Worldwide, it is estimated that the number of fetal deaths after week 20 of gestational age is around 2.6 million per year. Although the numbers have been decreasing in the past decades, the stillbirths' rate still ranges from about 1 in 250 births in developed countries and 1 per 33 in South Asia and Sub-Saharan Africa (data from 2009), according to Cousens et al. (1).

Cardiotocography (CTG) combines fetal heart rate (fHR) measurement, obtained through a uterine contraction monitoring probe and a Doppler ultrasound probe for fHR, recorded using an abdominal pressure transducer. In developed countries, clinical decisions during labor are firmly based on fHR monitoring (2, 3), being CTG the most used tool to assess fetal well-being since the early '60s according to Spencer (4). However, the information provided by CTG is limited since a complete electrocardiogram (ECG) signal of the fetus is not available. Moreover, the CTG is highly sensitive to both fetal and maternal movement. The use of an electrode placed on the fetus's scalp is more reliable as it retrieves fetal electrocardiogram, containing not only fHR but also other crucial clinical parameters (5, 6). On the other hand, this is an invasive method only possible during labor, after the beginning of cervical dilatation and the membranes' rupture, carrying with it risks of infection (7, 8). However, other methods for fetal monitoring are used such as fetal phonocardiography (9–11), fetal echocardiography (12, 13), and fetal magnetocardiography (14, 15). Each one of the methods has its own advantages and disadvantages. For more detail on this matter, see Jaros et al. (16) and Hoyer et al. (17).

Electronic fetal monitoring came with high expectations since it offered continuous monitoring, compared to the intermittent auscultation done until then. However, a meta-analysis of large multicenter studies did not prove any significant improvement. Also, electronic fetal monitoring became the main suspect for the increased rate of cesarean sections (18). These procedures result in a slight increase in poor outcomes in low-risk pregnancies. The cesarean sections also require a longer time to heal than a vaginal birth and present increased risks, including baby breathing problems, amniotic fluid embolism, and postpartum bleeding for the mother (19). Despite the importance of the fetus and mother well-being assessment, low concordance between physicians is still present, even among experienced obstetricians, resulting in a high rate of false-positives (2, 20, 21). In daily practice, fHR is subject to the clinician visual interpretation, even when following the guidelines provided by the International Federation of Obstetrics and Gynaecology (FIGO) (22, 23), which although being associated with high sensitivity but low specificity (24), might leads to a chance of more harmful than beneficial adherence to conventional guidelines (25).

The autonomic nervous system (ANS) is involved in the control of almost every organ system, and the beat-to-beat variation of fHR reflects the influence of the fetus' ANS and its components (sympathetic and parasympathetic) and, therefore, is an indicator of fetal well-being (8). A certain level of unpredictable fetal heart rate variability (fHRV) reflects sufficient capabilities of the organism in search of optimal behavior. Reduced fHRV is linked with limited capabilities and mental disorders (26). The linear modeling approaches quantify sympathetic and parasympathetic control mechanisms and their balance by measuring spectral low and high-frequency components. However, it has been shown that not all information carried by beat-to-beat variability can be explained by these components (27). For this matter, in the past couple of decades, and with the fast development of computation, new signal processing, and pattern recognition methodologies have been developed and applied to many different fields, including the analysis of fHRV using non-linear parameters (28, 29). These approaches can reveal relevant clinical information not exposed by temporal or frequency analysis (30).

Variability and complexity are different terms. While a complex system requires variability, the other way around is not guaranteed. For example, a set of random notes in music can be interpreted as having high complexity for its non-predictability, whereas a set of consecutive notes is highly predictable, and both have high variability. Thus, complexity signals, such as those produced by self-regulatory physiological systems, present temporal or spatial structures over a varied range of scales. Because of their non-linearity and non-stationarity, conventional indicators, such as the mean and the standard deviation, do not fulfill their purpose (31). In the end, complexity is a property of any system that quantifies the amount of structured information.

