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Edited by: Felix Blankenburg, Freie Universität Berlin, Germany

Reviewed by: Dirk Ostwald, Freie Universität Berlin, Germany; Xiaoli Li, Beijing Normal University, China

*Correspondence: UnCheol Lee

This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) and the copyright owner are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.

The integrated information theory (IIT) proposes a quantitative measure, denoted as Φ, of the amount of integrated information in a physical system, which is postulated to have an identity relationship with consciousness. IIT predicts that the value of Φ estimated from brain activities represents the level of consciousness across phylogeny and functional states. Practical limitations, such as the explosive computational demands required to estimate Φ for real systems, have hindered its application to the brain and raised questions about the utility of IIT in general. To achieve practical relevance for studying the human brain, it will be beneficial to establish the reliable estimation of Φ from multichannel electroencephalogram (EEG) and define the relationship of Φ to EEG properties conventionally used to define states of consciousness. In this study, we introduce a practical method to estimate Φ from high-density (128-channel) EEG and determine the contribution of each channel to Φ. We examine the correlation of power, frequency, functional connectivity, and modularity of EEG with regional Φ in various states of consciousness as modulated by diverse anesthetics. We find that our approximation of Φ alone is insufficient to discriminate certain states of anesthesia. However, a multi-dimensional parameter space extended by four parameters related to Φ and EEG connectivity is able to differentiate all states of consciousness. The association of Φ with EEG connectivity during clinically defined anesthetic states represents a new practical approach to the application of IIT, which may be used to characterize various physiological (sleep), pharmacological (anesthesia), and pathological (coma) states of consciousness in the human brain.

Integrated information theory (IIT) postulates that consciousness is identical to integrated information and that a system's capacity for consciousness can be expressed by a quantitative measure referred to as Φ (Tononi,

In this study, we introduce a novel method to estimate the relative change of Φ and test its ability to predict levels of consciousness as modulated by various anesthetic agents (see Figure

Schematic diagram of experiments and analysis. The high-density EEG data were recorded from two experiments.

Glossary.

Integrated information (Φ) | Information that is specified by a system that is irreducible to the information specified by its parts. It is calculated as the distance between the conceptual structures specified by the intact system and that specified by its minimum information partition. |

Effective information (φ) | The repertoire specified by a mechanism in a state informs the possible past and future states of a system. Effective information is defined as the distance between effect repertoire and corresponding unconstrained probability distributions. |

Markovian integrated information (Φ_{DM}) |
Integrated information for discrete dynamic systems. Each partitioned state is measured with the reduced entropy by maximizing the entropy of the past state. |

Empirical integrated information ( |
Integrated information for a continuous time series derived from Markovian integrated information by using the assumption of a Gaussian distribution of time series and differential entropy formula. |

Auto-regressive integrated information ( |
Integrated information for systems with a non-Gaussian distribution of time series by substituting the covariance of the time series of the empirical integrated information to the prediction error of linear regression of time series. |

Mismatched decoding integrated information (Φ^{*}) |
The Φ^{*} is calculated with the difference between actual mutual information under the actual probability distribution of the system and the hypothetical mutual information under mismatched probability distribution where a system is partitioned into hypothetical independent parts. |

Relative changes of integrated information ( |
Estimation of the mean integrated information of randomly and globally sampled small sets of EEG channels. This method was introduced in the current study to investigate the relative change of the mean integrated information across states and its relationship with conventional EEG properties, rather than calculating the precise Φ of a system. |

Regional integrated information ( |
Evaluation of the contribution of a certain EEG channel to the |

This study was conducted at the University of Michigan Medical School and approved by the Institutional Board Review (HUM00061087 and HUM0071578); written informed consent was obtained from all participants.

In this study we conducted secondary analyses of high-density EEG data gathered in healthy volunteers during two independent studies; detailed methodology can be found in Vlisides et al. (Vlisides et al.,

