The data used for the present analysis were obtained from 25 female subjects in the age range 30-78 years who had undergone breast cancer surgery under general anaesthesia at Regional Cancer Centre, Trivandrum, Kerala, India. A written informed consent was obtained from all participating subjects and the study protocol was approved by the institutional medical ethical committee.

Each subject was pre-medicated with Alprazolam (0.25 to 0.5 mg), Pantoprazole (40 mg), and Domperidone (10 mg) at 10 PM the night before surgery and at 6 AM on the day of surgery. An intravenous line was started just before surgery and Glycopyrolate (0.2 mg), Midazolam (1 mg), and Fentanyl 1 $\mu$g/kg were given just prior to the start of surgery. Additionally, analgesic drugs like Paracetamol (1 g), Diclofenac sodium (75 mg), an intravenous anaesthetic drug propofol (2 mg/kg), and a muscle relaxant drug Vecuronium Bromide (0.1 mg/kg) were given during the surgery. TPatients were ventilated with oxygen (O $ {}_{2} $)-Sevoflurane and nitrous oxide (N $ {}_{2} $ O) to maintain anaesthesia for the duration of the surgery. Additional doses of Fentanyl, up to 0.5 $\mu$g/kg, were given if blood pressure (BP) or heart rate (HR) increased more than 20 percent above base line. If the BP or HR was not controlled by Fentanyl then Nitroglycerin (NTG) was administered to control BP and Metoprolol was used to control HR.

A BIS electrode was used to collect the EEG signal and BIS value from each subject. The EEG signal was sampled at 128 samples per sec. The collected EEG database was classified as awake, induction, maintenance, and recovery signal depending upon the time at which data was collected[22].

(i) Awake signal: EEG signals collected 5–10 minutes before administering intravenous anaesthetic agents. Corresponding BIS values ranged between 80–100.

(iii) Maintenance signal: EEG signals collected after insertion of endotracheal tube and administration of inhalation agent until the end of surgery. Corresponding BIS value ranged between 40-60.

(iv) Recovery signal: EEG signals collected after the cut off of inhalation agent and administration of reversal agent (Neostigmine and Glycopyrolate) until return of consciousness. Corresponding BIS values ranged between 60-80.

EEG signals corresponding to BIS values of 0-20 were not analyzed due to the possibility of hemodynamic instability of the patient during surgery and hence were beyond the scope of this study.

A 50 Hz notch filter was used to remove power line interference from the recorded EEG signals[3]. EEG signals were segmented using a uniform segmentation method that divides EEG signals into non-overlapping rectangular windows of eight second duration[23]. Fig.1 shows one segment of EEG signal corresponding to each different phase of anaesthesia. Amplitude of the EEG signal increases and frequency decreases with increase in DoA. Induction EEG signals are deep, maintenance EEG signals are moderate, and recovery EEG signals are light anaesthetic EEG signals. One segment of EEG signal was eight seconds of data or 1024 data samples.

The time and frequency distribution of the awake, induction, maintenance, and recovery EEG signals were analyzed using histograms and frequency distribution plots. Plots in Fig.2 shows the histogram and Fig.3 shows the frequency spectrum corresponding to an eight second EEG recording of a subject in each phase. The amplitude of the EEG signal increases and the frequency decreases when the DoA increases[24]. Amplitude variations were more visible in the histogram. For awake EEG signals the amplitude range was $-$15 to $+$15 $\mu$V, induction signal (very deep anaesthetic) range was $-$50 to $+$50 $\mu$V, maintenance signal (deep anaesthetic) range was $-$40 to $+$40 $\mu$V, and for recovery signal (light anaesthetic) the amplitude ranged from $-$25 to $+$25 $\mu$V. It is clear from the frequency spectrum shown in Fig.3 that frequency reduced when anaesthesia depth increased. The frequency spectrum EEG signals of the deep anaesthesia state (induction phase) contained lower frequency components, whereas, the awake EEG signal contained higher frequency components[22].

The major challenges for EEG based analysis of DoA are the inherent non-stationarities and complexity of the data. If surgery has a three hour duration, then the EEG data for a single subject consists of more than 13 lakh of data points (10800 second data duration). Analyzing all these data points is time consuming. Therefore, the EEG signal dimensionality was reduced by extracting the RWE. The extracted RWE feature discriminated the different anaesthetic states, awake, light anaesthesia, moderate anaesthesia, and deep anaesthesia.

