**5.1 Background**

242 Recurrent Neural Networks and Soft Computing

The network has been optimised in terms of its learning rate, momentum constant, and hidden layer size to achieve the minimum mean-squared error. The optimum learning rate is found to be 0.2. The optimum momentum constant is found to be 0.2. The single-hidden-layer has an optimum dimension of 6 x 6. The input to the first layer is the bispectral contours of the four transabdominally-measured ECG segments. The network is trained using the BIC templates. During the training phase, the input to the network is four template patterns. These are the BIC of four segments from one transabdominal cardiac cycle. For example the first is the maternal QRS-complex BIC, the second is the first fetal heartbeat BIC, the third is the QRS-free ECG BIC, and the fourth is the second fetal heartbeat BIC. The network is trained over ten templates of each of the four segments. The training terminates when the worst error in all patterns in one pass is less than 0.1. Typically the average error will be in the range of 0.001.

The main motivations behind the use of HOS are their ability to (i) preserve the phase of the signal frequency components (ii) suppress Gaussian noise, (iii) characterise and separate motion artefact (Nikias and Petropulu, 1993), and other non-Gaussian low frequency components, and (iv) detect and classify non-linearities. HOS algorithms are employed to develop discriminant contour patterns in the multi-dimensional phase of the polyspectra (polyphase) of normal looking ECGs in outpatients having weariness and general malaise or have recently had suspected angina. Similar polyphase patterns have been found in the ECGs of acute myocardial infarct patients with or without diagnostic S-T segment and T-wave changes. The polyphase computation is done in milliseconds but a temporal window of 10 ECG cycles is necessary in each of the polyspectral averaging process. The polyphase patterns can be displayed every 10 seconds. A high resolution three-lead ECG is adequate for polyphase discrimination. The results of a pilot study show that this is a potential diagnostic technique. Particularly in those 50% Pre-Infarction Syndrome cases which show perfectly normal 12-lead ECGs and will not be identified early enough to prevent them from developing acute myocardial infarction (AMI), (Struebe and Strube, 1989). The standard 12-lead ECG has poor sensitivity for the early detection for (AMI). Only 40-50% patients presenting with AMI show S-T segment and T-wave changes on the initial ECG. The rest might not receive the benefit of acute interventional therapies in the first hours after the event. The application of HOS to ECGs has shown fruition in positively identifying ischemic heart diseases (Strube and Strube, 1989, Zgallai, 2011a, Zgallai, 2011b, and Zgallai 2011c). The methodology involved decomposing the ECGs into linear and several non-linear component waves prior to identification and classification. Methods of validation employed clinical diagnoses and other apriori clinical information spanned over a number of years. Using other HOS discriminant patterns, the focus is on the identification of coronary artery disease, solely from its polyphase contour patterns. Polyphase patterns are obtained using the standard three-lead ECG, a multi-channel low-noise amplifier, an interface card and a PC. Sampling frequency is 0.5 KHz and a resolution of 12 bits. Recurrent neural networks have been used to classify the patterns in Fig 4.1 c and d, respectively (**Rizk et al., 1999b**). The employed neural network has an input layer, a middle layer, and an output layer. The input layer has 64 neurons, the middle layer has 16 neurons, and the output layer has 8 neurons. The network size has been optimised using trial and error with an MSE threshold of

**3.9.2 Parameters of the single-hidden layer perceptron** 

**4. ECG abnormality classification using polyphase** 

0.001. The learning rate and momentum constant are, respectively, 0.7 and 0.9.

The relationship between myocardial infarction (MI) and short-duration high-frequency components occurring around the terminal end of the QRS complex in the cardiac cycle of

Detection and Classification of Adult and

adjacent one.

network.

**5.3 Design of the neural classifier** 

**5.3.1 Block adaptive weight adjustment** 

types of abnormalities.

third-order statistics adds more complexity to the network.

Fetal ECG Using Recurrent Neural Networks, Embedded Volterra and Higher-Order Statistics 245

pinpoint the high-level low-frequency QRS spectral peaks (LFQRSSPs) per cycle, but also performs the preliminary spotting of the low-level high-frequency late potential components over a range of frequencies from 100-250 Hz. Detection of late potential highfrequency spectral peaks is carried out off-line every 5 LFQRSSPs to allow appropriate segmentation between the R-R marking in the time domain processing which runs almost synchronisingly with the MUSIC routine. A detailed procedure for segmentation involves calculating the bicoherence squared and mapping a particular region for each individual segment to confirm existence of quadratic non-linearity before moving on to interrogate another segment or skip a few segments up to the next R peak. This controlled skipping helps to avoid the highly non-linear T wave of the present cycle and the P wave of the

The Volterra filtering can be used to partially suppresses motion artifact only in those cases of missing LFQRSSPs and the MUSIC routine is repeated over the same cardiac cycle for confirmation of the presence or absence of QRSs. This has been found to be necessary in extreme cases and in the absence of QRS waves (ventricular fibrillation). Offline calculations of the cumulant diagonal and wall 1-d slices are performed on those segments suspected of having LPs as depicted in Fig. 5.1. It is clearly seen that abnormality is manifested in the eminent petal pattern (a horizontal slice has a petal shape) in the cumulant domains. Five thousand cardiac cycles of normal and abnormal ECGs were put to the test. An arbitrarily chosen non-linear function modifies the envelope of the so-called 'petal pattern' to enhance its peculiarity against background artifact. The non-linear function is then sampled across the input layer of the neural

Fig. 5.2 shows the network preceded by a preprocessing unit which performs the task of determining a set of meaningful and representative features in the HOS domains. A sigmoid logistic function is used to describe the input-output relation of the non-linear device. The neural network is designed to classify two classes; normal and abnormal third-order cumulants. The combined use of skewness and kurtosis can provide more accuracy in difficult cases.The utility of the diagonal slice of the fourth-order cumulant can be of more help when used in the desired response for the third output. The use of higher than the

Initially the classification was attempted by feeding cumulant slices of short ST segments of the order of 10 to 30 samples at 500 Hz sampling rate. This attempt was 80% successful as the network missed low profile petal patterns with low levels of signal-to-noise ratios in their vicinity as a result of short data segmentation. A function was introduced to strengthen the relative magnitude of the discriminant cumulant slice features. The function is sampled across the input layer and its parameters (,) can be adaptively changed for each cumulant slice fed during the training phase which usually takes up to 10 modified cumulant slices every 1000 cardiac cycles. Obviously the shape of function can be changed to cater for other

the ECG has been investigated by a number of dedicated research workers (Gomis et al., 1997). The high frequency components are associated with late potentials (LPs) emanating from areas of delayed conduction and outlast the normal QRS period (80-100 msec). LPs are linked with malignant ventricular tachycardia (VT) after a myocardial infarction (dead zone or scar tissue in the ventricular muscle). The later is highly correlated with sudden cardiac death. Common methodology for detecting LPs in the time domain involves temporal scanning of the S-T region of the cardiac cycle and relies upon accurate identification of the QRS boundaries (Li et al., 1995). The detection problem is exacerbated by the fact that LP's are relatively weak (mv) and often below the noise floor. In the frequency domain, secondorder statistics can offer a limited success. The shapes of power spectra of normal and abnormal (malignant VT) ECGs are invariably broadly similar and without significant features above the noise floor, at approximately -70 dB (Rizk et al., 1998). LPs are essentially non-linear transient events (Gomis et al., 1997) and consequently interact with the inherent non-linearity of the cardiac waves as well as certain class of recursive non-linearly attributed to external factors such as motion artefact (Zgallai et al., 1997).

Previous work (Zgallai et al., 1997) showed that results obtained using HOS offer some empirical evidence that: (i) ECG signals contain intrinsic as well as quadratic and higherorder non- linearities, (ii) the QRS wave is predominantly linear non-Gaussian, the P and T waves are characterized by having quadratic and cubic non-linearities, (iii) the QRS wave can be totally resolved from the motion artifact in the bispectrum domains and (iv) disproportionately high-frequency non-linearity in the bicoherence squared is indicative of abnormality in an otherwise innocent looking ECG. However, non-linear filtering and a high resolution technique such as the spectral MUSIC incorporates an optimised window must be applied to a short duration data sample (without compromising the variance), prior to the application of HOS (Zgallai et al., 1997). Third-order Volterra filtering applied to raw data can be beneficial in isolating quadratic and cubic non-linearity in the higher-domains (Zgallai et al., 2007).

The higher-order statistical features are selected and enhanced using sampled weights of a non-linear function based on a priori information about distinguished abnormality signatures in the higher domains. The function is modified adaptively during the training of the neural network which employs ten 1-d cumulants every 1000 or less cycles per patient. After this the updated version of the function parameters are fixed over the next 1000 cardiac cycles. Subsequently, a simple neural network classifier based on a modified version (Jacobs, 1988, and Hush and Salas, 1988) of the back-propagation algorithms performs accurate LPs and even ischemic ECG classification (Zgallai, 2011 a, Zgallai, 2011 b, and Zgallai, 2011 c).
