A new simple efficient classification technique for severity of sleep apnea with mathematical model and interpretation

Abstract

BACKGROUND:

Obstructive Sleep Apnea (OSA) is the cessation of breathing during sleep due to the collapse of the upper airway. Polysomnographic recording is a conventional method for detection of OSA. Although it provides reliable results, it is expensive and cumbersome. Thus, an advanced non-invasive heart rate variability (HRV) signal processing technique other than the standard spectral analysis, which also has efficiency limitations, is needed for identification of OSA and classification of apnea levels.

OBJECTIVE:

The main purpose of this work was to predict the severity of sleep apnea using an efficient method based on the combination of time-domain and frequency-domain analysis of the HRV to classify sleep apnea into three different levels (mild, moderate, and severe) according to its severity and to distinguish them from normal subjects.

METHODS:

The statistical signal characterization of the FFT-based spectrum of the RRI data is used in this work in order to rank patients to full polysomnography. Data of 20 normal subjects, 20 patients with mild apnea, 20 patients with moderate apnea and 20 patients with severe apnea were used in this study.

RESULTS:

Accuracy result of 100% was obtained between severe and normal subjects, 100% between mild and normal subjects, and 100% between apnea (mild, moderate, severe) and normal subjects. This perfect accuracy is obtained using the parameter mean (mt). The physiological interpretation of the SSC parameters has been derived using a mathematical model system.

CONCLUSIONS:

An efficient method for screening of sleep apnea with 100% efficiency in classification of sleep apnea levels, is investigated in this work.

Keywords

Obstructive sleep apnea severity of apnea HRV statistical signal characterization FFT spectral

1. Introduction

Sleep apnea is complete cessation of breathing during sleep. Obstructive Sleep Apnea (OSA) is the commonest form of apnea that occurs when the upper airway is obstructed due to the relaxation of dilating muscles [1]. Hypopnea is a form of nocturnal obstruction where the airway partially collapses and causes 50% reduction of airflow [2]. The severity of the apnea is measured by Apnea Hypopnea Index (AHI), which indicates the number of apneas and hypopneas episodes per hour of sleep. OSA is said to be mild if AHI is between 5 and 15 per hour, moderate if AHI is between 15 and 30 per hour, and severe if AHI is greater than 30 per hour. If AHI is less than 5 per hour, the case is considered normal [3].

The most commonly used technique for sleep analysis is an overnight polysomnographic recording, which requires overnight hospitalization for monitoring of patients’ body functions during sleep. Such functions are brain activity, eye movements, muscle activity, leg and arm movements, heart rate, respiration effort, airflow, snoring, and blood oxygen level. These activities are measured by several special electrodes and sensors attached to the body and connected to a polyrecorder.

The diagnosis of the recording is done automatically by a specialized software, edited by a skilled technician and reviewed by a specialized physician. Although the polysomnographic recording can be inconvenient to the patient, it provides reliable results for diagnosis of sleep disorders. It is a demanding and consumable procedure which requires a large team of manpower and expensive equipment [4]. In Sultan Qaboos University Hospital (SQUH), which has the only sleep laboratory in the Sultanate, the waiting list for Polysomnography keeps increasing with the increased awareness of OSA by doctors and patients. The waiting list is now up to 4 months [5].

The development in computer and biomedical signal processing technology has led several researches to propose alternative noninvasive methods for apnea detection and screening that involve processing and manipulation of one or more of the body activities such as heart rate (HR) or R-R interval (RRI); Electrocardiogram (ECG), and breathing signals. This has led to the use of less electrodes and to made the screening process easier and more convenient.

The spectrum of HRV or RRI data is divided into three bands: very low frequency (VLF) ( $\leqslant$ 0.04 Hz), low frequency (LF) (0.04–0.15 Hz) and high frequency (HF) (0.15–0.4 Hz) bands [6]. The frequency domain analysis of RRI data is mainly dependent on finding and comparing the power contents of these bands.

Theoretically, in OSA the cessation of breathing will cause the respiration center in the brain to activate its autonomic components (sympathetic and parasympathetic) which send feedback impulses to the heart to compensate for the lack of oxygen and low blood pleasure [3]. This interaction between the heart and brain is reflected into the beat-to-beat variation of heart rate. The HF band is contributed to the parasympathetic activity and respiration sinus arrhythmia (breathing frequency); the LF can be due to both sympathetic and parasympathetic activities. The VLF could be related to thermoregulation and low frequency periodicities in respiration [3, 4, 5, 6].

Many frequency domain studies have shown that OSA patients tend to have spectral peaks within the VLF band (0.01 to 0.05 Hz) of RRI spectrum [7]. In [8], the fast Fourier transform (FFT) was applied directly on the RRI signal leading to classification accuracy of 90% when applied to the MIT data set. The short-time Fourier transform (STFT) was applied on the RRI data using the ratio between the power of LF band to the power of HF band (LF/HF) [9]. The LF/HF ratio was found to be higher in patients with severe OSA compared to those with mild OSA and normal subjects [9, 10].

The soft-decision power spectral estimation technique based on sub-band decomposition and [11, 12] wavelet-decomposition [13] was implemented successfully in many applications among them identification of patients with obstructive sleep apnea and congestive heart failure using RRI data [14, 15, 16, 17, 18].

The standard FFT spectrum analysis method and the soft-decision wavelet-based technique have been used to rank patients to full polysomnography [19]. Data of 20 normal subjects and 20 patients with mild apnea and 20 patients with moderate apnea and 20 patients of severe apnea are used in this study. The data is obtained from the sleep laboratory of Sultan Qaboos University hospital in Oman. Accuracy result of 90% was obtained between severe and normal subjects and 85% between mild and normal and 83.75% between normal and patients. The VLF/LF power spectral ratio of the wavelet-based soft-decision analysis of the RRI data after a high-pass filter resulted in the best accuracy of classification in all versions.

The main purpose of this work is to predict the severity of sleep apnea using a new method that combines a time-domain method named statistical signal characterization (SSC) and the standard frequency-domain method (FFT) using the same data used in [19].

The organization of the paper is as follows: in Section 2, the data used in the work is described. In Section 3, the methods implemented in the work are investigated. Section 4 contains the main results of classifying apnea into its different levels. Section 5 introduces a physiological interpretation model to understand the correlation between SSC parameters and HRV spectral parameters. Section 6 concludes the work.

2. Data acquisition

2.1 Subjects

This study received approval from the Institutional Research and Ethics Committee on 20 October 2010, with the reference number MREC380. All subjects gave informed written permission for participation and use of the data in analysis. Strict confidentiality was maintained.

Eighty subjects were included in this study. Their data were collected from SQUH sleep laboratory including information about their: age, sex, BMI, AHI, sleep efficiency, and the number of rapid eye movement (REM) cycles (REM is a normal stage of sleep characterized by the rapid movement, low muscle tone and a rapid low-voltage EEG) occurring during their sleep. The past medical and medication history of those patients were obtained from hospital information system of SQUH.

The subjects selected are of age ranging between 15–75 years, with sleep efficiency of more than 50% and with at least one REM cycle. Subjects taking drugs for hypertension or drugs that affect the heart were excluded. As well as subjects having prolonged severe asthma or have previously underwent a cardiac surgery.

According to the AHI, the eighty subjects included in the study were divided into four groups: control, mild, moderate and severe OSA.

2.2 Data pre-processing

The data are initially recorded by polysomnographic recording machine running Gamma PSG Software at the hospital of Sultan Qaboos University in Oman. Out of the polysomnogarphic overnight recorded signals (between 4 to 6 hours of recording), only ECG signals sampled at 100 samples/sec are extracted in text format using the Gamma PSG software itself. The following pre-processing steps are implemented on the ECG signals [19] :

1.
Resample the ECG data at 200 samples/sec and convert them from text format to WFDB format using the WaveForm DataBase (WFDB) software [20]. The (WFDB) is a software package provided by Harvard-MIT Division of Health and Technology for the analysis and manipulation of digitized signals of ECG, blood pressure, respiration, EEG and EMG signals, as well as to analyze the annotation files that normally associated with these signals.
2.
Generate the RRI data using the QRS detector tool which is part of the Physionet tools [21]. The detector operates on a single channel of ECG data (WFDB format) sampled at 200 samples/sec. Therefore, the data must be in WFDB format and re-sampled at 200 samples/sec before applying the detector.
3.
Reconvert the RRI data from WFDB format to text format using (WFDB) software.
4.
Remove the outliers of the RRI data using 41-points Moving Average Filter (MAF).
5.
Resample at 1 Hz and substitute the missed peaks by using linear interpolation in MATLAB. This step is done to generate equally spaced RRI data and preserve the temporal sequence that is necessary for frequency domain analysis.
6.
Band-pass filtering with 0.01–0.09 Hz bandwidth to screen the apnea oscillations by implementing a high-pass filter followed by a low-pass filter in MATLAB.

3. Data analysis method

A new modified version of the Statistical Signal Characterization (SSC) – method is applied on the spectrum of the RRI signal. The basis of this approach is to be briefly explained in the following subsection.

Figure 1.

Segments amplitudes and corresponding times characteristics.

3.1 Statistical Signal Characterization

The SSC is a method that characterizes a waveform not only as a function of the frequency-component amplitudes, but also as a function of the relative phases of its frequency components [22, 23]. The input waveform to the SSC process is basically divided into segments where each segment is bounded by two extrema: maxima and minima as shown in Fig. 1.

The segment amplitudes $A_{n}$ and the segment periods $T_{n}$ are defined as follows: Segment amplitude of the $n$ -th segment:

$\displaystyle A_{n}=|a_{n}-a_{n-1}|,\quad n=1,2,\ldots,N_{s}$ (1)

where $a_{n}=$ waveform amplitude at the concluding extremum of the $n$ -th segment, $a_{n-1}=$ waveform amplitude at the beginning extremum of the $n$ -th segment, $N_{s}=$ total number of segments, which varies for any given signal.

Segment period of the n-th segment:

$\displaystyle T_{n}=t_{n}-t_{n-1}$ (2)

where $t_{n}=$ time instant at the concluding extremum of the $n$ -th segment, $t_{n-1}=$ time instant at the beginning extremum of the $n$ -th segment.

Figure 2.

Segments amplitudes and corresponding frequencies characteristics.

Four SSC parameters can then be computed from the amplitude and period vectors of the signal under consideration. These parameters are the amplitude mean (ma), the period mean (mt), the amplitude-mean deviation (da), and the period-mean deviation (dt):

$\displaystyle\textit{ma}=\sum_{i=1}^{N_{s}}(A_{i}/N_{s})$ (3) $\displaystyle\textit{mt}=\sum_{i=1}^{N_{s}}(T_{i}/N_{s})$ (4) $\displaystyle\textit{da}=\sum_{i=1}^{N_{s}}(|A_{i}-M_{a}|)/N_{s}$ (5) $\displaystyle\textit{dt}=\sum_{i=1}^{N_{s}}(|T_{i}-M_{t}|)/N_{s}$ (6)

The SSC process is usually applied to a time-domain signal, as described above.

In this work, it is modified and applied to the spectrum of the time-domain signal. For example, similar to Fig. 1, a magnitude spectrum can be plotted by considering the spectral maxima and the minima, as sketched in Fig. 2. Hence, corresponding changes have to be applied to Eqs (4) and (6) by replacing any time point by a frequency point. The phase information in the original time-domain algorithm is included in the modified algorithm in the differences between the successive frequency locations of the critical points of the amplitude spectrum.

3.2 Implementation process

In our work, the time-domain RRI signal is divided into 80 sections. The following 12 derived parameters are computed as average or maximum or minimum of the main SSC parameters of the 80 sections.

1.
Average of amplitude mean: Mean (ma)
2.
Maximum-amplitude mean: Max (ma)
3.
Minimum-amplitude mean: Min (ma)
4.
Average of amplitude-mean deviation: Mean (da)
5.
Maximum amplitude-mean deviation: Max (da)
6.
Minimum amplitude-mean deviation: Min (da)
7.
Average of period mean: Mean (mt)
8.
Maximum-period mean: Max (mt)
9.
Minimum-period mean: Min (mt)
10.
Average of period-mean deviation: Mean (dt)
11.
Maximum period-mean deviation: Max (dt)
12.
Minimum period-mean deviation: Min (dt)

3.3 Classification versions and performances

In this study, only binary classification is considered, e.g. classification between two different cases termed “positive case” and “negative case”.

