Extraction of Fetal ECG from the Composite Abdominal Signal

Transcription

1 Extraction of Fetal ECG from the Composite Abdominal Signal Group Members: Anand Dari ( ) Venkatamurali Nandigam ( ) Utpal Pandya ( ) Abstract A wavelet transform-based method can be used to extract the fetal electrocardiogram (ECG) from the composite abdominal signal. This is based on the detection of the singularities obtained from the composite abdominal signal, using the modulus maxima in the wavelet domain. Modulus maxima locations of the abdominal signal are used to discriminate between maternal and fetal ECG signals. In this approach, at least one thoracic signal is used as thea prior to perform the classification. A reconstruction method is utilized to obtain the fetal ECG signal from the detected fetal modulus maxima. The proposed technique is different from the classical time-domain methods, in that the most distinct features of the signal is exploited, leading to more robustness with respect to signal perturbations. Index terms Fetus ECG, singular point, wavelet transform. I INTRODUCTION The analysis of the electrocardiogram (ECG) signal has been known as a fairly reliable technique for cardiac disease diagnosis. ECG, recorded from maternal abdomen, can in principle be used to monitor the electrical activity of the fetal heart during pregnancy period. However, fetal ECG signal has very low power and mixed with several sources of interference. These include the maternal ECG, maternal muscular and respiratory activity noise and power line interference. The ECG signals measured at the chest leads primarily contain information about the maternal ECG (MECG). Furthermore, it is known that the ECG signal energy at the abdominal leads, extracted in the latest gestation months, contains information about the fetus ECG (FECG), though the signal energy is typical small relative to that of MECG. By comparing the chest and abdominal composite signals, a method may be devised for extracting information about the FECG from the composite signal. This is highly desirable due to the noninvasive nature of the process. Different methods have been proposed for the detection and (or) extraction of FECG. These can be classified based on the principle signal processing methodologies that are employed. A method employing the auto-correlation and cross-correlation properties has been used. Linear weighted combination of signals from multiple leads, and adaptive filtering are used. Here a scheme based on the singular-value decomposition (SVD) is proposed 1

2 which exploiting various assumptions, these methods each use different signal features and (or) characteristics. The main drawbacks of these techniques are their underlying simplistic assumptions, namely the additive model for the composite signal and the assumed high correlation between the chest and the mother-component of abdominal signal profiles. In particular, the validity of the latter assumption can be questioned due to a variety of complex effects from the different body layers that each signal passes through [1]. 1) Fetus ECG II BACKGROUND THEORY ECG signal is a measurement of the electrical activity from the heart muscles, i.e., myocardiac. Intercardiac signals, generated by the action potentials of the different cardiac parts, pass through various body layers, and are finally picked up as the ECG signal by electrodes on the skin surface. It is important to note that the signal has to penetrate through a complex system, experiencing various effects. In a pregnant woman, the ECG signals are commonly measured at two locations; the chest and the abdomen (see Fig. 1). The FECG is commonly extracted from multiple leads information. One particular method involves making three chests (maternal) and five abdominal (composite) measurements.the abdominal leads pick up a composite signal, consisting of the contributions from both the MECG and the FECG. The energy of the latter has been estimated as less than one quarter of the total signal energy. The amplitude of FECG signals changes during pregnancy: it increases during the first 5 weeks, experiences a marked minimum toward the 3 nd week, and increases again afterwards []. Figure 1. (a) Lead locations of ECG signal measurements in a pregnant woman. (b) Sample examples of the signals from the chest leads (top four) and an abdominal lead (bottom) [1]. An ECG profile depends on the position where the signal is recorded. The different paths, from the heart to the various lead locations on the skin surface, can modify the intracardiac signal distinctively. The electrical activity of the heart can be modeled as being induced by a time-dependent current dipole, variable in both amplitude and

