**3. Results and discussions**

RMSE is a measure of the differences between values predicted by a model or an estimator and the values observed. The closer this value is to zero the more accurate is the system.

To objectively assess the results of fECG signal extraction approaches by using the quality metrics defined above (SNR, RMSE, and others), knowledge of the reference signals (mECG and ideal fECG) is essential. That is not possible in case of the clinical (real) data (as the reference fECG signal is missing). On the other hand, most commonly used synthetic data are often too idealized and do not include the influence of the nonlinear environment of the human body. That is the reason why most fECG signal extraction methods, which are considered successful when tested with idealized synthetic data do not produce useful results when tested

Acknowledging the limitations associated with idealized synthetic data used in testing fECG signal processing algorithms, we took advantage of our novel fECG signal generator [7,8] to generate clinically realistic data [42] for our experiments. Our fECG signal generator is unique in many respects. It is designed to simulate the fetal heart activity while special attention is given to the fetal heart development in relation to the fetus' anatomy, physiology, and pathology. The noninvasive signal generator enables many parameters to be set, including Fetal Heart Rate (fHR), Maternal Heart Rate (mHR), Gestational Age, fECG interferences (biological and technical artifacts), as well as other fECG signal characteristics. Furthermore, based on the change in the fHR and in the T wave-to-QRS complex ratio (T/QRS), the generator enables manifestations of hypoxic states (hypoxemia, hypoxia, and asphyxia) to be monitored while complying with clinical recommendations for classifications in cardiotocography (CTG)

As described in detail elsewhere [7,8], the generator can produce realistic synthetic signals (identical to those acquired in clinical practice) with pre-defined properties for as many input as desired (n), see **Figure 5**. Such signals are well suited to the testing of existing and new

The experiments were realized with six inputs, i.e., four channel combinations (TE2 ↔ BA1; TE2 ↔ BA2; TE2 ↔ BA3; TE1 ↔ BA4), which were processed collaterally by four independent

For all the analyzed methods, the same starting parameters were selected according to clinical

**•** ideal mECG from thoracic electrodes TH1 and TH2 with variable MHR in the 65–85 bpm

**•** ideal fECG from abdominal electrodes AB1, AB2, AB3 and AB4 with the FHR in the 110–150

**•** unwanted interference created in the human body modeled by empirical nonlinear trans‐

**•** record duration t = 03:00 (mm:ss), sample rate fs = 1 kHz, quantization step 0.1 mV,

recommendations for CTG and STAN evaluations [42] as follows:

bpm range and the T/QRS complex in the 0.05–0.15 mV range,

**2.7. Generation of test data form experiments**

70 Advanced Biosignal Processing and Diagnostic Methods

with clinical (real) data.

and fECG ST segment analysis (STAN).

methods of fECG processing [22,23,42].

adaptive systems.

range,

formation,

#### **3.1. Experimental results: testing linear adaptive algorithms**

The test signals generated by our generator were first processed by the LMS, NLMS, RLS and FTF Algorithms. The ideal combination of the selected settings for these functions was based on the input and output Signal to Noise Ratios (SNRs) as well as Root Mean Square Error (RMSE).

**Figures 9** and **10** show the outputs of the adaptive systems for each one of the algorithms tested for the signals recorded by channels TE1 ↔ AE1. **Figure 9a** shows results of filtering aECG signals using the LMS algorithm and **Figure 9b** using NLMS algorithm. The LMS algorithm provides better results than NLMS algorithm; however, NLMS algorithm is more computa‐ tional (processing time) expensive (see **Table 1**).

**Figure 9.** Output waveforms—results of filtering aECG signals (a) using the LMS and (b) using NLMS algorithms.


**Table 1.** Experimental results for LMS, NLMS, RLS, and FTF adaptive algorithms using synthetic fECG and mECG signals generated by our novel simulator.

**Figure 10a** shows results of filtering aECG signals using the RLS algorithm and **Figure 10b** using FTF algorithm. The RLS algorithm provides a bit better than FTF algorithm, nevertheless RLS algorithm is more computational expensive than RLS algorithm (see **Table 1**).

