Wavelet Based Fluctuation Analysis on ECG Time Series

In this paper the correlation behavior and multifractal properties of electrocardiogram (ECG) signals were investigated through the wavelet based fluctuation analysis method to classify patients and healthy subjects. For this purpose the ECG time series data of five patients suffering from congestive heart failure (CHF) and five healthy humanbeing were obtained from Physionet online database. From the results, we observe that the presence of persistent behavior and strong multifractal nature in all the time series. Also we found that the calculated Hurst scaling exponents distinguishes the healthy signals from patients with CHF. We suggest that this approach may be useful for diagnosis and prognosis of heart disease. Keyword: ECG signals, wavelet analysis, Hurst exponent, classification. INTRODUCTION Fractals analysis on natural time series has made tremendous applications in areas ranging from financial markets to physiological systems [1-4]. It characterizes the fluctuations dynamics through scaling laws. In recent years, the study of scaling and correlation behavior in time series analysis is an active area of research. Various methods have been developed to characterize the time series featuring irregular dynamics with sudden and intense bursts of high frequency fluctuations. Among those, rescaled range analysis [5], structure function [14], wavelet transform modulus maxima [8], average wavelet coefficient [9], detrended fluctuation analysis and its variants [6,7], detrended moving average methods and its variants [10,11], wavelet based fluctuation analysis methods [12,13] etc. were in use to study the correlation behavior and fractal characteristics in time series analysis [5-13]. These methods were applied in various fields ranging from finance, physiology, engineering and natural sciences [14-27]. A large number of studies have been carried out to analyze electrocardiogram (ECG) signals that provide information about cardiac activity and also in identifying the various heart diseases and heart abnormalities. Among those, the congestive heart failure (CHF) is a high risk disease which is triggered due to damaged heart valves, blocked blood vessels, excess toxic exposure etc. Treating patients with such disease is a challenging task for physicians to categorize the disease severity that in turn motivates the researchers in development of different methodologies to characterize the ECG signals. Until now, various studies have been carried out in analyzing the ECG signals using the methods such as Fourier power spectral analysis [28], detrended fluctuation analysis and its variants [29-34], cumulative variation amplitude analysis [35], Hilbert and wavelet transform based analysis [36,37], complex networks [38], permutation entropy [39-41], ordinal pattern statistics and symbolic dynamics [42] etc. In this paper, we investigate the correlation properties and multifractal behavior in the ECG signals using the recently developed wavelet based fluctuation analysis method for classification of patients and healthy subjects. For the purpose, we have obtained the ECG data of congestive heart failure (CHF) and healthy human-being from Physionet online database. In section 2 the information about the data and the wavelet based fluctuation analysis method are described and in section 3 we provide the results and discussion. The conclusion to our study is in section 4. DATA AND METHODOLOGY ECG data collection We have collected the ECG data of five patients suffering from congestive heart failure (CHF) and five healthy humanbeing from Physionet online database [43]. The obtained data was the filtered version of the original time series where the outliers (i.e. abnormal beats) were removed [44]. The measured RR interval (heart beat) is in seconds for each data set and its lengths ranges between 70,000 to 110,000 data points. The healthy human ECG was recorded from 2 male of age 32 and 45 and 3 female of age 20, 32, 20 where as the ECG of CHF patients were recorded from 5 male of age 71, 63, 48, 51, 61. Wavelet based fluctuation analysis method The procedure of wavelet based fluctuation analysis method is as follows: Let us assume the time series x(i), where i = 1, 2,...,N and N is the length of the time series. Step 1: (Initially L=1) Decompose the signal using the desired discrete wavelet filters belonging to Daubechies (Db) family which effectively capture the polynomial trend in a variable window size from the time series. The high-pass and low-pass coefficients represents about the fluctuations and the trend of signal respectively. Step 2: Discarding the high-pass coefficients perform the reconstruction only with the low-pass coefficients that provides the local trend of the signal. Now, the fluctuations can be extracted at each level by subtracting the trend from