3 orientation. As a result, both assumptions of additivity and high correlation between the chest and the mother-component of abdominal signals become questionable. In fact, though the locations of the waveforms constructing a full cycle of the ECG (i.e., P, QRS complex, and T) remain relatively unchanged for various lead positions, the degree of resemblance varies drastically among the signal profiles. In order to extract the fetus signal from the composite signal robustly, it is desirable to employ those features of the signal that remain relatively invariant with respect to the lead position. ) Wavelet Transform The wavelet transform (WT) of a signal x() t is defined as where (ο) denotes the convolution operation, the basis function ψ () t is the so-called mother wavelet, and s is a scale factor. The input signal x() t and the output wavelet coefficients and L ( R ) W (, ) x s t belong to the measurable and square integral spaces, respectively. For applications in the discrete domain, the scale factor is chosen from the dyadic L ( R) s =,( Z) sequence, where Z denotes the space of integers. A sampled signal x( n) can be viewed as the representation of x() t at the scale, = 0 and the corresponding wavelet coefficients are denoted by W ( x s, n ). Time (or sample) and scale are the two dimensions of the wavelet representation. Choosing a wavelet function that optimally fits the signal depends on the application and the signal itself. There are several characteristics that should be considered. The first two are the ability to reconstruct the signal from the wavelet decomposition and to preserve the energy under the transformation. Another characteristic is symmetry, which is important in avoiding a drift of the information. The length of the wavelet filter depends on the regularity of the signal to be decomposed. For more regular signal the wavelet filter must be longer, the calculation time of the process increases and, in addition, the localization accuracy decreases [4]. In this application, a bi-orthogonal quadratic spline wavelet with compact support 1 and one vanishing moment is considered. The dyadic WT of a digital signal f( n) can be calculated with Mallat algorithm as follows [4] [7]. 1 S f n h S f n and W f( n) = g 1 ( ) ks f n 1 ( ) = 1 ( ) k k z k z Where S is smoothing operator and S 0 f( n) = d n, dn is the digital signal to be analyzed [7]. The Fourier transforms of the wavelet function of this type is given by, 3

4 sin( w / 4) ψ ( w) = w /4 where i = 1. The dyadic WT of a digital signal x( n) can be calculated by two filter banks (i.e., analyzing and synthesizing) which are implemented using the three discrete filters, hgk,, with Fourier transforms 3 / ( ) He e cos = / ( ) 4 Ge sin w = ie 4 () 1 He ( ) Ke ( ) = Ge ( ) The analyzing filter bank F consists of + 1 filters, as follows: a (3) G(e ) G(e )H(e ) F (e )= a -1 - G(e i w )H(e i w )...H(e ) -1 - i w i w H(e )H(e )...H(e ) = 1 = < J = J+ 1 (4) The wavelet coefficients of the signal x( n ) are the output of the high-pass filter, for J 1 F + a = 1, and band pass filters, for 1 J. The low-pass filter is used for calculating the low frequency component of the original signal x( n ), denoted by S ( J x, n ), which is needed for perfect reconstruction of x( n ). The above computation can be performed in the time-domain, by calculating the convolution between the signal x( n ) and time domain coefficients of the filter, denoted by f F a a 4

5 F(e )= s K(e ) K(e )H(e ) -1 - i w i w G(e )H(e )...H(e ) -1 - i w i w H(e )H(e )...H(e ) = 1 = < J = J + 1 (6) The synthesizing filter bank also consists of J + 1 filters, shown in (6). To reconstruct x( n) perfectly, the sequence of discrete signals, must be used, as follows : where f s denotes the time-domain coefficients of the filter with Fourier transform F s. The number of scales J is usually chosen to be log ( N), where N is the length of the discrete signal x( n ).Each filter in the analyzing and synthesizing filter banks is a FIR filter with a generalized linear phase. This alleviates the effect of noise due to the quantization of the wavelet coefficients. This type of wavelet has been proven to be the most appropriate for the detection of singularities and using them for the signal reconstruction. Singularity Detection with Wavelet Singularity detection is an important application of wavelet analysis. According to the reported research work of Mallat, when an edge appears in a signal, the local extrema of the wavelet transform of the signal correspond to the edge[].thus the edge can be determined by detecting the local maxim of a signal s wavelet Transform. We know that every uniphase wave, like the (a) or (b) waves in Fig. 1, corresponds to a positive maximum negative minimum pair of W f( n) at different scales. The wave rising edge corresponds to a negative minimum, and the dropping edge corresponds to a positive maximum at different scales. The moduli of these maxima or minima corresponding to the same edge are named as the modulus maximum line [5]. 5

