**7. Conclusion**

248 Recurrent Neural Networks and Soft Computing

ECG signals are predominantly non-Gaussian (Rizk and Zgallai, 1999 and Rizk et al., 1995), and exhibit quadratic and higher-order non-linearities supported by third- and fourth-order statistics, respectively. ECG signals do contain measurable quantities of quadratic and cubic non-linearities. Such quantities if not synthesised and removed before any further processing for the purpose of signal identification and classification could lead to poor performance with regard to fetal QRS-complex detection rates. The non-linearity in the ECG signal can be detected using the bicoherence squared. The bicoherence squared has peaks at the frequency pairs of (6 Hz,15 Hz) and (14 Hz,14 Hz) for the fetal scalp cardiac cycle, (15 Hz,15 Hz) for the maternal chest cardiac cycle, and (7.5 Hz,7.5 Hz) for the maternal transabdominal cardiac cycle. These bicoherence peaks support non-linearity (Zgallai, 2007). There is a general consensus that individual cardiac cycles are locally stationary. However, when applying a highly dimensional signal such as the transabdominal ECG that have several individual non-linear and deterministic signals overlapping both in the time and frequency domains, all coexisting in a cocktail of noise and motion artefact, it is prudent to re-examine the validity of the stationarity assumption in relation to such signals. It is only natural to expect that the proximity of two non-linear signals such as the maternal and fetal QRS-complexes would result in non-linear (quadratic and higher-order) coupling and this in turn would invoke non-stationarity. The bispectral OT region is insepcted (Nikias and Petropulu, 1993) for the maternal bispectral contour maps at a level of -30 dB. When the two R-waves of the maternal and fetal QRS-complexes are separated by 200 msec, the resultant bispectrum does not support the OT region (Zgallai, 2007). However, the situation is totally different when the two R-waves are as close as 35 msec. The OT region of the bispectrum is fully occupied and non-stationary (Zgallai, 2007). Hence, conventional signal processing techniques to separate the maternal and fetal QRS-complexes cannot be used. This problem has been adequately solved by linearising (at least removing quadratic coupling) the

transabdominal signal before attempting to separate individual QRS-complexes.

high as 42 Hz (Zgallai, 2007).

method is within the range of -0.1 to +0.1.

Correlartion-based second-order statistics do not show any distinguishable features that could be used to differentiate between maternal QRS-complex, fetal heartbeat with maternal contribution, and QRS-free ECG contributions. The FFT method reveals a fetal scalp electrode ECG principal spectral peak at 30 Hz (Zgallai, 2007). The FFT method for the transabdominal cardiac cycle reveals the maternal principal spectral peak of 15 Hz (Zgallai, 2007). However, the FFT does not clearly show fetal spectral peak from the segmented transabdominal signal. There could be a shallow peak as low as 28 Hz or a shifted peak as

Statistical analysis of ECG data, including Pearson's correlation analysis and higher order moments have been carried out (Rizk and Zgallai, 1999). The value of Pearson's productmoment correlation coefficient for both the third-order cumulant and the bispectral contour

The Receiver Operating Characeteristics (ROC) analysis has been used to statistically analyse the results of the two propsoed detection methods, third-order cunulant and bispectral contour, compared to the second-order statistics method. The Area Under Curve (AUC) has been used as a measure for diagnostic accuracy and discriminating power. The second-order statistics-based, third-order cumulant slice, and the bispectral controue

**6. Statistical analysis of ECG detection methods** 

The sensitivity, specificity and classification rate for the third-order slice cumulant matching hybrid system have been calculated . The technique has been evaluated for diagonal, wall, or arbitrary TOC slices, employing both the LMF-based quadratic and cubic Volterra filters. The results indicate that a linear combination of diagonal and wall slices of the TOC can improve the detection rate by up to 1% over and above the 77.8% obtainable using only either slice. Using two more arbitrary slices off-diagonal and off-wall would result in a further improvement of up to 1%. Using two slices instead of only one results in an two-fold increase in the CPU time of 1 msec using Unix WS. Further improvement of 6% to 8% is attainable with maternal transabdominal ECG signal linearisation employing second- and third-order Volterra synthesisers, respectively. Based on the first hybrid system using TOC slices for signal processing and subsequent single-hidden-layer classification, 100% and 86.16% classification rates have been achieved for maternal QRS-complex and fetal heartbeats, respectively. Note that the classification rates for coincident and non-coincident maternal and fetal QRS-complexes are 0% and 95.55%, respectively. The remaining undetected 13.84% fetal heartbeats include 9.8% overlap with the maternal QRS-complexes and 4% occur during depolarisation of the maternal T-waves. Those events unavoidably lead to significant distortion of the fetal TOCs. This means that the cumulant signatures will not be close to the TOC template signature stored in the database. Examples of false negatives and false positives have been found in the following cases, respectively, (i) a fetal heartbeat with maternal contribution TOC diagonal slice was wrongly matched to a QRSfree ECG TOC diagonal slice template, and (ii) a QRS-free ECG TOC diagonal slice was wrongly matched to a fetal heartbeat with maternal contribution TOC diagonal slice template.

Results obtained for the bispectral contour matching hybrid system from 30 cases using the non-invasive transabdominally-measured ECG signal, with the simultaneous fetal scalp electrode ECG signal as a reference, show that the method has a classification rate of 100% for normal, healthy maternal QRS-complexes and 90.12% for fetal heartbeats. It has been

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shown that an improvement of 1% to 3% is attainable with ECG signal linearisation employing second- and third-order Volterra synthesisers, respectively. Conventional methods (based on the power spectrum) of fetal heartbeat detection have a success rate in the range of 70%. The second hybrid system has a significantly higher classification rate. The classification rate of fetal heartbeats for non-coincident maternal and fetal QRScomplexes is 99.21%. The classification rate of fetal heartbeats for coincident maternal and fetal QRS-complexes is 0%. This means that the hybrid bispectral contours technique fails to resolve the fetal beat when both the mother and fetal QRS-complexes are synchronised. The bispectral contour template matching technique improved the classification rate by approximately 4% over and above that of the third-order cumulant template matching technique. The difference in performance is not due to better resolvability of the latter over the former in the case of coincident maternal and fetal QRS-complexes, as both techniques fail in this respect. But, it is due to the fact that the BIC template matching technique can resolve a few of the fetal QRS-complexes occurring within the T-wave region of the mother.

Non-invasive classification of a particular type of ECG abnormality, late potentials, was investigated. This has been achieved by the prudent use of their third-order cumulant 1-d slices. A four-layer neural network classifier based on modified back-propagation algorithm and incorporating adaptive feature enhancement weights applied to its input layer during its learning phase has been successfully tested. Classification rate obtained from 3000 cardiac cycles of normal, confirmed, and suspected abnormal subjects is 90%. In a separate study conducted on the same data a sophisticated recurrent back-propagation network achieved less that 80% success rate. However, the instability issues of the latter network have not been fully investigated.