EEG was acquired with 128-channel HydroCel nets, Net Amps 400 amplifiers, and Net Station 4.5 software (Electrical Geodesics, Inc., USA). The EEG was digitized continuously at 500 Hz with a vertex reference. Per manufacturer recommendations, channel impedances were kept at <50 kΩ, and the net was wrapped with gauze to optimize contact between the electrodes and scalp. Baseline and recovery EEGs in the ketamine experiments were recorded for 5 min. EEG during exposure to subanesthetic ketamine was recorded during an infusion of 0.5 mg/kg administered over 40 min. EEG during ketamine anesthesia was recorded after an intravenous bolus of 1.5 mg/kg ketamine until return of responsiveness. Baseline and recovery EEG in the propofol-isoflurane experiments was recorded for 5 min. The propofol administration sequence was recorded for 15 min. Deep anesthetic state EEG with isoflurane was recorded for ~180 min. After the recording, 32 channels on the lower part of the face and head were removed, leaving 96 channels in place, to avoid confounds in the analysis of occipital and prefrontal channels due to contamination from contact with the bed and facial movements. The average reference was used for referencing and the windowed sinc-FIR filter was used to avoid a possible shifting of the signal phases (in the MATLAB toolbox from EEGLAB). For EEG analysis, we chose a clean 2-min EEG epoch for each state (baseline, sedated, anesthetized, and recovery), and segmented it into 6-s long EEG epochs. Noisy epochs were excluded by visual inspection based on power spectrum and EEG signal.

In this study, we differentiated deep anesthesia (non-responsive with burst suppression) from general anesthesia (non-responsive state). Burst suppression is a well-known EEG characteristic observed in the deeply anesthetized state. The EEG pattern is characterized by periods of high voltage electrical activities alternating with minimal activity. We used the burst suppression ratio (BSR: the fraction of EEG in suppression per epoch) of 0.3 to determine the burst suppression period (Vijn and Sneyd,

For all selected periods within each subject, spectral power was computed based on the short-time Fourier transform using the “spectrogram.m” function in the MATLAB Signal Processing Toolbox (time window: 3 s hamming window, overlap: 50%). The relative power was then computed for each experimental period at each of five frequency bands (delta: 0.1–4 Hz, theta: 4–8 Hz, alpha: 8–13 Hz, beta: 13–25 Hz, gamma: 25–45 Hz), for all 96 channels. The difference in relative power among the different states was tested with linear mixed model analysis.

The integrated information theory defines

where X is the system, x is a state, and P is a partition P = {^{1}, …, ^{r}}.

Identifying the MIP requires searching all possible partitions and comparing their effective information φ. This is the most time consuming process in the application to high density EEG. Furthermore, considering the fact that the EEG recorded during anesthetic state transitions are non-Gaussian and continuous time series, it is important to choose a valid version of Φ (Φ_{DM}, ^{*}). In Table

Markovian integrated information (Φ_{DM}) is defined for a discrete dynamic system (Balduzzi and Tononi, _{DM}) is measured with the reduced entropy by maximizing the entropy of the past state; the lowest value of effective information among the partitions is defined as Φ_{DM}.

where X is a discrete system, and M represents the subsets. Barrett and Seth modified Φ_{DM}, and introduced empirical integrated information (_{E}), which works for a continuous time series.

where τ is the time delay between the past and present states, and ^{1, 2} are the bi-partitioned subsets. To make the calculation of (4) easier, the entropy terms

For the application to non-Gaussian time series,

where τ is the time delay between the past and present state^{1, 2} are the bi-partitioned subsets. _{t} = α + A·_{t−τ} +_{t}. ^{Mk}) is the determinant of the covariance (∑) of predictions errors (^{Mk}). The

Although many improvements have been made in the algorithms of Φ over the last decade, the computation time is still unrealistic because of the need to search an enormous number of partitions to identify the MIP.

Here we suggest a method to circumvent the fundamental problem by considering the average features of many small sample units rather than trying to identify the MIP and its effective information for all EEG channels. A sample unit consists of a small number of EEG channels randomly selected with the total number of sample units large enough to represent the behavior of the entire high-density EEG montage. In this study, we directed our interest only to the relative changes of Φ values across states (baseline, sedation, anesthesia, burst, suppression, and recovery), rather than to the exact Φ value of the brain for each state, which is impossible with the superficial and spatially imprecise brain activity recorded by EEG.

For each sample unit, we were able to calculate the MIP and its effective information φ, that is, the Φ of the sample unit. For instance, in this study, we selected 8 random EEG channels for a sample unit, and acquired 600 sample units that were randomly selected from the baseline states. The same 600 sample units determined in the baseline were then compared across states to investigate the increase or decrease of Φ values. Since the number of possible bipartitions of 8 channels is

The average

where _{i}(_{surr}(_{i}(

Since the random selection of EEG channels can produce variable

where the total number of the sample

We also estimated the contribution of a single EEG channel

To reconstruct a network from EEG data, we used weighted Phase Lag Index (wPLI), which is robust to the EEG volume conduction problem (Stam et al.,

where the signed PLI is the numerator normalized by denominator, the imaginary part of cross-spectrum.

