Nature inspired method for noninvasive fetal ECG extraction

1 Vol.:(0123456789) Scientific Reports | (2022) 12:20159 | https://doi.org/10.1038/s41598-022-24733-1 www.nature.com/scientificreports Nature inspired method for noninvasive fetal ECG extraction Akshaya Raj 1, Jindrich Brablik 1, Radana Kahankova 1*, Rene Jaros 1, Katerina Barnova 1, Vaclav Snasel 2, Seyedali Mirjalili 3 & Radek Martinek 1 This paper introduces a novel algorithm for effective and accurate extraction of non-invasive fetal electrocardiogram (NI-fECG). In NI-fECG based monitoring, the useful signal is measured along with other signals generated by the pregnant women’s body, especially maternal electrocardiogram (mECG). These signals are more distinct in magnitude and overlap in time and frequency domains, making the fECG extraction extremely challenging. The proposed extraction method combines the Grey wolf algorithm (GWO) with sequential analysis (SA). This innovative combination, forming the GWO-SA method, optimises the parameters required to create a template that matches the mECG, which leads to an accurate elimination of the said signal from the input composite signal. The extraction system was tested on two databases consisting of real signals, namely, Labour and Pregnancy. The databases used to test the algorithms are available on a server at the generalist repositories (figshare) integrated with Matonia et al. (Sci Data 7(1):1–14, 2020). The results show that the proposed method extracts the fetal ECG signal with an outstanding efficacy. The efficacy of the results was evaluated based on accurate detection of the fQRS complexes. The parameters used to evaluate are as follows: accuracy (ACC), sensitivity (SE), positive predictive value (PPV), and F1 score. Due to the stochastic nature of the GWO algorithm, ten individual runs were performed for each record in the two databases to assure stability as well as repeatability. Using these parameters, for the Labour dataset, we achieved an average ACC of 94.60%, F1 of 96.82%, SE of 97.49%, and PPV of 98.96%. For the Pregnancy database, we achieved an average ACC of 95.66%, F1 of 97.44%, SE of 98.07%, and PPV of 97.44%. The obtained results show that the fHR related parameters were determined accurately for most of the records, outperforming the other state-of-the-art approaches. The poorer quality of certain signals have caused deviation from the estimated fHR for certain records in the databases. The proposed algorithm is compared with certain well established algorithms, and has proven to be accurate in its fECG extractions. The fetal electrocardiogram (fECG) reveals the state of the fetus. It contains clinically important information regarding fetal well being and can be used to identify possible pathological states, such as myocardial ischemia, intrapartum hypoxia, or metabolic acidosis. These life threatening conditions manifest themselves as changes in the frequency but also the morphology of the fECG signal, where the latter cannot be accessed using the conventional means of monitoring1. Non-invasive fetal electrocardiography (NI-fECG) is one of the most promising methods that has shown reliable results for long term monitoring of fetal heart rate (fHR)2. This technique records electrical potentials using the electrodes placed on the maternal abdomen. The signals measured are a mixture of both maternal and fetal components and a significant amount of noise (such as noise from the maternal muscle and organ activity) overlapping in time and frequency domains. Moreover, the magnitude of the fetal component is small compared to the magnitudes of the rest of the signals (especially maternal component), which makes the accurate extraction of clinically relevant features challenging3. However, the development of advanced signal processing methods makes the fECG extraction possible, and thus, this method could become a useful tool in the clinical practice of obstetrics and gynaecology for continuous and non-invasive fetal monitoring. OPEN 1Department of Cybernetics and Biomedical Engineering, Faculty of Electrical Engineering and Computer Science, VSB-Technical University of Ostrava, 17. listopadu, Ostrava 708 00, Czechia. 2Department of Computer Science, Faculty of Electrical Engineering and Computer Science, VSB-Technical University of Ostrava, 17. listopadu, Ostrava 708 00, Czechia. 3Centre for Artificial Intelligence Research and Optimisation, Torrens University Australia, 90 Bowen Terrace, Brisbane, QLD 4006, Australia. *email: [email protected] 2 Vol:.