Computational Intelligence and Neuroscience

Volume 2016, Article ID 2304356, 12 pages

http://dx.doi.org/10.1155/2016/2304356

## Spectral Gini Index for Quantifying the Depth of Consciousness

^{1}Department of Electronic Engineering, Soongsil University, Seoul 06978, Republic of Korea^{2}Department of Anesthesiology and Pain Medicine, Asan Medical Center, University of Ulsan College of Medicine, Seoul 05535, Republic of Korea^{3}Department of Clinical Pharmacology and Therapeutics, Asan Medical Center, University of Ulsan College of Medicine, Seoul 05535, Republic of Korea

Received 14 June 2016; Revised 13 September 2016; Accepted 26 September 2016

Academic Editor: Saeid Sanei

Copyright © 2016 Kyung-Jin You et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

We propose indices that describe the depth of consciousness (DOC) based on electroencephalograms (EEGs) acquired during anesthesia. The spectral Gini index (SpG) is a novel index utilizing the inequality in the powers of the EEG spectral components; a similar index is the binarized spectral Gini index (BSpG), which has low computational complexity. A set of EEG data from 15 subjects was obtained during the induction and recovery periods of general anesthesia with propofol. The efficacy of the indices as indicators of the DOC was demonstrated by examining Spearman’s correlation coefficients between the indices and the effect-site concentration of propofol. A higher correlation was observed for SpG and BSpG (0.633 and 0.770, resp., ) compared to the conventional indices. These results show that the proposed indices can achieve a reliable quantification of the DOC with simplified calculations.

#### 1. Introduction

The depth of anesthesia (DOA) must be precisely and appropriately controlled according to the surgical procedure and the patient’s medical condition. For example, inadequate anesthesia may provoke stress responses of the body such as hypertension, tachycardia, sweating, lacrimation, increased skeletal muscle tone, and spontaneous movement [1]. Tachycardia and hypertension can lead to various side effects such as a cardiovascular event. In contrast, an anesthetic agent overdose can cause hypotension, which can lead to hypoperfusion of the heart and brain in susceptible patients. Owing to the interpatient variability of the dose-response effect of anesthetic agents, the administration of an adequate amount of anesthetics and the maintenance of an appropriate DOA are challenging. Therefore, an objective and reliable method of evaluating the DOA is needed to maintain a stable level of anesthesia.

General anesthesia (GA) includes two independent components: hypnosis and analgesia [2]. Several methods of measuring the DOA are based on the changes in the autonomic nervous system, such as the degree of muscle relaxation, hemodynamics, sweating, and lacrimation [3, 4]. Methods using the heart rate variability reflect the changes in brainstem function [5, 6]. However, these parameters are poorly correlated with the cerebral cortex functions, are closely related to consciousness, and constitute poor indicators of the depth of consciousness (DOC) [7, 8]. Intraoperative awareness can occur without monitoring the DOC. Intraoperative awareness is the unexpected explicit recall of sensory perceptions during GA [9] and may occur in 0.1–0.2% of patients receiving GA [10]. Such awareness can lead to mental sequelae and posttraumatic syndrome [11]. Therefore, the parameters that monitor the DOC must focus on the electroencephalogram (EEG), which reflects the action of the cerebral cortex, of the thalamus, and of the brainstem. Many studies have attempted to develop indices for a quantitative, immediate, and continuous indicator of the DOC based on (sub)cortical electrical activities.

Information theoretical approaches, such as the spectral entropy [12–14], permutation entropy (PE) [15], and approximate entropy (AE) [16] methods, consider that the irregularity of the EEG change during anesthesia is expressed by information quantity. Although the spectral entropy approach has been clinically applied [17], these methods have the drawback that the estimation of the probability distribution, which is the theoretical basis of these methods, can be biased. The detrended fluctuation analysis (DFA) as a fractal dimension method was applied to EEG to assess the DOA [18]. Recently, [19] compared twelve entropy indices as indicators of the DOA that is induced by GABAergic agents and showed that the PE and AE outperformed the others. Other studies have focused on bispectrum-based methods using a higher order spectrum [20–23]. The bispectral approach measures the coupling between the phases of the spectral components. The bispectral index (BIS) has been verified in terms of efficacy and is being used in clinical practice [24]. However, the exact algorithm for the BIS has not been reported and is partially unknown [25]. Furthermore, bispectrum analysis, which is the core descriptor of the BIS, requires extensive calculations [26].

