Monitoring the Depth of Anesthesia Based on Phase-Amplitude Coupling of Near-Infrared Spectroscopy Signals

Accurate monitoring of the depth of anesthesia (DOA) is essential to ensure the safety of the operation. In this study, a new index using near-infrared spectroscopy (NIRS) signal was proposed to assess the relationship between the DOA and cerebral hemodynamic variables. Methods: Four cerebral hemodynamic variables of 15 patients were collected, including left, right, proximal, distal, oxygenated (HbO $_{{2}}{)}$ and deoxygenated (Hb) hemoglobin concentration changes. The Phase-Amplitude coupling (PAC), an adaptation of cross-frequency coupling to reflect the modulation of the amplitude of high-frequency signals by the phase of low-frequency signals, was measured and the modulation index (MI) was obtained to monitor the DOA afterwards. Meanwhile, the BIS value based on electroencephalogram is also measured and compared. Results: Compared with awake period, in anesthesia maintenance period, the PAC was strengthened. The analysis of receiver operating characteristic (ROC) curve showed that the MI, especially the MI of rp-HbO2, could effectively discriminate these two periods. Additionally, during the whole anesthesia process, the BIS value was statistically consistent with the MI of cerebral hemodynamic variables, and cerebral hemodynamic variables were immune from interference by clinical electric devices. Conclusion: The MI of cerebral hemodynamic variables was appropriate to be used as a new index to monitor the DOA. Significance: This study is of great significance to the development of new modes of anesthesia monitoring and new decoding methods, and is expected to develop a high-performance anesthesia monitoring system.


I. INTRODUCTION
G ENERAL anesthesia is an important part of the clinical operation process, which is usually caused by the temporary anesthetic suppression of central nervous system. Maintaining an appropriate depth of anesthesia (DOA) is essential to ensure the safety of operation. When the DOA is too shallow, there will be intraoperative awareness, which will have a serious impact on the patient's physiology and psychology. Too deep anesthesia will lead to liver damage, stroke, long recovery time, and even increased mortality after surgery [1], [2]. Therefore, the accurate monitoring of DOA can not only provide guidance to the anesthesiologist's dosage, but also have important significance for providing a safe and stable surgical environment.
The DOA during surgery is mainly judged by the anesthesiologist according to various physiological indicators of patients. This method is greatly influenced by the level and experience of anesthesiologists and easily affected by external interferences, for example, blood pressure and heart rate and other cardiovascular indexes may vary depending on the disease and surgical techniques [3]. Because electroencephalogram (EEG) is a comprehensive reflection of spontaneous This work is licensed under a Creative Commons Attribution 4.0 License. For more information, see https://creativecommons.org/licenses/by/4.0/ and rhythmic electrical activity of brain cell population, since the 1990s, the method of monitoring the DOA through the index calculated by EEG has been widely developed and applied [4]. However, because the EEG signal itself is susceptible to interference from high-frequency electric knife and other equipment, in some cases, the DOA monitoring method based on the EEG signals will become invalid [5]. The near-infrared spectroscopy (NIRS), by which the cerebral perfusion can be assessed through continuously cerebral tissue oxygen saturation measurements, has been proven to be a reliable method to represent the activities of the brain due to the neurovascular coupling mechanism in an indirect way [6], [7]. Therefore, NIRS is suitable for monitoring the DOA.
As NIRS measures the cerebral hemodynamic variables based on the optical spectrum, it is not easily interfered by electrical equipment during operation [8]. Chaix et al. found that, compared with bispectral index, mean arterial pressure, mean blood velocity of the middle cerebellar artery, NIRS values were less susceptible to cardiovascular disease [9]. Also, as NIRS is a safe, noninvasive, and portable method that requires relatively few physical constraints, it can be used for monitoring the DOA of the children [10], even the infants [11]. However, most of the methods of monitoring the DOA with NIRS are based on the original values of NIRS, i.e. the concentration changes of oxyhemoglobin (HbO 2 ) and deoxyhemoglobin (Hb), regional cerebral oxygen saturation (rSO 2 ) [12], [13]. The cerebral hemodynamic variable is a weak-stationary signal after all, so Wang et al. applied the non-linear algorithm of entropy algorithm to analyze the relationship between the cerebral hemodynamic variable and DOA under general anesthesia [14], [15]. These entropy algorithms only analyze the cerebral hemodynamic signal in a single frequency band independently, ignoring the correlations between different frequency bands, so in this study, a cross-frequency coupling (CFC) method was introduced.