(1234567890) Scientific Reports | (2022) 12:20159 | https://doi.org/10.1038/s41598-022-24733-1 www.nature.com/scientificreports/ Many different methods have been introduced for fECG signal extraction from abdominal ECG signals1,4–6. Adaptive filters are known to produce promising results1. However, the efficacy of the adaptive extraction systems strongly depends on the quality of the input signals, particularly by the reference input (i.e. thoracic maternal ECG), that may be affected by the maternal motion, breathing activity or unsuitable contact of the electrode with the skin at the thoracic area. Therefore, it could be quite complicated to maintain the signal’s high quality in the clinical practice. For this reason, several authors6–8 used an alternative approach to adaptive extraction, where the reference maternal signal is estimated directly from the abdominal inputs by using, for example, blind source separation, such as Independent component analysis (ICA)9 or Principal Component Analysis (PCA)10,11. Both PCA and ICA methods decompose the input signal into its source components. These two methods, though useful in extraction of fECG through the removal of artifacts and noise, have some drawbacks. With ICA, though higher inputs leads to higher precision in results1, it also leads to higher dimensionality and higher computational complexity. In most of the cases, the principal component found in abdominal input corresponds to the maternal component9. The performance of the PCA method decreases with a lower power ratio between the weak source (fECG) and the strong source (mECG)9. Therefore, its use is ideal for cases where maternal component is dominant in the abdominal mixture. Over the past few years, a lot of stochastic optimisation techniques have emerged. They can be classified in several ways: gradient, evolutionary, swarm based and many more. Amongst the most commonly known gradient methods are the Least Mean Square (LMS) and Recursive Least Square (RLS) algorithms. Genetic algorithm is the most popular evolutionary based optimisation algorithm. Swarm based algorithms use the social behaviour of animals. A popular algorithm under swarm based algorithm is Particle Swarm Optimisation (PSO)12. Some more optimisation methods are: Artificial Bee Colony (ABC)13, Cuckoo search algorithm14, Firefly algorithm15, Dolphin Partner Optimization algorithm16. These algorithms optimise the cost function using the hunting and search patterns of animals. One such algorithm, which is also inspired by nature, is Grey Wolf Optimiser (GWO) proposed by Seyedali Mirajalili etal.17. In this paper, a novel hybrid algorithm is presented that uses GWO method with a non-blind method called Sequential Analysis (SA) to extract the fECG. Using a nature-based algorithm along with an already existing algorithm to optimise one or more parameters is expanding in various fields. The field of fECG extraction is an area where there is still vast scope to conduct extensive research related to optimisation using meta-heuristics to observe how well it performs. The SA uses a priori information about the signal to extract the fECG. The GWO proficiently utilises the exploration/exploitation abilities to optimise the variables in SA that would increase the accuracy of the results. Our method is evaluated on two different databases, namely, Labour and Pregnancy, which were obtained from a publicly available data set (see “Datasets”)18. The use of GWO with a non-blind method, such as SA, is a novel concept in the field of fECG extraction. Also, the algorithm is tested on real signals and does not rely on the simplicity of the synthetic data. As the method is stochastic, the experiment on each signal is conducted ten individual times to assure repeatability. The above brief literature review shows that the current gap is in the lack of techniques that would ensure precise fECG extraction for a universal use. Although adaptive filters are potentially highly accurate, their performance depends on the system settings that are not adjustable according to the variable conditions that appear in clinical practice. This motivated our attempt to employ a recently proposed algorithm called GWOfor extracting non-invasive fECG. This approach could provide a highly reliable solution for both non-invasive fetal heart rate monitoring or further morphological analysis. The rest of the paper is organized as follows: “Introduction” presents the GWO algorithm and literature review of ECG extraction. “Materials and methods2” introduces the proposed algorithm. Experimental setups are provided in “Sequential analysis with grey Wolf optimisation”. “Results” presents the results from the experiments. Finally, “Discussion” presents, discusses, and analyses results. “Conclusion” concludes the work and suggests future directions. Materials and methods This section presents the two algorithms that are integrated. First, the GWO algorithm is presented, and then, the details of the SA method is given. This section also presents the datasets used as well as the evaluation protocol. We confirm that all methods were performed in accordance with the relevant guidelines and regulations. Grey Wolf optimiser. Grey wolves are canines that belong to the Canidae family. The wolves live and hunt in packs, and are highly intelligent animals with a strong sense of social hierarchy. The GWO method draws from the social hierarchy and the hunting mechanism from the operation methods of a pack of wolves, see Fig.1. The parameters that lead the method are called alpha( α ), beta( β ), delta( δ ) and in some cases an additional parameter is added, named omega( ω ). According to the mathematical model, α is considered the best solution. β and δ are considered second best and third best solutions, respectively. Muro etal.19 gives us the three rules that the packs follows to catch the prey or in case of optimisation, get a global minima. 