DETECTING QRS COMPLEX IN ECG USING WAVELETS AND CUBIC SPLINE INTERPOLATION

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1 DETECTING QRS COMPLEX IN ECG USING WAVELETS AND CUBIC SPLINE INTERPOLATION Luiz Carlos Rodrigues, Maurício Marengoni Universidade Presbiteriana Mackenzie, São Paulo, Brazil Corresponding authors( lcfrod@hotmail.com, mmarengoni@mackenzie.br) Abstract Due to its easy application and low cost, the eletrocardiogram (ECG) is a resource with large application in the heart health assessment and, among all the ECG components, the QRS Complex is the most significant fiducial point. A fundamental step in any study of digital signal processing of ECG, as well heart beats classification, is the QRS complex detection. Several works on QRS detection are available in the literature, however the robustness and high level of precision is still a matter of studies. In this work we present a QRS detector relying in Daubechies wavelets transform and cubic spline interpolation. Using waveletes transform, the ECG is first pre-processed for noise removal and baseline wandering and then, combining wavelets and cubic spline interpolation, the QRS complex is enhanced and other noise components are attenuated. This signal is submitted to a peak detector module whose purpose is to identify the R wave. For development and validation of this work we used the Massachusetts Institute of Technology-Beth Israel Hospital(MIT-BIH) Arrithmias database. The final result showed a sensitivity level above 96.5% in most of the tested records, this results are presented at the end of this work. Key words - biomedical signal processing; health care information systems; ECG; QRS complex,wavelets. I. INTRODUCTION Since its creation in 1903 by Willem Einthoven, Nobel Prize of Medicine in 1924, the electrocardiogram (ECG) has been considered an instrument of excellent cost-benefit for the prevention, diagnostic and treatment of cardiac diseases. As a non-invasive test, low cost and its easy application the ECG is listed among the most applied resource in medicine for heart health conditions assessment. The ECG consists of a graphical register produced by a galvanometer that measures the electrical signal generated during the activity of cardiac muscles and represent them as a function of time and amplitude. These electrical signals are stored in digital files, making possible its later study in a way that is beyond the simple visual analysis. In the study presented here, the wavelet transform was used for noise removal, baseline wandering and to identify the main features that characterize a cardiac cycle. These points are considered fiducial points and have a fundamental role in the identification of abnormalities such as the disturbance of rhythm, electrical conduction or detection of ischemia. The QRS detection has been studied by many researchers and several approaches have been proposed. Chen et al. [3] described a combination of discrete wavelet transform and adaptive thresholding method to identify the QRS complex. Quing et al [5] developed an algorithm were the ECG signal is decomposed with the equivalent filter of a biorthogonal spline wavelet by Mallat pyramid algorithm [8] and the signal singularity s Lipschitz exponent was used to analyze the relationship between the signal singularity (R wave) and the zero-crossing point of the modulus maximum pair of its wavelet transform. Zhang et al. [4] presented in their study an algorithm for wearable ECG device in body area network which utilizes the multistage multiscale mathematical morphology filtering to suppress the impulsive noise and uses multiframe differential modulus accumulation to remove the baseline wandering and enhance the signalžs fiducial points. In the work presented here, all the 48 records of MIT- BIH arrhythmia database were used for the development and testings of the algorithm [1]. Each record was submitted to Daubechies 4 Wavelet Transform for denoising and removal of baseline wandering. The schematic representation of the whole process is shown in Fig. 1. ECG Remove Baseline wandering Remove Noise Wavelet Transform B-Spline Interpolation QRS Detection QRS Figure 1. Schematic representation of the whole process of QRS detection describe in this study. A. ECG : Waves and Intervals For analysis purpose the cardiac cycle is represented graphically through waves, intervals and segments [2]. The waves, the fiducial points, are peaks of electrical activity, captured by electrodes on the human body surface and reflected the depolarization of the cardiac cells, as well their repolarization. A normal ECG, with its waves and intervals, considered normal is shown in Fig. 2 The Fig. 2 shows the series of peaks and waves that correspond to ventricular or atrial depolarization and repolarization, with each signal segment representing a different event within the cardiac cycle. The cardiac cycle is triggered

