**3.8.1 The maternal QRS-complex classification rate**

238 Recurrent Neural Networks and Soft Computing

Fig. 3.2. The effect of changing (a) the learning rate, (b) the momentum constant, and (c) the middle layer size on the classification rate of the maternal QRS-complexes (l.h.s.) and fetal heartbeats (r.h.s.) from transabdominally-measured ECG signals using bispectral contours and their templates to be matched using a single-hidden-layer perceptron back-

propagation algorithm with momentum. Data length = 250 msec. The optimised parameters for the BIC classification are: learning rate = 0.2, momentum constant = 0.2,

and middle-layer size = 6 x 6. (Code: 5-1-100).

Table 3.1 shows a top classification rate of 100% for maternal QRS-complexes using bispectral contours for signal processing and single-hidden-layer perceptron classification. The 100% maternal QRS-complex classification rate has been achievable with or without linearisation. It makes no difference to the results. A brief description of the optimised parameters required for the linearisation process is given. To calculate the maternal heart rate an auxiliary method to pinpoint the R-wave is needed. For this application an adaptive thresholding method has been employed. Note that this is not very accurate when one deals with deformed QRS-complexes in heart patients. All maternal ECGs, however, exhibit normal-to-the-patient QRS-complexes. The instantaneous maternal heart rate is calculated by dividing 60 by the R-to-R interval (in seconds). The application of this auxiliary routine leads to a maternal heart rate with an accuracy of 99.85%.

*Parameters:* The second-order Volterra parameters are: filter length = 6, step-size parameters = 0.005, and 0.0004 for linear and quadratic parts, respectively, delay = 3. The third-order Volterra parameters are: filter length = 6, step-size parameters = 0.001, 0.0002, and 0.0004 for linear, quadratic and cubic parts, respectively, delay = 4. A dual-band-pass filter is applied to the bispectrum, the first has a band-pass of 10 Hz to 20 Hz and the second has a bandpass of 25 Hz to 40 Hz. Optimised Kaiser windows centred at frequencies of 15 Hz, 16 Hz, 17 Hz, 18 Hz, and 19 Hz for the maternal spectrum, and at frequencies of 28 Hz, 29 Hz, 30 Hz, 31 Hz, 32 Hz, 33 Hz, 34 Hz, 35 Hz, 36 Hz, 37 Hz, and 38 Hz for the fetal spectrum are used in both the power spectrum and the BIC.

#### **3.8.2 Fetal heartbeat detection quality and classification rate for the bispectral contour template matching technique**

Table 3.2 summarises the results of the fetal heartbeat detection using the power spectrum method (second-order statistics), and the bispectrum contour template matching technique. Optimised adaptive LMF-based second- and third-order Volterra synthesisers are employed. The power spectrum method has a classification rate of 71.47%. Using the second hybrid system, the classification rate increased to 87.72% without linearisation, and to 88.28% and 90.12% using second- and third-order Volterra synthesisers with LMF update, respectively. The second hybrid method has an improvement of 19% and 4% in the classification rate over and above that achieved with the second-order statistics and the TOC template matching technique, respectively. The classification rate of the coincident maternal and fetal QRS-complexes is 0%. The classification rate of non-coincident maternal and fetal QRS-complexes is 99.21%.

Detection and Classification of Adult and

Fetal ECG Using Recurrent Neural Networks, Embedded Volterra and Higher-Order Statistics 241

horizontally cut at a maximum number of 10 levels, a good quality discriminant picture can be made available for the neural network classifier. For example, it is very unlikely that maxima and troughs are missed because of any changes in their respective positions. Approximately 50,000 maternal cardiac cycles have been included in the analysis. The numbers of bispectral contours compound templates are 10 for the maternal chest, 10 for the fetal scalp, and 140 for the transabdominally-measured 250 msec segments, respectively. Each bispectral compound template is made of 10 horizontal templates at different levels.

The maternal transabdominal ECG signal is linearised using an optimised LMF-based secondor third-order Volterra synthesiser. The second-order Volterra synthesiser parameters are: filter length = 6, step-size parameters = 0.005, and 0.0004 for linear and quadratic parts, respectively, delay = 5. The third-order Volterra synthesiser parameters are: filter length = 6, step-size parameters = 0.001, 0.0002, and 0.0004 for linear, quadratic and cubic parts, respectively, delay = 5. The transabdominal ECG signal is segmented into four segments containing; (I) The maternal QRS-complex, (II) the first fetal heartbeat with maternal contribution, (III) QRS-free ECG, and (IV) the second fetal heartbeat with maternal contribution. To segment the transabdominal ECG signals, the window length is carefully chosen to; (i) Yield an acceptable upper threshold of both the deterministic and stochastic noise types inherent in the higherorder statistics of the ECG signals encountered, and (ii) allow the detection of one, two, three, or

The classification procedure starts by matching the bispectral contours of the segments to those of the templates until the first and the second maternal QRS-complexes are detected and their R-waves are pinpointed. The maternal heart rate is accurately calculated from the knowledge of the current and previous R-wave positions. Then, the search for the fetal heartbeat starts at 50 msec before the first maternal R-wave and continues until the second maternal R-wave is reached. Although the ECG bispectral contour template matching technique is very effective in detecting the occurrence of the fetal heartbeats as a whole in the frequency domain even when it is completely buried in noise, it cannot locate the R-wave in the time domain over a window length of 250 msec. However, the maternal heartbeats can be measured fairly accurately and calculate the instantaneous heart rate for the mother. Hence, by counting the number of fetal heartbeats that have occurred between two successive maternal

R-waves, one can easily calculate the averaged FHR within the maternal cardiac cycle;

**3.9.1 The effect of window length on the bispectral contour variance** 

100 bpm. The latter has resulted in an 30% decrease in segment size.

The average FHR = MHR x Number of FHBs / number of maternal heartbeats the instantaneous maternal heart rate is previously known with some degree of accuracy, and the relative fetal to maternal heartbeat is also known within the maternal cardiac cycle. Hence, the averaged fetal heart rate can be calculated within each maternal cardiac cycle.

The variance of the bispectrum for the optimum window length of 250 msec with FHB occurrence ranges from 0.47 to 3.3 with an average value of 1.716. The variance of the bispectrum is smaller than that of the third-order cumulants. A further 15% increase in the variance of the bispectrum is due to an increase in the maternal heartbeat from 60 bpm to

Starting from a normalised 0 dB and going down in steps of 1 dB each to a – 10 dB.

four fetal heartbeats (FHBs) within one maternal transabdominal cardiac cycle.

*Parameters:*The second-order Volterra parameters are: filter length = 6, step-size parameters = 0.005, and 0.0004 for linear and quadratic parts, respectively, delay = 5. The third-order Volterra parameters are: filter length = 6, step-size parameters = 0.001, 0.0002, and 0.0004 for linear, quadratic and cubic parts, respectively, delay = 5. A dual-band-pass filter is applied to the bispectrum, the first has a band- pass of 10 Hz to 20 Hz and the second has a bandpass of 25 Hz to 40 Hz. Optimised Kaiser windows centred at frequencies of 15 Hz, 16 Hz, 17 Hz, 18 Hz, and 19 Hz for the maternal spectrum, and at frequencies of 28 Hz, 29 Hz, 30 Hz, 31 Hz, 32 Hz, 33 Hz, 34 Hz, 35 Hz, 36 Hz, 37 Hz, and 38 Hz for the fetal spectrum are used in both the power spectrum and the BIC.


Table 3.1. The classification rate for the maternal QRS-complex using maternal transabdominally-measured ECGs and their respective power spectrum and bispectral contours.


Table 3.2. Fetal heart detection quality and classification rate using transabdominallymeasured ECG and their respective power spectrum and bispectral contours with and without linearisation. The total number of fetal heartbeats is 120,000 and the total number of maternal ECG recordings is 30. The performance was assessed against synchronised fetal scalp heartbeats. All mothers were during the first stage of labour at 40 weeks of gestation.
