Depth of Anaesthesia Assessment Based on Spectral Entropy

Anaesthesia is a state of temporary controlled loss of awareness induced for medical purposes. An accurate assessment of the depth of anaesthesia (DoA) has always been required. However, the current DoA algorithms have limitations such as inaccuracy or inflexibility. In this study, for more reliable DoA assessment, pre-denoised electroencephalograph (EEG) signals are divided into ten frequency bands ( α, β1, β2, β3, β4, β, βγ, γ, δ and θ ), and the basic complexity measure is done by using spectral entropy (SE). SE from beta-gamma frequency band (21.5 - 38.5 Hz) and SE from beta frequency band show the highest R squared value (0.8458 and 0.7312, respectively) with currently the most popular DoA index, bispectral index (BIS). A new DoA index is developed based on these two SE values for monitoring the DoA and evaluated by comparing with the BIS index. The highest Pearson correlation coefficient is 0.918, and the average is 0.80. In addition, the proposed index shows an earlier reaction

than BIS index when the patient from deep anaesthesia to moderate anaesthesia, and the consistency in the case of poor signal quality (SQ) while the BIS Index exhibits inflexibility with cases of poor SQ.

Introduction
Monitoring the patients' depth of anaesthesia (DoA) is one of the current challenges in medicine. An accurate assessment of the DoA is crucial as the patient under-dosage may lead to intraoperative awareness with recall, while the over-dosage may lead to prolonged recovery and an increased risk of postoperative complications for the patient. Various human and animal researchers confirmed that electrical brain activities significantly correlated with the DoA during surgery. Most of brain electrical activities can be represented by the electroencephalograph (EEG) signals. EEG monitoring methods are typically non-invasive, with small metal discs with thin wires (electrodes) placed on the scalp, and then send signals (voltage fluctuations resulting from ionic current within the neurons of the brain) to a computer to record the results. EEG patterns change during stages of anaesthesia, and, as the level of anaesthesia becomes deeper, EEG signals gradually shift toward higher-amplitude and lowerfrequency activity. The DoA monitoring using EEG improves patient treatment outcomes by reducing the incidences of intra-operative awareness, minimizing anaesthetic drug consumption and resulting in faster wake-up and recovery [22,6]. Consequently, most of the recent research has been turned their attention to developing and finding non-invasive ways to monitor the DoA based on electrical brain activities.
When using EEG signals to measure the DoA, the bispectral index (BIS) monitor is commonly the primary indicator for anesthesiologists. The BIS index is a statistically based, empirically derived complex parameter, which is a weighted sum of several EEG sub-parameters, including a time domain, frequency domain, and high order spectral sub-parameters [1]. The BIS takes an EEG complex signal and provides the result into a single dimensionless number, which ranges from 0 (almost flat EEG activity) to 100 (awake). An appropriate level for general anaesthesia takes place in a BIS value between 40 and 60 [8].
However, the BIS has limitations, such as being delayed, not robust with different anesthesia medications, and not accurate across patients [6]. There are some possible improvements in the algorithms. Different attempts have been made to construct a new index using EEG signals to provide a more reliable reference to the DoA for clinical practitioners. Various methods have been developed to decompose and extract features of a frequency segment of the raw EEG over recent years. While several algorithms have been used in clinical studies and applied to EEG analysis, an algorithm based on spectral entropy (SE) is proposed in this study and its performance is compared with a method applying permutation entropy (PE). A window segmentation technique [28] is also employed with decomposing its frequency bands of an EEG signal, and then each EEG segment is divided into a number of small blocks. The parameters (SE and PE) are calculated from the blocks and averaged over each segment. Then, the selected parameters are trained, tested, and evaluated by the Pearson correlation coefficient to build a new DoA index model.

Methods
In this research, the original EEG signals were de-noised using a nonlocal means method [3]. EEG signals are hard to be processed due to the great complexity and non-stationarity. Decomposing an EEG signal into a set of signals with different frequency bands is one efficient strategy to analyse it. Then, one EEG signal is partitioned into small segments using a window segmentation technique [28]. The window size in this paper was 56 second (s) with overlapping of 55s. EEG segment was divided into a number of blocks. The parameters (SE and PE) are calculated from the above blocks and averaged over each segment. These values can be used in time-domain methods to calculate their correlations with their changing anaesthetic states. The methods for a new DoA index design are demonstrated in Fig. 1.

Experimental Data
The EEG data were collected at Toowoomba St Vincent's Hospital from 24 adult patients. The demographics information of all the participants who involved in this study is explained in Table 1  alpha to gamma (8 Hz-60 Hz) are extracted using FFT [19]. Applying a simple classifier such as Knearest neighbor (KNN) with that frequency domain offered a maximum mean classification accuracy of 91.33 % on the beta band [19]. In this study, WT was not necessary for frequency discrimination because time-series filtering by Fourier transform was applied to obtain different frequency components of denoised EEG datasets.