2 Figure 2. Schematic representation of a wave form considered normal in an ECG. The cardiac cycle starts with the P-wave, corresponding to atrial depolarization, that is followed by the QRS complex, composed by Q, R and S waves, corresponding to ventricular depolarization, and the cycle ends with the T-wave, corresponding to the ventricular repolarization. The U-wave may, or may not, be present. Between the waves we can see the intervals. Adapted from [6] by the sinoatrial node in the right atrium. This first event is not detected by the ECG because the sinoatrial node has not a mass of cells large enough to create an impulse to be detected by the electrodes. The depolarization of the sinoatrial node is conducted rapidly throughout both the right and the left atria, what is registered by the the electrodes and represented by te P-wave. After about 200 milliseconds from the beginning of the P-wave the right and left ventricles begin to depolarize resulting in the recordable QRS complex, which has a duration of approximately 100 milliseconds. If present, the first negative deflection of the signal is the Q-wave and the large positive deflection is the R-wave. And if there is a negative deflection after the R-wave, it is called the S- wave. As the QRS complex ends, the ventricles are completely depolarized and its contraction starts, pumping blood. The ventricles then repolarize after the contraction, giving raise to the T-wave, normally the last event detected in cardiac cycle and for this reason it is followed by the next P-wave, repeating the whole process[2]. a smoothing function θ(t), it can be shown [7] [19] that the wavelet transform of a signal x(t) at scale a is: + ( ) 1 t b W (a, b) = f(t) ψ dt (2) a a where θ(t) = ( 1 a θ t a ) is the scaled version of the smoothing function. The wavelet transform at scale a is proportional to the derivative of the signal filtered version with a smoothing impulse response at scale a. Therefore the zero crossing of the WT corresponds to the local maxima or minima of the smoothed signal at different scales and the maximum absolute values of the wavelet transforms are associated with maximum slopes in the filtered signal. In this study we are interested in ECG waves which are composed of slopes and local maxima (or minima) at different scales occurring at different time instants within the cardiac cycle. The scale factor a or the translation parameter b can be discretized. The usual choice is to follow a dyadic grid on the time-scale plane: a = 2 k and b = 2 k l. This transform is called dyadic wavelet transform with basis functions [21] ψ k,l (t) = 2 ( k 2 ) ψ(2 k t l); where k, l Z + (3) For discrete-time signals, the dyadic discrete wavelet transform(dwt) is equivalent, according to Mallat s algorithm [8], to an octave filter bank and can be implemented as a cascade of identical cells, low-pass and high-pass finite impulse response [FIR] filters, as illustrated in Fig. 3. From the transformed coefficients W 2 kx[2 k l] and the low-pass residual, the original sign can be rebuilt using a reconstruction filter bank. The down samplers after each filter in Fig.3 remove the redundancy of the signal representation. As side effects, they make the signal representation time variant and reduce the temporal resolution of the wavelet coefficient for increasing scales. A. Wavelets Transform (WT) II. MATHEMATICAL SUPPORT The wavelet transform is a signal decomposition as a combined basis functions set, obtained by dilation(a) and translations (b) of a single prototype wavelet ψ(t). Thus, the WT of a signal x(t) is defined as + ( ) 1 t b W (a, b) = f(t) ψ dt (1) a a The greater the scale factor a is, the wider is the basis function and consequently, the corresponding coefficients gives information about lower frequency components of the signal, and vice versa. In this way, the temporal resolution is higher at high frequencies, achieving the property that the analysis window comprises the same number of periods for any central frequency. If the prototype wavelet ψ(t) is the derivative of Figure 3. Mallat s algorithm for the two filter bank implementation of DWT. B. Cubic Spline Interpolation Mathematically, interpolation is any method to obtain new data points within the range of a discrete set of data points. In engineering and science, we often have a time serie of data, for example, values obtained by the electrodes when recording an ECG at some defined rate. It is often required to estimate the value for an intermediate value between points of this serie. This task is named interpolation and may be achieved by curve fitting or regression analysis. In practice, when the ECG sensor has not a satisfactory rate, interpolation can be used to increase the signal resolution. There are several interpolation methods available, such as linear interpolation,