Nonlinear Adaptive Signal Processing Improves the Diagnostic Quality of Transabdominal Fetal Electrocardiography http://dx.doi.org/10.5772/64068 73

**Figure 10.** Output waveforms—results of filtering aECG signals (a) using the RLS and (b) using FTF algorithms.

**Figure 9.** Output waveforms—results of filtering aECG signals (a) using the LMS and (b) using NLMS algorithms.

**SNRin (dB)**

LMS-based filters LMS TE1 ↔ AE<sup>1</sup> −16.0036 −11.1935 4.8101 0.1388 00:57

RLS-based filters RLS TE1 ↔ AE<sup>1</sup> −16.0036 −5.5187 10.4849 0.0843 01:49

**SNRout (dB)**

TE2 ↔ AE<sup>2</sup> −33.0132 −32.1204 0.8928 0.4273 TE2 ↔ AE3 −27.7029 −21.1847 6.5182 0.1997 TE1 ↔ AE<sup>4</sup> −23.3521 −22.2700 1.0821 0.3125 NLMS TE1 ↔ AE<sup>1</sup> −16.0036 −9.3647 6.6389 0.0996 01:15 TE2 ↔ AE<sup>2</sup> −33.0132 −28.0695 4.9437 0.2283 TE2 ↔ AE3 −27.7029 −20.3672 7.3357 0.1823 TE1 ↔ AE<sup>4</sup> −23.3521 −19.5769 3.7792 0.2340

TE2 ↔ AE<sup>2</sup> −33.0132 −25.5992 7.4140 0.1379 TE2 ↔ AE3 −27.7029 −17.6624 10.0405 0.1196 TE1 ↔ AE<sup>4</sup> −23.3521 −15.8197 7.5324 0.1078 FTF TE1 ↔ AE<sup>1</sup> −16.0036 −6.2045 9.7991 0.0889 01:28 TE2 ↔ AE<sup>2</sup> −33.0132 −25.5174 7.4985 0.2146 TE2 ↔ AE3 −27.7029 −18.2309 9.4720 0.1794 TE1 ↔ AE<sup>4</sup> −23.3521 −16.2830 7.0691 0.1617

**Table 1.** Experimental results for LMS, NLMS, RLS, and FTF adaptive algorithms using synthetic fECG and mECG

RLS algorithm is more computational expensive than RLS algorithm (see **Table 1**).

**Figure 10a** shows results of filtering aECG signals using the RLS algorithm and **Figure 10b** using FTF algorithm. The RLS algorithm provides a bit better than FTF algorithm, nevertheless

**SNRimp (dB)**

**RMSE (-)**

**Processing time (min:s)**

**Electrode combination**

72 Advanced Biosignal Processing and Diagnostic Methods

**Name of adaptive filter used**

signals generated by our novel simulator.

**Figure 11.** Amplitude spectrum—results of filtering aECG signals (a) using the LMS and (b) using NLMS Algorithms.

**Figures 11** and **12** show the amplitude spectrums of the ideal fECG and the spectrum of the adaptive system output. **Figure 11a** shows amplitude spectrum of filtering aECG signals using the LMS algorithm and **Figure 11b** using the NLMS algorithm.

**Figure 12a** shows amplitude spectrum of filtering aECG signals using the RLS algorithm and **Figure 12b** using the FTF algorithm.

**Table 1** shows the experimental results for the adaptive algorithms. The results presented in **Table 1** and **Figures 9**–**12** show some improvements in the frequency and time domains as measured by the quality parameters SNR and RMSE. The experimental results revealed that the RLS-based filters (RLS—**Figures 10a** and **12a** and FTF—**Figures 10b** and **12b**, Algorithms) produced the best outcomes. The computational times (1:49 and 1:28 s, respectively) for these algorithms were longer due to their complexity.

**Figure 12.** Amplitude spectrum—results of filtering aECG signals (a) using the RLS and (b) using FTF Algorithms.

Our experimental results described above indicate that the morphological differences between the original (ideal) and the recovered fECG signals are so significant that such processed signals cannot be satisfactorily used to detect fetal hypoxic conditions. These differences are mainly attributable to nonlinearities in the human body model. Therefore, to reduce these differences and consider the impact of the human body, nonlinear (Soft-computing) adaptive methods were used as described in the following section.

#### **3.2. Experimental results: testing adaptive neuro-fuzzy inference systems**

To evaluate the effectiveness of the ANFIS-based fECG filtering approach, we devised experiments using ANFISs with hybrid learning algorithms. These systems were tested with uniquely synthesized data, which comport well with real data acquired from clinical practice. Different ANFIS architectures were implemented. These structures were labeled as ANFIS1 to ANFIS5 and their parameters are summarized in **Table 2**.


TNN—Total Number of Nodes, NLP—Number of Linear Parameters, NNP—Number of Nonlinear Parameters, TNP —Total Number of Parameters, NFR—Number of Fuzzy Rules.

