DOI 10.1007/s10527-016-9583-5 Biomedical Engineering, Vol. 50, No. 1, May, 2016, pp. 4043. Translated from Meditsinskaya Tekhnika, Vol. 50, No. 1, Jan.Feb., 2016, pp. 2831. Original article submitted May 4, 2015.
A Robust Method for Detecting the QRS Complex of the ECG Signal A. A. Fedotov
This work was devoted to a robust method for detection of the QRS complex of the ECG signal based on the appli cation of a bandpass filter with a linear phase characteristic, the Hilbert transform, and an adaptive threshold ing algorithm. The efficiency of various QRS complex detectors in the presence of pronounced artifacts was stud ied. The efficiency of the suggested method was verified using different ECG records available from the MIT PhysioNet open access database.
Introduction
Theory
Detection and processing of ECG signals are widely used in medical diagnosis. Progress in the development of cardiac monitoring systems based on the variability of cardiac rhythm parameters is increasing the demand for reliable methods of detection and processing of the QRS complexes of the ECG signal. Such methods are neces sary to minimize the measuring error of the RR interval of the ECG signal under conditions of exposure to noise and artifacts of various origin [1, 2]. At the same time, the method and algorithms for the detection of the QRS complex of the ECG signal should be relatively simple in their implementation to be used in portable monitoring systems with low energy consump tion and low calculation speed. The variety of algorithms for detection of the QRS complex of the ECG signal used in current medical prac tice are mainly based on the calculation of the first and second derivatives, bandpass filtering, wavelet trans form, matched filtering and neural networks, as well as various combinations of these methods [35]. The goal of this work was to describe a relatively sim ple method for detection of the QRS complex of the ECG signal providing high sensitivity and low error. This method includes three successive stages of digital processing of the ECG signal: bandpass filtration, the Hilbert transform, and an adaptive algorithm for the peak detection.
The primary stage of processing of the ECG signal involves bandpass filtering reducing the baseline drift of the biosignal and the effect of motion artifacts and high frequency noise. Correct selection of the frequency filter passband ensures adequate isolation of the highfrequen cy QRS complex of the ECG signal against the back ground of the lowfrequency P and T waves of the signal, lowfrequency noise, and 50Hz power line artifacts. The dependence of the spectral power of various components of the ECG signal on frequency (measured in relative units) is shown in Fig. 1 [4].
Samara State Aerospace University, Samara, Russia; Email:
[email protected]
Fig. 1. Dependence of the spectral power of various components of the ECG signal on frequency.
S, relative units
ECG QRS complex
Motion artifacts Myogram P and T waves f, Hz
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00063398/16/50010040 © 2016 Springer Science+Business Media New York
A Robust Method for Detecting the QRS Complex
Analysis of the results demonstrates that isolation of the QRS complex of the ECG signal based on the prin ciple of frequency selection can be very effective. The sensitivity and specificity of detection of the QRS com plex of the ECG signal was analyzed. It was demonstrat ed that the optimal passband of the filter was 820 Hz [6, 7]. The essence of the Hilbert transform is the determi nation of the orthogonal component of the signal [8]. The Hilbert transform of the ECG signal allows the biosignal to be represented as analytical and its envelope to be isolated. This improves the quality of detection of the QRS complex of the ECG signal. The envelope of the analytical signal is determined by calculating the signal modulus.
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t, s
t, s
t, s
t, s
Materials and Methods The method for detection of the QRS complexes of the ECG signal suggested in this work consists of a sequence of operations: 1) the Hilbert transform of the output signal of the band filter is performed to obtain an analytical signal; 2) the modulus of the analytical signal is calculated to determine its envelope; 3) the modulus of the analytical signal is squared to provide additional amplification of highamplitude com ponents corresponding to the QRS complexes of the ECG signal. In this work, an eighthorder Butterworth digital fil ter with correction of the nonlinear phase characteristic was used at the stage of the frequency filtering of the ECG signal. The frequency band of the filter was 820 Hz. To provide a linear phase characteristic, the output signal of the Butterworth filter should be repeatedly filtered in the reverse order of signal readings. In this case, the order of the filter is doubled [9]. Real ECG signal curves at different stages of pro cessing by the method suggested in this work are shown in Fig. 2 (A1 – initial ECG signal; A2 – ECG signal after bandpass filtering; A3 – modulus (envelope) of the ana lytical signal; A4 – squared modulus of the analytical sig nal). After the first two processing stages, the resulting sig nal A4 is applied to the input of the adaptive circuit used for detection of the signal peaks serving as reference points of the QRS complex. The R wave is selected as the most distinct marker. This method of the ECG signal pro cessing using a band filter with a linear phase characteris tic and further Hilbert transform allows the phase distor tion and time delay to be eliminated.
Fig. 2. ECG signal curves at different stages of processing.
The essence of the adaptive algorithm for peak detection is the formation of a 2s sliding window within which the peaks reaching above the given threshold level (Lev) are sought. The threshold level is determined indi vidually for each sliding window based on the following threshold function:
where Ω is the value of the mean square deviation of the signal amplitude readings within the limits of the given sliding window and max is the maximal value of the signal amplitude readings within the limits of the given sliding window. The numerical values of the threshold function parameters were selected empirically based on the exper imental data for the criterion of correct detection of QRS complexes and minimization of false detection and omis sion. The peak detector determines the time position of the signal peak within the time interval of the search if the following conditions are observed simultaneously: А4(n) > Lev & A4(n) > A4(n + 1) & A4(n) > А4(n – 1). The QRS detector suggested in this work was veri fied using the PhysioNet ECG signal database of the Massachusetts Institute of Technology (http://phys ionet.org). The efficiency of detection of QRS complex es was estimated using the following statistical parame ters:
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Fedotov
TABLE 1. Efficiency of Detection of QRS Complexes of the ECG Signal 100
104
105
Mean value averaged over 48 fragments
Signal fragment
1 2 3 4
P T, %
P F, %
Per, %
P T, %
P F, %
Per, %
P T, %
P F, %
Per, %
P T, %
P F, %
Per, %
99.9 100 100 100
0.09 0.05 0 0
0.1 0.06 0.07 0
98.2 99.5 99.7 99.8
0.1 0.08 0.07 0.06
0.25 0.2 0.18 0.17
98.2 99.5 99.7 99.8
0.12 0.04 0.03 0.02
0.3 0.2 0.21 0.22
98.9 99.6 99.8 99.8
0.08 0.05 0.02 0.02
0.24 0.2 0.19 0.18
1) probability of detection of reference points PT:
with highamplitude noise (records 104 and 105) were specially selected for the tests [10].
PT = (NT/N)⋅100%; 2) probability of detection of false reference points PF: PF = (NF/N)⋅100%; 3) parameter of the detection error level Per: Per = ([Nm + NF]/N)⋅100%, where NT is the number of correctly detected QRS com plexes, NF is the number of falsely detected QRS com plexes, N is the total number of QRS complexes, and Nm is the number of omitted QRS complexes. Used in the tests were ECG signal samples available from the MITBIH Arrhythmia Database, which con tains 48 fragments of actual ECG signals (30 min each); one sample with low noise (record 100) and two samples A
Results Comparative analysis of the QRS complex detection efficiency was carried out using the following detectors: 1) the Pan–Tompkins detector [11]; 2) a detector based on a matched filter [12]; 3) a detector based on wavelet transform [13]; 4) the detector suggested in this work. The results of quantitative evaluation of the efficien cy of the detector suggested in this work as compared with currently used approaches to processing of actual ECG signals are presented in Table 1. Actual ECG curves with pronounced motion arti facts and baseline drift are shown in Fig. 3 (A – fragment of initial ECG signal; B – output signal of band filter; C – input signal of adaptive circuit for peak detection using sliding windows; the adaptive threshold is shown as a straight line, and R waves of the ECG signal are marked with crosses).
Conclusion t, s
t, s
B
C
t, s Fig. 3. Processing of an actual ECG curve fragment with pro nounced motion artifacts and baseline drift.
It follows from the results obtained in this work that the detection of QRS complexes of the ECG signal based on bandpass filtering and the Hilbert transform is an effective method for processing ECG signals measured under actual clinical conditions. The method suggested in this work made it possible to achieve 100% errorfree detection in a lownoise 30minlong ECG signal sam ple. In a noisy ECG signal, the detection error level was no more than 0.2%. The advantages of the method for QRS complex detection described in this work are easy implementation, a high speed for modern computer systems, a high rate of correct detection of QRS complexes, and a low incidence of errors caused by false detection and omission.
A Robust Method for Detecting the QRS Complex
This work was supported by the Ministry of Education and Science of the Russian Federation (State Targeted Program for Scientific Research, Project No. 12.2013.2014/K, State Registration No. 114121670017).
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