3 cosine interpolation and polynomial interpolation, to cite just a few ones [9]. One of the most important interpolation method is the cubic spline technique. In terms of mathematics, spline means a piecewise polynomial satisfying continuity conditions between curve segments. Consider the following sequence : X = x 0, x 1,..., x n then the piecewise polinomial would take the form as follows [9]: S 1 (x), x 1 x x 2 ; S 2 (x), x 2 x x 3 ; f(x) =. (4). S n 1 (x) x n 1 x x n ; where S 1 (x), S 2 (x),..., S n 1 (x) are cubic polynomials and can be written as follow: S i = a i x 3 + b i x 2 + c i x + d i i = 1, 2,..n S(x) must satisfy the following rules : 1) Every point of the sequence should be in the curve. 2) S(x), as well its first and second derivative of S(x) should be continuous then any interpolation can be computed for any x between x 0 and x n. In this case S(x) exists and can be determined. Figure 4. Normalized record of ECG with noise of low and high frequencies. The low frequency component, that causes the baseline variations, was isolated and represented by the green line. Signal adapted from [22]. coefficients values of the Daubechies 4 (Daub4) wavelet. After the replacement of these values, the inverse transform is calculated and the signal is rebuilt, now without the baseline wandering. III. METHODS We now present the steps executed during the development of this work. It started with the reading of a MIT-BIH ECG record. The record was submitted to a pre-processing consisting in the baseline wandering and the high frequency noise removal. To enhance the QRS Complex and attenuate the other components, the pre-processed record was decomposed in wavelet coefficients levels and the 3 first levels were interpolated and merged in a summation. The record with enhanced QRS Complex was submitted to a Peak detector that distinguished the QRS peaks from the non-qrs peaks. The details for each step are described in this section. A. Removal of the Baseline Wandering Among the artifacts that degrade the correct reading and analysis of any digital signal, in general, and of the ECG, in particular, are the low frequency artifacts, that cause the signal oscillations above and below its base line. This variation is a kind of noise that can lead to a low performance of the system detecting R waves, as well as the classification of these heart beats. For example, the ST Segment, an important fiducial point in ECG for identifying ischemia, is a low frequency wave and may be completely distorted by this oscillation [10] The Fig. 4 presents a normalized ECG time serie, acquired from a patient that occasionally presents arrhythmia episodes. The fluctuations of low frequency, shown on the picture by the green line, are known as baseline wandering, which is caused by the patient breathing [22]. The method here adopted for baseline wandering removal, described in [12], consists on the complete decomposition of the signal in scales of the wavelets coefficients and then its elimination, replacing them by zero, of the sixth level Figure 5. Same signal shown in Fig. 4, rebuilt, now without the Baseline wandering. In order to prevent the distortion of the ST Segment, the American Heart Association [13] recommends a cut-off frequency of up to 0.05Hz for low-frequency ECG filtering. The central frequency (F c ) for Daubechies 4 wavelet is Hz and the sampling period for the MIT-BIH database is 1/360 seconds. We can use the relationship between scale and frequency given by (5) to select the most convenient scale to remove the baseline wandering. F a = (5) a We can see that if we choose the scale 6 to be fulfilled by zeros, we would be eliminating from the signal the frequency, as shown below : F a = 0, / Hz B. Removal of Noise The electrocardiograms signals are very easily and frequently contaminated by different sources of high frequencies noise during its acquiring and recording. Among these unwanted signals, the more recurrents are : F c