6 Figure. The relation between the characteristic points of simulation waves and those of their WT's at different scales. The uniphase wave (a) is symmetric and T a = = 7 points. The uniphase wave (b) is not symmetric and T b - T a, = points. Complex (c) is symmetric and T c = T a = 7 points. Here waves (d) and (e), Td1 <Te1, Td < Te. Tel = = 7 points and Te = = points [6]. 3) Relation between the signal singularity and its WTs Signal singularities often carry the most important information. It is important to find the location of singularity and characterize the singular degree in signal processing. The singular degree is often described with the Lipschitz exponent [7]. On the pioneer work of Grossman, Mallat founded the relation between the WT's and singularities of signals.if wavelet ψ ( x) is the first derivative of a smooth function, then scale s is small enough, so the maxima of Wf s ( x) indicate the locations of sharp variation signal points and the function f ( x ) is Lipschitz α (0 α 1) < < over [, ] α constant A such that for all x [ ab, ], W f( x) A( ). III ALGORITHM FOR FETAL ECG EXTRACTION ab, if and only if there exists a Based on the previous discussions, there are two approaches in extracting the FECG from the composite ECG taken from an abdominal lead. As stated, this composite signal contains a strong maternal ECG component, the fetal ECG, and a considerable amount of noise due to muscular and respiratory activities, etc. This method uses at least one thoracic signal as the a priori information for the extraction procedure. The chest ECG with little/no contribution from the FECG is exploited to extract the a priori information about the modulus maxima locations of the maternal component existing in the composite signal, recorded by the abdominal lead. Thus, a minimum of two leads, i.e., one abdominal and one thoracic, must be used. The FECG extraction procedure is as follows [3]. 6

7 Step 1) The signals from the two leads are arranged as batches with arbitrary length N, the wavelet coefficients for each scale,1 log( N) are calculated, and the corresponding modulus maxima are found. Step ) Comparing the modulus maxima locations of the thoracic and abdominal at all the scales, the common ones, assumed to belong to the MECG, are discarded from the composite abdominal modulus maxima set. Step 3) The remaining modulus maxima set of the composite signal is used to reconstruct the FECG. For the step 1, the quadratic spline wavelet is employed. The modulus maxima in the wavelet domain are located by finding the maxima of the wavelet coefficients absolute values; see Fig. 3. In step, a method is devised to compare the modulus maxima locations accurately and robustly, by taking advantage of fuzzy membership functions. This method also accommodates the use of more than one chest signal, where available. In particular, it provides tolerance with respect to misalignments in the modulus maxima, from different leads at various scales, which do not coincide in practice. Figure 3. (a) Original signal. (b), (c), (d), (e), and (f)wavelet coefficients at scale,1 5 (g) Signal at the highest scale 5, which with the wavelet coefficients, are needed for a perfect reconstruction. (h), (i), (), (k), and (l) Modulus maxima of wavelet coefficients at scale,1 5 [1]. 7

8 For each of the maxima locations, we can define a triangular fuzzy membership function. The widths of the membership functions for different scales are varied, allowing more uncertainty at the higher scales. We can select a fuzziness width twice the sampling rate on each side of the modulus maxima at the lowest scale, and this proportionally varies with the scale. Integration of all available information from different thoracic leads can be done by calculating the union of the fuzzy sets associated with the modulus maxima locations of these signals. To describe the method more precisely, we define two-dimensional functions C µ (, n), for each thoracic signal C=1,..p, and a µ (, n), for the composite abdominal signal. These functions consist of triangular membership functions centered at all the existing modulus maxima (see Fig. 4). The maternal modulus maxima fuzzified locations are expressed by the union of the functions calculated for each thoracic signal c. Figure 4. Fuzzy reasoning method for detection of FECG modulus maxima [1]. (8) We can use c µ (, n) to mask out the maternal modulus maxima in the composite signal. 8

9 To do this, we determine the mask M m by applying the intersection operation to the thoracic and abdominal modulus maxima fuzzified locations. (9) The mask M m consists of crisp values in the interval [0,1] at modulus maxima locations of l the composite signal m, and it is zero elsewhere. Similarly, we define the fetal mask M that is derived from: (10) f The modulus maxima of the composite abdominal signal W l (, m ), are labeled as those l l belonging to the FECG, W (, m ) and the maternal component MECG, W (, m ), as follows: f a m (11) The above process is illustrated in the example of Fig. 4.For the step 3, the time-domain FECG signal is reconstructed from the modulus maxima. The flow chart in Fig. 5 depicts the various steps of the algorithm. Additionally, it is required to cancel out the effect of high-frequency noise from the power line and maternal macular activities. This can be done by applying the denoising algorithm introduced in [8], prior to the reconstruction. This method removes the noise modulus maxima, hypothesized to be the ones, whose amplitudes increase (on average) when the scale is decreased, or that do not propagate to larger scales. The low frequency noise introduced by baseline drift and maternal respiratory activity, which mostly affect the composite ECG at the higher scales can also be removed/ reduced. To do this, the low-frequency signal at the highest scale is zeroed out, in the FECG reconstruction process. This causes the reconstructed FECG to be built on zero base line. 9

10 . Figure 5. Flow chart of algorithm described above IV CONCLUSION The reconstruction of the fetal ECG from the maternal ECG signals recorded at chest and abdomen is possible by exploiting the information from the singular points of these signals. A wavelet transform-based approach has been undertaken to detect these singularities from the modulus maxima in the wavelet domain, to identify those belonging to the fetal signal, and to finally reconstruct the fetal ECG from its modulus maxima. The high performance that has been achieved is primary due to the fact that the very robust features of the ECG signals, namely their singular points, are exploited. Another benefit of this technique is the relaxation of the assumptions underlying alternative methods. 10

11 References [1] A.Khamene and S. Negahdaripour, A New Method for the Extraction of Fetal ECG from the Composite Abdominal Signal IEEE Trans. Biomed.Eng., Vol.47, pp , April 000, [] M. Jafari and J. Chambers, Fetal electrocardiogram extraction by sequential source separation in the wavelet domain IEEE Trans. Biomed.Eng.,Vol.5,pp , March 005. [3] Y. Datian, C. Yu and G. Qin, Wavelet analysis method for processing and recognition of abdominal fetal ECG waveform IEEE conference on electronics, circuits and systems,vol.3, pp , [4] B. Castro, D. Kogan and A. Geva, ECG feature extraction using optimal mother wavelet IEEE conference on electrical and electronic engineers in Israel 000, pp , [5] J. Sahambi, S. Tandon and R. Bhatt, Using wavelet transforms for ECG characterization IEEE Engg.Medicine and Biology.,Jan./Feb, pp , 005. [6] C. Li, C. Zheng and C. Tai, Detection of ECG characteristic points using wavelet transforms IEEE Trans. Biomed.Eng., Vol.4, January, pp.1-8,1995. [7] S. Mallat, Zero-crossings of a wavelet transform IEEE Trans. Inform. Theory, Vol.37, pp ,1991. [8] S. Mallat and S. Zhong, Characteization of signals from multi-scale edges IEEE Trans. Pattern Anal. Machine Intell., Vol.14, pp , July,