Heart Rate Variability-Derived Features Based on Deep 2 Neural Networks for Monitoring Depth of Anaesthesia

11 Background: Estimating the depth of anaesthesia (DoA) is critical in clinical 12 anaesthesiology. Electroencephalograms (EEGs) have been widely used for monitoring the 13 DoA; however, they may be inaccurate under certain conditions. 14 Methods: In this study, we propose a novel method to evaluate the DoA based on multiple 15 heart rate variability (HRV)-derived features combined with a discrete wavelet transform 16 and deep neural networks (DNNs). Four features were extracted from an 17 electrocardiogram, including the HRV high-frequency power, low-frequency power, 18 high-to-low-frequency power ratio, and sample entropy. Next, these features were used as 19 inputs for the DNN, which used the expert assessment of consciousness level as the 20 reference output. Finally, the DNN was compared with the logistic regression (LR), support 21 vector machine (SVM), and decision tree (DT) models. The data of 23 anaesthesia patients 22 were used to assess the proposed method. Results: The results demonstrated that the accuracies of the four models, in distinguishing 24 the anaesthesia states, were 86.2% (LR),87.5% (SVM),87.2% (DT), and 90.1%(DNN). Our 25 method outperformed the LR, SVM, and DT methods. 26 Conclusions: The proposed method could accurately distinguish between different 27 anaesthesia states, thus, providing an alternative or supplementary method to EEG 28 monitoring for the assessment of DoA.

DoA [11,12]. Moreover, there are various shortcomings related to this approach. First, these 56 indices were developed using adult patients, and are unsuitable for infants and children.

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Second, these indices are not recommended for use with some general anaesthetics, such as 58 ketamine and nitrogen dioxide [13]. In addition, EEG signals are subject to interference 59 originating from the noise of the medical equipment in the operating room. Therefore, it is 60 essential to seek new methods of DoA monitoring to overcome the drawbacks of 61 mainstream methods based on EEG signals [14] and improve DoA monitoring accuracy.

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Electrocardiograms (ECGs) are internationally used in standard monitoring during 63 general anaesthesia [15]and provide important physiological signals, such as heart rate assist anaesthesiologists in evaluating the DoA. In addition, there are certain advantages in 66 the use of ECGs. On the one hand, ECG signals are more stable and less susceptible to noise 67 than EEG signals. On the other hand, in comparison with the EEG, the electrode sensors 68 used for ECG signal acquisition are cheaper, rendering ECG a more cost-effective method.

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More importantly, ECG signals are closely related to DoA. During general anaesthesia, 70 different anaesthetic drugs affect ECG signals [16,17]. Previous studies have found that 71 heart rate variability (HRV) derived from an ECG is regulated by the central nervous and 72 autonomic systems, and closely related to the DoA during surgery [18][19][20].Therefore, HRV 73 may be used as an alternative or important supplementary method of EEG monitoring in 74 terms of DoA evaluation [13,21].

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Owing to the strong nonlinear characteristics of the EEG and ECG, nonlinear analysis 76 methods may be used in studies of anaesthesia [22,23]. Sample entropy (SampEn) is a 77 typical nonlinear analysis method that was developed to study HRV [24,25] and provide 78 an improved assessment of DoA during surgery [26,27]. In addition, three features of HRV, 79 including the high-frequency power(HF), low-frequency power(LF), and ratio of 80 high-to-low-frequency power(HF/LF), are related to the autonomic nervous system and 81 have been implemented in anaesthesia research [28,29].

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As a result of the complicated changes in patient vital signals during different 83 anaesthesia states, it is necessary to use multiple physiological features to evaluate DoA.

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Recently, several studies based on multiple EEG features have been conducted to assess 85 DoA. Ferreira et al. used

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All patients underwent preoperative fasting for at least 8 h. After the electrodes were 109 placed on the patient chest wall, anaesthesia was usually induced by intravenous 110 midazolam, propofol, sufentanil, and cisatracurium. Sevoflurane together with propofol and remifentanil were used to maintain anaesthesia. Additional drugs (such as sufentanil 112 and atropine) were administrated when approaching the end of surgery. Table 1 113 summarises this information in detail. Physiological signals(such as ECG, BP, HR, and 114 SpO2) were measured to guarantee the safety of the patients under different anaesthesia 115 states. The attending anaesthetist adjusted the DoA accordingly, using these observed 116 signals and their own experience.

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In this study, ECG signals were recorded from twenty-three adult patients under general 118 anaesthesia. The signals were recorded using a Philips MP60 monitor (Intellivue; Philips,

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Foster City, CA, USA). The operation time was 1-3 h. Raw ECG data were sampled at a 120 500-Hz sampling frequency.