4 The signals of Electromyogram(EMG), a high frequency component generated by muscular contraction, electrodes instability or patient s body movement. Interference of power line of 50 or 60 Hz. The isolation and elimination of these spurious components become a scientific challenge when we know that the spectrum of a QRS Complex (5 to 15 Hz) overlaps with the noise generated by the muscles [14]. For noise removal, this project implemented the method described in [15]. This method is based on wavelets transforms and the application of a threshold to the coefficients obtained in the wavelet decomposition. The signal is decomposed in levels of wavelets coefficients in their respective scales then applying thresholds only to the coefficients of the selected level leaving intact all other coefficients. The Donoho s algorithm [22] is summarized as follows: 1 o Consider the vectors W 1,...W J 0, with wavelets coefficients obtained from the signal decomposition, with N samples, by wavelets transform until the level J 0 is selected. This level depends on the frequency to be filtered. 2 o Calculate the median absolute deviation or (MAD), with the values of the selected level. In this study, the level 1 was selected, were the highest frequencies of the signal were found. The MAD is then calculated dividing the median of the level 1 by 0,6754, an estimator for standard deviation for Gaussian white noise. ˆρ (mad) median{ W 1, 0, W 1, 1,... W 1, N 2 1 } 0, o Apply the result of the MAD (6), to obtain the threshold ˆδ (u), to be applied to the level J 0, according (7): ˆδ (u) 2ˆρ (mad) log (N) (7) (6) Figure 6. At the top the signal contamined with high frequency noise and at the bottom the same signal after the application of the hard thresholding method. described, the task of QRS detection is not trivial [18]. In this work an adaptation of the algorithms described in [14] and in [16] was developed. The first step in our system development was the selection of the method for the ECG signal analysis. Instead of choosing a tradicional digital signal processing technique which would require an specific filter for the frequency of the record [17], we have selected wavelets transforms due its ability to separate the QRS Complex from the other ECG components and noise in the time-scale plane. There are a variety of wavelets families available for this purpose, like Haar, Daubechies, Biorthogonal, Coiflets, Symlets, Morlet, and many others Real or Complex wavelets groups [19] [20]. From these methods Daubechies 4 wavelet prototype, Fig. 7, was selected because its compact support and shape similarity to the QRS Complex waveform. 4 o For each value of W j, t, j = 1,..., J 0 e t = 0,..., N j 1 apply the rule named hard thresholding, calculating the new coefficient values according to the rule (8): { 0.0 if Wj, W j, t = t W j, t Otherwise ˆδ (u) Fig. 6 shows the signal before and after the noise removal process. Note that the filtering process used here has the the task of QRS Complex detection, after filtering the signal is useless for diagnostic purpose. C. QRS Complex Detection The dominant characteristic of the ECG is a cyclic pulse in a waveform called QRS Complex, that corresponds to the instant in which the ventricular cardiac cells, after be crossed by an ionic current, loose their conditions of electric equilibrium. The QRS Complex is one of the most important fiducial points for the ECG monitors system. Several studies have been done for the creation of a universal solution for the problem of the QRS detection. However, due the huge diversity of waveforms, waveforms abnormalities and interference, above (8) Figure 7. Daubechies 4, also known as Db4 or Daub4, wavelet function. The computation starts with the wavelet Multi Resolution Analisys (MRA) of the signal, decomposing 2 N samples, in this work N = 11 or a 2048 MRA vector. Since the MRA produces N/2 J coefficients for each level J(0 J N), the result are three vectors with 1024, 512 and 256 wavelets coefficients. These coefficients are interpolated using cubic spline method to rebuilt the vectors of 2048 positions, that are then summed, as Fig. 8 shows. After obtaining the merged vector, the result is submitted to a moving integration filter, to eliminate the double peaks (9). The value for the moving average may depend on the length of the vector. After some experiments, the best performance of the peak detector was achieved with the value of n = 0, 03 seconds.

5 2048 Db4 MRA Interpolate levels 1,2 and 3 Merge levels 1,2 and Figure 8. MRA of 2028 ECG data samples, interpolation of the 1st, 2nd and 3rd levels which are summed. y(n) = n k=n M+1 Below are the rules implemented for the QRS peak detection: 1) Ignore all peaks that precede or follows larger peaks by less than 200 milliseconds. 2) If the peak occurred within 360 milliseconds of a previous detection verify if the derivative of the raw signal was at least half of the derivative of the previous detection. If not, the peak is considered to be a T-wave. 3) If the peak is larger than the detection threshold, classify it as a QRS complex, otherwise ignore it. The detection threshold is obtained by calculating the mean of the last eight pass QRS complex. Every time a peak is classified as QRS complex it is added to a buffer containing the eight most recent QRS peaks. The threshold is the mean of these eight peaks. 4) If no QRS has been detected within 1.5 R-to-R intervals, there was a peak that was larger than half the detection threshold, and the peak following the preceding detection by at least 360 milliseconds, classify this peak as a QRS complex. The beat detection needs the threshold to work, so we need to inform some initial threshold estimate. In order to make an initial estimate,the mean of the eight maximum peaks in a interval of 5 seconds was detected. IV. EXPERIMENTAL RESULTS Fig. 9 shows the detection result of 2048 samples extracted from the record 101 of the MIT-BIH Arrythmia Database. The green lines are visual indicators of the point were the algorithm has detected a QRS. Figure 9. Vertical green lines indicates the detection of the QRS Complex The system presented here was assessed by comparing the results with those annotated in MIT-BIH Arrythmia Database. The MIT-BIH Arrythmia Database makes available 48 halfhour segments of two channel ambulatory ECG records that are sampled at 360 Hz. Only the first channel, MLII (Modifiel Lead II) was considered for this study. MIT-BIH also makes (9) available programs for the generation of the statistical results. These programs, like bxb.exe that compares, beat to beat, the reference and the test annotation, are available in the Physionet library. The beat annotations do not need to coincide precisely with the reference beat annotation, since the evaluation protocol allows a time difference of up 0.15 second between each pair of matching beat annotation. Any beat annotations existent in the first five minutes of the record, the "learning period", are ignored in the evaluation process. The remainder of the record must be fully annotated. Two evaluation parameters are calculated by Physionet tools: the Sensitivity (Se) (10). Se = T P T P + F N and the Positive Predictivity(+P) (11). +P = T P T P + F P (10) (11) where T P is the number of true positives detections, F N corresponds to the number of false negative detections and F P corresponds to the false positive detections. The complete result of all 48 records from MIT-BIH database are shown in table I V. CONCLUSION AND DISCUSSION The ECG is one of the most important resource for the heart health assessment and Daubechies 4 wavelet Multi Resolution Analysis has been proved to be a suitable tool to extract information from an ECG for diagnostic of rhythm disturbance as well other cardiopathies. Currently, more and more automatic arrhythmias detection systems have been researched to achieve the highest level of accuracy and robustness. Accuracy and robustness are crucial factors for any healthcare computational applications and for this reason the search for a robust QRS detector is still open. This paper proposed a technique for heart beat detection using Daub4 wavelet transform of the Daubechies family associated with QRS detection rules and adaptive thresholds. It was demonstrated that Daub4 wavelets can be very useful for removing high-frequencies in ECG, and is an efficient tool for removing the baseline wandering. Although less complex than the algorithms described in table I, our method was capable to get a Positive Predictivity (+P) above 98% and Sensitivity (Se) above 94% and it can be improved with more rules for QRS complex detection. Another way to improved our results is adding more rules for detection of QRS complex, possibly achieving the same rates of Sensitivity and Positive Predictivity reached by more complex and sophisticated algorithms. All the 48 records of MIT-BIH Arrythmia Database were tested during the assessment of the algorithm here described. VI. ACKNOWLEDGEMENTS The authors thank Fundo Mackenzie de Pesquisa (Mackpesquisa) from the Universidade Presbiteriana Mackenzie for the financial support for this research.

