An improved QRS complex detection method having low computational load

Biomedical Signal Processing and Control 42 (2018) 230–241

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Biomedical Signal Processing and Control journal homepage: www.elsevier.com/locate/bspc

An improved QRS complex detection method having low computational load Önder Yakut a , Emine Do˘gru Bolat b,∗ a b

Department of Information Technologies, Kocaeli University, Izmit, Kocaeli, Turkey Department of Biomedical Engineering, Faculty of Technology, Kocaeli University, Umuttepe Campus, 41380, Kocaeli, Turkey

a r t i c l e

i n f o

Article history: Received 20 July 2017 Received in revised form 19 January 2018 Accepted 4 February 2018 Keywords: Electrocardiogram (ECG) QRS complex detection Digital FIR filter Biomedical signal processing Dynamic threshold

a b s t r a c t In this study, an improved QRS complex detection method having low complexity is proposed. This method includes two stages as preprocessing and decision making. The preprocessing stage consists of a band-pass digital FIR filter, squaring operation, moving average, normalization steps whereas the decision stage includes only one phase realizing the QRS complex detection. In the preprocessing stage, the unwanted frequency components of the Electrocardiogram (ECG) signal were reduced by using the digital FIR filter. The filtered signal was enhanced with the squaring operation and finally integrated and smoothed by moving average step. In the decision making stage, R peaks were detected employing a dynamic threshold process incorporating with the preprocessing stage for determining the QRS complex components. The R peaks were detected by comparing the time intervals between two successive R peaks with the calculated time range. For assessing the performance of the proposed method, it was tested using the ECG recordings (about 1.3 million beats) taken from the five standard databases as MIT-BIH Arrhythmia, Fantasia, MIT-BIH Noise Stress Test, QT and European ST-T. In this study, 1296137 beats of 272 cases were tested for QRS detection and the average sensitivity, Se was obtained as 99,60%, while the average positive predictivity, +P was provided as 99,77%. The contribution of the proposed method is that the training, selection, setting and prediction processes are not required while determining the necessary parameters. Therefore, this contribution reduces the complexity of the method resulting in decreasing the computational load as well without compromising on high performance indices (Se and +P). Since the proposed method provides low complexity and computational load together with high accuracy, it can be implemented as a QRS detector for applications of telemedicine and embedded systems easily in contrast to the algorithms having higher complexity. © 2018 Elsevier Ltd. All rights reserved.

1. Introduction ECG signal carries the information of how much the heart can perform its functions electrophysiologically. ECG is one of the most common noninvasive tools used for the diagnosis of the heart diseases by the clinicians. Therefore, measuring and processing of the ECG signal have a vital importance. The ECG is a rhythmic signal proceeding regularly. It is composed of basic characteristic waveforms as P wave, QRS complex and T wave.

∗ Corresponding author. E-mail addresses: [email protected] (Ö. Yakut), [email protected] (E.D. Bolat). https://doi.org/10.1016/j.bspc.2018.02.004 1746-8094/© 2018 Elsevier Ltd. All rights reserved.

The segments and intervals representing the electrophysiological change of the heart of the ECG waveform are depicted in Fig. 1. These segments and intervals are used for analyzing the ECG signal. When the characteristic components of the ECG signal are compared, the most significant waveform is QRS complex having a higher amplitude than P and T waveforms. An accurate and reliable detection of R peak of QRS complex enables the clinicians to observe and diagnose the cardiac abnormalities. Detection of R peaks promotes the determination of characteristic components Q, S, P and T waveforms. So, determination of all components of the ECG signal delivers solution to a significant issue for the analysis of the electrical activity of the heart. QRS detection has been a research topic for more than thirty years. Numerous algorithms, methods and tools based on different approaches have been developed by researchers during this period. These approaches are based on mathematical morphology

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231

Fig. 1. A single cardiac cycle of the ECG signal [1].

[2,3], digital filters [4–9], wavelet transform [10–14], time dependent entropy method [15], S-Transform method [16], empirical mode decomposition [17], knowledge based method [18], singular value decomposition [19], phase-space method [20], body sensor network [21], Hilbert Transform method [22,23], derivative method [24–26], delay-coordinate mapping method [27], movingaveraging method [28] and Teager Energy Operator (TEO)[29]. When the existing methods are examined, the QRS complex is detected, removing the noise from the ECG signal using various types of filters. Similarly, the QRS complex is detected employing the combinations of different types of filters such as wavelet transform. During this process, since there is no general rule for the operations such as determining the related frequency intervals and selecting the wavelet type, some additional operations are required by trial. Moreover, when the other methods are analyzed, the necessity of additional process steps such as training, settings and prediction of model parameters increases the complexity in computational load/cost [6]. In this study, an improved QRS complex detection method having a low computational load is proposed. This method includes minimum preprocessing steps and an adaptive threshold based simple decision making rules. Therefore, it doesn’t require the additional operations mentioned in the previous paragraph. In preprocessing stage of this method, undesired frequency components, influences of P and T waves accepted as noise, baseline wander [30] of the ECG signal were reduced by a band-pass digital FIR filter, then, the signal was enhanced by squaring operation and finally it was integrated and smoothed by moving average step. High frequency components such as electromyographic (EMG) and power line interference artifacts of ECG signal were depressed in moving average step [30]. The obtained smooth ECG signal was applied to the adaptive thresholding step used in decision making stage of R peak detection process. After the R peak detection process was realized, Q and S points were detected using windowing operation. The proposed QRS detection method was verified/proved analyzing the ECG recordings of the MIT-BIH Arrhythmia Database (AD) [31], Fantasia Database [32], MIT-BIH Noise Stress Test Database [33], QT Database [34] and European ST-T Database [35]. So, a use-

