Wireless Pers Commun DOI 10.1007/s11277-017-4791-1
On the detection of Cardiac Arrhythmia with Principal Component Analysis Harjeet Kaur1 • Rajni Rajni1
Springer Science+Business Media, LLC 2017
Abstract The Electrocardiogram (ECG) signal is used to record the electrical activity of heart. The subtle variations in ECG attributes are used by cardiologists for diagnosis of heart anomalies. But, for prognosis of cardiac ailments feature extraction from electrocardiographic signal becomes extremely difficult due to presence of noise. With the aim of noise reduction, a hybrid technique involving Extended Kalman filter along with Discrete Wavelet transform for effectively improving signal quality is focused as a powerful tool. The performance of denoising algorithm is evaluated in terms of signal to noise ratio and mean square error. On denoised signal, a quick, simple and effectual approach based on Principal Component Analysis is proposed for R-peak and QRS complex detection. The beat detector performance is validated with MIT-BIH arrhythmia database, yielding a sensitivity of 99.93%, positive predictivity of 99.98% and a 0.079% detection error rate, being a positive outcome in comparison with recent researches. Later, different types of arrhythmias are detected on the basis of heart rate and morphological characteristics of ECG waveform. Keywords Electrocardiogram Denoising Principal component analysis QRS complex Arrhythmia
& Harjeet Kaur
[email protected] Rajni Rajni
[email protected] 1
Department of Electronics and Communication Engineering, Shaheed Bhagat Singh State Technical Campus, Ferozepur, Punjab, India
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1 Introduction The Electrocardiogram (ECG) is a recorded graphical trace demonstrating the variation of bio-potential versus time. The ECG is a widely available diagnostic tool used to understand and investigate cardiac health condition. The nonstationary ECG signal is captured with the aid of ECG machine by placing electrodes at specific locations on the surface of human body. Each heartbeat (cardiac cycle) in the ECG signal consists of three main deflections: P wave, QRS complex (formed of Q, R and S waves) and T wave [1]. In ECG signal, heartbeat patterns changes considerably with time and varying physical conditions for same individual [2]. Among all three waves, generally QRS complex has higher value of amplitude than T and P waves [3]. A typical ECG waveform with these events is shown in Fig. 1 [4]. The detection of constituent waves in ECG is related to diagnosis of various cardiovascular diseases [5]. Additionally, it can reveal the identity of a person [6]. The precised R-peak or QRS complex detection is necessary for accurate examination of patient’s heart rate [3, 5]. However, accurate detection of R wave or QRS complex becomes a challenging task due to presence of different noisy indices. The extraction of these clinically useful features from noisy ECG indications requires consistent signal processing methods [7]. For denoising ECG signals, several attempts have been reported in literature, including filter banks [8], adaptive wavelet with Wiener filtering [9], adaptive Kalman filter [10] and adaptive filtering [11]. The method of Empirical Mode Decomposition (EMD) has been applied for separating noise from ECG signal [12]. In EMD, selection of proper intrinsic mode functions is essential for reducing noise content. A great attention has been drawn by wavelet transform in denoising ECG signals [15]. For QRS detection authors have implemented real time algorithm in assembly language. This QRS detector failed to detect 0.675% of beats [16]. The QRS complex detection based on zero-crossing method, first derivative and empirical mode decomposition has been analyzed in [17–19]. Recently, Discrete Wavelet Transform (DWT) has been utilized for feature extraction in [5, 20, 21]. Till now, an extensive number of ECG denoising and beat detection techniques have been reported by analysts and the consistent diligent work for their improvement is still in progress. It proves that a solution which is able to be universally acceptable has not been found yet. The proposed work focuses on the application of Principal Component Analysis
Fig. 1 The ECG wave pattern [4]
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(PCA) along with thresholding for detection of QRS complex, R-peak and heart rate for arrhythmia detection. As it is complex to analyze ECG signal in the presence of noise, hybrid method involving two influential tools extended Kalman filter (EKF) with DWT is provided for noise eradication. The novelty of proposed work is the approach of adopting the three different prevailing tools, i.e. EKF, DWT and PCA for denoising, extraction of constituent components, prominent peaks of the ECG signal, detection of heart rate, arrhythmia and achieving superior results in comparison to other techniques. This paper is organized in five Sections. The introduction of topic of interest and work done in relevant field by researchers is covered in Sect. 1. The materials and methods as well methodology for proposed work are explored in Sects. 2 and 3 respectively. The results for presented work are provided and discussed in Sect. 4. Finally, Sect. 5 concludes the paper.
2 Materials and Methods 2.1 Extended Kalman Filter (EKF) The conventional Kalman filter is merely applicable for systems with linear models [22]. For nonlinear structures, an extension of conventional Kalman filter has been developed known as extended Kalman filter (EKF) [23, 24]. For a discrete-time nonlinear system xkþ1 ¼ f ðxk ; wk Þ and its observation yk ¼ gðxk ; vk Þ, linear approximation near a reference point ð^ xk ; w^k ; v^k Þ can be formulated [25, 26] as in Eq. (1). xkþ1 f ðx^k ; w^k Þ þ Ak ðxk x^k Þ þ Fk ðwk w^k Þ ð1Þ yk gðx^k ; v^k Þ þ Ck ðxk x^k Þ þ Gk ðvk v^k Þ where xk is the state vector, wk represents state noise with Qk ¼ E wk wTk covariance matrix. yk definesthe observation vector, the parameter vk is measurement noise with associated Rk ¼ E vk vTk covariance matrix. The function f ð:Þ represents state evolution and gð:Þ describes relation between observations and state vector. Ak , Fk , Ck and Gk are the Jacobian matrices as shown in Eq. (2). 8 ^k Þ of ðx; w of ðx^k ; wk Þ > > > A ¼ F ¼ k < k ox xk ¼x^k ow w¼w^k : ð2Þ ogðx; v^k Þ ogðx^k ; vÞ > > > C ¼ G ¼ k : k ox ov x¼^ xk v¼^ xk Hence, equations for implementing EKF algorithm are expressed in Eqs. (3) and (4). x^k=k1 ¼ f x^k1=k1 ; 0 ð3Þ Pk=k1 ¼ Ak Pk1=k1 ATk þ Fk Qk FkT 8 < x^k=k ¼ x^k=k1 þKk yk g x^k=k1 ; 0 1 K ¼ Pk=k1 CkT Ck Pk=k1 CkT þ GTK : k Pk=k ¼ Pk=k1 Kk Ck Pk=k1
ð4Þ
where Kk is the gain of the filter, x^k=k1 ¼ Efxk jyk1 ; yk2 ; . . .::; y1 g is state vector estimate at kth time instant given y1 to yk1 observations. x^k=k ¼ Efxk jyk ; yk1 ; . . .::; y1 g is state
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vector estimate at kth instant using y1 to yk observations. Pk=k1 and Pk=k are described in similar manner. The EKF facilitates linearization and denoising of ECG signals [27] and provides estimation of RR interval with nearest match to that present in the actual signal [28].
2.2 Discrete Wavelet Transform (DWT) The wavelet transform (WT) due to its flexibility becomes a promising tool to study nonstationary signals such as ECG [29]. The WT describes a signal in its time–frequency domain [5, 30] and can be perceived as an extension of Fourier transform because instead of single scale, WT works on multi-scale basis [31]. The constituent waves of ECG become clearly noticeable when subjected to multiresolution investigation [5]. The WT of a signal vðtÞ is expressed as Eq. (5) given below [32]: 1 1 tb dt ð5Þ Wa vðbÞ ¼ pffiffiffi r vðtÞw a a 1 where a and b are dilation and translation parameters respectively, wðtÞ is a wavelet function. In recent years, DWT has been established as a well known tool in signal processing since it provides good time and frequency resolution [21]. In DWT, a signal is decomposed by using filter banks. There are two types of filters in DWT: a high pass filter and a low pass filter. The input signal is convoluted with designed filters to produce a decomposed version of signal. The filtered signal is then down sampled. The signal decomposition results in detail and approximation coefficients [20]. The two-level wavelet decomposition of a signal yðnÞ is depicted in Fig. 2.
2.3 Hybrid Linearization Technique (HLZT) The HLZT involves application of EKF in combination with DWT to successfully improve the quality of ECG signals, meanwhile preserving the significant morphological characteristics of the signal. The EKF filters the ECG to some extent. Further, HLZT algorithm is implemented for providing an improved signal available at EKF output. The Bior3.1 wavelet is favored over other wavelet functions. This wavelet function is preferred because it provides lower values of percentage root mean square difference, mean square error and higher values of peak signal to noise ratio and signal to noise ratio [15]. The performance
Fig. 2 Two level wavelet decomposition of a signal
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of HLZT algorithm is evaluated by two parameters: signal to noise ratio (SNR) and mean square error (MSE). SNR and MSE are calculated in Eqs. (6) and (7) respectively [25]. ! Ri jyðiÞj2 ð6Þ SNRðdBÞ ¼ Ri jyðiÞ y^ðiÞj2 MSE ¼
Ri ðyðiÞ y^ðiÞÞ2 N
ð7Þ
where yðtÞ is original ECG signal, y^ðtÞ is reconstructed version of the signal and N signifies the number of samples in the signal. Different steps for implementing HLZT are given below: • Acquisition of ECG signals and loading in MATLAB environment. • The ECG signal filtration with EKF. Compute SNR and MSE. • Apply DWT on filtered signal and thresholding is done. Compute SNR and MSE for output signal.
2.4 Principal Component Analysis (PCA) In ECG signal processing, feature extraction is a recent application of PCA. The PCA is a statistical technique that involves projection of data along the direction of highest variance [33]. The concept of PCA is interested in describing the covariance configuration of datasets. The general steps for performing PCA [33–36] include acquisition of the data, mean calculation and subtracting mean from original data. Afterwards covariance matrix is computed and decomposed to obtain eigenvectors and eigenvalues. Finally, row feature vector is adjusted to drive new data set. Data is projected along the direction of sorted eigenvectors.
3 Proposed Methodology The presented work focused on ECG signal analysis for denoising and detection of R-peak, QRS complex, heart rate and arrhythmia. The different stages that are involved in the processing of ECG signal are explained pictorially in Fig. 3.
Fig. 3 Flow of stages involved in proposed methodology
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3.1 Denoising and Wave Detection In pre-processing stage, a total of 15 signals have been considered randomly from MIT-BIH arrhythmia database [37] and loaded into MATLAB environment. The different ECG signals have been selected from MIT-BIH arrhythmia database with the aim to extract features, detect arrhythmia and to present a comparative performance of proposed work with recent past. The ECG records in the database are sampled at 360 Hz and duration of each record is of 30 min 5.556s [37, 38]. While recording, ECG signal gets contaminated with different types of artifacts and noise [39], making pre-processing of the signal essential for accurate analysis. Thus, next step in ECG processing is denoising i.e. removal of low and high frequency noise. For removing baseline wander (due to coughing and respiration etc.), artifacts (induced due to electrode motion) and other noises, HLZT algorithm is applied as presented in Sect. 2. The Bior3.1 wavelet is used for signal decomposition. The detail and approximation coefficients are extracted and global thresholding is done. The performance of denoising technique is computed in terms of SNR and MSE. Thereafter, PCA is applied on noise free ECG signal for extraction of R-peak and QRS complex. R-peak is the most important wave in ECG signal and can be easily detected due to its high amplitude [5]. The maximum information is concentrated in the region around this peak. The ECG signal is decomposed using PCA and during detection process, eigenvalues are squared for minimizing smaller values and maximizing larger values. Then thresholding is performed to retain R-peaks and their positions are stored for detection of other waves. With reference to detected R-peaks, Q and S peaks are extracted. Since for any patient QRS complex width is not greater than 160 ms, the denoised signal is scanned for 80 ms on left as well as on right of R-peak indexes [36]. Afterward minimum values on either side of reference peak are achieved. These minimum values on left and right correspond to Q-peak and S-peak respectively, hence forming a complete QRS complex. For performance analysis of beat detection algorithm, Sensitivity (Se), Positive Predictivity (P?) and Detection Error Rate (DER) parameters are used. Se, P? and DER are expressed in Eqs. (8), (9) and (10) respectively. Se ¼
True positive 100% True positive þ False negative
Fig. 4 a Original ECG signal and b denoised signal of record 100
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ð8Þ
On the Detection of Cardiac Arrhythmia with Principal… Table 1 Performance evaluation of denoising method ECG record
EKF
DWT
SNR (dB)
MSE
SNR (dB)
HLZT MSE
SNR (dB)
MSE
100
3.8286
5.1e-03
6.9326
2.0e-03
17.4590
1.15e-04
101
3.5305
3.28e-04
3.7445
3.12e-04
11.7044
2.53e-05
102
7.0377
8.3e-03
10.2807
1.8e-03
18.9089
9.13e-05
103
4.1280
1.04e-02
8.4883
6.0e-03
18.1110
3.61e-04
104
8.7102
8.3e-03
8.9980
6.1e-03
19.3092
4.41e-04
111
8.8224
7.0e-02
9.3417
5.1e-03
19.9982
5.31e-04
112
3.5660
1.5e-03
6.6893
7.15e-04
15.0421
5.05e-05
113
3.2994
1.3e-03
7.1855
1.1e-03
15.4151
3.67e-05
115
4.8433
1.4e-03
7.3859
7.89e-04
17.4115
4.94e-05
117
5.2256
1.81e-02
8.7776
8.0e-03
18.3845
5.70e-04
121
5.3583
7.5e-03
9.9772
2.6e-03
18.8628
2.21e-04
122
3.1873
4.0e-03
3.7663
3.5e-03
12.0947
2.65e-04
123
4.3027
1.0e-02
8.9304
3.5e-03
18.0581
2.40e-04
230
6.2581
1.58e-02
9.0610
1.24e-02
18.4892
5.45e-04
231
6.2719
8.0e-03
8.5448
4.7e-03
18.9004
3.13e-04
Fig. 5 a Detected QRS complex and b detected R-peak of sample number 103
Pþ ¼
True positive 100% True positive þ False positive
ð9Þ
DER ¼
False positve þ Fasle negative 100% True positive
ð10Þ
where True Positive (TP) is the correctly detected R-Peak, False Positive (FP) refers to misdetections and False Negative (FN) indicates undetected R-Peak.
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H. Kaur, R. Rajni Table 2 Performance of beat detection algorithm for MIT-BIH arrhythmia database ECG record
Total beats
Detected beats
TP beats
FP beats
FN beats
Se (%)
P? (%)
DER (%)
100
2273
2265
2265
0
8
99.6
100
0.353
101
1865
1865
1865
0
0
100
100
0
102
2187
2185
2187
2
0
100
99.9
0.091
103
2084
2084
2084
0
0
100
100
0
104
2230
2228
2229
1
1
99.9
99.9
0.089
111
2124
2121
2121
0
3
99.8
100
0.141
112
2539
2538
2538
0
1
99.9
100
0.039
113
1795
1795
1795
0
0
100
100
0
115
1953
1953
1953
0
0
100
100
0
117
1535
1535
1535
0
0
100
100
0
121
1863
1861
1862
1
1
99.9
99.9
0.107
122
2476
2476
2476
0
0
100
100
0
123
1518
1516
1516
0
2
99.8
100
0.131
230
2256
2255
2256
1
0
100
99.9
0.044
231
1573
1570
1570
0
3
98.8
100
0.191
30,271
30,247
30,252
5
19
99.93
99.98
0.079
Total
Table 3 Arrhythmia detected for different ECG records ECG record (gender/age)
HR (bpm)
124 (M/77)
50
232 (F/76)
55
105 (F/73)
84
116 (M/68)
80
201 (M/68)
123
203 (M/43)
115
106 (F/24)
59
119 (F/41)
57
210 (M/89)
105
213 (M/61)
105
Characteristics
Arrhythmia
HR is \60 bpm
BC
Premature QRS complex followed by compensatory pause
PVC
HR is more than100, absence of P wave and presence of fibrillating waves
AFib
Continuous alteration of long and short waves
VB
HR is [100 bpm
TC
3.2 Arrhythmia Detection The term ‘Arrhythmia’ refers to irregular or abnormal electrical activity of human heart [40]. The abnormal activity of heart leading to different cardiac arrhythmias may be of minimal impact or may also signify an irreparable damage to the heart. Arrhythmias can influence the heart rate (HR) [41]. The HR measured from ECG signal is widely accepted as one of the significant features in clinical aspects. The HR as well as
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On the Detection of Cardiac Arrhythmia with Principal…
Fig. 6 a Original ECG signal and b detected BC of record 124
Fig. 7 a ECG signal and b detected PVC of record 105
Fig. 8 a ECG signal and b detected AFib of record 201
morphological characteristic changes in the ECG waves can be used to deduce significant physiological information [42]. The final stage in proposed work is to calculate HR and detect arrhythmia from ECG on the basis of calculated HR and its
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H. Kaur, R. Rajni
Fig. 9 a ECG signal and b detected VB of record 119
Fig. 10 a ECG signal and b detected TC of record 210
characteristics. The HR is measured in beats per minute (bpm) and is defined as the count that how many times heart beats in 1 min. The expression for calculating HR [21] is given in Eq. (11). Heart rateðHRÞ ¼
60 bpm average RR interval
ð11Þ
where RR-interval is distance between two adjacent R-peaks (QRS-peaks).
4 Results and Discussion The ECG analysis essentially begins with pre-processing of signal. Being electrical in nature, ECG signal is much prone to disturbances such as muscle artifacts and baseline wandering. Hence extraction of pure physiologic indices from the signal becomes complex. Several methods have been developed and applied to denoise ECG signal like adaptive filters and Weiner filter. In literature, it has been revealed that EKF denoises ECG signal to some extent. The WT has been explored as a convenient tool for analysis of non-stationary signal. The reported approach exploits the potentials of both EKF and DWT to extract
123
99.8
99.6
NR
P?
DER
Banerjee et al. [5]
0.65
99.65
99.70
Lin et al. [20]
Beat detector methods
Se
Para-meters in (%)
0.221
99.92
99.85
Kaur et al. [21]
Table 4 Comparison of proposed work with other reported works
0.54
99.82
99.64
Zidelmal et al. [29]
2.57
98.96
98.47
Madeiro et al. [32]
NR
99.71
96.28
Rodriguez et al. [36]
4.12
97.24
98.68
Chouakri et al. [43]
0.54
99.80
99.66
Choi et al. [44]
0.079
99.98
99.93
Proposed work
On the Detection of Cardiac Arrhythmia with Principal…
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noise free signal from contaminated ECG indices, thereby providing accurate signal processing. The ECG signal of record mitdb/100 and its denoised waveform are depicted in Fig. 4a, b respectively. Results of EKF, WT and HLZT filtering for comparison are provided in Table 1. As seen from Table 1 HLZT algorithm is able to provide superior results in terms of SNR and MSE. Although each ECG sample is of 30 min duration but for simplification it is shown for 10 s. After denoising, the next step is R wave detection which forms the basis for detection of QRS complex. QRS complex varies according to age and gender of the person. Figure 5a demonstrates the QRS complex detected from ECG record mitdb/103 and Fig. 5b depicts the detected R wave for same signal. The performance analysis of beat detection algorithm is provided in Table 2. Table 2 depicts the total number of beats, number of detected beats, True Positive beats, False Negative and False Positive beats. Thereafter five different types of arrhythmias: bradycardia (BC), tachycardia (TC), atrial fibrillation (AFib), ventricular bigeminy (VB) and premature ventricular contraction (PVC) have been identified. The HR and characteristics corresponding to different arrhythmias for different ECG signals are provided in Table 3. In Table 3, F and M indicates female and male respectively. The waveforms of original ECG record mitdb/124 along with detected bradycardia are shown in Fig. 6a, b respectively. Figure 7a depicts original mitdb/105 and its detected premature ventricular contraction is shown in Fig. 7b. Figure 8a illustrates the original ECG signal of record mitdb/201 along with its detected atrial fibrillation in Fig. 8b. The waveform of original ECG record mitdb/119 is shown in Fig. 9a with its detected ventricular bigeminy in Fig. 9b whereas Fig. 10a, b depict the actual ECG signal of sample mitdb/210 and its detected tachycardia respectively. The value of term Se in Table 2 shows that 99.93% of heartbeats have been correctly recognized by the algorithm and value of P? indicates that 99.98% of detected heartbeats are real heartbeats. Therefore, accurate results for beat detection have been successfully achieved with the PCA. A comparison of proposed feature extraction algorithm with previous methods for MIT-BIH arrhythmia database is shown in Table 4. In Table 4, NR signifies not reported. From Tables 2 and 4 it is clearly evident that proposed algorithm outperforms many methods referred in the literature.
5 Conclusion In this paper, ECG signal is analyzed through HLZT and PCA. The first stage of denoising has been carried out through the new approach of HLZT which yields improved SNR and MSE proving the applicability of HLZT for denoising ECG signals. Further, detection of QRS complex and R-peak is a significant part of ECG signal analysis. The detection is performed using PCA and thresholding. The parameters used to access the performance of beat detection, yields 99.93% of Se, 99.98% of P? and DER of 0.079%. Later arrhythmia is detected on the basis of heart rate and abnormalities such as bradycardia, tachycardia, atrial fibrillation, ventricular bigeminy and premature ventricular contraction have been identified successfully. The outcomes presented in Table 2 depicts that presented algorithm achieves accurate detection rates. The values of SNR, MSE for denoising and sensitivity,
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positive predictivity, error detection rate for peaks in ECG waveform inferred that the novel algorithm is superior to many others referred in the literature. Compliance with Ethical Standards Conflict of interest The authors declare that they have no conflict of interest.
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On the Detection of Cardiac Arrhythmia with Principal… Harjeet Kaur has done her M. Tech and B. Tech from SBS State Technical Campus, Ferozepur, Punjab, India. Her area of interest includes Biomedical Signal Processing.
Rajni Rajni is currently Professor at SBS State Technical Campus Ferozepur, India. She has done her M.E. from NITTTR, Chandigarh, India and B.Tech. from NIT, Kurukshetra, India. She has done her Ph.D. in Metamaterial antennas from SLIET Longowal in August 2016. She has approx. 19 years of academic experience. She has authored a number of research papers in International journals, National and International conferences. Her areas of interest include Wireless communication, Biomedical signal processing and Antenna design.
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