To reduce spurious connectivity of EEG, 20 surrogate data sets were generated with a random shuffling method, in which a time point is randomly chosen in each EEG channel; the EEG epochs are then shuffled before and after the time point. The shuffled data has almost the same amplitude distribution and power spectrum of the original EEG but disruptions of the original connectivity between two EEG signals. The non-zero wPLI from the shuffled data is regarded as spurious connectivity. We expected that different EEG frequency bands and different states would have different levels of spurious connectivity (Lee et al.,

where _{i} and _{j} are the node degrees, m is the total number of links in the network, and _{i} = 1 if node _{i} = −1 if it belongs to group 2 for a particular division of the network into two groups.

The overall strengths of

Linear mixed-effects model analysis was used to evaluate the significance of the results (Pinheiro and Bates,

where Y is the known vector of observation, β is an unknown vector of fixed effects, u is the unknown vector of random effects, ε is an unknown vector of random errors, and X and Z are known design matrices relating the observations Y to β and u, respectively. The analyzed properties (integrated information, degree, number of modules, and relative power) were set as observation vector Y, the states and epochs were set as fixed effect, and the epochs with subject numbers were set as random effects. The MATLAB function ‘fitlme.m’ was used to test all states pair-wise. Data from experiment 1 (ketamine) and experiment 2 (propofol-isoflurane) were calculated separately. Performance of the statistical tests was assisted by Consulting for Statistics, Computing & Analytics Research (CSCAR, University of Michigan).

To determine the significance of

Configurations of

The changes of power, connectivity, modularity, and Φ of the conventional frequency bands of EEG after anesthesia with ketamine and propofol.

Relative power of spectrogram | |||||

Integrated information ( |
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Average degree (weighted PLI network) | |||||

Number of modules (modular structure) | |||||

To find a relationship between

There was a strong negative correlation between

We estimated the contribution of a single EEG channel on

Topographic structures of

The EEG connectivity and

Multi-dimensional parameter space based on EEG connectivity and

According to IIT, the level of consciousness is related to the system's functional differentiation and overall integration, mathematically expressed by Φ. The physical quantity and spatiotemporal grain necessary to measure Φ empirically is unclear. To test if there was a relationship between Φ estimated from EEG and various states of human consciousness, we modulated the state of healthy human volunteers with different anesthetics in two independent experiments. We introduced a method to estimate the relative change of Φ across states of consciousness referenced to the baseline, rather than calculating the precise Φ of a state. The method is based on estimating the mean integrated information

The alpha band was associated with the highest node degree and long-range functional connectivity (Figures

When data from EEG burst and suppression periods were analyzed separately, the Φ of the EEG bursts is similar to or even larger than wakeful consciousness. This could suggest a similar or higher level of consciousness during the burst period in deep anesthesia. However, other evidence suggests alternative interpretations. First, the topographical structures of node degree and

Obviously, the separation of burst and suppression periods into independent states may not be clinically relevant. Without such separation, the

The multi-dimensional parameter representation (Figure

The recovery of responsiveness following anesthesia in the absence of a full recovery of integrated information implies that there may be a threshold of integration above which subjects regain purposeful responsiveness (Tononi,

In this study, Barrett and Seth's algorithm,

Oizumi et al. attempted to solve the theoretical problem of calculating Φ from empirical time series with a new approach called “mismatched decoding,” but the method is subject to the limitation of a Gaussian assumption (Oizumi et al., ^{*} from Oizumi et al. Both measures with a Gaussian assumption showed similar patterns to each other across the five states, which are also comparable with ^{*} of the suppression period was much higher than zero (in Supplementary Figure

This study introduced a novel and practical method to estimate Φ from high density EEG and applied it to various states of consciousness altered by general anesthesia induced by ketamine and propofol-isoflurane. The investigation of the EEG properties corresponding to large and small

AH, GM, HK, and UL wrote the manuscript; UL designed research; HK and UL developed the computational methods; HK analyzed data; JL curated data; GM and the ReCCognition Study Group acquired data; All authors reviewed the manuscript.

The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest. The reviewer DO and handling Editor declared their shared affiliation, and the handling Editor states that the process nevertheless met the standards of a fair and objective review.

ReCCognition Study Group members include: Michael S. Avidan, Tarik Bel-Bahar, Stefanie Blain-Moraes, Goodarz Golmirzaie, Ellen Janke, Max B. Kelz, Paul Picton, Vijay Tarnal, Giancarlo Vanini, Phillip E. Vlisides.

The Supplementary Material for this article can be found online at: