Blind Source Separation Based on Pearson-ICA of Atrial Fibrillation Signal Separation

Transcription

1 Journal of Computational Information Systems 11: 7 (2015) Available at Blind Source Separation Based on Pearson-ICA of Atrial Fibrillation Signal Separation Gang LI 1, Dengao LI 2,, Haifang LI 1, Lingyan ZHOU 2 1 College of Computer Science and Technology, Taiyuan University of Technology, Taiyuan , China 2 College of Information Engineering, Taiyuan University of Technology, Taiyuan , China Abstract Atrial activity extracted from surface electrocardiogram (ECG) during atrial fibrillation (AF) episodes is the most important part of noninvasive research of electro physiologic mechanism of AF. When fast independent component analysis (FastICA) algorithms are used to extract AF wave from electrocardiogram signal (ECGs) of persistent atrial fibrillation, serious distortion exists in F wave QRST segment. To reduce this distortion, a new algorithm based on Pearson-ICA is proposed. This algorithm is based on negative entropy FastICA algorithm with the purpose of extracting atrial fibrillation signal, and removes mixed Gaussian signal mixed in atrial fibrillation through the Pearson system model. Through this method of extraction of F wave, the distortion of the QRST segment is significantly reduced. Keywords: Surface Electrocardiogram; Atrial Fibrillation; FastICA; Pearson-ICA 1 Introduction Atrial fibrillation (AF) is one of the most common arrhythmias diseases [1]. About a third of the arrhythmia is caused by atrial fibrillation. About 0.4% 1% of the general population may occurs AF, and the incidence statistically of 70 years old man is as high as 10%. In patients with heart disease, the patients with atrial fibrillation s mortality are 2 times as the patients with other disease. In addition, atrial fibrillation can also cause a stroke, heart failure [2] disease. In recent years, the research of atrial fibrillation has gained more and more attentions by the research community and medical workers. ECG is an important nondestructive measurement technology which can be used to study the cardiac electrical physiological. The typical ECG is composed for P wave and QRST wave group: P wave is mainly produced by atrial activity, QRST wave is mainly produced by ventricular Project supported by Natural Science Foundation of China (Grant No ); Scientific Research Project for the Returned Overseas Chinese Scholars of Shanxi Province (Grant No ); International Cooperation Project of Shanxi Province (Grant No ). Corresponding author. address: lidengao@tyut.edu.cn (Dengao LI) / Copyright 2015 Binary Information Press DOI: /jcis13223 April 1, 2015

2 2316 G. Li et al. /Journal of Computational Information Systems 11: 7 (2015) activities. The AF patients ECG shows the normal sinus P wave disappeared, and unequal size and different form atrial disorder excited waves (F wave) appeared. I, II, III and avf guide group are relatively obvious [3]. F and QRST wave are overlapped in time domain. The amplitude [4], spectrum of F wave [5] is widely used in the diagnosis of atrial fibrillation. At the same time, F wave has important meanings in AF mechanism [6, 7] and flutter location positioning [8] research. As discussed above, this paper takes F wave as the objective signal to extract the heart disease information. The remainder of this paper is organized as follows. Section 2 delineates related work of F wave extracting and ICA algorithm. Section 3 describes the Pearson-ICA blind source separation including the ECG signal analysis and Pearson system model for F wave extracting. Section 4 presents the experimental work, specifies the data results and the performances discussed in depth. Section 5 summarizes the validation of the complete system, concludes and outline future work. 2 F Wave Extracted by ICA Ventricular electrical signals and atrial electrical signals accord with transient superposition model in the body [9], and satisfy the application of ICA s three assumptions: the source signals can have a Gaussian source commonly; each output signal are linear mixed from source signal s instantaneous linear mixed; each source signal are mutual independence. F wave can be extracted by ICA, shown as Fig. 1. Fig. 1: Block diagram of ICA algorithm for F wave extraction X means twelve lead electrical signals which are pretreated, and means corresponding separation vector of F wave. F wave can be separated by the following formula S F = W F X (1) However, there is a shortcoming in the ICA method extracting AF signal at present. During the ICA separating process, it mainly uses the signal s high order statistics, but the high order cumulant of Gaussian signal is zero, so the ICA can not separates Gaussian signal. So the basic condition is one of the source signals can be Gaussian source signal. If there are more than one the Gaussian source, the separation effection of ICA is poor, even failure. Atrial signal is sub-gaussian signal, but its kurtosis value is very low, closes to zero, so it can be regarded as

3 G. Li et al. /Journal of Computational Information Systems 11: 7 (2015) sup-gaussian signal [10]. Therefore, a disadvantage of the AF separation based on ICA method is that a certain amount of Gaussian signal (noise) will be mixed in the extracted AF signal. In this paper, a method based on ICA combines with Pearson system model is designed, to obtain more accurate F wave and reduce the atrial fibrillation signal s local distortion. 3 Blind Source Separation Based on Pearson-ICA A new method of Pearson-ICA blind source separation is proposed in this paper, it includes two steps, shown as Fig. 2. Fig. 2: Pearson-ICA based on blind source separation algorithm Step 1: Independent Component Analysis. The ECG signal can be taken as a linear instantaneous mixture of the ventricular signal, the atrial signal and the Gaussian signal [11]. In the extraction process of the AF signal, the ventricular signal and a Gaussian signal are the interference signals, and these signals need to be removed during the extraction procession. As the ICA extraction algorithm, the ECG signal is processed by ICA in the first step. ECG source signal is not directly separated ventricular signal and atrial signal, but divided into the ventricle source signal and non-ventricular source (atrial signal and Gaussian noise) at first [12]. Most energy of ventricular component in ECG is removed, and the remaining non-ventricular signal is left to second-step treatment. Due to the existence of the QRST wave group, the ventricular source signal s peak value is high. As the quasi- Gaussian signal, atrium signal s peak value is very close to zero, so the Kurtosis can be used as a distinguishing ventricular signal component and non-ventricular determination threshold value of the signal component. According to a large number of experiments, 1.25 is an appropriate threshold kurtosis, to remove QRST wave [12]. Step 2: Pearson model. When the number of Gaussian source signal is more than one, the signals separated by the ICA will be mixed in a certain Gaussian signals. In the AF signal practical application, the atrium signal can be correctly extracted, but Gaussian source signal is mixed, for example, thermal noise, etc. [13]. In this paper, the Pearson system model is used for the biased source signal or approximate Gaussian distribution to eliminate Gaussian signal which is mixed in separated signal. The Pearson System has a very extensive distribution, including asymmetric distribution family. It is more suitable for the asymmetric distribution and the distribution closed to Gaussian

4 2318 G. Li et al. /Journal of Computational Information Systems 11: 7 (2015) source signal separation [14, 15]. The Pearson system model is a four-parameter tuft distribution, the differential equations of the form P (y n ) = (y n a)p (y n )/(b 0 + b 1 y n + b 2 y 2 n) (2) where P (y n ) is a probability density function, P (y n ) is P (y n ) partial derivatives, a, b 0, b 1 andb 2 are the parameters of the distribution function. Another modification of the differential form P (y n ) = (a 1 y n a)p (y n )/(b 0 + b 1 y n + b 2 y 2 n) (3) a 0, a 1, b 0, b 1 and b 2 are distribution function parameters, and the advantages of this expression is, which can be 0. When Gaussian distribution belongs to the Pearson system, the mean value m and variance σ 2 satisfy Pearson system, the parameters a 0 = 12(σ 2 ) 3 m (4) a 1 = 12(σ 2 ) 3 (5) b 0 = 12(σ 2 ) 4 (6) b 1 = b 2 = 0 (7) From the formula (2), the cost function of Pearson system mode can be deduced as f(y n ) = (a y n )/(b 0 + b 1 y n + b 2 y 2 n). (8) 4 Experimentation and Discussion The method of simulation F wave generation introduced in the literature [16] is referred. The simulation of F wave is superimposed on the normal ECG to simulate the body surface ECG of patients with atrial fibrillation. The new proposed algorithm and traditional ICA method were used to extracte the analog ECG s F waves, and then compare the results of the test. Step 1: Initializing the separation matrix W, usually we take the unit matrix; selecting the most simple form of a diagonal matrix B as the identity matrix, and n = 1. Step 2: Whiten the observed signals to obtain the whitened observed signals X. Step 3: ICA decomposition, calculating the kurtosis value of the signal S after the separation. If the kurtosis values>1.25, we get the ventricular wave S F ; If the peak value of atrial fibrillation wave, mixed-signal and noiseare S M are got. Step 4: According to the current data y M = W T n S M. Calculate the second, third, and fourthorder matrix m 2, m 3 and m 4. Step 5: Calculating the nonlinear function g(y M ) g(y M ) = y 2 Msign(y M ) (9) Step 6: According to the second, third, and fourth-order matrix m 2, m 3 and m 4. When 2.5<m 4 <m , the nolinear function f(y M ) = (a y M )/(b 0 + b 1 y M + b 2 ym 2 ) is choiced.

5 G. Li et al. /Journal of Computational Information Systems 11: 7 (2015) Step 7: Calculate. Step 8: Use the following iterative algorithm to calculate the separation matrix W n+1. W + M+1 = W MG 1 M B (10) W M+1 = (W + M+1 (W + M+1 ) 1/2 )W + M+1 (11) Step 9: If W M+1 W M > ε, let M = M + 1, then turn to Step 4, otherwise, end algorithm. Fig. 3, Fig. 4, Fig. 5 are the results during the above experiment. Fig. 3: The simulation of the normal ECG signal and fibrillation atrial signal Fig. 4: Atrial fibrillation signal extracted by ICA algorithm Compare Fig. 4 and Fig. 5, the the distortion of the QRST segment is significantly reduced by our algorithm, which means the extracted AF signal by proposed algorithm has less distortion, the results are desired.

6 2320 G. Li et al. /Journal of Computational Information Systems 11: 7 (2015) Fig. 5: Atrial fibrillation signal extracted by our algorithm When atrial fibrillation hanppens, exact value of the F wave in body surface ECG is unknown. It is difficult to estimate whether the actual signal evaluation algorithm is effective. Nevertheless, we still try to use more macro indicators to measure the effect of various algorithms: AF signal spectrum concentration of SC, the performance index PI and the SNR as performance indicators, comparing the experimental results of the Pearson-ICA and ICA. Table 1: The performance index of Pearson-ICA and ICA algorithm in extracting F wave SC(%) P I SNR P earson ICA ICA In above table, the larger value of SC indicates the better separation effect; the smaller PI value signifies the better separation effect. And the greater SNR, the better the separation effect. From the experimental results, the separation of the Pearson-ICA algorithm is superior to the ICA algorithm. 5 Conclusion This article is based on ICA algorithm combined with the mathematical model Pearson, which is used to reduce the interference signal of Gaussian signal in atrial fibrillation. Through the experiment discovered, this algorithm can obtain more accurate signal of atrial fibrillation. By the way of two kinds of methods of simulation signal extraction, the new algorithm extracted F wave has less distortion, faster convergence speed, easy to atrial fibrillation signal extraction. References [1] Zeng Yujie, Wei Fengning. Atrial fibrillation anticoagulation therapy status quo and new progress [J]. Journal of Diseases of the heart and brain, 2009, 11 (12): (China). [2] FUSTER V, RYDEN L E, CANNOM D S, et al. ACC/AHA/ESC 2006 Guidelines the management of patients with atrial fibrillation [J]. Circulation, 2006, 48 (4): e149-e246.

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