ful QRS detection method is proposed for analyzing ST segment, QT interval and various heart diseases such as irregular heart rhythm, atrial fibrillation. QRS detection algorithms are required for storing, processing the ECG signal and realizing the real time diagnosis of the cardiac abnormalities or critical situations of the heart automatically. These algorithms should have low complexity and computational load to be implemented in mobile/smart phones, e-health applications, wireless sensor based systems and embedded platforms by being integrated into a modular ECG monitoring system for analyzing the ECG signal. So, the proposed algorithm provides the ECG signal to be analyzed with a high accuracy and reliability and it can also be realized in the devices having lower processing capacity. The rest of the paper is organized as follows. A brief explanation of the proposed QRS detection method is presented in Section 2. The implementation of the proposed method including the related graphs is explained in Section 3. The detailed experimental results and the performance comparison of the proposed method with similar studies are given in Section 4. The overall experimental results are discussed in Section 5 and finally Conclusions are given in Section 6.

2. Materials and methods QRS complex detection algorithm consists of two main processes named as preprocessing and decision making stages as depicted in Fig. 2. Both two stages are composed of various substages. QRS complex of the ECG signal is detected utilizing these sub-stages performing some calculation or assessment processes.

2.1. Preprocessing stage The Preprocessing Stage includes a band-pass digital FIR filter, squaring operation, moving average and normalization processes. These processes are explained in the following subsections.

232

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Fig. 2. Block diagram of the QRS Complex Detection Method.

2.1.1. Digital FIR filter FIR filters are utilized in case the output value depends on the input signal. The denominator of the transfer function is equal to one in FIR filters. The transfer function expresses the effect of the system to the input signal and the filter effect. General difference equation of FIR filters is given in Eq. (1) [36]. The coefficients of FIR filters are real or integer numbers in general. Utilizing FIR filter with integer coefficients in R peak detection methods provides computational simplicity [8]. Therefore, bk , the coefficient of the function having length K is taken as integers in this Equation and bk values are given in the related sections. x(n) is the input while y(n) is the output signal. y(n) =

K 

bk x(n − k)

(1)

k=0

Since all the poles of the FIR filters are in z = 0 region, this filter is always stable guaranteeing the linear phase. Thus, they are quite beneficial in the case of phase distortions such as voice and ECG analysis applications. The difference equation of the system was provided as in Eq. (2). The Eq. (2) is based on the principle of difference equation formed by placing zeros on the unit circle with K equal intervals in the zplane. In this Equation, y0 (n) is the ECG output signal, x(n) is the raw ECG signal and x(n-K) is K shifted raw ECG signal. K parameter was obtained using sampling frequency, fsample and line frequency, fline which were employed while recording the ECG signal as shown in Eq. (3). fsample , fline , and K values for the databases are given in the related sections below. y0 (n) = x(n) − x(n − K)

(2)

K = fsample ⁄fline 

(3)

2.1.3. Moving average operation Numerous QRS complexes having abnormal amplitudes and intervals were formed in the squared ECG signal. The Moving Average approach was applied to prevent this condition to cause a problem during the Decision Making Stage. With this approach, the QRS complex in the moving average window became more distinctive by suppressing P and T waves and finally, a soft/simple QRS complex interval having a single peak was provided. The width of the moving average window is quite significant for the R peak detection process. When it is selected too narrow, numerous unnecessary peaks arise in the QRS complex. If it is selected too wide, this results in misdetection of the R peaks because of the existence of the T waves in the window. Therefore, faulty results were prevented taking the width of the moving average window as equal to the widest possible QRS complex given as 150 ms by Pan and Tompkins. The width of the moving average window, N was derived from Eq. (5) in terms of sample [7]. In this Equation, QRSwidth expresses the widest QRS duration and it was utilized as 150 ms in this study. N = fsample × QRSwidth 

(5)

The output signal, y2 (n) of the moving average process was obtained employing Eq. (6). In these equations, N obtained utilizing Eq. (5) shows the width of the moving average window as samples. 1 y1 (n − i) N N

A band-pass FIR filter having a difference equation given in Eq. (2) was designed for removing the baseline wander and suppressing P and T waveforms, enhancing the QRS complex of the ECG signal. The developed FIR filters are in a band-pass structure having frequency ranges given in Section 4. 2.1.2. Squaring operation Each sample of the ECG signal was subjected to a squaring operation as shown in Eq. (4). y1 (n) = [y0 (n)]2

with the application of nonlinear signal amplifying process to each sample value of the ECG signal. As the result of this operation, QRS complex was discriminated with respect to P and T waves having lower amplitude.

(4)

Negative valued samples were converted to positive with this operation. So, it was enabled that the FIR filter output was amplified

y2 (n) =

(6)

i=1

2.1.4. Normalization operation The amplitude values of the ECG signal change depending on the age and gender of the person, diseases affecting the cardiovascular system directly or indirectly. So, for the aim of preventing the misleading effects of these changes in R peak detection process, normalization process was applied. y(n) =

y2 (n) − y2min y2max − y2min

(7)

Min-max normalization process was applied using Eq. (7). Undesired effects which change depending on the person, were

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Rpeak (n) =

2.2. Decision making stage

After the candidate R peaks in QRS complex, were detected, a window width, WQRS shown in Fig. 3(a) and (b) was determined from Rsi value using Eq. (12). This Equation is used for finding out the midpoint of the WQRS width taking Rsi value as odd. The candidate R peak was located in the center of this window having WQRS width for detection of Q, S and extrema points of the candidate R peak as seen in Fig. 3(a). Then, in this Figure, the intervals having WQRS /2 samples on the left and right side of the window were analyzed. To determine whether the direction of the QRS complex was positive or negative, dirR (n), the average value of the 20 samples taken from both two sides of the candidate R peak was calculated utilizing Eq. (13.a). In case of the calculated dirR (n) (direction of the R peak deflection) value was positive or negative, the extremum point having a maximum or minimum amplitude value in the window was determined as an R peak. Rpeakmax (n) given in Eq. (13.b) includes the location data of the extrema of the raw ECG signal as shown in Fig. 3(a).

The approaches and assessments for detecting R peaks, Q and S points of QRS complexes are explained in the Decision Making Stage. An adaptive thresholding method was employed in the R peak detection process as given in Eq. (8). This method was utilized for the aim of the adaptation of the changes in the signal. The QRS complex region of the signal obtained from the output of the moving average was easily determined by the applied thresholding method. In Eq. (8), thv(n) variable represents the current calculated adaptive threshold value. N parameter is the width of the moving average window. thv(n-1) variable is the previous adaptive threshold value and y(n) is the current ECG sample value. While the initial value of thv(n) was being calculated, thv(n-1) was taken as 1 in Eq. (8).

 WQRS =

temploc , if

Rpeak (n − 1) − temploc ≥ Rsi



inhibited applying the normalization process to the output signal of the moving average process. In Eq. (7), y(n) is the normalized value of the nth sample of the ECG signal, y2 (n) expresses the nth sample value of the ECG signal before normalization process, y2min is the minimum value of the ECG data set, y2max is the maximum value of the ECG data set.

(11.b)

(Rsi − 1) , ifRsi iseven.

(12)

Rsi , ifRsi isodd.

⎛

⎞ L  1 dirR (n) = ⎝ Rpeak(n − j)⎠ > 0 , L = 10 (L, the number of samples) 2×L

 Rpeak max (n) =

thv(n) =

(N − 1)thv(n − 1) + y(n) N

 

QRSduration = (2 × QRSwidth ) = 240ms



n, if (y(n) ≥ thv(n))

 



, dirR (n) > 0

min x

Rpeak (n) − WQRS /2 : Rpeak (n) + WQRS /2

, dirR (n) < 0

 

(8)

(13.b)

For detecting the locations of the Q and S points, the extremum point of R peak detected in Fig. 3(a) was placed in the center of the window as seen in Fig. 3(b). Then, the required calculations using Eqs. (14) and (15) were executed employing the window having WQRS width. In these Equations, Qpoint and Spoint contain the locations of detected Q and S points respectively. The locations of the Q and S points were detected according to the location of the R peak as given in Fig. 3(b). This operation was realized as similar to that of the R peak detection process as seen in Fig. 3(a).

(9)

(10)

The R peak detection process started with the thresholding step considering the peaks of the signal having a higher amplitude than the threshold value thv(n) using Eq. (11.a). Then, the peak was accepted as a candidate R peak if the R-R interval was bigger than or equal to the Rsi as given in Eq. (11.b). Otherwise, the peak was evaluated as noise and eliminated. The locations of the obtained candidate peaks were near to the annotated R peaks in the raw ECG signal. temploc =



Rpeak (n) − WQRS /2 : Rpeak (n) + WQRS /2

The significant period and amplitude values of normal ECG sinus rhythm are shown in Tables 1 and 2 respectively [37]. The features given in Tables 1 and 2 are extracted from a healthy man’s ECG signal having 60 beats per minute. In Eq. (10), Rsi sample interval value gives the minimum time interval between the two successive R peaks in terms of samples. Calculated Rsi value was compared with the sample interval detected between two adjacent R peaks. Rsi = QRSduration × fsample 

 

max x

While calculating the minimum duration between consecutive R peaks detected in thresholding process, the upper limit of normal QRSwidth value given in Table 1 was multiplied by 2 as given in Eq. (9) and QRSduration was obtained from this equation in milliseconds. QRSwidth = 100 + 20 = 120ms

(13.a)

j=−L

(11.a)

Table 1 The significant period values of normal ECG sinus rhythm of a healthy male adult with a heart rate of 60 bpm [37]. Properties

Normal Value

Normal Limit

Pwidth PRinterval QRSwidth QTinterval

110 ms 160 ms 100 ms 400 ms

±20 ms ±40 ms ±20 ms ±40 ms

Table 2 The significant amplitude values of normal ECG sinus rhythm of a healthy male adult with a heart rate of 60 bpm [37]. Properties

Normal Value

Normal Limit

Pamplitude QRSheight STlevel Tamplitude

0,15 mV 1,5 mV 0 mV 0,3 mV

±0,05 mV ±0,5 mV ±0,1 mV ±0,2 mV

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Table 3 The frequency ranges of the pass bands according to the developed filters.

+P =

K Values

First Pass Band

Second Pass Band

Third Pass Band

6 5 4

15–45 Hz 12,5–37,5 Hz 15,625–46,875 Hz

75–105 Hz 62,5–87,5 Hz 78,125–109,375 Hz

135–165 Hz 112,5–125 Hz –



min

 

Qpoint (n) = max

 



 



x

Rpeak max (n) − WQRS /2 : Rpeak max (n)

x

Rpeak max (n) − WQRS /2 : Rpeak max (n)

 

, dirR (n) > 0 , dirR (n) < 0

(14)



min

 

Spoint (n) = max

 



 



x

Rpeak max (n) : Rpeak max (n) + WQRS /2

x

Rpeak max (n) : Rpeak max (n) + WQRS /2

 

, dirR (n) > 0 , dirR (n) < 0

(15)

3. The implementation of the proposed QRS complex detection method Schematic diagram of the QRS complex detection process of which details are explained above is shown in Fig. 4. This Figure includes block diagram of the proposed method together with the related output signals of each step. MIT-BIH AD was employed as the ECG signal to be processed in Fig. 4 The preprocessing and decision making stages of QRS complex detection employing MIT-BIH AD record 103 (ML-II) is depicted in Fig. 5. 4. Experimental results

TP TP + FP

Se value represents the algorithm’s detection capability of real heart beats. +P value represents the algorithm’s distinguishing capability between true and false beats. TB (Total Beats) is the total number of R peaks of the ECG recordings. TP (True Positive) value shows the number of total R peaks detected correctly. FN (False Negative) value is the total number of undetected R peaks. FP (False Positive) value represents the number of R peaks detected incorrectly. In experimental studies, the R peaks were detected exactly or quite close to the marked times in the annotation file. The interval between the detected R peak and related annotated time was taken as 27.8 ms (10 samples) [16] for the databases utilizing a sampling frequency of 360 Hz, while it was used as 40 ms (10 samples) for the databases having a sampling frequency of 250 Hz. When detected R peaks were within 27.8 ms from the annotated time, these were accepted as TP. Otherwise, the peaks were missed and evaluated as FN. Finally, remaining peaks were assessed as FP. The K values were achieved as 4 (Fantasia, QT Database), 5 (European ST-T Database) and 6 (MIT-BIH AD, MIT-BIH Noise Stress Test Database) of which the details are given in the related sections below. The frequency ranges of the pass bands according to the developed digital band-pass FIR filters are shown in Table 3. 4.1. MIT-BIH arrhythmia database In this study, 48 subjects of which each having 30 min recordings taken from the MIT-BIH database were used in experiments [31]. The performance of the proposed method was tested utilizing the first channel of two-channel ECG recordings. The ECG signals of the database are measured at a frequency of 360 Hz (fsample ) while fline frequency is 60 Hz and K parameter was calculated as 6 according to Eq. (3). The coefficient values of bk giving the best results and used in Eq. (1) are depicted in Eq. (18). bk = {1, 0, 0, 0, 0, 0, −1}

The proposed method was assessed using various databases mentioned above. The performance of this method was evaluated in terms of Sensitivity Se and Positive Predictivity +P, of which equations are shown in Equation (16) and (17) respectively. Se =

TP TP + FN

(16)

(17)

(18)

The performance results, obtained from the experiments of the MIT-BIH AD based on the proposed method, are given in Table 4. The validity of the performance results was verified comparing the detected R peaks of QRS complexes with the recorded values specified in the annotation file. Se and +P were calculated using the TP, FP and FN values determined before.

Fig. 3. The window utilized for the detection of QRS complex components of raw ECG signal (a) Detection of both the direction of the QRS complex and extremum point of the R peak (b) Detection of the locations of Q and S points.

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Fig. 4. Schematic diagram of the QRS complex detection process together with the output signals of each step.

235

236

Ö. Yakut, E.D. Bolat / Biomedical Signal Processing and Control 42 (2018) 230–241 Table 4 QRS Detection performance results for the MIT-BIH AD.

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 Total

Record

TB

TP

FP

FN

Se(%)

+P(%)

100 101 102 103 104 105 106 107 108 109 111 112 113 114 115 116 117 118 119 121 122 123 124 200 201 202 203 205 207 208 209 210 212 213 214 215 217 219 220 221 222 223 228 230 231 232 233 234 48 Subjects

2273 1865 2187 2084 2229 2572 2027 2137 1763 2532 2124 2539 1795 1879 1953 2412 1535 2278 1987 1863 2476 1518 1619 2601 1963 2136 2980 2656 1860 2955 3005 2650 2748 3251 2262 3363 2208 2154 2048 2427 2483 2605 2053 2256 1571 1780 3079 2753 109494

2273 1863 2187 2084 2225 2556 2027 2134 1748 2532 2123 2539 1795 1874 1953 2404 1535 2278 1987 1863 2476 1518 1618 2597 1948 2133 2955 2653 1850 2941 3004 2638 2747 3249 2257 3361 2202 2153 2048 2424 2482 2604 2038 2256 1571 1780 3078 2749 109310

0 3 0 1 9 12 8 0 34 0 0 0 0 3 0 11 0 1 0 0 0 0 0 2 8 6 22 0 4 9 0 6 0 0 1 1 2 0 0 2 3 0 30 0 0 3 1 0 182

0 2 0 0 4 16 0 3 15 0 1 0 0 5 0 8 0 0 0 0 0 0 1 4 15 3 25 3 10 14 1 12 1 2 5 2 6 1 0 3 1 1 15 0 0 0 1 4 184

100 99,89 100 100 99,82 99,38 100 99,86 99,15 100 99,95 100 100 99,73 100 99,67 100 100 100 100 100 100 99,94 99,85 99,24 99,86 99,16 99,89 99,46 99,53 99,97 99,55 99,96 99,94 99,78 99,94 99,73 99,95 100 99,88 99,96 99,96 99,27 100 100 100 99,97 99,85 99,83

100 99,84 100 99,95 99,60 99,53 99,61 100 98,09 100 100 100 100 99,84 100 99,54 100 99,96 100 100 100 100 100 99,92 99,59 99,72 99,26 100 99,78 99,69 100 99,77 100 100 99,96 99,97 99,91 100 100 99,92 99,88 100 98,55 100 100 99,83 99,97 100 99,83

The proposed method is compared with the well-known QRS detection methods in Table 5. It was observed that the proposed method detected 109310 TP, 182 FP and 184 FN beats among total 109494 beats taken from the MIT-BIH AD resulting in overall QRS detection sensitivity, Se and positive predictivity, +P as 99,83% and 99,83% respectively as seen in this Table. These results are better than or similar to that of the previous studies.

4.2. Fantasia database

Fig. 5. The output signals of preprocessing and decision making stages of QRS complex detection using the MIT-BIH AD record 103 (ML-II). (x(n): raw ECG signal, y0 (n): output signal of the digital FIR filter, y1 (n): output signal of the squaring operation, y2 (n): output signal of the moving average operation, y(n): output signal of the normalization,thv(n): output signal of the adaptive threshold, Rpeak(n): candidate R peaks, Rpeakmax (n): Detected extrema of the raw ECG signal, QRS complex: determination of Q and S points. Marking of QRS points (‘*’, ‘ˆ’ and ‘x’ respectively). A.U., is arbitrary unit.)

Fantasia database includes 2 groups having rigorously screened healthy subjects [32]. These groups consist of 20 young (21–34 years old) and 20 elderly (68–85 years old) subjects. The recordings named (f1y01,. . .,f1y10 and f2y01,. . .,f2y10) were taken from the young group and the recordings named (f1o01,. . .,f1o10 and f2o01,. . .,f2o10) were obtained from the elder group. 120 min of continuous ECG signals of the subjects were recorded when they were in supine resting position. Measured signals were digitized at a frequency of 250 Hz (fsample ) while fline was 60 Hz and K parame-

Ö. Yakut, E.D. Bolat / Biomedical Signal Processing and Control 42 (2018) 230–241 Table 5 Comparison of the performance of the proposed method with other algorithms for the MIT-BIH AD. QRS Detector

Cases

TB

FP

FN

Se(%)

+P(%)

This Work Yazdani et al. [2] Sharma et al. [4] Mourad et al. [10] Farashi [15] Yochum et al. [11] Castells-Rufas [5] Gutiérrez-Rivas et al. [26] Pangerc et al. [8]a Pangerc et al. [8] Ding et al. [9] Zidemal et al. [16] Li et al. [17] Dohare et al. [6] Elgendi [18] Zhang et al. [3] Jung et al. [19] Ghaffari et al. [13] Adnane et al. [24] Cvikl et al. [27] Chen et al. [28] Martinez et al. [14] Hamilton and Tompkins [25] Pan and Tompkins [7]

48 48 48 48 48 48 48 48 48 48 48 48 48 48 48 48 48 48 48 48 45 48 48 48

109494 109494 109488 106310 109965 109491 109494 109949 109494 109494 109494 108494 109497 109966 109985 109510 109541 109428 109494 109494 102654 109208 109267 109809

182 108 428 48 163 574 353 289 92 125 73 97 137 728 124 199 579 89 393 200 529 153 248 507

184 137 509 259 273 160 614 502 114 125 134 171 67 870 247 279 583 61 253 200 459 220 340 277

99,83 99,87 99,50 99,76 99,85 99,85 99,43 99,54 99,90 99,89 99,93 99,84 99,94 99,21 99,78 99,76 99,47 99,94 99,77 99,82 99,55 99,80 99,69 99,75

99,83 99,90 99,56 99,95 99,75 99,48 99,67 99,74 99,92 99,89 99,87 99,91 99,87 99,34 99,87 99,82 99,47 99,91 99,64 99,82 99,49 99,86 99,77 99,54

a

The algorithm [8] processed both ECG signals.

Table 6 QRS Detection performance results for the Fantasia database. TB

TP

FP

FN

Se(%)

+P(%)

f1a f2b Over All

141117 142630 283747

141100 142481 283581

26 32 58

17 149 166

99,98 99,90 99,94

99,99 99,99 99,98

a

The group of young subjects. The group of elder subjects.

Table 7 Comparison of the performance of the proposed method with other algorithms for the Fantasia Database. QRS Detector

Cases

TB

FP

FN

Se(%)

+P(%)

This Work Sharma et al. [4] Elgendi [18] Pan and Tompkins [18]

40 40 40 40

283747 160844 278996 278996

58 148 315 N/R

166 152 50 N/R

99,94 99,9 99,98 89,16

99,98 99,91 99,97 99,89

N/R: Not Reported.

Record

TB

TP

FP

FN

Se(%)

+P(%)

118e24 118e18 118e12 118e06 118e00 118e 6 119e24 119e18 119e12 119e06 119e00 119e 6 Total

2278 2278 2278 2278 2278 2278 1987 1987 1987 1987 1987 1987 25590

2271 2260 2205 2152 2041 2004 1982 1975 1871 1853 1770 1573 23957

5 16 53 87 158 184 4 7 71 142 291 371 1389

7 18 73 126 237 274 5 12 116 134 217 414 1633

99,69 99,21 96,80 94,47 89,60 87,97 99,75 99,40 94,16 93,26 89,08 79,16 93,62

99,78 99,30 97,65 96,11 92,81 91,59 99,80 99,65 96,34 92,88 85,88 80,92 94,52

Table 9 Comparison of the performance of the proposed method with other algorithms for the MIT-BIH Noise Stress Test Database. QRS Detector

TB

Se(%)

+P(%)

This Work Dohare et al. [6] Elgendi [18] Pan and Tompkins [18] Plesnik et al. [20] Wei et al. [21]

25590 25590 26370 26370 25590 N/R

Benitez et al. [23]

N/R

93,62 88,20 95,39 74,46 72,11 90,66 98,75 93,48

94,52 89,19 90,25 93,67 82,48 87,19 77,60 90,6

sented in Table 8. The sampling frequency, fsample was 360 Hz, while fline was 60 Hz and K parameter was achieved as 6 for this database. The coefficient values of bk giving the best results and used in Eq. (1) are depicted in Equation (18). The proposed method detected 23957 TP, 1389 FP and 1633 FN beats of total 25590 beats taken from the MIT-BIH Noise Stress Test Database, resulting in overall QRS detection sensitivity, Se and positive predictivity, +P as 93,62% and 94,52% respectively as depicted in Table 8. The comparison results of the performance of the proposed method with that of other algorithms are presented in Table 9 and it is observed that the obtained results are higher and similar to other previous works. 4.4. QT database

ter was obtained as 4 for this database. The coefficient values of bk giving the best results and used in Eq. (1) are depicted in Eq. (19). bk = {1, 0, 0, 0, −1}

Table 8 QRS Detection performance results for the MIT-BIH Noise Stress Test Database.

N/R: Not Reported.

Record

b

237

(19)

The proposed method detected 283581 TP, 58 FP and 166 FN beats of total 283747 beats taken from Fantasia database providing overall QRS detection sensitivity, Se and positive predictivity, +P as 99,94% and 99,98% respectively as presented in Table 6. The proposed method and other algorithms are compared in Table 7 for the Fantasia database. The performance of the proposed method was obtained higher than or similar to the other previous works as observed in Table 7. 4.3. MIT-BIH noise stress test database The MIT-BIH Noise Stress Test Database consists of twelve 30 min-recordings with different Signal-to Noise Ratio (SNR) values derived from 118 and 119 recordings of the MIT-BIH AD [33]. The performance results of the proposed method using the all ECG (118e24,. . .,118e 6 and 119e24,. . .,119e 06) recordings are pre-

The QT database consists of ECG recordings chosen to represent a wide variety of QRS and ST-T morphologies for challenging QT detection algorithms with real world variability [34]. Recordings were selected from the existing databases MIT-BIH AD, the European Society of Cardiology ST-T Database and several other ECG databases. The QT database contains 105 15-min of two-channel ECG recordings recorded with a sampling frequency of 250 Hz. Since 23 of 24 sudden death ECG recordings did not have annotation files, they were not considered in experimental studies. The performance of the proposed method was obtained using 82 of 105 ECG recordings of QT database. The sampling frequency, fsample was considered as 250 Hz. Because the majority of 82 records (49 records) were taken from the MIT-BIH database, 60 Hz (which is the line frequency of MIT-BIH database) was accepted as the line frequency fline of QT database. Thus, K parameter was derived as 4 from Eq. (3) for this database. The coefficient values of bk giving the best results and used in Eq. (1) are depicted in Eq. (19). The proposed method determined 86649 TP, 39 FP and 92 FN beats of total 86741 beats taken from QT database, having overall QRS detection sensitivity, Se and positive predictivity, +P as 99,89%

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Table 10 Comparison of the performance of the proposed method with other algorithms for the QT Database. QRS Detector

TB

TP

FP

FN

Se(%)

+P(%)

This Work Dohare et al. [6] Elgendi [18] Pan and Tompkins [18] Ghaffari et al. [13] Martinez et al. [14] Moody and Mark [38]

86741 87679 111201 111201 86892 86892 86892

86649 87572 N/R N/R 86854 86824 84458

39 41 N/R N/R 70 107 459

92 107 N/R N/R 38 68 2434

99,89 99,87 99,99 97,99 99,96 99,92 97,20

99,96 99,95 99,67 99,05 99,92 99,88 99,46

N/R: Not Reported.

Table 11 Comparison of the performance of the proposed method with other algorithms for the European ST-T Database. QRS Detector

TB

TP

FP

FN

Se(%)

+P(%)

This Work Mourad et al. [10] Dohare et al. [6] Luigi et al. [12] Ghaffari et al. [22] Martinez et al. [14] Moody and Mark [38]

790565 788772 790559 788050 787103 787103 787103

787514 786207 774180 N/R 784210 784059 748768

1371 1258 2190 3511 3554 4077 10405

3051 2760 3679 1483 2893 3044 38635

99,61 99,65 99,53 98,81 99,63 99,61 95,09

99,83 99,84 99,72 99,56 99,55 99,48 98,63

N/R: Not Reported.

and 99,96% respectively as given in Table 10. The performance of the proposed QRS detection method was provided higher than and comparable to other algorithms. 4.5. European ST-T database The European ST-T Database was developed for analyzing ECG abnormalities, ST and T waves [35]. This database contains 90 twohour excerpts of two-channel ambulatory ECG recordings from 79 subjects, having 90 annotation files, 250 Hz sampling frequency and 12 bits resolution over a nominal 20 mV input range. The sampling frequency, fsample was 250 Hz, while fline was 50 Hz and K parameter was obtained as 5 from Eq. (3) for this database. The coefficient values of bk giving the best results and used in Equation (1) are shown in Eq. (20). bk = {1, 0, 0, 0, 0, −1}

(20)

The proposed method was tested on 90 full-length data of the European ST-T Database. This method ascertained 787514 TP, 1371 FP and 3051 FN beats of total 790565 beats, obtaining overall QRS detection sensitivity, Se and positive predictivity, +P as 99,61% and 99,83% respectively as presented in Table 11. These results give significantly improved performance compared to other algorithms tested on the European ST-T Database as seen in Table 11. 5. Discussion The performance of the proposed QRS detection method was tested on several standard databases as MIT-BIH AD, Fantasia Database, MIT-BIH Noise Stress Test Database, QT Database and European ST-T Database. The performance results obtained from the experimental studies are compared with the several studies in literature and are presented in Tables 5, 7, 9–11 respectively. To illustrate the performance and the robustness of the proposed system, the graphs on the records 108, 203 and 228 having abnormal beats and severe artifacts are depicted in Fig. 6(a)–(c) respectively. These are the most difficult records on which are worked [2,16,19]. Furthermore, the worst segments of these records are plotted in this Figure. R peaks detected as TP(), FN(*) and FP(o) from the raw ECG signal are represented here. Record 108 which is one of the most distorted records, includes borderline degree auriculo-ventricular (AV) block, sinus arrhyth-

mia, multiform Premature Ventricular Contractions (PVC), severe noise, morphological changes and baseline shifts [2,16,44]. Selected segment has R peaks with low-amplitude as depicted in Fig. 6(a). The record 203 has multiform PVCs, QRS morphology changes, muscle artifacts and baseline shifts [16,19,44]. The reference [44] stated that “It is a very difficult record, even for humans!”. This can be seen from Fig. 6(b). The record 228 contains first degree AV block, multiform PVCs, baseline shift and R peaks with low-amplitude as shown in Fig. 6(c) [16,44]. Due to the abnormalities of the records 108, 203 and 228 mentioned above, the FP and FN values were obtained higher than that of other records as seen in Table 4 for the MIT-BIH AD. High frequency muscle noise, R peak waves with low-amplitude, sudden changes of amplitude and baseline shifts complicate the QRS detection process. The proposed algorithm can be improved to decrease these FP and FN values. But, this makes the algorithm more complicated and increases the computational load. Since the main goal of this study is to propose a low-cost and realizable QRS detection algorithm in embedded systems, these obtained high FP and FN values are acceptable for the most difficult records such as 108, 203 and 228. The summary of the obtained performance results of the proposed QRS detection method for the five different databases is shown in Table 12. For testing the performance of the proposed method, total 1296137 beats of 272 ECG recordings were analyzed obtaining 1291011 TP, 3039 FP and 5126 FN beats. It was observed that the satisfying high values as 99,60% of the overall QRS detection sensitivity, Se and 99,77% of positive predictivity, +P were obtained using standard databases as presented in Table 12. The proposed method was developed using MATLAB 2015b (The MathWorks, Inc., Natick, MA, USA) in a personal computer with the specifications of Intel(R) Core(TM) i5–3230 M CPU 2.60 GHz processor and 4 GB RAM. For the analysis of ECG recordings taken from standard databases to test the proposed method, the recording length, the Elapsed Time Range (ETR) (consumed computational time) and the average ETR values are presented in Table 13. Kohler et al. [39] grouped the algorithms into categories low, medium and high according to the computational complexity. Since the exact computational requirements of the algorithms were not

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Fig. 6. Representation of performance of the proposed method on the abnormal records (a)108, (b) 203 and (c) 228 from the MIT-BIH AD.

Table 12 The summary of the proposed QRS detection method results for the MIT-BIH Arrhythmia, Fantasia, Noise Stress Test, QT and European ST-T databases. Database

Cases

TB

TP

FP

FN

Se(%)

+P(%)

MIT-BIH Arrhythmia DB Fantasia DB MIT-BIH NST DB QT DB European ST-T DB Total

48 40 12 82/105 90 272

109494 283747 25590 86741 790565 1296137

109310 283581 23957 86649 787514 1291011

182 58 1389 39 1371 3039

184 166 1633 92 3051 5126

99,83 99,94 93,62 99,89 99,61 99,60

99,83 99,98 94,52 99,96 99,83 99,77

Table 13 The average computational times for MIT-BIH Arrhythmia, Fantasia, Noise Stress Test, QT and European ST-T databases. Database

Record Length(min)

Elapsed Time Range (ETR)

Average ETR

MIT-BIH Arrhythmia DB Fantasia DB MIT-BIH NST DB QT DB European ST-T DB

30 120 30 15 120

9–17 s 20–31 s 8–12 s 2–5 s 19–25 s

13 s 25,5 s 10 s 3,5 s 22 s

available, they categorized the algorithm according to their experience. However, they stated that these categories might be useful about the required processing power for researchers studying on the QRS detection. Dohare et al. [6] also considered these computational load categories suggested by Kohler et al. [39] and compared their proposed method with other algorithms and they declared that the computational load of their proposed algorithm was in the low category. When we compared our proposed QRS detection method to the study of Dohare et al. [6] according to the computational complexity categories, computational times obtained from three standard databases utilizing our proposed method were lower than the values provided by Dohare et al. [6] as seen in Table 14. So, the computational load category of our method can be accepted as low, according to the values given in this Table. It is obvious that the computational load increases together with the increase in performance of the algorithm in most of the studies. But, the important issue is to achieve the highest possible performance with a low computational load for requiring less system

resources while it is being realized. The algorithm in this study was proposed as a solution to this issue, providing a low computational load/cost with satisfying and comparable performance indices (Se and +P) with the existing works. So, based on our experiences achieved from our previous studies on embedded systems referred as [1,40–43], it can be said that the proposed algorithm can be realized in embedded systems having limited resources. This makes the proposed method more advantageous to the existing algorithms regarding to the required system resources. Gutiérrez-Rivas et al. [26] proposed a differentiation based approach at the preprocessing stage for providing the input ECG signal. The derivative parameter of the proposed algorithm was obtained by the observations of the test results. They suggested the optimum combination with the estimation of the required parameters. For discriminating the QRS complex with respect to P and T waves, Dohare et al. [6] took the power of the ECG signal up to the sixth power by comparing each power with the others at the preprocessing stage. They finally utilized the sixth power of the ECG signal as an optimum power in their study. Yazdani et al. [2] provided a 99,87% Se and 99,90% +P value while our algorithm enabled 99,83% Se and 99,83 +P values for the MITBIH AD as seen in Table 5. In their Pre-processing and Decision Making Stages, they proposed a complicated algorithm, including Mathematical Morphology, feature signal analysis and peak detection, structuring element and parameter updates causing a high computational load comparing to our algorithm and there is a slight difference (0,04% of Se and 0,07% of +P) between their algorithm’s performance and that of ours.

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Table 14 Comparison of ETR values of this work to the study of Dohare et al. [6]. Database

MIT-BIH Arrhythmia DB QT DB European ST-T DB

Elapsed Time Range (ETR)

Length of Each Record (min) 30 15 120

The algorithm of Ghaffari et al. [13] obtained the highest performance indices providing 99,94% Se(0.11% higher than ours) and 99,91% (0,08% higher than ours) +P as seen in Table 5. Their main concern in this paper was to achieve a high performance. So, their algorithm, including DWT (Discrete Wavelet Transform), MHOM (Multiple Higher Order Moments), nonlinear amplification and so on, is quite more complex and complicated than ours. An algorithm having a high computational load was proposed by Pangerc et al. [8]. Especially the pre-processing stage included detailed processes such as feature extraction, detection functions, morphological analysis and signal repair increasing the algorithm’s complexity. Their Decision Making Stage contained detection step I, repetitive learning phase, Merging ECG heart beat annotation streams, detection step II, Regularity test. They achieved a 99,90% of Se (0,07% higher than ours) and 99,92% of +P (0,09% higher than ours) as seen in Table 5. The proposed algorithm enables comparable high performance indices using much lighter processing steps and lower computational load. The algorithm proposed by Ding et al. [9] included adaptive threshold and sifting processes containing complicated mathematical expressions such as autoregressive model and score function which require more system resources. They provide 99,93% of Se (0.1% higher than that of ours) and 99,87 of +P (0,04% higher than that of ours). In the proposed method, K parameter (given in Equation (3)) used in Equation (2) was derived from the sampling frequency, fsample of the ECG signal and line frequency, fline of which the recordings were done. The proposed algorithm does not include complicated mathematical expressions needing a high processing capability unlike the existing studies as [2,6,8,9,13,26]. If the performances are compared, the performance indices of the studies [2,8,9,13] are higher than that of ours. However, our proposed method does not require any additional processes such as setting, training, selection, testing and prediction of model parameters unlike the studies similar to [2,6,8,9,13,26]. The proposed algorithm is simple, executable step by step, realizable easily and efficiently. So, the performance difference between our algorithm and the algorithms having higher success is not significant considering the devices/platforms having limited system resources. An algorithm having a low computational load and satisfying and comparable performance indices (Se and +P) to the existing works was proposed in this study as seen in Table 5. The decrease in the computational complexity of the proposed method results in a decrease of the computational load as well without compromising on high performance indices (Se and +P). With this advantage, the proposed method can be used in any ECG recording system without needing any extra processes and computations. This is one of the most important contributions of the proposed method to the literature and shows this algorithm can be implemented in embedded systems. 6. Conclusion In this study, an improved QRS complex detection method having a low computational load was proposed. In the preprocessing stage of the proposed method, the undesired frequency components were reduced and an enhanced ECG signal was obtained. At

Dohare et al. [6]

This Work

80–85 s 22–26 s 230–250 s

9–17 s 2–5 s 19–25 s

the Decision Making Stage, an adaptive thresholding was applied to the ECG signal. The proposed method was tested on standard databases such as MIT-BIH Arrhythmia, Fantasia, MIT-BIH Noise Stress Test, QT and European ST-T. Satisfying good results were obtained from the novel proposed method and the performance indices were higher or comparable to similar studies in the scientific literature. The proposed method works properly as a QRS detector for the employed databases without downsampling. It can be used as a real time QRS detector with the properties of flexible, low cost and easy to realize. The proposed QRS detector provided a satisfying high performance in difficult distorted records of 108, 203 and 228 from the MIT-BIH AD, although it included a simple algorithm having no complex processes such as learning, training and prediction. Most of the algorithms in similar studies employ parameter definitions, including operations such as setting, training, selection, testing and prediction of model parameters. These methods require additional processes, increasing both the computational load and time. In the proposed method, this issue was taken into consideration and the parameter definition was provided employing the features of the ECG signal. Thus, the proposed method can be utilized for any ECG recording system without any additional processing load. The proposed method has low complexity and computational time presenting a high performance approach for telemedicine, remote monitoring systems, mobile/smart phone applications, embedded systems as single board computers and wireless sensor network based medical devices. It offers a satisfying efficient and reliable method for many clinical applications, providing 99,60% overall sensitivity, Se and 99,77% overall positive predictivity, +P. And it also enables a high accuracy with low computational load at the same time.

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