Frequency bands of EEG signals
The EEG signals are normally classified into five basic frequency bands (α, β, γ, δ and θ) [20]. The EEG characteristics analysis is mostly based on the different frequency bands, and DoA algorithms are usually designed upon the frequency bands dynamics [31]. For the BIS index, the phase coupling between high frequency (40 to 47 Hz) and a broader frequency range (0.5 to 47 Hz) of EEG waves is quantified, and the ratio of higher frequency waves (30 to 47 Hz) to other waves of lower frequency (11 to 20 Hz) is measured to compute the bispectrum [10]. In this study, the frequency bands are divided and filtered into ten frequency bands group (α, β1, β2, β3, β4, β, βγ, γ, δ, and θ) by FFT methods to find parameters which have a higher correlation with anaesthetic states.

Spectral entropy
Extracting features simplifies the amount of data needed to describe a huge set of data accurately. In addition, features extraction is important to minimize the loss of essential information embedded in a signal. Various methods have been used to extract the features from EEG signals. Among those methods are entropy [16], detrended moving average (DMA) [21], isomap-based estimation [11], Bayesian [35], and so on [4]. In the past decade, entropy algorithms have been widely used for features extraction in EEG signals during anaesthesia. EEG patterns during the course of anaesthesia are time series and nonlinear, and entropy algorithm is a measure of complexity that can be easily applied to any type of time series nonlinear data of complexity, including physiological data such as heart rate variability and EEG data. One of the entropy methods, SE quantifies the amount of potential information conveyed in the power spectrum of a given signal. Zhang et al. (2015) evaluated the inter-session prediction performance of the sensorimotor rhythm-based brain-computer interface using a SE predictor, and their results showed that the average classification accuracy of the inter-session prediction is up to 89 % [34].
Das and Bhuiyan (2016) also investigated the efficiency of several SE-based features in a comprehensive analysis of focal and non-focal EEGs [5]. When the log energy entropy values were utilised as features in a KNN classifier to classify the signals, it provided 89.4% accuracy and with 90.7% sensitivity, which was higher than those by some state-of-the-art methods [5]. Xu et al. (2006) studied the SE from rats' EEG to investigate and measure brain activity variations under different DoA.
They found that the SE of EEG would decrease quickly while the DoA was from light to deep and vice versa [32]. However, despite numerous researches engaged with entropy-based algorithms, few articles among them were related to SE in human-related DoA assessment. Hence, this research examines the SE of each frequency band from an EEG signal and also investigates a PE to compare their performances from features extraction.
The SE of a signal is a measure of its power spectrum distribution [30]. The SE takes the signal's normalised power spectrum distribution in the frequency domain as a probability distribution and calculates its Shannon entropy. The equations for SE are derived from the equations for the power spectrum and probability distribution for a signal. For a signal x(n), the power spectrum is S(m) = |X(m)| 2 , where X(m) is the discrete Fourier transform of x(n). According to Ulrych [30], the probability distribution P(m) is then: The SE (H) follows as: (2) Normalizing (3) where N is the total frequency points. The denominator, log2N, represents the maximal SE of white noise, uniformly distributed in the frequency domain. If a time-frequency power spectrogram S(t, f) is known, then the probability distribution P(m) becomes: (4) Then the SE at time t (H(t)) is:

Features extraction based on SE and PE
The parameters (SE and PE) are calculated from blocks in a segmented EEG and averaged over each segment. The SE or PE values in time domain analysis methods should be highly correlated with changing anaesthetic states. These correlations should also be robust for different patients. The degree of their correlation is measured by the coefficient of determination (R 2 ) in this research. The R 2 indicates the degree of the variance in the dependent variable that the independent variables explain collectively.
The SE and PE values are calculated from 10 frequency bands (α, β1, β2, β3, β4, β, βγ, γ, δ, and θ) of each EEG episode and the R 2 is used to evaluate the correlation between parameters and anaesthetic states (referring to the BIS in this study). The definition of the R 2 [14] is: Where yi is a data set, ̅ is the mean of a data set, and fi is a set of predicted values. The greater the R 2 is, the higher correlation between the parameter and BIS value is.

Regression Models and Evaluation
where x is the new index value, ̅ is the mean of new index, y is the corresponding BIS value, and ̅ is the mean of BIS. The value of r is between [-1 1]. If r is closed to 1 or -1, it means that the two indexes are highly correlated. If r equals 0, it means that there is no correlation at all between the indexes.
The RMSE is a square root of MSE [18]. The definition of the MSE is as follows : Where n is the number of data points, is a set of observed values, and ̂ is a set of predicted values.

Features selection
Before parameters are calculated from different frequency bands, SE and PE values are calculated from EEG signals of channel 2 (Ch2) and the sum of EEG signals of channel 1 and channel 2 (Ch1+Ch2) to select the channel so that the experimental design can be simplified but more efficient. As shown in Fig. 2, the R 2 of SE and PE from Ch2 and Ch1+Ch2 (the reference is the BIS index) have very close to each other. Therefore, the EEG signals from Ch1 or Ch1+Ch2 are not necessary to be analyzed when the EEG signals from Ch2 are analyzed.  The average R 2 value of SE and PE in each frequency band from 13 patients (randomly chosen) of EEG signals are shown in Fig. 4.    Fig. 6 (a)). In addition, the RMSE from the linear regression analysis is lower than any other analytical methods in this study. The lowest RMSE from the linear regression of these samples is 10.16 ( Fig. 6 (b)). The execution time is also an important factor of selecting analytical methods because the execution time for analysis is crucial in the real-time measurements of the DoA.
The average execution time for each regression analysis is measured and shown in Table 2. The linear regression analysis records the shortest execution duration (0.5 seconds), and SVM takes the longest time for the analysis (186 seconds).

New DoA design and evaluation by linear regression
The selected parameters (SE calculated from β and βγ) of the EEG data from ten subjects (patient ID:

Patient's state in the case of poor signal quality
The signal quality indicator (SQI) is an index for signal quality which is calculated based on impedance data, artefacts, and other variables. The BIS index is not capable of calculating the valid values on the screen when SQI is lower than 15. In these cases, the value -3276.8 was labeled as a notice "excessive artefact detected in signal" [23]. The performance of the new index in poor signal quality cases (according to SQI) is also evaluated. The new index produces the DoA values when SQI is lower than 15, where the BIS index could not calculate the index. In Fig. 8 and Fig. 9, for patient ID 3, the BIS index is -3276.8 from 611 to 629 seconds and from 1294 to 1301 seconds. In Fig. 10 Fig. 10. The index value 35 is assumed to be the point at which the anaesthetic states transfers from deep anaesthesia to moderate anaesthesia. We can observe that the upward transit of the BIS from 20 to 50 is lethargic and delayed than the new index in the graph below (Fig 10). The time difference for 14 patients are provided in Table 3.  Table 3 The time response comparison between the new index and the BIS   Patient ID  4  7  9  10  11  12  13  14  16  17  19  21  24  25  Time  difference   200  75  258  231  41  116  331  100  6  157  288  266  132  14

Discussion
Extracted features reduce the number of data points needed to describe a huge set of data accurately as well as minimize the loss of essential information embedded in signals. The features extraction based on SE in this study successfully leads to develop a reliable DoA algorithm for accurate DoA assessment.
The denoised EEG signals were, firstly, divided into ten sub-frequency bands (α, β1, β2, β3, β4, β, βγ, γ, δ, and θ), and then the basic complexity measure was done by using SE and PE. The SE from βγ frequency band and the SE from the β frequency band yield the highest R 2 value (0.8458 and 0.7312, respectively) with the BIS in this study. Frequency bands decomposition from EEGs were enabled by the FFT, and SE values were obtained from ten sub-frequency bands. WT was not necessary for time-domain frequency bands decomposition in this study because software MATLAB offers an FFT filter, which performs time-series filtering by using an FFT to analyse the frequency components in the input data sets. There are six types of filters available in the FFT filter function, and the band-pass filter function was used to separate the frequency bands in this study.
This study proves that the results of the experiment by Xu et al. [32], which showed that SE was sensitive to the states of rats' light and deep sleeps. Some studies [9,24] [27] proposed that the PE is the promising parameter selecting algorithm discriminating different levels of consciousness during anaesthesia. The PE showed a high correlation (the highest R 2 = 0.793) with the BIS index, but the SE presented an improved correlation (the highest R 2 = 0.846) than PE in this study. Along with other studies that were related to the analyses of the human brain activity [26,34], the SE was proved to be a useful algorithm to monitor the stages of human anaesthesia during surgery.

Conclusions
The new DoA index was developed based on two SE values (from β and βγ) for monitoring the DoA.
It was evaluated by comparing with the BIS index. The highest r value is 0.918, and its average value In conclusion, SE of the EEG is highly sensitive to the levels of anaesthesia. Therefore, an improvement can be expected with SE application in the accuracy of DoA assessment in the future.