2.3.1. Relative Wavelet Energy

The time-frequency representation of a signal can be done effectively obtained by wavelet transform (WT). At low frequencies, a WT gives a lower temporal resolution and high frequency resolution, whereas, at high frequencies it gives a high temporal resolution and lower frequency resolution[22]. Most biomedical signals are non-stationary, thus a WT is best suited for locating transient events. The present study employed wavelet based feature extraction and multiresolution analysis to analyze the various transient events in the EEG of awake and anaesthetized subjects. Multiresolution analysis decomposes EEG signals into a number of frequency bands. Discrete wavelet transform (DWT) with Mallat's fast algorithm is commonly used for EEG signal analysis[25].

The RWE feature extraction algorithm is described by [22, 26]:

(1) Decomposition of EEG signals into detail and approximation coefficients using DWT is given by

(1)$cA_{j} (n) =\sum g(l-2n) cA_{j-1}(l)\\[15pt]$ (2)$cD_{j} (n) =\sum h(l-2n) cD_{j-1}(l)$

Here $ {cD }_{j} (n)$ and $ {cA}_{j} (n) $ give the detail and approximation coefficients of an EEG signal and $ {g} $ and $ {h} $ provide low and high pass filters for the EEG signals.

(2) Calculation of wavelet coefficient total energy (3) $E_{m, \rm total} = \sum\limits_{j=1}^{4}\sum\limits_{k=1}^{m} | cD_j (k) |^2 = \sum_j E_{m,j}$ where $ {m} $ is the window length of the EEG segment, $ {j} $ is the level of decomposition and $ {E}_{m, j} $ is the energy of the $ {k} $th sample is given by

(4) $E_{m,j} = \sum\limits_{j=1}^{4} |cD_{j} (k) |^2$

(3) Relative wavelet energy is obtained from

(5)$\rho_{m,j} = \frac{E_{m,j}}{E_{m, \rm total}}$

The goals of wavelet based RWE feature extraction are (i) decompose EEG signals into their constituent frequency bands, (ii) provide the concept of RWE associated with EEG frequency bands, and (iii) determine the degree of importance of different frequency bands during the different anaesthetic phases.

The Kruskal-Wallis statistical test was employed to determine whether the extracted RWE features discriminate the different anaesthetic levels as awake, light anaesthesia, moderate anaesthesia, and deep anaesthesia.

2.4.1. Kruskal-Wallis test

The Kruskal-Wallis test or one-way ANOVA on ranks is a non-parametric method for testing whether samples originate from the same distribution[27,28]. It is employed to determine the statistically significant differences between two or more groups of an independent variable and a continuous or ordinaly dependent variable. The test determines whether the groups are statistically different or not.

An adaptive neuro-fuzzy inference system artificial neural network based on the Takagi-Sugeno fuzzy inference system was employed. ANFIS integrates neural network and fuzzy logic principles and has the potential to capture the benefits of both paradigms in a single system. Its inference system consists of a set of fuzzy IF-THEN rules and has the ability to approximate nonlinear functions[29]. In ANFIS, membership function parameters are extracted from the data set that describes system behavior. The ANFIS learns features from the data set and adjusts system parameters according to an error criterion[30]. In the present study ANFIS utilizes a fuzzy c-means (FCM) clustering method to learn and adjust its parameters. In this clustering algorithm, introduced by Bezdek et al. [31], each data point belongs to a cluster to a degree specified by the membership grade.

RWE features measure DoA based on relative energy across its frequency bands and varyies with the transformation in depth of anaesthesia. EEG signals corresponding to the BIS value range of 0-20 were not obtained during surgery for reasons of patient safety and hence were not analyzed.

3.1.1. Relative Wave Energy (RWE)

Awake and anaesthetised EEG signals were decomposed into the frequency ranges delta, theta, alpha, beta, and gamma using multiresolution analysis by WT. RWE was then extracted from the required frequency ranges for each subject. DWT with a Doubechies-4 mother wavelet was used for the decomposition and the decomposition level was four. The decomposition of the EEG signal into its frequency bands was obtained by successive convolution with high-pass and low-pass filtering of the signal. The low frequency components were obtained from the approximation coefficients and high frequency components from the detail coefficients. Fig.4 shows the four-level decomposition of EEG signals with a sampling frequency of 128 Hz. CA1, CA2, CA3, and CA4 are the approximation coefficients and CD1, CD2, CD3, and CD4 are the detail coefficients obtained after successive decomposition. Frequency bands corresponding to four-level decomposition of EEG signals are shown in Table 1. The sub-band frequencies obtained from the DWT coefficients of the awake EEG signal of a subject and its four detail (CD1-CD4) and approximate (CA4) frequency band signals are shown in Fig.5. The relative wave energies RWE1, RWE2, RWE3, RWE4, and RWE5 are computed using energies of the CD1 to CD4 and CA4 frequency band signals. Similarly, the RWE1, RWE2, RWE3, RWE4, and RWE5 features were computed from induction, maintenance, and recovery EEG signals and their DWT decomposition. RWE feature extracted from a single segment of EEG signal from four anaesthetic phases of a subject are shown in Table 2.

From the Table 2 it is clear that the values of RWE1 are high in the awake phase because when a subject is awake high frequency components will be more active due to anxiety and stress. However, when anaesthetized, the RWE values of low frequency components become active. Therefore, during the deep anaesthetic state (induction phase) RWE5 is high. In the maintenance phase RWE values of theta and delta, i.e. RWE4 and RWE5, show almost similar values and in recovery phase, RWE values of the alpha band (RWE3) are active compared to the other bands.

The RWE distribution of a subject during six continuous segments of different anaesthetic phases are shown in Fig.6. It can be seen from the figure that during the awake phase RWE values of gamma, beta, and alpha frequency bands are high, which is usually seen in the conscious state. During induction the patient loses consciousness and the RWE values of delta and theta increase with prominent delta activity values. There are decreased RWE values for alpha, beta, and gamma activity. Also seen are the waxing and waning effects of the RWE values of alpha, theta, and delta. In the maintenance phase the inhalational agent sevoflurane induces the predominant RWE values of theta and delta activity with reduced RWE values for alpha, beta, and gamma. During recovery, sevoflurane is curtailed and the subject starts to regain consciousness after the effects of the anaesthetic drugs. Thus, there is a sudden increase in the RWE values of alpha, beta, and gamma activity, with prominent alpha activity.

3.1.2. Statistical analysis

The discriminative ability of the features RWE1-RWE5 extracted from all 25 subjects during the entire surgery was tested by application of the Kruskal-Wallis statistical test to the features RWE1-RWE5. The output groups for the discrimination are Awake, Light Anaesthesia, Moderate Anaesthesia, and Deep Anaesthesia which is the anaesthetic depth given for each subject by the attending anaesthetist. The p-values obtained from the Kruskal-Wallis tests are given in Table 3. The highest p-values are for the feature RWE4 and RWE3 which indicates that RWE4 and RWE3 had the lowest discriminative ability when compared to other features. On the other hand RWE1, RWE2, and RWE5 had the highest discriminative ability. The features RWE4 and RWE3 were eliminated from further processing because of their poor discriminative ability. Box plots of the features RWE1-RWE5 during different anaesthetic depths are shown in Fig.7a-7e. From the box plots it is clear that the RWE values of RWE1 and RWE2 are inversely proportional to the depth of anaesthesia, as it increases the RWE values decrease. On the other hand, RWE5 shows a direct relation to anaesthetic depth and their values increase with increased in depth.

An adaptive neuro-fuzzy inference system was implemented to generate an index that continuously measured the anaesthetic depth based on extracted RWE features. The features RWE1, RWE2, and RWE5 were given as inputs to the neuro-fuzzy system. This study utilized an ANFIS-Fuzzy c-means clustering method to generate the DoA index. In conventional fuzzy inference systems the membership functions and the rules are decided by experts who have a thorough knowledge about the inputs and outputs. In the present ANFIS-FCM model, membership functions (MFs) and rules were realized by training a data set of input-output pairs. However, the number of MFs were assigned empirically[32,33].

The architecture of the ANFIS-FCM model for the estimation of DoA is shown in Fig.8. The data sets for training and validation incorporated the extracted features RWE1, RWE2, and RWE5 from the EEG signals of 25 patients consisting of 17,935 3-D vectors. 13,166 3-D vectors were utilized for construction of the model by training, and the remaining 4,373 3-D vectors were used for evaluating the performance of the ANFIS-FCM model that was developed. Fig.9 shows the membership functions of the input parameters RWE1, RWE2, and RWE5 and Table 4 shows the specification of the ANFIS-FCM model. This model was implemented to generate a dimensionless index ranging from 0 to 100 similar to a BIS index where 0 indicates no brain activity and 100 indicates the fully awake state. The RWE and ANFIS-FCM based DoA index of patient-12 is shown in Fig.10.

The Pearson correlation between the proposed DoA index and the BIS index for the particular patient is 81.6%. The average Pearson correlation obtained for all 25 patients is 79.7%.