Continuous Wavelet Transform in ECG Analysis. A Concept or Clinical Uses

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1 1143 Continuous Wavelet Transform in ECG Analysis. A Concept or Clinical Uses Mariana Moga a, V.D. Moga b, Gh.I. Mihalas b a County Hospital Timisoara, Romania, b University of Medicine and Pharmacy Victor Babes Timisoara, Romania Abstract Most of the clinically useful information carried by the ECG is found in the morphology of the QRS complexes and in the T wave, measured as amplitude, deformations and duration. During the last years, wavelet transform has proven to be a valuable tool in many applications areas for analysis of non-stationary signals, and the ECG in particular. Our study was performed in the light of the assessment of ECG signals from the medical point of view. We are interested to detected after wavelet transform, ECG like waves, which are composed of slopes and local maxima (or minima) at different scales, occurring at different time instants within the cardiac cycles. For this purpose we used the continuous wavelet transform, under MATLAB 6.5 software, on ECG signals from the MIT-BIH Arrhythmia and ESC-ECG databases. The sampling frequency of this ECG signals was 250 Hz. In our study we used the Morlet, Mexican Hat and Complex frequency B spline wavelets. Our study was made from the medical point of view, and has not impose to be an automatic detection method, its seems to be useful to compare the obtained data, with other parameters, like power spectral density. We compared, using statistically accepted methods, correlation between the QRS duration and power spectral density parameters (Pearson method). Long QRS duration is correlated well with the very low and low power spectra of the studied ECGs, sympathetic mediated. In conclusion, we prove the value of a mathematical technique in the field of the biomedical science. It is important to notice that the continuous wavelet transform provides a rich description of the ECG signals. Keywords: Continuous Wavelet transform, ECG spectrogram, Power spectral density 1. Introduction In the last decades, and also in present, cardiovascular diseases are in the EU and also non- EU counties, on the top, as concerning the causes of morbidity and mortality. The analysis of the ECG is widely used for diagnosing many cardiac diseases, ischaemic heart diseases and arrhythmias. Most of the clinically useful information carried by the ECG is found in the morphology of the QRS complexes and in the T wave, measured as amplitude, deformations and duration. The ECG signal is characterized by a cyclic occurrence of patterns with different frequency content (QRS complexes, P and T waves). The QRS complex is the must characteristic waveform of the ECG signal, reflecting the left ventricular depolarization, as expression of the electrical activity within the heart during the ventricular activation. Its shape, duration (0.6 1 sec.) and time of occurrence provide valuable information about the current state of the heart.

2 1144 Cardiologists can use features of these signals to obtain important data about the clinical condition of their patients. These features are reflected by the morphology and duration of the individual waves of the ECG (P, QRS complex, and T waves). Since from the clinical (ex. cardiologists, other specialties) point of view, the ECG analysis it is a milestone in the assessment of a patient, we consider the clinical criteria for determining the starting points and endpoints of the P wave, QRS complex and T wave as essential. But in the mean time, we consider also that in the body surface ECG lays more information. From this point of view, we used in our paper, the wavelet transform as an alternative method for the clinically ECG analysis. During the last years, wavelet transform has proven to be a valuable tool in many application areas for analysis of nonstationary signals, and the ECG in particular. The wavelet transform is two-dimensional in time and frequency, and allows data in both domains to be analysed at the same time. The wavelet transform provides a time frequency representation of the signal that offers a graphical representation, spectrogram, of the ECG signal, at different scales with different resolutions. 2. Method The wavelet transform is a suitable tool to analyse the ECG signal, which is characterized by a cyclic occurrence of patterns with different frequency content (P wave, QRS complex, T wave). In our study, that was performed at the Informatics Department of the County Hospital No1 Timisoara, Romania, we analysed ECG signals obtained from the databases (i.e. MIT-BIH Arrhythmia, ESC databases). For this purpose we selected ECGs in sinus rhythm, with normal QRS duration (<= 120 ms) at different values of the heart rate and also ECGs from the congestive heart failure databases, in which we analysed ECGs with QRS > 120 ms duration, i.e., left bundle branch block, anterior myocardial infarction. The sampling frequency of those signals is 250 Hz. We u00sed the Matlab 6.5 on Windows 2000 Professional ; using the wavelet toolbox from the Wave menu performed the wavelet transform. Our study was performed in the light of the assessment of ECG signals from the medical point of view. We are interested to detected after wavelet transform, ECG like waves, which are composed of slopes and local maxima (or minima) at different scales, occurring at different time instants within the cardiac cycle. The transition in the input ECG signal corresponds to local maxima in the decomposition modulus at different scales. The frequency content of the ECG characteristic waves is different, so they are distinguished at different decomposition scales. The wavelet transform is designed to give good time resolution and poor frequency resolution at high frequencies, and good frequency resolution and poor time resolution at low frequencies. This approach is useful for ECG signals; signals with high frequency components for short durations, and low frequency components for long durations. The wavelet transform is a decomposition of the signal as a combination of a set of basis functions, obtained by means of dilation (a) and translation (b) of a single prototype wavelet; there are several wavelet functions (mother wavelet with different properties) like Morlet or Mexican Hat wavelets or complex frequency B spline wavelets that we are used in our study (figure 1).

3 1145 Figure 1 - Continuous wavelet transform. Mexican Hat wavelet. Spectrogram. Wavelet analysis is done by breaking up of a signal into a shifted and scales version of the original wavelet. We can define a continuous wavelet transform (CWT) as the sum overall time of the signal multiplied by a scaled and shifted version of the wavelet function. From a one-dimensional input signal, in our case the ECG signal, the continuous wavelet transform is a two-dimensional function of a scale parameter (a 1/frequency > 0) and a translation parameter (b=time localization), at which the signal is analysed (figure 2). Figure 2 - Continuous wavelet transform in congestive heart failure. Mexican Hat wavelet 3. Results In our study we used Morlet, Mexican Hat and Complex frequency B spline wavelets. The Morlet family wavelets have a high frequency resolution and the Mexican Hat wavelets family has a good time resolution, conversely the Complex frequency B spline wavelets describe better the spectrogram of the ECG signals. Consequently, we analysed the morphological characteristics and the position of the ECG signal components (P wave, QRS complex, T wave) in normal sinus rhythm and in ECGs of patients with congestive heart failure (figure 1&2). The greater the scale factor a is the wider is the basis function and consequently, the corresponding coefficient gives information about lower frequency components of the signal, and vice versa. In this way, the temporal resolution is higher at high frequencies than at low frequencies (figure 3).

4 1146 Figure 3 - ECG decomposition with Complex frequency B spline wavelet in congestive heart failure patients. After decomposition the original signal is reconstructed. The scale factor a and/or the translation parameter b can be discretized. The usual choice is to follow a dyadic grid on the time-scale plane: a = 2k and b = 2kl. The transform is then called dyadic wavelet transform (figure 4). Figure 4 - Dyadic wavelet transform, a = 26. Visualization of the QRS complex energy spectra. We consider that the energy of the QRS complex usually is highest at scale 6 (a = 26). Using of other types of wavelets, like Gaussian, Daubechies, or even Morlet wavelets, they will induce distortions in the decomposed signal. We made also correlations between the duration of the QRS complexes and the power spectral density (PSD) parameters in some of the studied ECG signals (figure 6). As measure of the PSD we used the pmusic expression, from the signal processing tool of Matlab Discussion and Conclusions As we mentioned above, the ECG signal contains components with high frequencies, with short duration and low-frequencies components with long duration. For ECG signal processing performed by the CWT, the most useful wavelet is the Mexican Hat wavelet, since this type of wavelet does not induce alterations in the basic signal. In relation with the type of the wavelet that we use to decompose an ECG signal, we notice, after CWT, the W max wave as a positive maxima that correspond to a negative minima (W min ) reflecting the

5 1147 QRS complex. The delay between the W max of the decomposed ECG signal and the original signal is depending on the scale for decomposition (figure 5). Figure 5 - Dyadic wavelet transform of an ECG signal, the delay is depending on the scale (a = 26). Some wavelet types are able to generate some artificial waves in the morphology of the original signal as seen in figure 1, 4, and 5. Analyzing these artificial waves, from medical point of view, they appear to be an amplified Q wave and notches on the T wave. Those amplified signals could offer data for analysing the significance of the duration and the morphology of these new waves in relation to ischaemic heart diseases, atrio-ventricular conduction duration and pathways and with the autonomic control of the heart function. Since our study was made from the medical point of view, and has not impose to be an automatic detection method, its seems to be useful to compare the obtained data, basically the ECG spectrogram and the CWT parameters, with other parameters, like the power spectral density of the studied ECG signals. Measuring the QRS complexes duration, and the power spectral density parameters, in the light of former works that studied the relation between the autonomic tone and heart rate variability parameters, we can observe that in condition in which the QRS complex is wide (>120 ms), like left bundle branch block, myocardial infarction, the duration of the QRS complex is correlating well with absolute value of the power spectrum density parameters (Table 1). Long duration of QRS complexes seems to be well correlated with PSD parameters that express very high frequencies and are under sympathetic control. Table 1 - The correlation between the QRS duration (ms) and the PSD parameters. QRS complex duration (ms) ms 2 x10 3 /Hz ms 2 x10 3 /Hz r: -0.66; p: 0.01 Recent studies explores time-frequency methods for pattern recognition in the context of a relevant clinical problem in cardiology; the identification of high-risk patients by analysing the signals through surface electrocardiogram (ECG). Concerning this problem, cardiologists have focused their interest in determining what provokes the onset of ventricular fibrillation,which is almost always preceded by an episode of ventricular tachycardia. This early detection of such a phenomena could eventually help to reduce the number of patients who are predisposed to sudden cardiac death. To analyse the

6 1148 characteristics of these cardiac arrhythmias,a Continuous Wavelet Transform (CWT) was used in order to retain both temporal and spectral information. Results have shown that wavelets have a great potential in the field of biomedical signals processing. In conclusion, our study proves the value of a mathematical technique in the field of the biomedical science. Even if we used a medical determination of the starting points and endpoints of the component waves of the ECG, we consider that we have presented a valuable tool for research and clinical practice. Our work is suitable to analyse nonstationary signals, especially physiological signals, like the ECG, in various conditions. The wavelet transform offers an insight of the ECG signals as an alternative method to Fourier transform. It seems important that parameters like the duration of the QRS complex could correlate with spectral parameters of the PSD and the continuous wavelet transform, although more complicated mathematically than other techniques provides a rich description of the ECG signals. 5. References [1] Antoine JP, Vandergheynst P, Murenzi R. Two-dimensional directional wavelets in image processing. Int J Imaging Sys and Tech. 1996; 7: [2] Ishikawa Y. Wavelet Theory-Based Analysis of High-Frequency, High-Resolution Electrocardiograms: A New Concept for Clinical Uses. Progress in Biomedical Research, 2002: Vol. 7, No. 3; [3] Mallat S. Wavelet Tour of Signal Processing, 2 nd ed. San Diego: Academic Press. 1998: , [4] Marco A Reyna-Carranza, Raimon Jane-Campos. Análisis Multi-Wavelet para la detección de conductividad ventricular anormal en señales ECG de alta resolución. Revista Biomédica 2001; 12: [5] Moga M, Moga VD, Luca CO, Mihalas Gh. Wavelets as method for ECG signal processing. Timisoara Medicala [6] Morlet D, Couderc JP, Touboul P, et al: Wavelet analysis of high-resolution signal averaged ECGs in postinfarction patients: Role of the basic wavelet and of the analysed lead. Int J Biomed Comput. 1995; 39: [7] P.W. MacFarlane. Recent developments in computer analysis of ECGs., Clinical Physiology, Vol. 12 (1992), pp [8] Toledo E, Gurevitz O, Hod H, Eldar M, Akselrod S. Thrombolysis in the Eyes of the Continuous Wavelet Transform. Computers in Cardiology 2002; 29: Address for correspondence Mariana Moga, V.D., County Hospital Timisoara, Romania, mvmoga@yahoo.com