6 Table I TEST RESULTS OF THE QRS DETECTION ALGORITHM ECG Table Column Head Record Beats FP FN Se(%) +P(%) Average Table II COMPARISON OF QRS COMPLEX DETECTION RESULTS OBTAINED BY OTHER METHODS Comparison of Results with other methods Authors Se (%) +P(%) Chen et al. [3] 99,55 99,49 Chen et al. [4] ,80 Zhan et al. [5] n/a This Method Available in: < /> [2] Dupre, A.; Vieau, S.; Iaizzo, P. A. Handbook of Cardiac Anatomy,Pshysiology, and Devices. 2nd. ed. Minnneapolis, USA: Springer, [3] Chen, S.W; Chen, H.C; Chan H.L, A real-time QRS detection method based on moving-averaging incorporating with wavelet denoising Computer Methods and Programs in Biomedicine, v. 82, n. 3, p , [4] Zhan F., Lina Y, QRS detection based on multiscale mathematical morphology for wearable ECG Devices in body area networks IEEE Transactions on Biomedical Circuits and Systems, v. 3, n. 4, p , [5] Chen Q., Liu J,Li G., QRS wave group detection based on B-Spline wavelet add adaptive threshold 2010 International Conference on Computer, Mecatronics, Control and Eletronic Engineering (CMCE), p , [6] CORP, M. S.. D. The Merck manual for healthcare professionals. The Merck Manuals Online Medical Library, Available in: < // Last Access: 1 fevereiro [7] Burrus, C. S.; Gopinath, R. A.; Guo, H. Introduction to Wavelets and Wavelets Tranforms - A Primer. New Jersey: Prentice Hall, Inc, [8] Mallat, S. G. A Theory for Multiresolution Signal Composition: The Wavelet Representation. IEEE Transactions on Pattern Analysis and Machine Intelligence, v. II, n. 7, p , [9] Howard, A. S; Rorres, C. Elementary Linear Algebra - Applications Version. New Jersey: Cambridge University Press, [10] Jane, R. and Laguna, P. and Thakor, N. V. and Caminal, P. Adaptive baseline wander removal in the ECG: Comparative analysis with cubic spline technique.computers in Cardiology. Proceedings, p , [11] Percival, D. B.; T.Walden, A. Wavelets Methods for Time Series Analysis. New Jersey: Cambridge University Press, [12] Jansend, A.; Cour-Harbo, A. Ripples in Mathematics The Discrete Wavelet Transform. New York,USA: Springer, [13] Klingfield, P. et al. Recommendations for the Standardization and Interpretation of the Electrocardiogram: Part I: The Electrocardiogram and Its Technology: A Scientific Statement From the American Heart Association Electrocardiography and Arrhythmias Committee, Council on Clinical Cardiology; the American College of Cardiology Foundation; and the Heart Rhythm Society Endorsed by the International Society for Computerized Electrocardiology. Circulation, v. 115, n. 10, p , Available in: < /10/1306> [14] Pan, J.; Tompkins, W. J. A real-time qrs detection algorithm. IEEE Transactions on Biomedical Engineering, BME-32, p , [15] Donoho, D. L. De-noising by soft-thresholding. IEEE Transactions on Information Theory, v. 41, n. 3, p , August [16] Rudnick, M.; Strumillo, P. A real-time adaptive wavelet transform-based qrs complex detector. In: ICANNGA (2). [S.l.: s.n.], p [17] Haykyn, S.; Veen, B. V. Signals and Systems. 2nd. ed. New York, NY, USA: John Wiley & Sons, Inc., 2002.ISBN [18] Elgendi, M. et al. A robust qrs complex detection algorithm using dynamic thresholds. In: Proceedings of the International Symposium on Computer Science and its Applications. Washington, DC, USA: IEEE Computer Society, p [19] Burrus, C. S.; Gopinath, R. A.; Guo, H. Introduction to Wavelets and Wavelets Tranforms - A Primer. New Jersey: Prentice Hall, Inc, [20] Daubechies, I. Orthonormal bases of compactly supported wavelets. Communications on Pure and Applied Mathematics, v. 41, p , [21] Addison, Paul S. Wavelet transforms and the ECG: a review. Physiological Measurement,n.5,v. 26, p , [22] Percival, D. B.; T.Walden, A. Wavelets Methods for Time Series Analysis. New Jersey: Cambridge University Press, [23] Gene H. Golub and Charles F. van Van Loan. Matrix Computations(Johns Hopkins Studies in Mathematical Sciences) The Johns Hopkins University Press, 3rd edition, October REFERENCES [1] Goldberger, A. L. et al. Physiobank, physiotoolkit, and physionet: Components of a new research resource for complex physiologic signals. Circulation, v. 101, n. 23, p. e215 e220, Circulation Electronic Pages: