**1. Introduction**

224 Recurrent Neural Networks and Soft Computing

Yu, H.; Chung, I.H. & Moreira, J. (2006). Topology Mapping for Blue Gene/L

ACM Press, New York, NY, USA, pp. 5264

Supercomputer, *Proceedings of the 2006 ACM/IEEE conference on Supercomputing*,

The fetal heart rate (FHR) is a useful tool in the assessment of the condition of the fetal before and during labour. Fetal Electrocardiography (FECG) (Sureau, 1996) uses noninvasive surface electrodes placed on the maternal abdomen is another tool for FHR recording (Sureau, 1996). The fetal signal is weak relative to the maternal signal and to the competing noise. Widrow et al. (Widrow et al., 1975) proposed an adaptive filtering and adaptive noise cancellation method to extract the FECG from the composite maternal ECG signal. Auto-correlation and cross correlation techniques (Van Bemmel, 1968) and spatial filtering techniques (Van Oosterom, 1986, and Bergveld and Meijier 1981) have been proposed. These methods require multiple maternal thoracic ECG signals. Other methods were proposed for the rejection of the disturbing maternal ECG signal (Sureau, 1996). The automated long-term evaluation of FECG is regarded as less robust than CTG. A failure rate of approximately 30% is quoted as an almost unanimous norm (Herbert et al., 1993). The advantage of FECG is that it can be implemented in small and relatively low-cost devices (Lin et al., 1997).

A proposed technique employing wavelet transform (Khamene and Negahadariapour, 2002) exploits the most distinct features of the signal, leading to more robustness with respect to signal perturbations. The algorithm is validated using high SNR data. Dynamic modelling has been proposed (Schreiber, and D Kaplan, 1996). The data has comparatively high SNR and the fetal heartbeats can be detected by an adaptive matched filter and requires much shorter data samples than the dynamic modelling. The dynamic modelling apparent success at high SNR is offset by the required lengthy data. Due to the beat-to-beat fluctuations of the shape and duration of the ECG waveform, the normal ECG cannot be considered to be deterministic. Determinism is found in adult and fetal ECGs for data lengths of 10,000 samples (Rizk et al., 2002). The independent component analysis (ICA) has been carried out under assumptions (Lathauwer et al., 2000), the validity of each has been challenged (Rizk et al., 2001).

Detection and Classification of Adult and

been developed (Zgallai, 2007).

x

performance with regard to fetal QRS-complex detection rates.

from a time sequence {y(k). The output of the filter is expressed as

1 i

N

1i

**2.3 LMF quadratic and cubic volterra** 

updates the weights as follows:

Fetal ECG Using Recurrent Neural Networks, Embedded Volterra and Higher-Order Statistics 227

c ),()}k(X),k(X),k(X{Cum)(r <sup>x</sup>

where r 2,1() and r 1,2() represent 1-d wall and diagonal slices, respectively. The former can be obtained from Eq. (2.1) by assuming 1 = 0. The later obeys the condition 1 = 2. Employing 1-d slices will have the effect of reducing the CPU time by reducing the complexity of the operations. The calculations of TOC slices are comparable to those of autocorrelation and take CPU time of approximately 1 msec unlike TOCs, which take 1 sec to calculate. For a sampling rate of 0.5 KHz and an FHR of the order of 120 bpm, a real-time system can be implemented. An algorithm which calculates any arbitrarily chosen off diagonal and off wall one-dimensional slice, and hence reduce the CPU time by 99%, has

Adequate knowledge of the TOC of both the maternal and fetal ECG signals must first be acquired in order to pave the way for fetal QRS-complex identification and detection. There are several motivations behind using TOC in processing ECG signals; (i) ECG signals are predominantly non-Gaussian (Rizk and Zgallai, 1999), and exhibit quadratic and higherorder non-linearities supported by third- and fourth-order statistics, respectively. (ii) Gaussian noise diminishes in the TOC domains if the data length is adequate (Nikias and Petropulu, 1993). It is possible to process the ECG signal in Gaussian noise-free domains. For ECG signals a minimum length of 1 sec is adequately long to suppress Gaussian noise in the TOC domains, whilst not long enough to violate Hinich's criterion of local stationarity (Brockett et al., 1988). In general, ECG signals are non-stationary in the statistical sense, but relatively short data can be successfully treated with conventional signal processing tools primarily designed for stationary signals. When dealing with individual cardiac cycles, nonstationarity is not an issue but when one takes on board the heart rate time series which is chaotic and multi-dimensional then it is not wise to assume stationarity for analysis purposes. (iii) In the TOC domain all sources of noise with symmetric probability density functions (pdfs), e.g., Gaussian and uniform, will vanish. The ECG signals are retained because they have non-symmetric distributions (Zgallai et al., 1997). (iv) ECG signals contain measurable quantities of quadratic and, to a lesser extent, cubic non-linearities. Such measurable quantities of non-linearity, if not synthesised and removed before any further processing for the purpose of signal identification and classification, could lead to poor

The Volterra structure is a series of polynomial terms (Schetzen, 1980) which are formed

xa)n(y ....xxa N

N

1i

Adaptive conventional Volterra is updated using the Least-Mean Squares (LMS) criterion. The LMS algorithm minimises the expected value of the squared difference between the estimated output and the desired response. A more general case is to minimise E{e(n)2N} (Wallach and Widrow, 1984). N = 2 is the Least-Mean-Fourth (LMF). The LMF algorithm

2 i,i

1ik1ik

(2.4)

2121

1i

1

1ik

1 2 <sup>11</sup>

3

2,1 (2.3)

This chapter investigates the application of recurrent neural networks to the detection and classification of ECG signals. Third-order cumulants, bispectrum, polyphase, and embedded Volterra are utilised. The chapter develops methodology for adult ECG detection using the higher-order statistics. It extends that to non-invasive fetal heartbeat detection, during labour. The work is also extended to classify adult heart abnormalities based on the phases of the higher-order statistics. The chapter is organised as follows; Sections 2 and 3 employ third-order cumulant slices and bispectrum contours, respectively, to detect adult and fetal ECG signals. Section 4 introduces a method of ECG abnormality detection using polyphase. Section 5 shows how third-order cumulants could be utilised for the detection of late potentials. Section 6 summarises the conclusions.
