Automated Recognition of Sleep Apnea-Hypopnea Syndrome Using Continuous Wavelet Transform-Based Multiscale Dispersion Entropy of Single-Lead ECG Signal

2.1 The ECG data description

PysioNet is a physiological signal database that may be utilized in biomedical research. Both of the databases we utilized are accessible via the web site, allowing an easy examination and evaluation of our technique. The databases used in this research allow us to have more records in order to obtain different classes of SAHS [21].

2.1.1 The apnea-ECG database

This work uses the Apnea ECG database, which is available on the Physio website [8], to diagnose SAHS. The data consists of 70 recordings separated into a learning set (a01-a20, b01-b05, c01-c10) and a test set (x01-x35) with 35 records each. Each of these recordings is related to a single channel ECG signal (lead) with a sampling frequency of 100 Hz and a resolution of 16 bits, for a period of time (less than 7 h to approximately 10 h). Additionally, the ECG signals were collected based on the following factors: age, gender, weight, height, apnea index (AI), hypopnea index (HI), and apnea hypopnea index (AHI). They are classified into three groups based on the AHI value (a, b, c). When the AHI value is less than 5, it is classified as normal; when the value is greater than 10, it is classified as apnea; and when the value is less than 10, it is classified as boundary.

2.1.2 UCD database

The St. Vincent’s University Hospital/University College Dublin Sleep Apnea Database (UCD database) contains 25 complete overnight PSG records from people without heart disease or autonomic dysfunction and not taking any medication known to interfere with heart rate, each of which includes an ECG signal as well as other data. ECG signals are sampled at a rate of 125 Hz. Sleep technologists create annotations, which describe the onset and duration of all episodes of apnea and hypopnea. Two labeling standards are used to select the reference annotation on a one-minute basis. A similar method is used in the Apnea-ECG database. Each recording contains ECG signals that span 5.9 to 7.7 hours, as well as an annotation file that details the start time and length of each apnea or hypopnea event [22]. This database provides us with the options of normal and hypopnea groups.

2.2 Pre-processing

Accurate detection of the QRS complex is essential for producing optimal HRV signal from ECG recordings. The method we propose for the delineation of QRS complexes is based on a multi-resolution analysis by the wavelet transform. In wavelet applications, the mother wavelet chosen is extremely important. In reality, there is no well-defined criterion for selecting the mother wavelet, and this decision is highly dependent on the nature of the application and varies from one to the next. Several studies of wavelet analysis of the ECG signal have discovered that the 'Daubechies' wavelet family, specifically the wavelet 'db6,' is best suited for the treatment of the ECG signal since its form is comparable to the QRS complex [23].

As a result, the Daubechies mother wavelet ‘db6' will be used to breakdown the ECG signal throughout the remainder of this article. The level of decomposition chosen is also a factor to consider. In this algorithm, we have divided the ECG signal into nine levels [24]. This wise choice makes it possible to clearly distinguish the QRS complex, P waves, T waves and the baseline. The R peak detection is the most crucial stage in identifying the QRS complex since the accuracy of subsequent waves is dependent on this initial step. The db6 wavelet is used to produce nine levels of wavelet decomposition on the preprocessed ECG data. All information except D3 to D6 is preserved, while the rest are erased. The signal is therefore reconstructed from the details D3-D6, allowing the QRS complexes in the signal to be preserved while the other components at low and high frequencies are eliminated.

The Pan Tompkins method was used to identify the QRS complex from the previously filtered signal [25]. Once R peaks have been identified, HRV signal may be generated easily and precisely. The variation in successive RR intervals yields an HRV signal.

2.3 Feature description

2.3.1 Continuous wavelet transform (CWT)

The CWT is a robust time-frequency conversion method, which uses a set of wavelet functions to deal with simultaneous filtering and segmentation in the time-frequency domain. Unlike STFT, CWT is one of the most advanced methods for STFT, as it can provide by adjusting scale and translation parameters high time resolution and low frequency resolution in the high frequency, and high frequency resolution and low time resolution in the low frequencies [26]. The CWT can be computed from the following expression:

$\mathrm{X}_{\mathrm{CWT}}(\mathrm{u}, \mathrm{s})=\frac{1}{\sqrt{\mathrm{s}}} \int_{-\infty}^{\infty} \mathrm{x}(\mathrm{t}) \psi^{*}\left(\frac{\mathrm{t}-\mathrm{u}}{\mathrm{s}}\right) \mathrm{dt}$    (1)

where, s is a scale parameter, u is a translation parameter, and ψ^*(t) is the mother wavelet. The scale can be converted to frequency by

$\mathrm{F}=\frac{\mathrm{F}_{\mathrm{c}} * \mathrm{f}_{\mathrm{s}}}{\mathrm{s}}$     (2)

where, F_c is the center frequency of the mother wavelet, f_s is the sampling frequency of signal x(t) [27].

