power [36, 38, 39] . In order to facilitate interpretation of our results we also computed the Complexity of Spontaneous EEG Decreases during General Anaesthesia PLOS ONE | 5 / 21 original signal and the imaginary part being the Hilbert transform of the signal. c) A synchrony time series is created for this pair of signals, being 1 at time t if the phases of the complex values of the analytic signals have similar magnitude at this time t. d) SCE (i) with respect to channel i is the entropy over columns (n × 1 synchronies) of the matrix Ψ i containing all n synchrony time series for channel i. The overall SCE is then the mean value of the SCE (i) across channels.