The cross-frequency coupling (CFC) is a recently discovered neural association of multiple cognitive and behavioral states, defined as related activities on different frequency bands, and has been studied for DOA monitoring using EEG signals [16]. An adaptation of Kullback-Leibler (KL) distance has been proposed to detect the CFC between two frequency bands of interest, i.e. the Phase-Amplitude Coupling (PAC) between the "phase-modulating" and "amplitude-modulated" frequency bands [17], [18]. Purdon et al. found slowwave (0.1-1Hz) phase-alpha (8-14Hz) amplitude coupling in propofol-induced anesthesia [19], [20]. Especially, the change from trough-max to peak-max appeared in the state transition from awake to anesthesia states, but the mechanism for this change remains to be an open question. Although NIRS hemodynamic signals are commonly considered as a supplement to the electrical monitoring system based on EEG signals [21], there has been no research on the application of PAC to NIRS signals so far.
In the current study, the process of anesthesia was monitored by cerebral hemodynamic changes using NIRS signals. With the calculation of the PAC between different frequency bands of NIRS signals, it is explored whether PAC occurs with the

A. Patients and Data Collection
Fifteen subjects participated in the project voluntarily. The experimental procedure was approved the 6 March 2015 by the Institutional Review Board of Xi'an Jiaotong University, China, ref. 2015-013. The subjects were selected based on the following inclusion criteria: (1) all patients were ASA class I or II; (2) the patients included were all over 30 years old, due to the differences in the absorption and scattering characteristics of near-infrared light in the brains of adults and children; (3) the patients underwent lower extremity surgery to facilitate the measurements of cerebral hemodynamics; (4) all patients had no history of cardiovascular and cerebrovascular diseases or hypertension in order to avoid affecting cerebral hemodynamic activities. All patients underwent surgery in the operating rooms of Xi'an Honghui Hospital (Xi'an, China) and had informed and written consent before study enrollment. The detailed clinical data of 15 patients are shown in TABLE I.
Before general anesthesia, the patient's personal information and vital signs were recorded first. At the beginning of the operation, propofol (2.5-4mg/kg), fentanyl (0.2mg) and cisatracurium (0.2mg/kg) were intravenously injected. Vital signs and induction duration were recorded during the injection. During the maintenance period of anesthesia, according to the changes in the patients' physiological parameters, the anesthesiologist continuously pumped propofol and fentanyl through the intubated trachea and injected atracurium intravenously. Important events such as body movements and the use of high-frequency electrosurgical units were recorded. The anesthetics was stopped after the operation. During the anesthesia recovery period, important events such as drug withdrawal time were marked.
The acquisition principle diagram of the NIRS signal and BIS value in this study is shown in Fig. 1. The NIRS signal was captured by a commercial NIRS device (NirsMpr, Xi'an Chenfang Sichuang Technology Co., Ltd., Xi'an, Shaanxi, P.R. China). This acquisition system consists of one recorder and two probe pads. Each probe pad contains one LED light source and two receivers 2cm and 3cm away from the light source, respectively. The wavelengths of light emitted by the LED light source is 735nm and 850nm, respectively. The two probe pads are usually pasted on the patient's left and right forehead with medical grade double-sided tape. In this study, only the right probe pad was used. The center of probe pad was located in the Fp2 position according to international 10-20 system. The cerebral hemodynamic activity was recorded at a sampling frequency of 100Hz. Then the NIRS signal was converted into a digital signal via a 24-bit AD converter and down sampled to 10Hz. Finally, the modified Beer-Lambert law was used to calculate the cerebral hemodynamic variables of Hb and HbO 2 concentration changes [22]. In this study, a total of four cerebral hemodynamic parameters were collected, including the right, proximal, and distal Hb and HbO 2 concentration changes. The abbreviations for these four variables are illustrated in TABLE II. While the left forehead of the patient was pasted with a BIS Quatro sensor to acquire BIS value, which was acquired with a commercial BIS monitor module (Aspect Medical Systems) at 0.1 Hz as the reference standard of the patients' DOA.

B. Analysis Paradigm
The general anesthesia process would be divided into five periods: 1. the preoperative awake period, that was, from the beginning of the NIRS signal recording to the start time of intravenous anesthetics; 2. the anesthesia induction period, from the beginning of intravenous anesthetics to tracheal intubation; 3. the anesthesia maintenance period, from tracheal intubation to anesthetics withdrawal; 4. the anesthesia emergence period referred to the time from the withdrawal of anesthetics to the patient's recovery of consciousness; 5. the postoperative awake period, that was, from the patient regained consciousness to the end of NIRS signal recording. For further analysis, the anesthesia maintenance period and the awake period were selected, and the awake period consisted of the preoperative and postoperative awake period. While the two periods of anesthesia induction and anesthesia emergence were not analyzed in this study.
Due to the broad age range of patients involved in this study, ranging from 31 to 80 years old, the wavelength dependent differential pathlength factor (DPF) cannot be considered a constant, but should be corrected according to the general equation for the differential path length factor proposed by Scholkmann andWolf [23]. Then, according to the modified Beer Lambert Law, the obtained optical density data was transformed into the hemodynamic data.
For the acquired NIRS data, pre-processing of the signal was performed first. For general baseline shifts, linear trends were removed with detrend. And for complex movement artifacts (MAs), the most widely used movement artifact reduction algorithm (MARA) was used in this study [24], and the specific steps are as follows: first, the moving standard deviation of the original signal was calculated, and then the presence of the MA and its position in the signal time series, i.e., the start and end time points, were determined based on the threshold; next, based on the determined position of the MA, the time series containing the MA were segmented and then interpolated using cubic spline interpolation; then the segment containing the MA subtracted its spline interpolated segment, and the resulting residual signal was considered to be the segment with MA removed; finally, the residual signal was reconnected to the segments without MA in the original signal.
For exploring further information of cerebral hemodynamic variables, the phase-amplitude coupling algorithm was introduced. It is a simple form of cross-frequency interaction that reflects the fluctuation of power in a relative higher frequency band at a specific phase of a relatively lower-frequency band [25].
The detailed calculation process of phase-amplitude coupling is as follows: First of all, the recorded NIRS signals were filtered into a relatively high-frequency band f amp (amplitude frequency) and a relatively low-frequency band f ph (phase frequency) using a least-squares finite impulse response filter (MATLAB function firls).
Secondly, a Hilbert transform to extract the instantaneous amplitude of f amp and instantaneous phase of f ph , denoted as A amp and ph , respectively. In this study, the frequency band of f amp was 0.145-2Hz, and the frequency band of f ph was 0.0213-0.145Hz.
Then, a time-varying phase-amplitude modulogram, M(t, ϕ), was constructed as: where δt denotes the time period length of hemodynamic variables to be studied. δφ/N stands for the phase bin that divides whose phase segment (-π to π ) into N parts, namely δφ/N = 2π N . The meaning of this formula is to count the sum of the high-frequency amplitude corresponding to the phase range of φ − δφ 2 to φ + δφ 2 in the time range of t − δt 2 to t + δt 2 for each moment, and after the summation formula is performed, divide by A amp (t ′ )dt ′ factor to achieve the purpose of normalization. In this study, 1000 points, i.e. 100 seconds, were assigned as the period length for calculating MI. For δφ, the N was determined to be 18, which could meet the need for a sufficiently high MI maximum [20].
Thirdly, Modulation Index, namely MI, as the Kullback-Leibler divergence between M (t,ϕ) and the uniform phase distribution on its phase segment (-π to π ), the deviation of this histogram from the uniform distribution can be measured as: Note that, φ n = 2π * n N . Considering the two extremes, when the phase-amplitude coupling is concentrated on a certain phase φ n , the maximum value log 2 N is obtained from the MI; when the distribution of amplitude-phase coupling in the whole phase segment is evenly distributed, the minimum value of the MI is 0.
In the end, the MI was compared with the BIS value recorded simultaneously. The MI was between 0 to 4.1699 (log 2 18 ) and the BIS value ranged from 0 to 100, so the MI was first converted to the same range as the BIS value. Then, the consistency between the MI and the BIS value of rp-HbO 2 signal was evaluated by Bland-Altman method.

C. Statistical Analysis
In this study, the statistical analyses were performed with the SPSS software version 22.0 (Statistical Product and Service Solutions, IBM Inc.) with the significant level set to 0.05. If Levene's test results were not significant, paired-sample ttests were used to distinguish between performance during anesthesia maintenance and awake periods, and if significant, Wilcoxon rank sum test was used. All statistical descriptions are expressed as mean ± standard deviation.

III. RESULTS
For the calculation of phase-amplitude coupling, parameter selection is very important. First of all, for frequency bands, the signals with frequency 0.145-2Hz are commonly considered as physiological interference to the brain blood oxygen signals, and the signals with frequency lower than 0.145Hz can be considered as functional interference to the brain blood oxygen signals accordingly [26]. So, the relatively high-frequency band and the relatively low-frequency band selected in this study are 0.145-2Hz and 0.015-0.145Hz, respectively. In the selected frequency band, the center frequency of the pass band starts at 0.015Hz and grows exponentially to 2Hz, the length of a pass band is 0.01Hz, transition band is 0.01Hz, the least-squares finite impulse response filter with the 1762 filter order is used. The MI of rp-HbO 2 for each patient in the awake period and the anesthesia maintenance period and their difference were calculated under different time period length. As illustrated in Fig. 2, PAC exist between the phases of low-frequency signals and the amplitudes of highfrequency signals, and the stronger the coupling, the higher the related MI. Under time period length 90,100 and 110 seconds, the 99% MI differences were concentrated in 0.0215-0.0227Hz for relatively low-frequency band and 0.145-1.8279Hz for relatively high-frequency band. For the sake of determining the time period length, the MI of the rp-HbO 2 signal for 200 seconds were calculated for each patient during anesthesia maintenance period. Fig. 3 shows the mean values of MI of all patients with different time period lengths. And as shown in this very figure, the time period length to calculate MI was specified as 100 seconds in this study to produce reasonable statistical validity. In addition, because the 100s data for calculating the DOA would cause a considerable time delay during the complete anesthesia process, the sliding window technology was adopted to segment the cerebral hemodynamic variables and assigned the 100s signal to each overlapping 95s.
The M and MI of one patient during 2 periods of general anesthesia process are shown in Fig. 4. As shown in fig. 4(a) and 4(c), the phase-amplitude modulograms of anesthesia  maintenance periods are more concentrated in a relatively narrow phase range than those of awake periods. Thus, the MI during anesthesia maintenance period are higher than those during awake period in fig.4(b) and (d). It shows that the MI can well track the DOA in one patient with the changes of  awake and anesthesia periods. Fig. 5(a) shows the difference in the MI of four cerebral hemodynamic variables during the anesthesia maintenance period and the awake period of one patient. For all 4 cerebral hemodynamic variables, the average MI is between 2.5593 and 3.2436 during the anesthesia maintenance period, and between 0.5301 and 1.1492 during the awake period. The MI of all cerebral hemodynamic signals during the anesthesia maintenance period were higher than those during the awake period, and the differences between the two periods were all significant ( p < 0.05). Furthermore, the MI of cerebral hemodynamic signals of all patients were analyzed. As shown in Fig. 5(b), the MI of all patients between the two periods were significant different (p < 0.05). The above results indicated the MI of these 4 cerebral hemodynamic variables can be used to distinguish between the anesthesia maintenance period and the awake period.
Then, the receiver operating characteristic (ROC) curve analysis was carried out to further investigate which kind of cerebral hemodynamic variable has the best performance in distinguishing the anesthesia maintenance period from the awake period with the phase-amplitude coupling algorithm. According to a set of different binary classification patterns, ROC can be illustrated by a curve with sensitivity on the vertical axis and 1-specificity on the horizontal axis. Because the MI during the awake periods were lower than those during the anesthesia maintenance periods, the awake periods were defined as the negative data and the anesthesia maintenance periods were defined as the positive data. Therefore, True positive (TP) can be denoted as the number of correctly classified the anesthesia maintenance periods, false positive (FP) represents the number of the awake periods classified as the anesthesia maintenance periods, true negative (TN) can be expressed as the number of correctly classified the awake periods, and false negative (FN) indicates the number of the anesthesia maintenance periods classified as the awake periods. Through Sensitivity =TP/(TP+FN), the sensitivity can reflect the correct recognition ability of the MI to the anesthesia maintenance periods.
Through Specificity =TN/(TN+FP), the specificity can assess the ability of MI to correctly recognize the awake periods.
By calculating the area under the ROC curve (AUC), the ability of MI to distinguish between the anesthesia maintenance period and the awake period can be assessed. Generally, the AUC value is between 0.5 and 1, reflecting the ability to distinguish between the anesthesia maintenance period and the awake period. Fig.6 shows the comparison of AUC values for all 15 patients under various cerebral hemodynamic variables. The AUC values of these 4 cerebral hemodynamic variables were between 0.7893 and 0.9760. The AUC value of rp-HbO 2 was 0.9760 ± 0.0252, which was also the largest of the 4 cerebral hemodynamic variables. The lowest AUC value of the 4 cerebral hemodynamic variables was rd-Hb, which was 0.7893 ± 0.1831. With paired Wilcoxon rank sum tests, rp-HbO 2 , and rd-HbO 2 were significantly different from rd-Hb respectively ( p < 0.05).
The 4 kinds of variables recorded the cerebral hemodynamic information of different parts of the forehead of the patient. These variables could be divided into two groups,  namely the Hb and HbO 2 cerebral hemodynamic variables. The Hb variables consisted of rp-Hb and rd-Hb, and the HbO 2 variables consisted of rp-HbO 2 and rd-HbO 2 . Similar to the Hb and HbO 2 variables, proximal and distal variables could also be obtained by combining different cerebral hemodynamic variables. Fig.7 shows the AUC value differences of MI between HbO 2 and Hb, proximal and distal variables in a total of 15 patients. As observed, although there is no significant difference in the AUC value of MI between proximal and distal variables, the p value is 0.0995, which can be called marginal significance. The AUC values of proximal and distal variables were 0.9364 ± 0.0695 and 0.8289 ± 0.1640, respectively. Although the distal variables propagated deeper than the proximal variables, the signal-to-noise (SNR) of the distal variables was lower than that of the proximal variables, which might lead to the slightly weaker discrimination capability of the distal variables. The AUC values of the Hb and HbO 2 variables were 0.9222 ± 0.0868 and 0.8431 ± 0.1400, respectively, and the difference was significant (p = 0.0171). Because the SNR of the HbO 2 variable is often higher than that of the Hb variable, the recognition ability of HbO 2 variable in anesthesia maintenance period and awake period was stronger than that of Hb variable.
After the MI was converted to the same range as the BIS value, the MI of rp-HbO 2 signal was compared with the BIS value recorded simultaneously by Bland-Altman method. As shown in Fig. 8, the mean difference between the two DOA measurements is 2.6501, the 95% confidence interval is -17.5587 to 22.8590, and the percentage of data points within the 95% confidence interval was 95.22%. Therefore, during general anesthesia process, the BIS value and MI of cerebral hemodynamic variables were statistically consistent.

IV. DISCUSSION
In the present study, NIRS cerebral hemodynamic variables from a total of 15 anesthetized patients were collected and analyzed with PAC method. The phases of low-frequency signals and the amplitudes of high-frequency signal showed stronger couplings in the anesthesia maintenance periods than in the awake periods, and the MI could reflect this situation well. For the 4 kinds of cerebral hemodynamic variables, the distinguishing ability were all significantly enough. Then, the ROC curve was used to further explore the ability to distinguish between the anesthesia maintenance and the awake periods. The results showed that the AUC index of the rp-HbO 2 signal was the highest and had a significant difference from the rd-Hb signal. Meanwhile, the Bland-Altman plot illustrated the MI of rp-HbO2 signals had high consistency with the BIS values recorded simultaneously. These findings suggest that the MI of cerebral hemodynamic signal has sufficient capacity to be used for monitoring the DOA of the patients.
As widely known, by using anesthetics, the conduction of dendritic signals in pyramidal neurons can be interfered, resulting in the loss of consciousness and reduced connectivity along sensory pathways in the entire nerve system [27]. Due to the neurovascular coupling, such situation can be reflected by changes in cerebral blood flow, especially in the prefrontal cortex, which is the very reason that in this study the NIRS probes were placed on the Fp2 position [28]. During brain activities, the metabolism of brain nerve cells is supported through localized vascular response, so that the oxygenated blood flows into the active area and its surrounding tissues, which is manifested as an increase in [HbO 2 ] and a decrease in [Hb] [29]. Such hemodynamic response to brain activities can be measured by NIRS.
The NIRS signals in different frequency bands originate from different physiological activities [30]. The high-frequency band f amp , of which the signals are considered as the global interference to the brain activities, can be divided into 2 frequency bands, namely 0.145-0.6Hz and 0.6-2Hz. The former originates from respiratory activity, the latter originates from cardiac activity. And for the low-frequency band f ph , of which the signals are considered as the functional interference to the brain activities, it consists of 3 frequency bands, including < 0.021Hz originated from endothelial activity, 0.021-0.052Hz originated from neurogenic (sympathetic) activity, and 0.052-0.145Hz originated from intrinsic myogenic activity. Since neuronal oscillations of different frequencies can interact with each other, by calculating the MI of the f ph signal and the f amp signal, the PAC of the 2 signals can be assessed [20]. As shown in Fig. 4, when the patient changes from the awake to the anesthesia period, the amplitude of f amp gradually concentrated into a narrow phase band of f ph , which is the visualization of the PAC between f amp and f ph and similar to the Peak-Max state of EEG signals [31]. In the process of general anesthesia, anesthetics such as propofol hyperpolarize post-synaptic neurons, inhibiting the central nervous system and affecting myocardial and lung activity [32]. Thus, as illustrated in Fig. 2, the amplitude of most 0.145-1.8279Hz NIRS signals is modulated by the 0.0215-0.0227Hz NIRS signals. The former oscillation represents the global interference from heart and respiratory activities, and the latter oscillation originates from neurogenic activity [33].
Also based on the NIRS signal, the sample entropy representing time series complexity was also good at distinguishing between the anesthesia maintenance and the awake periods [14]. Therefore, the sample entropy values during the anesthesia maintenance and the awake periods were also calculated, and subsequently the AUC corresponding to its ROC curve were also calculated. After paired sample t-test, similar to the results of MI, the sample entropy values of anesthesia maintenance period (0.3519 ± 0.0434) were also higher than that of awake state (0.2015± 0.0768), and the difference was significant ( p < 0.05). However, the AUC of sample entropy (0.8688 ± 0.1837) is significantly lower than that of MI (AUC = 0.9760 ± 0.0975, p = 0.0375). This suggests that although sample entropy also has a good ability to distinguish between different anesthesia states, its discrimination ability is worse than MI.
The proximal measurements in this study were obtained with a 2 cm source detector separation (SDS), which is relatively small. However, there is a considerable amount of literature mentioning that the appropriate SDS range is 2-5cm for the NIRS data of the human brain [34], [35], [36]. At the same time, there are generally mature correction methods for scalp blood flow, the most common of which is to eliminate it through 2-channel or short-distance methods. For example, Saager et al. used a detector with a distance greater than 5 mm from the light source to form a channel to measure the "scalp only" data and correct the obtained NIRS signals [35]. Saager and Berger also believed that when performing physiological "noise" corrections with short-distance measurement, the "near" detector should only be 5 to 15mm away from the nearby source probe [37]. Gagnon et al. also stated that short-distance measurement must be located as close as 1.5cm, and when it exceeded 2cm, this short channel compression would not be very meaningful [38]. Therefore, it is believed that the proximal measurements of 2 cm SDS can provide reliable information on the hemodynamic changes within the brain. However, the proximal measurements maybe carry the signal components coming from skin blood flow except for the cerebral information. In the future, a near detector with a distance less than 15 mm would be used to correct the effect of skin blood flow changes on the proximal measurements.
The BIS values in the same time periods as MI under anesthesia maintenance and awake states were selected, and the AUC corresponding to ROC curve was calculated. It was found that the AUC of BIS was 0.9856 ± 0.0252, which was higher than that of MI (0.9760 ± 0.0143). However, the paired sample t-test showed that the difference between the two was not significant (p > 0.05). This suggests that MI is comparable to BIS in its ability to distinguish between the periods of anesthesia maintenance and awake, echoing the results of Bland-Altman consistency. Although the consistency of BIS values and MI calculated by the Bland-Altman method is as high as 95.47%, during the actual surgery operation, some commonly used surgical instruments such as the high-frequency electric knife that generates high-intensity heat for tissue resection through high-frequency electricity, which will affect the EEG signals, and thus affect the BIS monitoring of the DOA. Fig. 9 shows the changes of the MI of rp-HbO 2 and BIS values of one patient during the whole anesthesia process with the use of high-frequency electric knife in clinical surgery. The change trend of the two DOA measures is consistent, and the change range is 37-98. The BIS value disappeared due to the influence of electrical instruments, when the electric knife was operated in 18:16-18:40. Meanwhile, the MI of rp-HbO 2 can continue to change to indicate the patient's DOA. Therefore, unlike the BIS value based on EEG signals, the MI based on NIRS signals will not be disturbed by clinical electrical instrument when monitoring the DOA. In order to compare the predictive capability of the BIS and MI in wake-up, the BIS values and corresponding NIRS data during the anesthesia emergence period and the postoperative awake period were selected, and their MI values were calculated. As in the previous analysis, the AUC of the ROC curves corresponding to the BIS and MI values were calculated, with the former being 0.9035 ± 0.0328 and the latter being slightly higher at 0.9408 ± 0.0592. The paired sample t-test showed that the difference between the two was not significant (p > 0.05). This indicates that MI is slightly but not significantly higher than BIS in its ability to predict wake-up. In the future, DOA monitoring will be more reliable through the combination of EEG and NIRS signals.
It should be pointed out that there are some limitations in this study. Firstly, the number of samples is relatively small, only 15. Secondly, the selection of anesthesia states for research is relatively limited, for example, it can be extended to the anesthesia induction period. Thirdly, the impact of different anesthetics such as ketamine and sevoflurane on DOA monitoring should be considered.

V. CONCLUSION
In this study, the process of anesthesia was monitored by NIRS signals, and the relationship between the DOA and the PAC among different frequency bands was analyzed. Compared with the awake period, PAC in the anesthesia maintenance period was enhanced between the frequency band 0.0213-0.0227Hz and 0.145-1.8279Hz. Through ROC analysis, among the four hemodynamic variables, the MI of rp-HbO 2 had the strongest ability to discriminate the anesthesia maintenance and awake periods. In addition, compared with distal variables, the proximal variables had higher discriminate ability. Meanwhile the difference of discriminate ability between HbO 2 and Hb was not significant, but marginal. During the anesthesia process, the MI and BIS value showed statistical consistency. All these results indicate that the PAC between different frequency NIRS signals can be used as a new method for monitoring the DOA.