The synthesis of the complete or limited-range part of the signals is accomplished from the wavelet parameters by means of the inverse continuous wavelet transform (ICWT), defined as follows:

$x(t)=\frac{1}{C_{\psi}} \int_{-\infty}^{\infty} \int_{-\infty}^{\infty} X_{C W T}(u, s) \frac{1}{\sqrt{s}} \psi\left(\frac{t-u}{s}\right) d u \frac{d s}{s^{2}}$     (3)

where, C_ψis the admissibility condition obtained when ψ(t) fulfills all the requirements to be considered a mother wavelet.

2.3.2 Multiscale dispersion entropy

Dispersion entropy (DisEn) is a time series irregularity measurement approach based on nonlinear dynamic analysis. DisEn has a better anti-noise capability than sample entropy since a slight change in amplitude does not modify the associated class label in DisEn.

The stages of DisEn may be stated as follows [28, 29] for a given univariate time series $X=\left\{x_{1}, x_{2}, \ldots, x_{N}\right\}$ with length N:

• A normal cumulative distribution function (NCDF) is used to mapped the original time series X into $\mathrm{Y}=\left\{\mathrm{y}_{1}, \mathrm{y}_{2}, \ldots, \mathrm{y}_{\mathrm{N}}\right\}$.

$y_{j}=\frac{1}{\sigma \sqrt{2 \pi}} \int_{-\infty}^{x_{j}} e^{\frac{-(t-\mu)^{2}}{2 \sigma^{2}}} d t$     (4)

where, $y i \in(0,1)$, and µ and σ represent the mean and standard deviation of time series X, respectively.

• Using the linear transform, all elements of $\mathrm{Y}\left(\mathrm{y}_{\mathrm{i}}, \mathrm{j}=1,2, \ldots, \mathrm{N}\right)$ are mapped to c classes with integer indices ranging from 1 to c for each member of the mapped signal.

$\mathrm{z}_{\mathrm{j}}^{\mathrm{c}}=\mathrm{R}\left(\mathrm{c} \cdot y_{j}+0.5\right)$     (5)

where, $\mathrm{z}_{\mathrm{j}}^{\mathrm{c}}$ denotes the jth member of the classified time series, c means the number of classes, and R(·) represents the rounding function. Despite the fact that step (2) is linear, the entire mapping method is nonlinear due to the usage of NCDF in the first step.

• Time series $\mathrm{z}_{\mathrm{i}}^{\mathrm{m}, \mathrm{c}}$ are made with embedding dimension m and time delay d according to $\mathrm{z}_{\mathrm{i}}^{\mathrm{m}, \mathrm{c}}=\left\{\mathrm{z}_{\mathrm{i}}^{\mathrm{c}}, \mathrm{z}_{\mathrm{i}+\mathrm{d}}^{\mathrm{c}}, \ldots, \mathrm{z}_{\mathrm{i}+(\mathrm{m}-1) \mathrm{d}}^{\mathrm{c}}\right\}, i=1,2, \ldots, N-(m-$ 1)d [30]. 

Each time series $\mathrm{z}_{\mathrm{i}}^{\mathrm{m}, \mathrm{c}}$ can be mapped to a dispersion pattern $\pi_{v_{0} v_{1} \ldots v_{m-1}}$, where $\mathrm{z}_{\mathrm{j}}^{\mathrm{c}}=v_{0}, \mathrm{z}_{\mathrm{j}+\mathrm{d}}^{\mathrm{c}}=v_{1}, \ldots, \mathrm{z}_{\mathrm{j}+(\mathrm{m}-1) \mathrm{d}}^{\mathrm{c}}=v_{m-1}$. The number of possible dispersion patterns that can be assigned to each time series $\mathrm{z}_{\mathrm{i}}^{\mathrm{m}, \mathrm{c}}$ is equal to $c \mathrm{~m}$ as the signal has $m$ members, and each member can be one of the integers from 1 to $c$.