Three different versions of classification are implemented:

1.
Version 1: classification between 20 positive cases (mild) and 20 negative cases (normal). This classification version is very important to discover the obstructive sleep apnea at an early stage.
2.
Version 2: classification between 20 positive cases (severe apnea) and 20 negative cases (normal). This classification version is the classical version on which most of the researchers are concentrating.
3.
Version 3: classification between 60 positive cases (apnea: severe or moderate or mild) and 20 negative cases (normal). In our opinion, this classification version is more important than version 2 and must be considered as the classical classification version used for apnea detection.

The performance of a classifier is evaluated by three main metrics: specificity, sensitivity, and accuracy, as follows [24]:

$\displaystyle\textit{specificity}=\frac{\textit{TN}}{\textit{TN}+\textit{FP}}$ (7) $\displaystyle\textit{sensitivity}=\frac{\textit{TP}}{\textit{TP}+\textit{FN}}$ (8) $\displaystyle\textit{accuracy}=\frac{\textit{TP}+\textit{TN}}{\textit{TP}+% \textit{FP}+\textit{TN}+\textit{FN}}$ (9)

where the entities in the above equations are: TN (true negatives), TP (true positives), FN (false negatives), and FP (false positives).

Specificity indicates the ability of the classifier to detect negative cases. Sensitivity represents the ability of the classifier to detect the positive cases. Accuracy represents the overall performance of the classifier, which indicates the percentage of correctly classified positive and negative cases among the total number of cases.

For each SSC parameter, a threshold is found to separate between the two apnea levels under investigation. The threshold is found using the Receiver Operating Characteristic (ROC) [25].

ROC is a graphical technique that evaluates the performance of a classifier as the decision threshold of the classifier varies. ROC also compares between different classifiers. Therefore, it assists in selecting an optimal threshold for a particular classifier and the best classifier among many classifiers. Consequently, a user (a receiver) can setup the operating characteristics, an optimal classifier and an optimal threshold, of his algorithm.

The ROC space is defined by two coordinates, the x-axis represents the (1-sensetivity) and the y-axis represents the specificity. Each classifier is represented by a point (1-sensetivity, specificity) in the ROC. The ROC is also used to evaluate the performances of the different parameters.

Table 1
Results of classification of version 1 (mild and normal)

Parameter Specificity Sensitivity Accuracy Threshold

Mean (ma) 1.0 0.85 0.925 0.134

Max (ma) 1 0.95 0.975 0.253

Min (ma) 0.9 0.85 0.875 0.059

Mean (da) 1 0.90 0.95 0.096

Max (da) 1 1 1 0.181

Min (da) 0.9 0.9 0.9 0.048

Mean (mt) 1 1 1 0.009

Max (mt) 1 0.95 0.975 0.011

Min (mt) 1 1 1 0.007

Mean (dt) 1 1 1 0.0045

Max (dt) 0.95 0.95 0.95 0.007

Min (dt) 0.95 0.95 0.95 0.0024

Figure 3.
ROC and results of parameter mean (ma) for normal and mild apnea.

Figure 4.
ROC and results of parameter mean (da) for normal and mild apnea.

Figure 5.
ROC and results of parameter mean (mt) for normal and mild apnea.

Figure 6.
ROC and results of parameter mean (dt) for normal and mild apnea.

4. Results

4.1 Results of version 1: Classification between mild and normal

Table 1 shows the efficiency of classification between mild and normal in terms of specificity, sensitivity, and accuracy using the 12 derived parameters. The accuracy ranges from 87.5% to 100% from parameter to another. Figures 3–6 show the ROC results on left and classification results on right for parameters mean (ma), mean (da), mean (mt), and mean (dt), respectively.

4.2 Results of version 2: Classification between severe and normal

Table 2 shows the efficiency of classification between severe and normal in terms of specificity, sensitivity, and accuracy using the 12 derived parameters. Figures S1–S4 show the ROC results on left and classification results on right for parameters mean (ma), mean (da), mean (mt) and mean (dt), respectively. The accuracy ranges from 90% to 100% from parameter to another. Best results are obtained with parameters mean (mt), max (mt), min (mt), max (ma) and max (da).