This paper demonstrates that the DOC can be quantified using a novel index that utilizes the inequality in the powers of the EEG spectral components. The Gini index, which was originally used for measuring income inequality in economics, is incorporated in the proposed methods, to measure the inequality in EEG waves. To our knowledge, this is the first study showing that the Gini index could be effective in monitoring the DOC. As an indicator of the DOC, the efficacy was determined by examining Spearman’s correlation between the proposed measures and the effect-site concentration of propofol with simple calculations.

#### 2. Materials and Methods

##### 2.1. Subjects

After obtaining the approval of the Asan Medical Center’s Review Board and written informed consent, thirteen volunteers were enrolled in the study. The subjects were aged over 20 years and were previously healthy with no abnormal laboratory results.

##### 2.2. EEG Recordings

The EEG was recorded using a QEEG-8 system (LAXTHA Inc., Daejeon, Korea) with seven channels of frontoparietal montages (Fp1, Fp2, F3, F4, P3, P4, and Cz referred to A2 of the international 10–20 system) and digitized at a frequency of 256 Hz and 16 bits of precision. The EEG was continuously recorded from 5 min before the start to 60 min after the end of the anesthetics infusion. A ninth-order Butterworth filter was used to remove the frequencies above 48 Hz from the EEG signals. In our study, analyses use data from channel F3.

##### 2.3. Blood Sample Acquisition

Microemulsion propofol (Aquafol-MCT™, Daewon Pharm. Co. Ltd., Seoul, Korea) was used as the general anesthetic [27]. When the volunteers arrived at the operating theatre, electrocardiography, pulse oximetry, end-tidal carbon dioxide partial pressure, and noninvasive blood pressure monitoring was started and EEG electrodes were applied. An 18 G angiocath was placed at the vein for propofol infusion, and a 20 G angiocath was placed in the contralateral radial artery for frequent sampling. The volunteers were preoxygenated with % oxygen and then a facial mask with 4 L/min of oxygen was applied. Continuous infusion of intravenous propofol was maintained for 60 min at a fixed rate of 12 mg/kg/h. Blood samples of 4 mL were acquired from the artery and vein at preset intervals: immediately before (0 min) and at 0.5, 1, 1.5, 2, 3, 4, 6, 8, 10, 15, 20, 30, 40, 50, 58, 60, 62, 66, 70, 80, 90, 120, 150, 180, 240, 300, 600, 720, and 1200 min after the beginning of propofol infusion. Additionally, samples were collected at the loss of consciousness (LOC) and recovery of consciousness (ROC). The LOC was assessed by verbally instructing the subjects to close their eyes immediately after the start of propofol infusion and at 10 s intervals until the volunteers did not respond. The ROC was evaluated by instructing the volunteers to open their eyes immediately after the end of propofol infusion at 10 s intervals until the subjects responded. Samples were collected in ethylenediaminetetraacetic acid (EDTA) tubes, centrifuged for 10 min at 3500 RPM, and then stored at −70°C until assay. Details of the anesthetic procedure have been previously described in [28].

##### 2.4. Conventional Methods

We compared five conventional methods: spectral entropy, permutation entropy, approximate entropy, detrended fluctuation analysis, and SynchFastSlow, which were investigated in recent studies [19, 30]. Conventional frequency domain-based methods have the following process in common. For one epoch of EEG, the spectral componentis calculated using the -point discrete Fourier transform (DFT) for the EEG signal amplitude at the time point . In (1), and are the corresponding frequency and sampling frequency of the spectral component, respectively, and is the frequency index. If the frequency range is reduced to , the frequency of the spectral component is bounded by the band of interest, Hz. For example, when the sampling frequency is 256 Hz and the length of the epoch is 5 s, and are appropriate for the analysis within the frequency range 13–40 Hz. The power spectrum of the signal is calculated from the spectral component as follows:where indicates the complex conjugate. The normalized power spectrum is calculated so that the sum of all frequency powers is equal to 1; that is,

###### 2.4.1. Spectral Entropy (SpE)

The Shannon entropy represents the minimum information quantity that can soundly express all states of a discrete random variable [31]. SpE is defined as the normalized Shannon entropy of the probability of spectral component occurrence when the signal is considered as a stochastic process:If the signal consists of only one spectral component, the SpE is equal to 0. In contrast, if all spectral components are uniformly distributed, the SpE becomes 1. Generally, and are used for the estimation of the DOC [12].