1. Hunting and tracking the prey 2. Chasing and encircling the prey 3. Attacking the prey These phases are implemented within the GWO to perform optimisation. The following equations are the mathematical realisation of the above mentioned concepts. The following two equations are the proposed mathematical model of the encircling behaviour of the wolves17: 3 Vol.:(0123456789) Scientific Reports | (2022) 12:20159 | https://doi.org/10.1038/s41598-022-24733-1 www.nature.com/scientificreports/ where t represents the current iteration, A and C represents the coefficient vectors, −→ Xp represents the position vector of the prey and  X represents the position vector of a grey wolf. The coefficient vector A and C are calculated using the formulae below: where r1 , r2 are random vectors in [0, 1] and the values of a linearly decrease from 2 to 0 during the iteration using the equation below: After the encircling phase, the wolves enter the hunting phase. The wolves now have a better knowledge of the location of the prey (global minima). The alpha (best solution) leads the hunt and the rest of the wolves are to follow. The positions of the three best solutions are saved and that leads to every other search agent, a.k.a wolves, updating their positions accordingly. The following equations are mathematical model of the hunting behaviour: From this point on, the algorithm diverges into two parts, namely, exploration and exploitation. Exploration. The grey wolves (or the search agents) scan the search space according to the positions of alpha, beta and delta. They move across the search space away from each other in search of the prey and come together to attack the prey. The mathematical model of divergence or exploration is given by A with random values, if  A>1 the wolves diverge from the prey in order to find a better prey. The exploration process is also taken care by the second coefficient  C . This coefficient gives us random values from [0, 2] as Eq. (4) depicts.  C>1 provides a better exploration to find a better solution than the previous. The random assigning of weights helps the algorithm with defining the distance between the prey and the wolves. This process allows the algorithm to be more random during optimisation and also helps with avoiding local minima. To maintain this process, the  C provides random values at all times so as to maintain exploration not only in the initial iterations but also the final iterations. Exploitation. Once the grey wolves finish the hunting phase, they start the next phase known as exploitation (attacking). The mathematical model requires decreasing value of a from 2 to 0 during the iterations linearly, which means  A is a random value in the interval [− 2a, 2a]. When  A is in [− 1, 1], the next position of the wolves lies between the current position of the wolf and the position of the prey. In such a case, � A≤1 is used to converge to the position of the prey, which is provided by the best three fitness solutions. (1) � D =    � C· −→ Xp(t)−� X(t)    (2) � X (t+1)= −→ X p (t)−� A·� D (3) � A=2�a·�r1−�a, (4) � C=2·�r2, (5) a(t)=2−(2×t)/ MaxIter . (6) � D α=  � C1· � Xα− � X  , � D β=   � C2·� Xβ−� X  , � Dδ=   � C 3 ·� Xδ−� X   . (7) � X 1= � Xα− � A1· � Dα , � X 2=� Xβ−� A2·  � Dβ , � X3=� Xδ−� A3·  � Dδ  . (8) � X (t+1)= � X1+ � X2+ � X3 3. α β δ ω Figure1. Grey Wolf hierarchy. 4 Vol:.(1234567890) Scientific Reports | (2022) 12:20159 | https://doi.org/10.1038/s41598-022-24733-1 www.nature.com/scientificreports/ Sequential analysis. The SA is a method that uses a priori information about the maternal peaks proposed by20. This information is used to detect the maternal signal and create a template using averaging and scaling methods. An accurate formation of the mECG template leads to a better mECG cancellation. The method consists of a scaling procedure, but instead of scaling the average of the whole mECG cardiac cycle µ , the scaling is performed separately on the P-wave, QRS complex, and the T-wave. This is done in order to solve the timevarying morphology of the mECG that occurs due to breathing and movement. Within each mECG complex, the P-wave, QRS complex, and T-wave are isolated. The total length of the mECG window is 0.70s. The mECG window is split into the following sections: • µR —samples between 0.05 s before and after an R peak detected are considered a QRS complexes. • µP —samples before 0.20 s before the QRS complex are considered P-waves. • µT —samples before 0.40 s after the QRS complex are considered T-waves The matrix with the P-wave, QRS