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

Mitochondrial physiology

As the knowledge base and importance of mitochondrial physiology to evolution, health and disease expands, the necessity for harmonizing the terminology concerning mitochondrial respiratory states and rates has become increasingly apparent. The chemiosmotic theory establishes the mechanism of energy transformation and coupling in oxidative phosphorylation. The unifying concept of the protonmotive force provides the framework for developing a consistent theoretical foundation of mitochondrial physiology and bioenergetics. We follow the latest SI guidelines and those of the International Union of Pure and Applied Chemistry (IUPAC) on terminology in physical chemistry, extended by considerations of open systems and thermodynamics of irreversible processes. The concept-driven constructive terminology incorporates the meaning of each quantity and aligns concepts and symbols with the nomenclature of classical bioenergetics. We endeavour to provide a balanced view of mitochondrial respiratory control and a critical discussion on reporting data of mitochondrial respiration in terms of metabolic flows and fluxes. Uniform standards for evaluation of respiratory states and rates will ultimately contribute to reproducibility between laboratories and thus support the development of data repositories of mitochondrial respiratory function in species, tissues, and cells. Clarity of concept and consistency of nomenclature facilitate effective transdisciplinary communication, education, and ultimately further discovery

Mitochondrial physiology

As the knowledge base and importance of mitochondrial physiology to evolution, health and disease expands, the necessity for harmonizing the terminology concerning mitochondrial respiratory states and rates has become increasingly apparent. The chemiosmotic theory establishes the mechanism of energy transformation and coupling in oxidative phosphorylation. The unifying concept of the protonmotive force provides the framework for developing a consistent theoretical foundation of mitochondrial physiology and bioenergetics. We follow the latest SI guidelines and those of the International Union of Pure and Applied Chemistry (IUPAC) on terminology in physical chemistry, extended by considerations of open systems and thermodynamics of irreversible processes. The concept-driven constructive terminology incorporates the meaning of each quantity and aligns concepts and symbols with the nomenclature of classical bioenergetics. We endeavour to provide a balanced view of mitochondrial respiratory control and a critical discussion on reporting data of mitochondrial respiration in terms of metabolic flows and fluxes. Uniform standards for evaluation of respiratory states and rates will ultimately contribute to reproducibility between laboratories and thus support the development of data repositories of mitochondrial respiratory function in species, tissues, and cells. Clarity of concept and consistency of nomenclature facilitate effective transdisciplinary communication, education, and ultimately further discovery

Analysis of 25 k-medoids chosen electrodes for each of four lobes.

<p>Blue star is WR, red diamond is LOC. The red error bars indicate standard error. LZc and ACE score for all subjects higher for WR as opposed to LOC, SCE does so for 6/7 subjects. The measures behave similarly for different brain regions. If the effect size Cohen’s <i>d</i> < 0.8 for the scores of a given subject, the subject’s label is printed in red.</p

Schematic of the computation of Lempel-Ziv complexity LZc.

<p>a) <i>x</i>_<i>i</i> is the activity of the <i>i</i>^<i>th</i> EEG electrode, i.e. the <i>i</i>^<i>th</i> channel, and <i>a</i>_<i>i</i> is the (Hilbert) amplitude of <i>x</i>_<i>i</i>. b) <i>b</i>_<i>i</i> is binarized <i>a</i>_<i>i</i>, using the mean activity of <i>a</i>_<i>i</i> as binarisation threshold. c) After binarisation of all <i>n</i> channels, successive <i>n</i> × 1 dimensional observations are concatenated to obtain one binary sequence <i>s</i> in which patterns are searched and listed into a dictionary of binary words via a Lempel-Ziv algorithm. d) Lempel-Ziv complexity LZc is proportional to the size of this dictionary.</p

Schematic of the computation of SCE.

<p>a) Two time series. b) The analytic signals of these two, being complex signals with the real part being the 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 <i>t</i> if the phases of the complex values of the analytic signals have similar magnitude at this time <i>t</i>. d) SCE^(<i>i</i>) with respect to channel <i>i</i> is the entropy over columns (<i>n</i> × 1 synchronies) of the matrix Ψ_<i>i</i> containing all <i>n</i> synchrony time series for channel <i>i</i>. The overall SCE is then the mean value of the SCE^(<i>i</i>) across channels.</p

Effect size comparison per measure and state pair.

<p>For each measure and state pair, the three numbers correspond to how many subjects out of 7 had higher score for the left state with Cohen’s <i>d</i> > 0.8 (left digit), no substantial difference, <i>d</i> < 0.8, (middle) and higher score for the right state with Cohen’s <i>d</i> > 0.8 (right). The results were obtained from applying the measures to the broadband signal from 25 k-medoids chosen electrodes from the whole cortex. Here WRa is wakeful rest emerging from propofol sedation.</p><p>Effect size comparison per measure and state pair.</p

Channel selection from the high density (256 electrodes) EEG.

<p>The electrode layout is from manufacturer EGI [<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0133532#pone.0133532.ref040" target="_blank">40</a>]. The homogeneously distributed channel selection is shown for: a) analyses across the whole scalp; b) analyses restricted to a certain lobe. Chosen channels are indicated as black stars. See text for details.</p

LZc, SCE and ACE computed as averages over multiple 10sec segments of EEG of the 7 subjects before and during anaesthesia.

<p>States shown are wakeful rest (WR) before propofol, mild sedation (MS), LOC and wakeful rest emerging from propofol sedation (WRa, not shown for single subject results). Measures are computed across 25 channels spread evenly across the whole cortex. The measures score highest for shuffled WR data, and consistently across subjects higher for WR as opposed to LOC. Error bars indicate standard error across segments, cyan horizontal lines are example thresholds for each of the measures, separating WR from LOC for all 7 subjects. For each single subject plot, the mean and standard error across its 7 values per state is displayed in the narrow plot to its right, with the title ‘mean’. For these mean values across subjects, significant differences between state pairs are shown by a double asterisk if <i>p</i> < 0.01 and a single asterisk if <i>p</i> < 0.05 (Wilcoxon rank sum test, FDR corrected for multiple comparison). See <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0133532#pone.0133532.t001" target="_blank">Table 1</a> for effect size comparison.</p

Complexity measures for increasingly regular activation/synchrony matrices.

<p>Given a random binary matrix of activations (for ACE and LZc) or synchronies (for SCE), with increasing number of duplicated channels, the complexity measures monotonically decrease with the number of equal channels. See text for details.</p