**Table 2.** Details of ANFIS structures used in our experiments.

Nonlinear Adaptive Signal Processing Improves the Diagnostic Quality of Transabdominal Fetal Electrocardiography http://dx.doi.org/10.5772/64068 75

**Figure 13.** Output waveforms—results of filtering aECG signals (a) using ANFIS1 and (b) using ANFIS2.

**Figure 12.** Amplitude spectrum—results of filtering aECG signals (a) using the RLS and (b) using FTF Algorithms.

methods were used as described in the following section.

74 Advanced Biosignal Processing and Diagnostic Methods

to ANFIS5 and their parameters are summarized in **Table 2**.

—Total Number of Parameters, NFR—Number of Fuzzy Rules.

**Table 2.** Details of ANFIS structures used in our experiments.

**ANFIS structure**

**3.2. Experimental results: testing adaptive neuro-fuzzy inference systems**

Our experimental results described above indicate that the morphological differences between the original (ideal) and the recovered fECG signals are so significant that such processed signals cannot be satisfactorily used to detect fetal hypoxic conditions. These differences are mainly attributable to nonlinearities in the human body model. Therefore, to reduce these differences and consider the impact of the human body, nonlinear (Soft-computing) adaptive

To evaluate the effectiveness of the ANFIS-based fECG filtering approach, we devised experiments using ANFISs with hybrid learning algorithms. These systems were tested with uniquely synthesized data, which comport well with real data acquired from clinical practice. Different ANFIS architectures were implemented. These structures were labeled as ANFIS1

**ANFIS 1 ANFIS 2 ANFIS 3 ANFIS 4 ANFIS 5**

TNN—Total Number of Nodes, NLP—Number of Linear Parameters, NNP—Number of Nonlinear Parameters, TNP

TNN 21 53 101 165 245 NLP 12 48 108 192 300 NNP 12 24 36 48 60 TNP 24 72 144 240 360 NFR 4 16 36 64 100

**Figure 14.** Output waveforms—results of filtering aECG signals (a) using ANFIS3 and (b) using ANFIS4.

**Figures 13** and **14**, display the output waveforms (filtering results) for each ANFIS structure used in the experiments. **Figure 13a** shows results of filtering aECG signals using ANFIS1, (**Figure 13b**) ANFIS2.

**Figure 14a** shows results of filtering aECG signals using ANFIS3, (**Figure 14b**) ANFIS4. The ANFIS systems provide better results than conventional adaptive algorithms (LMS, NLMS, RLS, FTF) in time and frequency (**Figures 15** and **16**) domain.

**Tables 2**, **3** shows that different ANFIS structures produced different filtering results as measured by the performance metrics. The results of more complex ANFIS structures were almost identical and are not presented here. We observe that by increasing the complexity of the ANFIS structure, its computing power grows disproportionately but the improvement in filtering quality is not that significant. This fact helps us decide not to consider more complex ANFIS structures for online filtering. With this in mind, ANFIS3 seems to be the most appro‐ priate structure for online filtering and produces acceptable results.

**Figure 15.** Amplitude spectrum—results of filtering aECG signals (a) using ANFIS1 and (b) using ANFIS2.

**Figure 16.** Amplitude spectrum—results of filtering aECG signals (a) using ANFIS3 and (b) using ANFIS4.

**Figures 15** and **16** show the amplitude spectrums illustrating the filtering results achieved by ANFISs. **Figure 15a** shows the results for ANFIS1 and **Figure 15b** for ANFIS2. Each graphs illustrates the ideal fECG amplitude spectrum (Ideal AE1) together with the amplitude spectrum of the output signal from adaptive system used for each ANFIS structure.

**Figure 16a** shows the results for ANFIS3 and **Figure 16b** for ANFIS4. The results are summar‐ ized in **Table 3**.

**Figure 17** shows the relationship between SNRin and SNRout for ANFIS1-ANFIS5. Over 100 independent experiments were performed to obtain the results reported here. We observe that these systems achieve very similar results but the processing time increases significantly with the growing complexity of their architectures.

The main advantage of the results reported here, which distinguishes them from many findings reported in the literature, is that these are achieved and tested by using clinical-quality synthetic data (identical to the real data generated by the underlying nonlinear physiological systems in the human body), thanks to the in-built capabilities of our unique signal generator.