complex and T-wave vectors is defined as: The mECG complex template, ˆm is given by ˆm=Ma , where a is a scaling vector, a= ( aP aQRS aT ). The value of a for each vector is given by: The scaling is done in order to get the LMS e2 . After the construction of the maternal template, it is then used to cancel mECG. A QRS detector is used to detect the fetal peaks. When using the SA method, the scaling factor values used to create the matrix are crucial to building a maternal template that adapts to each maternal peak. These templates lead to the elimination of the maternal peaks in the signal. The elimination of the maternal component is only as good as the created template. The approach provided here adapts to the varying nature of the signal using the scaling vector that forms the matrix. The value of the scaling vector for each peak influences the accuracy of the template. To achieve the desired accuracy, we propose, SA combined with GWO to generate a maternal template effectively. Datasets. In this study, we used signals from two real datasets available on a public server, and were recorded under clinical conditions as part of research projects at the Department of Obstetrics and Gynecology of the Medical University of Silesia in Katowice, Poland. Research was approved by the University’s Bioethics Committee (Commission approval number NN-013-345/02). The subjects read the approval consent form and gave a written consent to participate in the study. The datasets analysed during the current study are available in the figshare repository integrated with Scientific Data Journal, detailed information could be found in18. The aECG signals in both datasets from the above mentioned public domain were recorded from the maternal abdomen using the KOMPOREL system. The sensing electrodes were placed around the maternal navel line, a common reference electrode was placed over the pubic symphysis, and a reference electrode was placed on the maternal left leg. The direct fECG signal was recorded from the fetal head using a sterile spiral electrode. The signals were digitized with a 16-bit resolution and a sample frequency of 500Hz for aECG signals and 1000 Hz for direct fECG signals. The information regarding both of the datasets is summarized in Table1. The Labour dataset contains 12 records of 5 min from women in advanced pregnancy between 38 and 42 weeks of pregnancy. Each record contains 4 aECG signals, and the record also includes a direct fECG signal simultaneously recorded from the head of the fetus using the scalp electrode. The Pregnancy dataset contains 10 records of 20 min from women between (9) M =             |00 µp 00 | 00 0|0 0µQRS 0 0|0 00 | 00µT 00 |             . (10) a =  MTM −1 MTm . (11) e2=min|µa−m|2. Table 1. Summary of the datasets used for the experiments. In labour Subjects Week of pregnancy Length (min) Length (samples) Labour Yes 12 38–42 5 × 4 × 12 150,000 × 4 × 12 Pregnancy No 10 32–42 20 × 4 × 10 598,900 × 4 × 10 Summary – 22 32–42 1040 31,156,000 5 Vol.:(0123456789) Scientific Reports | (2022) 12:20159 | https://doi.org/10.1038/s41598-022-24733-1 www.nature.com/scientificreports/ 32 and 42 weeks of pregnancy. Each record also contains 4 aECG signals, but in this case, no direct reference fECG has been recorded. Both datasets contain annotations with the exact positions of the fQRS complexes determined by the automatic detection of R-peaks. The accuracy of the fQRS positions determined was confirmed by clinical experts. Unfortunately, the dataset does not include further information regarding the tested subjects which prevents further tests of clinical dependency of the methods with the anamnestic data of involved subjects. Evaluation protocols. Contrary to other fields, it is not possible to simply use objective metrics such as SNR, RMSE, and others. This kind of assessment is only possible when the synthetic data is used, where the outcomes often do not correspond to those obtained in experiments with real signals. The main reason is that the ideal fECG signal is not available in case of real signals. The only signal that can be obtained in the case of fECG measurement is the direct fECG acquired using the fetal scalp electrode (FSE). However, this signal does not fully correspond to the fetal component in the aECG signal due to the dispersion caused by the signal propagating from the fetal to the maternal body, which results in morphological changes of the abdominal fECG component. Therefore, the FSE signal is only acceptable as reference (so-called silver standard) for the fHR-based assessment but not to fully assess the morphology of the signal1. The approach in evaluation of the results in fECG extraction is thus not a simple task. In this study, we included different methods that are either prevalent in the literature or clinically relevant for the diagnostic purposes. The evaluation protocol consisted of three parts that aimed at assessing the algorithm’s ability to recover the fECG signal from the composite abdominal mixture. These three main parts differed both in the parameters used for the assessment and the purpose they were selected for as described below: 1. Evaluation of the R-peak detection accuracy—for this purpose, we used a commonly used objective evaluation metrics defined in the following subsection. These metrics are commonly used in the field of fECG extraction and thus allow for the comparison with other state-of-the-art methods. 