**2.5.4 Averaged fetal heart rate calculation**

The instantaneous fetal heart rate is calculated by measuring the interval between two successive R-waves. This requires pinpointing accurately the R-point of the QRS-complex. Although the ECG TOC template matching technique is very effective in detecting the occurrence of the QRS-complex as a whole even when it is completely buried in noise, it cannot locate the R-wave over a window length of 250 msec which satisfies the criterion for the variance threshold. In most transabdominal ECG recordings (85%), the fetal QRScomplexes cannot be seen as they are completely masked by other signals and motion artefact. This obscurity accounts for the lower success rate of fetal heartbeat detection in other assessed fetal heartbeat detection techniques (Sureau, 1996). The adult heartbeats can be measured accurately and the instantaneous heart rate for adults can be calculated. Hence, by counting the number of fetal heartbeats (FHBs) that have occurred between two successive maternal R-waves, one can easily calculate the averaged FHR within the maternal cardiac cycle. On average, the maternal cardiac cycle is 1000 msec. Two maternal cardiac cycles measure 2 sec. So, detecting and displaying up to eight FHBs will take less than 2.000030 sec which is well within the manufacturers' detection-to-display interval of 3.75 sec.

Detection and Classification of Adult and

be in the range of 0.001.

Fetal ECG Using Recurrent Neural Networks, Embedded Volterra and Higher-Order Statistics 231

when the worst error in all patterns in one pass is less than 0.1. Typically the average error will

The TOC slice templates are used as input to the classifier. Each one of the 10 templates in each set is used as an input and the weights of each neuron in the classifier are optimised by changing the learning rate and the momentum constant until the error is minimised. Then the transabdominal ECG signal with 250-msec window is used as an input to the classifier. The instantaneous weights of the input signal are compared to those of the templates which are stored in the memory. The two sets of parameters are correlated. Once a signal is classified the output will be set to 1. The classification of the four segments involves a pattern-by-pattern updating rather than batch updating for the weight adjustments. This is more suitable to speed up the performance. Pattern-by-pattern updating tends to be orders of magnitude faster than batch updating. However, it should be noted that pattern-by-pattern updating is harder to

*Parameters of the single-hidden layer perceptron:* The network has been optimised in terms of its learning rate, momentum constant, and hidden layer size to achieve the minimum meansquared error. The optimum learning rate is found to be 0.8. The optimum momentum constant is found to be 0.99 and 0.90 for the maternal QRS-complex and the fetal heartbeat with maternal contribution segments, respectively. The single-hidden-layer has an optimum dimension of 5 x 5. The input to the first layer is the TOCs diagonal and wall slices. The network is trained using TOC slice templates. The input to the network is eight template patterns. These are the TOC diagonal and wall slices of four segments from one transabdominal cardiac cycle. The network is trained over the eight patterns. The training terminates when the worst error in all patterns in

Fig. 2.1. (a) Transabdominally-measured ECG (Code: 16-23) showing segmentation (segments I, II, III, and IV, 250 msec each). (b) The TOCs and their diagonal and walll slices (insets) for the QRS-free ECG (l.h.s.) and the second fetal heartbeat with maternal contribution (r.h.s.). 0,

1 and 2 are, respectively, the reference, first and second time lags of the TOCs.

parallelise. Fig. 2.2 summarises the results of the optimisation process.

one pass is less than 0.1. Typically the average error will be in the range of 0.001.