###### 2.4.2. Permutation Entropy (PE)

Permutation entropy [32] has been proposed as a complexity measure of epileptic EEG [33] and anesthetic EEG [15]. For the EEG signal amplitude at the time point , the vectors are defined aswhere is the time delay between samples and is the embedding dimension. Then, is expressed in the nondecreasing order:Each vector is mapped onto one of the permutation patterns. Then, the probability of the pattern occurring, , iswhere is the number of occurrences of the th permutation. In [32], PE is defined as and, in [15], it is modified asto include both slow and fast EEG oscillations. We used , as recommended in [15]. Because of the extensive repetition of ordinal patterns in slow waves, PE is dominated by the proportion of higher EEG frequencies.

###### 2.4.3. Approximate Entropy (AE)

Approximate entropy, as an approximation of the Kolmogorov-Sinai entropy, quantifies the randomness of a time series signal and has been evaluated [16] for application in the analysis of EEG signals associated with anesthetic effects. The vectors are defined aswhere is the embedding dimension that determines the dimension of the phase space. The fraction that expresses whether is within the filtering distance of is defined as The AE is defined by where The AE is known to decrease with increasing anesthetic concentration. We used the parameter set , , as recommended in [16].

###### 2.4.4. Detrended Fluctuation Analysis Exponent (DFA)

Reference [18] used the DFA technique to study the scaling behavior of the EEG. For EEG signal of length , the integrated series is defined asThen, is divided into nonoverlapping segments of length , and is the linear regression of the segment. The root mean square fluctuation of from the trend isExponent is the slope of the line in log-log representation, by using the linear regression of in function of , . We calculated with the segment length, , associated with 6.7–157.8 ms as recommended in [18].

###### 2.4.5. SynchFastSlow

The bispectrum approach is a method of measuring the degree of phase coupling between two spectral components contained in a signal. Unlike the SpE, which only uses the power spectrum, the phase information is not ignored. The bispectrum magnitude is defined aswhere is the spectral component of the th epoch. Although the relationship between the LOC and phase coupling has not been clarified, an increase in phase coupling has been observed during anesthesia. The bispectrum has been used to estimate the degree of anesthesia in clinical trials [25]. The bispectral index (BIS), a common indicator of the DOC, uses SFS which incorporates the bispectrum [20, 34]:This is approximately the logarithmic ratio of the bispectrum magnitude values in the delta, theta, alpha, beta, and gamma band versus that in the gamma band only.

##### 2.5. Proposed Methods

###### 2.5.1. Spectral Gini Index (SpG)

The Gini index [35] was originally used to quantify income inequality in the field of economics. If the income level of the th house is , the Gini index is calculated using the following equation [36]:If the incomes of all houses are equal, that is, , the Gini index becomes 0. Additionally, when only one house has income, that is, , the income inequality is maximum and the Gini index is equal to 1.

The proposed method incorporates the Gini index to quantify the inequality between power spectra in the range of interest, Hz. If each frequency of the power spectrum of the EEG signal is considered as an individual house and the power of the corresponding frequency is considered as the house income, we can quantify the spectral inequality in terms of the Gini index. Therefore, the proposed spectral Gini index (SpG) is expressed asThe SpG can measure the inequality in the spectral powers of the signal. For example, in a white Gaussian random signal, all spectral components have equal powers; thus the SpG becomes 0. In contrast, for a signal focused on a certain spectral component, the SpG approaches 1.

###### 2.5.2. Binarized Spectral Gini Index (BSpG)

Here, we introduce the Gini index of the binarized spectrum. Firstly, we define the binarized power spectrum :where is a parameter proportional to the average power of the EEG before injection. Then, the BSpG is defined asThe advantage of the BSpG is that its calculation is very simple. Considering a total of values, if values are equal to , (20) is simplified as follows:

Figures 1(a) and 1(b) show an example of the SpG and BSpG for various power spectra with different distributions. The power spectrum at the top of Figure 1(a) is mostly concentrated below Hz, showing an inequality with an SpG value of 0.84. In comparison, the spectrum in the middle exhibits less inequality and has a decreased SpG value of 0.66. The power spectrum at the bottom is uniform; therefore, the SpG is 0.00, the minimum value. The power spectra of Figure 1(b) show the binarized power spectra and the relevant BSpG. As shown in the upper left spectrum, the percentage of spectral components with powers below the threshold is 88%, and the BSpG value is 0.88. For the middle spectrum which exhibits less inequality, the BSpG has a smaller value. Finally, for the spectrum that shows perfect equality, the BSpG is equal to 0.00, as in the case of SpG. Thus, we consider that both the SpG and the BSpG can measure the inequality of spectral distributions.