**2.6.2.5 Classification rate for the hybrid technique**

### **Definitions**

232 Recurrent Neural Networks and Soft Computing

Fig. 2.2. The effect of changing (a) the learning rate, (b) the momentum constant, and (c) the middle layer size, on the classification rate of the fetal heartbeats with maternal contribution from transabdominally-measured ECG signals and employing TOC diagonal slices and their templates to be matched using a single-hidden-layer perseptron back-propagation with momentum. Segment length is 250 msec each. The optimised parameters are: learning rate =

Each one of the four transabdominal ECG segments (Data length = 250 msec) has ten corresponding templates used for matching. An optimised cubic Volterra structure is employed to synthesise the four transabdominal ECG segments and the corresponding

The classification rate is 100% for maternal QRS-complexes using the TOC template matching technique with single-hidden-layer classification. To calculate the maternal heart rate an auxiliary method to pinpoint the R-wave employing an adaptive thresholding has been used. Note that this is not accurate when one deals with deformed QRS-complexes in heart patients. The data obtained include all mothers' ECGs exhibiting normal-to-the-patient QRS-complexes. The instantaneous maternal heart rate is calculated by dividing 60 by the Rto-R interval (in seconds). The application of this auxiliary routine leads to a maternal heart

0.8, momentum constant = 0.9, and middle-layer size = 5 x 5.

**2.6.2.3 Cumulant matching of the fetal heartbeats** 

**2.6.2.4 The maternal heartbeat classification rates** 

rate with an accuracy of 99.85%.

templates.


Table 2.1 shows the fetal heart detection quality and classification rate using transabdominally-measured ECGs and their respective TOC diagonal or wall slices with and without linearisation. The combined diagonal and wall slices improve the classification rate by about 1% over and above that achieved by either slice. A further improvement of about 1% is achieved by using two off-diagonal and off-wall slices. A second-order Volterra synthesiser results in a higher detection rate of 83.49%.

The highest achievable classification rate for non-invasive fetal heartbeat detection using the first hybrid system is 86.16% when a third-order Volterra synthesiser is employed in conjunction with single-hidden-layer classifiers. Note that the classification rate for coincident maternal and fetal QRS complexes is 0%. The classification rate of non-coincident maternal and fetal QRS-complexes is 95.55%.


Table 2.1. Fetal heart detection quality and classification rate using transabdominallymeasured ECG and their respective TOC diagonal or wall slices 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.

Detection and Classification of Adult and

The bispectrum, n = 3, is defined as:

bispectrum is of the order of N3.

Hz will help to detect these peaks.

electrode ECG 250 msec window.

where 312 (,) *<sup>x</sup> <sup>c</sup>* 

Fetal ECG Using Recurrent Neural Networks, Embedded Volterra and Higher-Order Statistics 235

Linearisation is a key step in the signal processing and it is applied using an optimised third-order Volterra synthesiser to all the results included. Fig. 3.1 depict dual-band-pass filtered bispectra and their contours normalised to the maternal QRS-complex spectral peak for the transabdominally-measured ECG segments I, II, III, and IV. Segment I: predominantly maternal QRS-complex, segment II: the first fetal heartbeat with maternal contribution; segment III: QRS-free ECG, and segment IV: the second fetal heartbeat with maternal contribution. The dual-band-pass filter consists of two fifth-order Butterworth filters with cut-off frequencies of 10 Hz to 20 Hz, and 25 Hz to 40 Hz, respectively, a passband attenuation of 0.5 dB, and a stop-band attenuation larger than 70 dB. The sampling rate is 500 Hz. Optimised Kaiser weighting coefficients are used for the fetal and maternal ECGs to enhance their spectral peaks at 30 Hz and 17 Hz, respectively. The Kaiser windows are centred at frequencies of 15 Hz, 16 Hz, 17 Hz, 18 Hz, and 19 Hz for the maternal QRS-complex, and at frequencies of 28 Hz, 29 Hz, 30 Hz, 31 Hz, 32 Hz, 33 Hz, 34

Fig. 3.1 (I) shows the maternal QRS-complex principal bispectral peaks and contours centred at the frequency pairs (18 Hz, 5 Hz) and (18 Hz, 16 Hz). These maternal frequency pairs with a frequency peak at 18 Hz slightly deviate from the actual frequency of 17 Hz (Rizk et al., 2000), which is due to the BIC bias. The maternal optimised Kaiser window centred at 18 Hz will help to detect this deviated peak. Fig. 3.1 (II) shows the first fetal heartbeat principal bispectral peaks and contours at the frequency pairs (30 Hz, 5 Hz), (30 Hz, 18 Hz), and (30 Hz, 30 Hz). The fetal optimised Kaiser window centred at 30 Hz will help to detect these peaks. Note that these peaks are sharp. Fig. 3.1 (III) shows the QRS-free ECG bispectral peak and contours centred at the frequency pair (27 Hz, 15 Hz). Note that the BIC of the QRS-free ECG is at approximately -12 dB which is 3 dB and 6 dB lower than that of the first and second fetal heartbeats, respectively. Fig. 3.1 (IV) shows the second fetal heartbeat principal bispectral peak and contours centred at the frequency pairs (30 Hz, 5 Hz), and (30 Hz, 28 Hz). The fetal optimised Kaiser window centred at 30

The variance of the BIC is defined as the expected value of the squared difference in frequency (in Hz) between the computed BIC of the 250 msec flag window of the transabdominal ECG signal and the computed BIC from the synchronised fetal scalp

 

is the third-order cumulant sequence. The computational complexity of the

1 2

 

**3.3 Typical examples of bispectra and their contours** 

Hz, 35 Hz, 36 Hz, 37 Hz, and 38 Hz for the fetal heartbeat.

**3.4 Estimation of the bispectral contour matching variance** 

<sup>312</sup> <sup>312</sup> (,) (,) *x x <sup>j</sup> C c <sup>e</sup>*

 

11 22

( )

(3.2)

 