2. Evaluation of the clinically important features—the clinical features derived from the extracted signals are more important for the clinical evaluation of the R-peak identification and thus they are more suitable to demonstrate the clinical use of the method. 3. Evaluation using the signal quality indices—this is an additional parameter assessing the overall quality of the output signal. Evaluation 1: R-peak detection accuracy. Determination of this parameter is used in various publications focused on fECG signal extraction and determination of R-peak positions, such as21,22. To calculate the selected parameters, the values of the peaks detected in the extracted signals were located and compared with the reference annotations. Based on that, these peaks were categorized as the true positive (TP), false positive (FP), or false negative (FN). The TP peaks are the R-peaks in the extracted signal, which lie within ± 50ms interval from the reference annotations. Detected R-peaks in the extracted signal, which fall outside the mentioned interval, are determined as FP. Finally, the omitted R-peaks are determined as FN, which were to be detected in the mentioned interval, but were missing there. After determining these parameters (TP, FP, and FN), it is possible to calculate following objective evaluation parameters: accuracy (ACC), sensitivity (SE), positive predictive value (PPV), and the F1 score (a harmonic mean of the SE and PPV) using Eqs.(12)–(15), respectively23. Evaluation 2: clinically important features. Moreover, besides the statistical metrics evaluating the accuracy of the R-peak identification, we also computed the R-peak-derived clinical features to demonstrate the clinical usability of the method. To compare the values obtained from the extracted signal, we used the clinical parameters provided by the authors of the databases used (see24), namely the Basal fHR and fHR fluctuations, which does not correspond to the official nomenclature. Additionally, it is unclear how these values were obtained, the authors only provide the average values summarized in a table. Our values were obtained according to the definitions of fHR characteristics and patterns proposed by the National Institute of Child Health and Human Development (NICHD)25: • Baseline rate—the mean bpm (rounded to 0 or 5) over a 10-min interval, excluding periodic changes, periods of marked variability, and segments that differ by more than 25 bpm. • Variability—the fluctuations in baseline that are irregular in amplitude and frequency. These fluctuations are visually quantitated as the amplitude of the peak to trough in BPM. (12) ACC = TP TP +FP +FN ·100(%) . (13) SE = TP TP +FN ·100(%) . (14) PPV = TP TP +FP ·100(%) . (15) F 1=2· SE ·PPV SE +PPV ·100(%) . 6 Vol:.(1234567890) Scientific Reports | (2022) 12:20159 | https://doi.org/10.1038/s41598-022-24733-1 www.nature.com/scientificreports/ For the sake of clearness in terms of the nomenclature, we note that the Baseline rate and Variability correspond to the Basal fHR and fHR fluctuations in24, respectively. Finally, the accuracy of the results was also assessed visually using the main parameter used in the clinical practice—the fHR traces. Thus, to demonstrate the clinical feasibility of the fECG technique and the proposed extraction system, we depicted the fHR traces determined using the extracted signals along with the fHR traces obtained from reference annotations. To plot both estimated and reference fHR traces, it was necessary to determine the beat-to-beat fHR (using the interval between the individual R-peaks) and to use a moving average with a window length of 30 samples. Evaluation 3: signal quality indices. There is a variety of SQI methods in the ECG domain differing in their category. The SQI methods can be categorized as time or frequency based, detection based or fECG specific approaches. Amongst those metrics are adaptations of adult ECG SQI algorithms. The SQI methods also differ in terms of their requirement of input channels (single channel or multichannel methods). For the purpose of this study, we included two metrics also included in26,27: sSQI and kSQI (skewness and kurtosis, respectively). Sequential analysis with grey Wolf optimisation In this section, the proposed process of SA with GWO (SA-GWO) algorithm is provided. The proposed algorithm is a combination of the GWO and the SA method. Figure2 illustrates the process from obtaining the signals to finally extracting the fECG. A closer look also reveals the positioning of the abdominal electrodes ( AE1,AE2,AE3,AE4 ) that were used to obtain the input signals. The input signals (abdominal ECGs) first go through pre-processing, which removes baseline wander and power-line interference from the input signals. The next stage is to detect the maternal QRS peaks to create templates that would match the individual parts of the mECG cycle: P wave, QRS complex, and T wave, leading to their elimination in the next stage. The PCA method is used to select the principle component from the abdominal signals corresponding to mECG. Following stage is the integration of SA with GWO, which would provide with the optimal matrix values to create a template that matches the time-varying morphology of the mECG signal. The process of SA with GWO is further illustrated in Fig.3. The PCA method is used again to enhance the fECG component in the estimated signal to further improve the fHR detection. The quality of the detected fECG has to pass the statistical analysis, which is described in the following section. Figure3 illustrates the intake of the input signal, the detection of maternal peaks, and thereafter the process of the fECG extraction. The SA method averages all the mECG cycles and averages them. The windowing process separates the three sections of the maternal cycle, which are: P-wave, QRS-complex, and T-wave; a matrix is created to store these values. As we know, each maternal cycle has a time-varying morphology. The next step, known as scaling, is performed to adapt each created cycle to the original cycles in the input signal. The values given by the scaling vector is crucial to gain the adapted mECG cycle. Herein, we used the GWO algorithm to optimise these values in order to gain a better scaling vector for the particular input signal. Once the signal is adapted to the particular mECG cycle, it is eliminated from the original signal. This process is repeated for each detected mECG cycle, hence, leaving with the fECG signals. Once extracted, these fECG signal is sent for further quality assessment as shown in Fig.2. The reason to integrate SA-GWO is to obtain an optimal value of the scaling vector, a, described in the previous section. Three optimal values are selected for the three sections of the maternal cycle based on the updated position of the search agents. GWO algorithm within the SA functions in the following manner: Preprocessing (FIR filter) SA method PCA method ACC, SE, PPV and F1 fQRS detection fQRS annotations CWT detector GWO PCA method and CWT detector mQRS detection AE1AE2AE4 AE0 AE3 N aECG1 aECG2 aECG3 aECG4 fECGPCA PCA + mQRS fECG1 fECG2 fECG3 fECG4 Figure2. Block scheme of proposed experiment. 7 Vol.:(0123456789) Scientific Reports | (2022) 12:20159 | https://doi.org/10.1038/s41598-022-24733-1 www.nature.com/scientificreports/ step 1: The search agents are initialised by assigning random position value of the agents for the scaling vector, a. step 2: The grey wolf optimiser runs for each detected mECG to give the three optimal scaling factors, which is obtained from the alpha position for individual parts of the mECG cycle: P wave, QRS complex, and T wave. step 3: The newly created template is then used to eliminate the maternal component in the input signal. step 4: The grey wolf optimiser is given the following objective to minimise: Increasing the number of iterations and the number of search agents increases the complexity but can give a slightly higher accuracy at the cost of an increase in computational time. The computational complexity of the algorithm in such cases can be addressed by using the processing speed of a field-programmable gate array (FPGA), which would improve both time and power consumption28. Though we have selected GWO for the purpose of extracting fECG, we cannot conclude that GWO is the only optimiser fit to perform the task discussed in the paper. The results are further discussed in the following section. Results This section shows the results of the experiments on real data assessed using the evaluation protocols defined above. The results for the parameters ACC, SE, PPV and F1 are summarized in Table2 for both the Labour and the Pregnancy dataset. For the Labour dataset, according to the ACC parameters, a highly accurate extraction was achieved, i.e. a value higher than 95.00% , for all records except of record r03. For record r03, the value of the ACC parameter was low ( 58.13% ), which was caused by a high number of FN and FP values (169 and 225, respectively). Such a low extraction accuracy could probably lead to an inaccurate diagnosis of the fetal health state. For the Pregnancy dataset, the ACC values were lower than 95.00% for records r02, r06, r07 and r10, but in this case the drop in accuracy was not so significant (in all four cases the ACC values were ≥88.00% ), which should not affect the resulting diagnosis of the fetal hypoxia. Regarding SE, PPV and F1 parameters, values higher than 95.00% were achieved for all three parameters for all records except r03 (SE = 76.40% , PPV = 70.85% , F1 = 73.52% ) for the Labour dataset and for all records except r10 for the Pregnancy dataset. Additionally, no FP or FN values were detected for record r10 from the Labour dataset, and all four parameters reached the values of 100.00% . Similarly, the r08 record from the same dataset detected no FP values and only one FN value, resulting in a PPV of 100.00% . (16) J =min N  n=1 (input signal −mECG template)2  (17) J=MSE(input signal −mECG template) Detected mECG cycles mECG1 mECGn Averaged mECG cycle and windowing Matrix creation Subtraction Extracted fECG signal Input aECG signal fffff mmm Prepared mECG signal Scaling coefficients Adapted mECG cycle (M · a) . . . Figure3. Block scheme of the SA with GWO. 8 Vol:.