• For each $c^{\mathrm{m}}$ potential dispersion pattern $\pi_{v_{0}} v_{1} \ldots v_{m-1}$, the relative frequency can be obtained by:

$p\left(\pi_{v_{0} v_{1} \ldots v_{m-1}}\right)=\frac{\#\left\{\begin{array}{c}\frac{i}{i} \leq N-(m-1) d, \mathrm{z}_{\mathrm{i}}^{\mathrm{m}, \mathrm{c}} \\ \text { has type } \pi_{v_{0} v_{1} \ldots v_{m-1}}\end{array}\right\}}{N-(m-1)}$     (6)

where, # means cardinality. In fact, $p\left(\pi_{v_{0} v_{1} \ldots v_{m-1}}\right)$ shows the number of dispersion patterns of $\pi_{v_{0}} v_{1} \ldots v_{m-1}$  that is assigned to $\mathrm{Z}_{\mathrm{i}}^{\mathrm{m}, \mathrm{c}}$, divided by the total number of embedded signals with embedding dimension m.

• Based on the definition of Shannon entropy, the DispEn of X is computed by

The present paper describes a new method for detecting and classifying episodes of obstructive sleep apnea and hypopnea using ECG signal. This method is based on extracting the calculated the mean of the small (1 to 5), medium (6 to 10) and large (11 to 20) time scales of the multiscale dispersion entropy (MDE) directly from the VLF, LF, HF and TP sub-band signals. So that the VLF, LF and HF sub-band signals were obtained by analyzing the HRV signal using CWT followed by ICWT technique. The CWT enables for signal analysis at multiple scales and translations according to the problem (It allows extracting each band between specific frequency bands). The ICWT approach aided us in noise reduction, to be implemented in the wavelet domain and in the signal reconstruction that resulted after processing.

Figures 4-9 and Figure 10 represent the mean and standard deviation of the indices based on the method of calculating the MDE in the small (1 to 5), medium (6 to 10) and large (11 to 20) time scales of the sub-band signals. As can be shown, the DispEnLF and DispEnLF/HF indices indicate a rising tendency among normal, hypopnea, and OSA episodes. Between normal, hypopnea, and OSA episodes, the DispEnHF and DispEnpHF indices indicate a declining tendency. In the normal, hypopnea, and OSA episodes, the ShEnVLF and ShEnpVLF indices exhibit volatility in the three time scales of MDE.

Because LF is associated with sympathetic nervous system activity, variations in HRV's LF sub-band signal change significantly in the sympathetic nervous system. HF is thought on the other hand to be associated with parasympathic activity. The physiological meaning of the very low frequency factor (VLF) is still unclear, however, and was merely determined using long-term rhythms [37]. Because typical people's parasympathetic activity increases during nighttime sleep, the fluctuation patterns of the HRV increase inside the HF band, the texture of the HF sub-image of CWT and sub-signal of ICWT is complicated. The sympathetic activity inhibiting HF component diminishes by comparison, i.e. in normal episodes, the fluctuations of HRV decreases with LF band, thereby simplifying the texture of the CWT sub-band image and ICWT sub-band signal of LF. Parasympathetic activity is, however, inhibited for OSA patients due to predominant sympathetic activity. Thus, the oscillation features of the HRV are reduced in the HF band, while the range of LF is increased in comparison to ordinary episodes. As a consequence, the DispEnLF and DispEnLF/HF indices show an increasing trend between the normal, hypopnea and OSA episodes, while the DispEnHF and DispEnpHF indices show a decreasing trend between the normal, hypopnea and OSA episodes in both three time scales: small, medium and large. As the variation of HRV signals from normal to hypopnea and normal to hypopnea episodes was represented largely in the HF band and the LF bands, there were therefore substantial disparities in both normal and hypopnea or OSA episode, and there was no significant difference between OSA and a hypopnea episode.

As you know from Table 2 and Figure 9, the highest classification accuracy between the normal and OSA episodes is 98.58% using SVM classifier with Radial Basis Function (RBF) kernel and combination indices of the small, medium and large time scales. Because OSA causes breathing disorders during sleep and increases sympathetic nervous system activity, it's simpler to discriminate between the two types of normal and OSA episodes. In OSA episodes and hypopneas, the HRV signal has more turbulent vibrational properties, whereas the HRV signal in a healthy individual has more regular and tuned qualities. This difference can be seen by the distribution of the wavelet spectral power in the time-frequency domain of HRV signal. The accuracy for both normal and hypopnea episodes is 95.69% using the SVM-RBF classifier and the combination of the indices of the small, medium and large time scales, which is lower than the normal and OSA episodes due to the diminution turbulent vibrational properties of the HRV signal in the hypopnea episodes.

The accuracy between the OSA and the hypopnea is 87.04%, by means of the SVM-RBF classifier and combining small, medium and large time scales, which is less than in the previous two examples. The fluctuating features of the HRV signal shows some parallels between OSA and hypopnea episodes. The activity of the sympathetic nervous system, which may produce OSA episodes, is more important than the activity of the hypoventilation episodes, resulting a difference between the two OSA and hypopnea episodes.

The average classification accuracy of three episodes (normal, OSA, and dyspnea) in Table 3 and Figure 10 is 93.94% by using the multi-classification technique of SVM-RBF classifier and combining small, medium and large time scale indices. The decrease in accuracy is due to the increasing types of categorization, which increases the probability of categorizing data into similar groups.

Several classification tests were performed in the proposed study, with the three-category ECG dataset (normal episodes, OSA episodes and hypopnea) so that the most difficult to accurately classify were OSA episodes and hypopnea. The traditional OSA detection and classification approach is based on the use of HRV and EDR signals analysis using time and frequency domains either alone or in combination. Khandoker et al. [13] demonstrated the best results for identifying OSA using the classic OSA detection and classification approach, which uses time-frequency domain analysis and an ANN classifier. They were able to detect apnea episodes with 94.84% accuracy which is less than that obtained by our proposed method. In reality, exploiting temporal characteristics of signal in real-time applications might be beneficial since they are simple to extract and provide a low-complexity calculation. However, in order to meet the established criteria, they have to split the original signal into short (5 sec) segments. Splitting the signal into small pieces often leads to loss and spoilage of the general dynamics of the signal. Also, there is no mathematical equation that can be used to determine the threshold levels in order to separate the sudden rises from the noise. Furthermore, ECG signal is a sort of weak and unstable signal that is readily impacted by noise, and frequency band analysis is not a solution since the signal is not stable.

As a result, we concentrated our efforts in this study on the HRV signal, which may be utilized as markers of cardio-respiratory rhythm coordination during SAHS, and we sought to uncover their non-linear features like multiscale dispersion entropy. Other research that used the same database (the Apnea-ECG database) for training and testing were compared to the suggested automated OSA detection methodology. Chazal et al. [10] and McNames and Frazer [38] are both achieving highly accurate. The authors [10] utilized a high-dimensional feature matrix (128 features), which results in a complicated technique. Furthermore, fundamental flaw is that their classification processes are not automated [38]. Also, in the classification stage, they deleted borderline recordings (10 participants), which is not the case in our classification work. Varon et al. [39] and Bali et al. [40] achieved the best results (100% accuracy) among the approaches for automated OSA identification. The methods mentioned in the studies [17-18] derived different characteristics from the RR intervals and EDR signal with an accuracy of 85.26 percent and 82.07 percent, respectively. Furthermore, several other researches, such as [19, 38], have rejected some of the noisy recordings with poor data quality in the process. As a result of the noisy nature of physiological signals, these techniques require high-quality datasets, which are not readily available.

In summary, the study's novelty stems mostly from the use of multiscale entropy characteristics of the HF, LF, VLF and TP sub-band signals in SAHS detection. The 24 novel indices in this article allow OSA and hypopnea to be recognized. Furthermore, this article benefits from the fact that the OSA and hypopnea episode may be recognised just with 5 minutes of the ECG signal, and that SAHS can be screened by the OSA episode, but also the hypopnea episode. There are few studies to differentiate obstructive sleep apnea episodes from episodes of hypopnea. As a result of this research, the suggested new indices based on CWT and MDE can differentiate between OSA episodes and hypopnea episodes, and these indices perform well - Accuracy, Sensitivity, and Specificity, respectively, are 89.87%, 87.13%, and 92.86%.