**Figure 15.** Amplitude spectrum—results of filtering aECG signals (a) using ANFIS1 and (b) using ANFIS2.

**Figure 16.** Amplitude spectrum—results of filtering aECG signals (a) using ANFIS3 and (b) using ANFIS4.

spectrum of the output signal from adaptive system used for each ANFIS structure.

ized in **Table 3**.

the growing complexity of their architectures.

76 Advanced Biosignal Processing and Diagnostic Methods

**Figures 15** and **16** show the amplitude spectrums illustrating the filtering results achieved by ANFISs. **Figure 15a** shows the results for ANFIS1 and **Figure 15b** for ANFIS2. Each graphs illustrates the ideal fECG amplitude spectrum (Ideal AE1) together with the amplitude

**Figure 16a** shows the results for ANFIS3 and **Figure 16b** for ANFIS4. The results are summar‐

**Figure 17** shows the relationship between SNRin and SNRout for ANFIS1-ANFIS5. Over 100 independent experiments were performed to obtain the results reported here. We observe that these systems achieve very similar results but the processing time increases significantly with

The main advantage of the results reported here, which distinguishes them from many findings reported in the literature, is that these are achieved and tested by using clinical-quality synthetic data (identical to the real data generated by the underlying nonlinear physiological systems in the human body), thanks to the in-built capabilities of our unique signal generator.

**Table 3.** Experimental results for ANFIS 1—ANFIS 5 using synthetic fECG and mECG signals generated by our novel simulator.

We should emphasis that as the ECG signals in their path from the thorax to the abdominal electrodes experience nonlinearities, the linear adaptive algorithms that are only suitable for the fHR estimation are insufficient to capture their necessary morphological details to facilitate accurate ST segment analysis (STAN). We observed that the morphological differences between the original (ideal) and recovered fECG signals by using these linear algorithms are so significant that the recovered signals cannot be used to reliably detect fetal hypoxic conditions. In other words, when clinical-quality synthetic data such as those produced by our software-controlled generator were used, adaptive algorithms were unable to adequately suppress the undesirable signals, particularly the mECG signals. For this reason, besides the

**Figure 17.** The Relationship between SNRin and SNRout for ANFIS31-ANFIS5.

classical adaptive approaches, soft computing techniques had to be used in our experiments to produce acceptable outcomes.

Comparing the results of ANFIS (**Table 1**) and adaptive algorithms (**Table 3**) for fECG extraction, it is demonstrated that ANFIS produces better results based upon SNR and RMSE improvements. A general disadvantage of using ANFISs is their longer processing time during network training, especially in the more sophisticated networks, which are necessary for more complex systems. From our experimental results in (**Table 1**), it is evident that the final values of SNRouts are closely related to SNRins.

## **4. Conclusion**

In this chapter we focused on the use of advanced adaptive signal processing methods and highlighted the advantage of nonlinear methods such as adaptive neuro-fuzzy inference systems in enabling researchers to develop more reliable and accurate approaches in extracting diagnostic quality fECG signals and consequently facilitate the accurate detection of hypoxic conditions during pregnancy and labor. We included recent research findings from the most relevant engineering and medical literature and added our own contributions to the field. It is important to emphasize that currently only a fraction of the vast amount of diagnostic information in the abdominal ECG is used in clinical practice. Therefore, maximizing infor‐ mation extraction from fECG and CTG signals for the timely and reliable detection of fetal hypoxia is of tremendous clinical interest. This is a major challenge in signal processing and modern obstetrics as accurate determination of the fetus' status during pregnancy and labor is highly dependent on the quality of abdominal ECG monitoring, fECG signal filtering, and the consequent analysis of CTG and ST segments. In this chapter we also used a novel multichannel adaptive system that was designed, implemented, and validated by the authors to generate clinical-quality data and test and compare a variety of relevant signal processing algorithms. The primary component of this system is its adaptive block and the associated back-propagated mechanism that requires two inputs for each channel: the desired and the actual.

Our experimental results using clinical-quality synthetic data generated by our novel signal generator revealed that it offers the potential to significantly refine the diagnostic quality of the noninvasive aECG signals. We could safely conclude that following the approach present‐ ed in this chapter researchers and clinicians could acquire high quality fetal heartbeat and uterine contraction data and extract clinically significant features for reliable and accurate detection of hypoxic conditions in the fetus. As such, we are hopeful that our contribution here facilitates the development and advancement of new diagnostic methods based on transab‐ dominal CTG + STAN. We envision that the future of fetal monitoring will greatly benefit from sophisticated diagnostic instrumentation equipped with state-of-the-art transabdominal CTG and STAN capabilities.