(1234567890) Scientific Reports | (2022) 12:20159 | https://doi.org/10.1038/s41598-022-24733-1 www.nature.com/scientificreports/ Since the proposed algorithm is of stochastic nature, we ran the algorithm multiple times to record the minimum accuracy average and maximum accuracy average. We conducted 10 independent runs of the algorithm for each combination in both datasets to assure its repeatability under the same conditions. For the Labour dataset, the minimum accuracy achieved from the average of all the signal combinations was 94.07% , and the maximum accuracy achieved from the average of all the signal combinations was 94.60% . As for the other parameters, we obtained the average values as follows: F1 of 96.82%, SE of 97.49%, and PPV of 98.96%. The similar test was performed on the Pregnancy dataset. The minimum accuracy achieved from the average of all the signal combinations was 94.88% and the maximum accuracy achieved from the average of all the signal combinations was 95.66% . For the rest of the parameters, following average values were achieved: F1 of 97.44%, SE of 98.07%, and PPV of 97.44%. The reference and estimated values of the clinically significant parameters of baseline fHR and fHR variation were determined for both databases and summarized in Table2. The values of baseline fHR estimated from the extracted fECG signals in the Labour dataset deviated most from the reference value in record r03 (the difference was 23.02 bpm), in record r10 with a difference of 6.54 bpm and for recording r11 with a difference of 7.37 bpm. In the Pregnancy dataset, the biggest deviation was observed in the record r04 with a difference of 8.46 bpm and in record r03 with a difference of 5.68 bpm. For the other recordings, the deviation values were lower than 5 bpm and can therefore be considered negligible. The lowest difference was achieved in the Labour dataset in the case of the record r01 with a difference of only 0.42 bpm and in the Pregnancy dataset with record r05 with even lower difference of 0.32 bpm. For fHR fluctuations, the largest deviation in the Labour dataset was observed in the case of record r04 with a value of 6.40 bpm, followed by a deviation in the record r01 with a value of 6.37 bpm and a deviation in the record r03 with a value of 5.42 bpm. For the rest of the recordings, as well as for all the recordings from the Pregnancy dataset, the difference values were lower than 5 bpm and can also be considered negligible. The lowest difference was achieved for the Labour dataset at record r08 with a value of 0.70 bpm and for the Pregnancy dataset at record r06 with a value of 0.4 bpm. The results of kSQI and sSQI for both databases are summarized in Table3. As these are parameters that are used to evaluate mainly adult ECG, there are no established threshold values or ranges that could be used for fECG evaluation. For these reasons, we will use the knowledge that is used in the adult ECG. According to29, the higher the value of the kSQI and sSQI indices, the fewer outliers equivalent to noise the signal contains, and thus the signal is of better quality. For kSQI, if its value is higher than 5, the signal is of high quality. According to the results in Table3, the values of kSQI >5 were achieved for all recordings in both datasets, and according to this parameter, all extracted signals were of high quality. According to kSQI, the highest value, and thus the best extraction, was achieved for the Labour dataset with the r07 record with a value of 21.12 and for the Pregnancy dataset with the r04 record with a value of 55.09. Conversely, according to kSQI, the lowest quality extraction was achieved for the Labour dataset with record r03 with a value of 7.73 and for the Pregnancy dataset with record Table 2. Evaluation parameters of the R-peak detection accuracy obtained by SA-GWO algorithm tested on signals from labour dataset and the pregnancy dataset. Dataset Recording Parameters TP (–) FP (–) FN (–) ACC (%) SE (%) PPV (%) F1 (%) Labour r01 640 5 4 98.61 99.38 99.22 99.30 r02 612 5 25 95.33 96.08 99.19 97.61 r03 547 225 169 58.13 76.40 70.85 73.52 r04 671 13 10 96.69 98.53 98.10 98.32 r05 653 7 7 97.90 98.94 98.94 98.94 r06 676 6 8 97.97 98.83 99.12 98.98 r07 619 10 13 96.42 97.94 98.41 98.18 r08 644 0 1 99.84 99.84 100.00 99.92 r09 666 9 8 97.51 98.81 98.67 98.74 r10 627 0 0 100.00 100.00 100.00 100.00 r11 640 10 6 97.56 99.07 98.46 98.77 r12 655 3 2 99.24 99.70 99.54 99.62 Pregnancy r01 3101 19 17 98.85 99.45 99.39 99.42 r02 2684 51 107 94.44 96.17 98.14 97.14 r03 2461 21 96 95.46 96.25 99.15 97.68 r04 2760 6 14 99.28 99.50 99.78 99.64 r05 2762 7 2 99.68 99.93 99.75 99.84 r06 2814 102 65 94.40 97.74 96.50 97.12 r07 2962 117 134 92.19 95.67 96.20 95.94 r08 2864 64 33 96.72 98.86 97.81 98.33 r09 2787 39 29 97.62 98.97 98.62 98.79 r10 2427 175 156 88.00 93.96 93.27 93.62 9 Vol.:(0123456789) Scientific Reports | (2022) 12:20159 | https://doi.org/10.1038/s41598-022-24733-1 www.nature.com/scientificreports/ r07 with a value of 8.80. Regarding the sSQI, the best result was achieved for the Labour dataset with the r08 record with a value of 1.19 and for the Pregnancy dataset also with the r08 record with a value of 6.33. The worst results were achieved for the Labour dataset with the r10 record with a value of − 1.94 and for the Pregnancy dataset also with the r10 record with a value of − 1.82. Discussion The results presented in the previous section demonstrated high effectiveness of the proposed system in extracting the fECG signal. In the clinical practice, the fHR traces are monitored and visually assessed during the pregnancy and the labor to assess fetal health state. To demonstrate the applicability of the fECG technique and the proposed extraction system in the clinical practice, we plotted the fHR traces estimated from abdominal ECG records along with the fHR traces obtained from reference annotations. The resulting fHR traces for all records from the Labour and the Pregnancy dataset are shown in Fig.4a,c, respectively. In the case of the Labour dataset, the estimated fHR traces copy the trend of the reference fHR trace for all records except record r3. In the case of the Pregnancy dataset, the estimated fHR traces copy the trend of the reference fHR trace for all records except for record r10. This corresponds to the above results—these two records achieved the poorest results in most of the tested parameters. To investigate the reasons why some of the outputs were not as accurate as others, we carried out a detailed analysis of the extracted data. For this investigation we selected samples of the signals from recordings that achieved poor results (r3 form Labour dataset and r10 from Pregnancy dataset) and the signals from recordings associated with high accuracy (r5, Pregnancy dataset). In both cases, we plotted the input aECG signal with annotations and the SA-GWO output. One can notice that the input signals from recordings r3 and r10 were both of poor quality. They are either too noisy or the ratio between the maternal and fetal component was too low. Both led to the inability of the algorithm to extract fECG signal of sufficient quality. For r3 recording, the fetal peaks were hidden in the noise, which was of the same amplitude and thus they were incorrectly detected— this led to high amount of falsely detected peaks and thus higher fHR than the one in the reference signal. This is prominent also in the lower values of objective parameters (ACC = 58.13% , SE = 76.40% , PPV = 70.85% , F1 = 73.52% ). In r10 recording, the output signal contained maternal residue of amplitude comparable with the fetal peaks. These were falsely detected as fetal R-peaks and, similarly as in the previous case, led to higher fHR in the resulting trace. Again, this resulted in decreased values of the evaluation parameters (ACC = 88.00% , SE = 93.96% , PPV = 93.27% , F1 = 93.62% ) in comparison with the remaining records (except r03, which besides the maternal residue also contained significant amount of noise). In contrast, when inspecting the signals on the examples from the r5 recording, where the extracted signals are of high quality, the maternal component Table 3. Result of Basal fHR, fHR fluctuations, Kurtosis and skewness analysis for the labour dataset and the pregnancy dataset. Dataset Recording Baseline rate Variability kSQI (–) sSQI (–)Ref. (bpm) Est. (bpm) Ref. (bpm) Est. (bpm) Labour r01 129.04 129.46 7.20 13.57 10.58 1.12 r02 133.69 132.91 7.60 9.17 12.76 1.13 r03 148.83 171.85 14.70 20.12 7.73 − 0.30 r04 137.42 141.34 9.20 15.60 11.75 − 0.48 r05 133.05 134.00 6.90 8.80 15.45 − 1.52 r06 136.92 138.70 9.50 8.20 12.11 − 1.01 r07 126.88 126.09 6.40 8.30 21.12 − 1.47 r08 129.09 133.26 7.20 6.50 12.83 1.19 r09 134.93 138.26 9.00 4.60 9.93 − 0.85 r10 125.47 132.01 6.70 8.30 16.15 − 1.94 r11 130.40 137.77 7.10 8.70 15.75 0.88 r12 131.47 132.92 8.10 6.40 11.53 0.84 Pregnancy r01 156.56 157.53 14.10 12.80 13.56 − 1.62 r02 140.58 136.45 11.20 15.83 13.00 − 1.81 r03 128.92 123.24 7.20 7.70 17.08 1.79 r04 139.47 147.93 11.70 14.90 55.09 − 1.40 r05 138.88 139.20 10.50 9.40 15.63 1.99 r06 144.70 147.05 11.30 10.90 50.53 − 1.16 r07 156.04 157.70 15.41 11.40 8.80 − 0.71 r08 145.91 146.59 12.50 16.60 14.41 6.33 r09 143.44 145.38 11.60 9.20 37.38 0.97 r10 131.60 133.46 10.00 13.90 14.53 − 1.82