Table 2
Results of classification of version 3 (severe and normal)

Parameter	Specificity	Sensitivity	Accuracy	Threshold
Mean (ma)	1	0.95	0.975	0.134
Max (ma)	1	1	1	0.253
Min (ma)	0.90	0.95	0.925	0.059
Mean (da)	1	0.95	0.975	0.096
Max (da)	1	1	1	0.181
Min (da)	0.9	0.95	0.925	0.048
Mean (mt)	1	1	1	0.009
Max (mt)	1	1	1	0.011
Min (mt)	1	1	1	0.007
Mean (dt)	0.95	0.9	0.925	0.0045
Max (dt)	0.95	0.95	0.95	0.007
Min (dt)	0.95	0.85	0.9	0.002

Table 3

Results of classification of version 4 (apnea and normal)

Parameter	Specificity	Sensitivity	Accuracy	Threshold
Mean (ma)	1	0.95	0.963	0.134
Max (ma)	1	0.983	0.988	0.253
Min (ma)	0.9	0.933	0.925	0.059
Mean (da)	1	0.967	0.975	0.096
Max (da)	1	1	1	0.181
Min (da)	0.9	0.95	0.938	0.048
Mean (mt)	1	1	1	0.009
Max (mt)	1	0.983	0.988	0.011
Min (mt)	1	1	1	0.007
Mean (dt)	1	0.95	0.963	0.0045
Max (dt)	0.95	0.967	0.963	0.007
Min (dt)	0.70	0.666	0.675	0.002

Table 4

Results of modeling experiment

SSC Parameter	Case 1: Mean $\pm$ Std.	Case 2: Mean $\pm$ Std.
Mean (ma)	0.287 $\pm$ 0.011	0.430 $\pm$ 0.015
Mean (da)	0.366 $\pm$ 0.006	0.455 $\pm$ 0.012
Mean (mt)	0.080 $\pm$ 0.004	0.091 $\pm$ 0.001
Mean (dt)	0.057 $\pm$ 0.005	0.008 $\pm$ 0.004

4.3 Results of version 3: Classification between apnea and normal

Table 3 shows the efficiency of classification between apnea (severe or moderate or mild) and normal in terms of specificity, sensitivity, and accuracy using the 12 derived parameters. The accuracy ranges from 67.5% to 100% from parameter to another. Best results are obtained with parameters mean (mt), min (mt), and max (da). Figures S5–S8 show the ROC results on left and classification results on right for parameters mean (ma), mean (da), mean (mt) and mean (dt), respectively.

5. Physiological interpretation of results

Since the SSC parameters of HRV spectral have no previous physiological interpretation, it was a difficult task to find this interpretation directly. On the other hand, the standard HRV spectral parameters (LF, HF) have a clear physiological interpretation.

The power of the LF component increases with apnea level (moving from normal to mild to moderate to severe), and the power of the HF component decreases with apnea level. This fact has been identified by many researchers [26, 27, 28, 29, 30] and also has been proved in our previous work [19]. An attempt to link the SSC parameters to the LF and HF spectral components of HRV could be a good solution and gives an indirect physiological interpretation to the SSC parameters of HRV spectral. A mathematical model is selected to simulate the following two cases:

Case 1: A signal is simulated 200 times by adding two sinusoidal signals with two different frequencies. The first frequency is 0.1 Hz corresponds to the LF component of HRV spectral.

While the second frequency is 0.3 Hz corresponds to the HF component of HRV spectral. The sampling frequency is selected to be 1 Hz.

The number of sections of each signal is selected to be 20, while the length of each section is chosen to be 512 samples. The amplitude of each sinusoid is randomly changed between two values. The idea is to have the power of the LF sinusoid (with amplitudes vary between 0.6 and 0.8) high compared to the power of the HF sinusoid (with amplitudes vary between 0.1 and 0.2). Then, the SSC parameters are computed for the spectral of the simulated signal.

Case 2: The same procedure is repeated but the amplitudes of both sinusoids are interchanged so that the power of the HF sinusoid is higher than that of the LF sinusoid.

It has been noticed that all the parameters (mean (ma), mean (da), mean (mt), and mean (dt)) are 100% (200 times) of larger values in case 2 than in case 1. The mean values and the standard deviation of the four parameters are listed in Table 4 for both cases.

We can conclude from the result of the modeling system that: An increase in the power of the HF component with a simultaneous decrease in the power of the LF component results in higher values of the SSC parameters. While a decrease in the power of the HF component with a simultaneous increase in the power of the LF component results in lower values of the SSC parameters.

In other words, we conclude that the SSC parameters of the HRV spectral follow the same variation of the HF power of the HRV spectral (directly proportional) and the opposite variation of the LF power of the HRV spectral (inversely proportional). So that the SSC parameters are decreasing with the apnea level (more in normal than in mild, and more in mild than in moderate, and more in moderate than in severe OSA subjects).

6. Discussions and conclusions

The statistical signal characterization of the FFT spectrum of RRI data has been implemented very efficiently to screen OSA patients from normal subjects and to classify OSA patients into three levels mild, moderate, and severe.

The accuracy of identification of mild apnea from normal ranges from 87.5% to 100% from one SSC parameter to another.

The accuracy ranges from 90% to 100% from parameter to another in classification between normal and severe apnea. The accuracy ranges from 67.7% to 100% from parameter to another in classification between normal and apnea.

Best results (perfect classification 100%) are obtained with parameter mean (mt) in all three different versions of classification. Such perfect classification efficiency is much better than our previous results [19] (85% between mild and normal, 90% between severe and normal, and 83.5% between apnea and normal) using the wavelet-based spectral analysis of the heart rate variability.

The method of this paper deals with the statistical signal characterization of the spectrum of the heart rate variability. This method depends mostly on the morphology of the spectrum signal and how long or short the segments are (parameters mt and dt), and how much the difference between the amplitudes of the critical points of the segment (parameter ma and da).

It is very clear to notice that all 4 important parameters mean (ma), mean (da), mean (mt), and mean (dt) are of higher values in normal subjects compared to patients. Such a remark leads to an important physiological interpretation and suggests a direct proportional relation between those parameters and the power of the high frequency band of the heart rate variability and an inverse proportional relation with the power of the low frequency band of the heart rate variability. This relation has been proved using a physiological interpretation modeling system.

The novel idea shows successful results and needs to be tested for classification of other diseases such as congestive heart failure and also attempts are done to apply it for monitoring patients before and after coronary artery bypass grafting (CABG) operation to see whether those SSC parameters are also successful for identifying the status of patients.

Footnotes

Acknowledgments

The author would like to thank the Sleep Laboratory at Sultan Qaboos University Hospital for providing the data used in the work.

Conflict of interest

None to report.

Abbreviations

Appendix A: Results of version 2 and 3

Figure S1.

ROC and results of parameter mean (ma) for normal and severe apnea.

Figure S2.

ROC and results of parameter mean (da) for normal and severe apnea.

Figure S3.

ROC and results of parameter mean (mt) for normal and severe apnea.

Figure S4.

ROC and results of parameter mean (dt) for normal and severe apnea.

Figure S5.

ROC and results of parameter mean (ma) for normal and apnea.

Figure S6.

ROC and results of parameter mean (da) for normal and apnea.

Figure S7.

ROC and results of parameter mean (mt) for normal and apnea.

Figure S8.

ROC and results of parameter mean (dt) for normal and apnea.

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A new simple efficient classification technique for severity of sleep apnea with mathematical model and interpretation

Abstract

BACKGROUND:

OBJECTIVE:

METHODS:

RESULTS:

CONCLUSIONS:

Keywords

1. Introduction

2. Data acquisition

2.1 Subjects

2.2 Data pre-processing

4.1 Results of version 1: Classification between mild and normal

4.2 Results of version 2: Classification between severe and normal

Table 2 Results of classification of version 3 (severe and normal)

5. Physiological interpretation of results

6. Discussions and conclusions

Footnotes

Acknowledgments

Conflict of interest

Abbreviations

Appendix A: Results of version 2 and 3

References

Table 2
Results of classification of version 3 (severe and normal)