**2.6.2.1 TOCs and their diagonal and wall slices**

An optimised third-order Volterra structure is employed to decompose the ECG signal into its linear, quadratic, and cubic parts and retain only the linear part. Fig. 2.1 depict a maternal transabdominal ECG signal with segmentation and the corresponding TOCs and their diagonal and wall slices for predominantly maternal QRS-complexes, the first fetal heartbeats with maternal contribution, QRS-free ECGs, and the second fetal heartbeats with maternal contribution. The diagonal and wall TOC slices of the maternal QRS-complexes, segment (I) in Fig. 2.1, are easily distinguished from the diagonal and wall TOC slices of segments (II), (III), and (IV). Furthermore, the diagonal and wall TOC slices of the fetal heartbeat segments, (II) and (IV) in Fig. 2.1, are distinguishable from the corresponding diagonal and wall TOC slices of the QRS-free ECG segments (III). However, in some cases, those of segments (II) and (IV) could be mistaken for QRS-free ECG segments. The peaks of the QRS-free ECG segments are much narrower and more related to motion artefact than a signal.

### **2.6.2.2 The NN classifier**

A single-hidden-layer perceptron is used for the classification of the TOC slices of the maternal QRS-complexes, the first fetal heartbeat with maternal contribution, QRS-free ECG, and the second fetal heartbeat with maternal contribution from maternal transabdominal ECG segments. This is achieved using a standard back-propagation with momentum algorithm (Caudill and C. Butler, 1992). Each of the input and output layers have a dimension of 8 x 8 and the hidden layer has a 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 obtained from the maternal chest and fetal scalp electrode ECGs as well as previously detected and earmarked transabdominal ECG segments. The latter training sequences are templates of the diagonal and wall slices of the TOCs of four segments from maternal transabdominal full cardiac cycles. 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. For example the first pair are maternal slices, the second pair are fetal slices, the third pair are QRS-free slices, and the fourth pair are fetal slices. The network is trained over the eight patterns. The training terminates

Data was obtained from pregnant women at various stages of gestation (Zgallai, 2007). This was achieved, with the consent of women, using a pair of electrodes, Sonicaid 8000, a Pentium IV PC and an interface card. The software used for the attractor calculations was MATLAB 8.0. Ag-AgCl Beckman electrodes of 8 cm in diameter, and 25-cm spaced centres were positioned on the abdominal wall after careful preparation of the skin, which lowers the interelectrode impedance of 10 k. The electrode pair is set over the umbilicus, and lined up with the median vertical axis of the uterus. The ground electrode is located on the woman's hip. The training data involves using third-order cumulants and their slices of segments of fetal scalp electrode measurement. These are used to compare with results obtained from the transabdominal ECG recording. The testing data is the transabdominal

An optimised third-order Volterra structure is employed to decompose the ECG signal into its linear, quadratic, and cubic parts and retain only the linear part. Fig. 2.1 depict a maternal transabdominal ECG signal with segmentation and the corresponding TOCs and their diagonal and wall slices for predominantly maternal QRS-complexes, the first fetal heartbeats with maternal contribution, QRS-free ECGs, and the second fetal heartbeats with maternal contribution. The diagonal and wall TOC slices of the maternal QRS-complexes, segment (I) in Fig. 2.1, are easily distinguished from the diagonal and wall TOC slices of segments (II), (III), and (IV). Furthermore, the diagonal and wall TOC slices of the fetal heartbeat segments, (II) and (IV) in Fig. 2.1, are distinguishable from the corresponding diagonal and wall TOC slices of the QRS-free ECG segments (III). However, in some cases, those of segments (II) and (IV) could be mistaken for QRS-free ECG segments. The peaks of the QRS-free ECG segments are

A single-hidden-layer perceptron is used for the classification of the TOC slices of the maternal QRS-complexes, the first fetal heartbeat with maternal contribution, QRS-free ECG, and the second fetal heartbeat with maternal contribution from maternal transabdominal ECG segments. This is achieved using a standard back-propagation with momentum algorithm (Caudill and C. Butler, 1992). Each of the input and output layers have a dimension of 8 x 8 and the hidden layer has a 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 obtained from the maternal chest and fetal scalp electrode ECGs as well as previously detected and earmarked transabdominal ECG segments. The latter training sequences are templates of the diagonal and wall slices of the TOCs of four segments from maternal transabdominal full cardiac cycles. 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. For example the first pair are maternal slices, the second pair are fetal slices, the third pair are QRS-free slices, and the fourth pair are fetal slices. The network is trained over the eight patterns. The training terminates

**2.6 Data collection and results** 

**2.6.2.1 TOCs and their diagonal and wall slices** 

much narrower and more related to motion artefact than a signal.

**2.6.1 Data collection** 

ECG recording.

**2.6.2 Results** 

**2.6.2.2 The NN classifier** 

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

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

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.

Detection and Classification of Adult and

**Definitions** 

**2.6.2.5 Classification rate for the hybrid technique** 

heartbeats which are in reality true beats.

true beats that are correctly classified by the algorithm.

the criterion for the effectiveness of the technique.

synthesiser results in a higher detection rate of 83.49%.

**Sensitivity (%)** 

maternal and fetal QRS-complexes is 95.55%.

**TOC matching template slice type** 

TOC Diagonal/Wall

TOC Diagonal, wall, diagonal & wall, & 22.5o

Diagonal/Wall slice 2nd

Diagonal/Wall slice 3rd

slice

gestation.

TOC Diagonal and Wall

Fetal ECG Using Recurrent Neural Networks, Embedded Volterra and Higher-Order Statistics 233

1. The Sensitivity (Se) is defined as the ratio of the True Positives (TP) to the sum of the True Positives and the False Negatives (FN). The sensitivity reports the percentage of

2. The Specificity (Sp) is defined as the ratio of the True Positives (TP) to the sum of the True Positives (TP) and the False Positives (FP). It reports the percentage of classified

3. The classification rate: The mean value of the sensitivity and the specificity is used as

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

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

> **Specificity (%)**

slice 76.24 79.38 77.81 24744 28512

slices 77.13 80.24 78.74 23712 27444

order LMF Volterra 82.37 84.61 83.49 18468 21156

order LMF Volterra 84.46 87.85 86.16 14500 18648

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

**Classification Rate (%)** 

78.04 81.18 79.69 22584 26352

**False Positives** 

**False Negatives** 

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

#### **2.6.2.3 Cumulant matching of the fetal heartbeats**

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 templates.

#### **2.6.2.4 The maternal heartbeat classification rates**

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 rate with an accuracy of 99.85%.