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The EACL is the average value of the DoA assessment score determined by five

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Therefore, data preprocessing is essential for evaluating DoA, and can normalize and 143 facilitate subsequent analysis. Preprocessing usually includes data format conversion, noise 144 cancellation, and data rearrangement. In this study, the outliers beyond the threshold (85 145 ms) were first removed by comparing the current RR interval, the interval between R peaks 146 in two adjacent heartbeats of the ECG, in the ECG signal with the average of the previous 147 ten sampling points. The RR interval is shown in Fig.1

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The definition of [26] is as follows:

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The HRV power was defined as the sum of squares of the time domain coefficients at a 198 certain frequency after the DWT. The calculation formula for the HRV power is as follows: The discrete time signal ( ) is defined as: where ( ) is the n th digit in the sequence , and is an integer.

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LR is a classification algorithm used to predict the probability of classifying dependent 203 variables. In this study, this is a combination algorithm of a linear and sigmoid function.

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The linear function is defined as: where is the weight of each feature, and stands for the transpose of the vector.

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The sigmoid function is given by: where is the natural logarithm. The ( ) maps the linear prediction result to the range 208 of 0-1, indicating the probability of the prediction result. The mean squared error of the 209 sigmoid function was used to measure the difference between the actual and predicted 210 values.

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The optimal regression function is as follows: Therefore, the parameter can be described as a linear combination of the prediction 213 observations.
Conditional entropy represents the uncertainty of the random variable under the 230 condition that the random variable is known.

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Therefore, the formula of the information gain is as follows:

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The DNN used in this study contains one input layer, two hidden layers, and one output

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Performance Analysis

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The 23 datasets in this study were divided into training and test datasets. Eighty percent 251 of the data were used to train the model, and 20% of the data were used to test the model.
Where i represents the three anaesthesia states (anaesthesia induction, anaesthesia 261 maintenance, anaesthesia recovery).

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Recall is where m is the actual number of one anaesthesia state.

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Classification accuracy is defined as the ratio of the total number of correctly identified

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nonparametric Wilcoxon signed-rank test may be applied to non-normal distribution data.

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Therefore, the four classification methods were compared using the Wilcoxon signed-rank 279 test. p < 0.05 was considered statistically significant.

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Fifty-two adult patients were enrolled in this study; twenty-three were analysed and 282 twenty-nine were excluded. Among the excluded patients, thirteen were excluded because 283 they declined to participate in the study, eight were excluded as they did not meet the  Table 1.

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In this study, RR interval resampling, discrete wavelet transformation of the ECG

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The DNN structure used in this study consisted of four layers: an input layer with four 314 nodes, a hidden layer with ten nodes, a second hidden layer with seventeen nodes, and an 315 output layer with one node (as shown in Fig.6). The data of 23 patients were processed 316 simultaneously for training and testing to avoid over-fitting and improve classification 317 accuracy.

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In this study, four features of the HRV were selected as the input of the DNN model.

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Specifically, these were the HF, LF, HF/LF ratio, and the SampEn of the RR interval; the 320 EACL was used as the reference output. Figure

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The correlations between the four features and the EACL are depicted in Fig.8

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These parameters can be used for the construction of the DNN model. Therefore, our 339 method is expected to provide a reliable reference for anaesthesiologists to accurately 340 assess the DoA. The most striking finding in Figure 8 is the low correlation between the 341 four features and the target EACL. In addition, the four parameters are mainly distributed 342 in the EACL value range of 40 _ 80, which is consistent with the actual clinical conditions.

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To compare the performance of the four models and EACL, the precision, recall, and

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Accurate monitoring of the DoA is crucial to guarantee the safety of surgery patients.

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Anaesthesiologists use physiological vital signs and their own experience to evaluate 367 levels of consciousness during operations. The key parameters of interest are generally BP,

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HR, and SpO2[13], although these parameters cannot accurately reflect the actual DoA.
New methods such as BIS, Narcotrend, and Entropy were developed to evaluate the 370 DoA[8-10], and are effective to some extent but bring certain drawbacks. Furthermore,

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HRV based on ECG signals is correlated with autonomic nervous system function and can 372 be used with general anaesthesia [18][19][20].These facts are widely accepted in the field of 373 anaesthesia, and ECG monitoring has been used in the present DoA study.

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To improve the accuracy of DoA estimation based on ECG signals, we proposed a 375 practical HRV-derived method designed to correspond with the EACL, the highly accurate