Chaffin et al. (32), in 1991, were the first to use non-linear analyzes in fHR. The authors applied fractal analysis (correlation dimension) to study 12 normal fetuses' well-being in labor. Later, in 1992, Pincus and Viscarello (33) found statistically significant results using approximate entropy (ApEn) when comparing a group of acidemic fetuses with non-acidemic ones. These results supported the hypothesis that regular fHR patterns are associated with acidemia. Datian and Xuemei (34), in 1996, introduced a new wavelet analysis method used to detect fetal electrocardiogram from the abdominal signal and compared to other methods in practice. Signorini et al. (35), in 2005, applied data compression (Lempel Ziv complexity) for the first time in the fHR analysis to improve the early detection of fetal distress conditions such as intrauterine growth restriction. The same authors, also in 2007 (36), used the Lempel Ziv complexity to successfully discriminate between severe intrauterine growth restriction (IUGR) (premature birth) and non-severe IUGR (term delivery) and normal fetuses. In the subsequent year, using a compressor-based clustering algorithm called normalized compression distance (NCD), Santos et al. (37) managed to clustered abnormal and suspicious tracks, regardless of the monitoring system used. Barquero-Pérez et al. (38) also used NCD for automatic detection of perinatal hypoxia.

The main contribution of this article is to provide a systematic review of articles that apply entropy, compression, fractal, and wavelet analysis to study the dynamics of fHR and analyze the research objectives of these articles. As far as we know, there is no systematic review for this purpose in the literature.

We begin by describing the methodology used, specifying the sources of information, the eligibility criteria, the study selection, data extraction, and quality assessment in section 2. Based on the systematic review results, we describe in detail the most commonly used non-linear methods to assess the dynamics of fetal heart rate and analyze how the study of the complexity of fHR has evolved over the years (section 3). In section 4, we describe the most frequent goals in research. We analyze the evolution of the non-linear methods' applications to these objectives and probe how the research objectives are related to non-linear methods. In section 5, we reflect on some open questions regarding the application of non-linear measurements to fHR dynamics. We finish this paper with the main conclusions in section 6.

This systematic review focused on original papers that include non-linear analysis, such as complexity measures, fractal approaches, and wavelets, of human fetal heart rate during ante and intrapartum. The online search was performed on Medline, through PubMed, and the Web of Science databases, searching all the papers published until the 4th of October 2020. The following terms were used as descriptors/Mesh: “non-linear dynamics,” “entropy,” “data compression,” “complexity,” “fractals,” “wavelets,” “fetal heart rate,” “foetal heart rate.” The queries used in each database can be found in Table 1. This study was conducted according to the Preferred Reporting Items for Systematic Reviews and Meta-analyses (PRISMA) statement (39). The review protocol was not registered prospectively.

Inclusion criteria for selecting studies were the following: observational or experimental papers presenting complexity analysis of fetal heart rate; abstract found online; reported original research in peer-reviewed journals; at least one measure from the following was used in the analysis (entropy, compression, fractal, or wavelet). Papers using non-human fetal heart rate analysis, papers without an English version, reviews, case studies, dissertations, and thesis were excluded (see Figure 1).

All authors were involved in the selection of studies, data extraction, and quality assessment. Two authors independently assessed each title and abstract found in the databases. The full texts of potentially relevant studies have been retrieved and revised in depth. Disagreements between reviewers were resolved by consensus or by the decision of a third independent reviewer. For each article, the following data were collected: year of publication, study design, objective, sample size, measure(s) used to analyze fHR, and conclusions. Both reviewers made sure that all included papers met the criteria defined in the first stage.

A total of 603 abstracts were assessed, 368 of which retained for full-text screening. Two hundred and seventy papers were then included in the review after meeting all the criteria. Figure 1 contains the PRISMA flow diagram for study selection, including reasons for exclusion. The most used non-linear analysis measures to study the dynamics of fHR obtained in the systematic review are also represented in Figure 1.

Although linear indices have been extensively used in fetal monitoring for the past decades, it is established that biological systems are more complex than they appear. Non-linear measures based on concepts of chaos, fractality, and complexity have gained space and demonstrated promising results in the analysis of fetal well-being and the prediction of pathologies. The application of non-linear measures to study the dynamics of fHR has increased over the years. The non-linear methods covered by this review are entropy, compression, fractal analysis, and wavelet analysis. The results show that entropy is the most applied measure in fetal heart rate, followed by fractal analysis, wavelet analysis, and the least applied is the compression (see Figures 1, 2). Although the application of entropy methods stands out, we can see that compression and wavelet analysis methods have been increasingly used in recent years (see Figure 2).

In the following sections, the most applied non-linear methods are described. In our systematic review, other non-linear methods were found, such as, Poincaré plot (in 18 papers), symbolic dynamics (in 12 papers), phase rectified signal average (in 10 papers), Lyapunov exponents (in 6 papers), and recurrence plot analysis (in 6 papers). However, due to the reduced number of uses, they were not described in detail. For this review, we decided to describe only the measures most applied to fHR.

There is no doubt of the importance of non-linear measures in fetal monitoring, as they enrich the signal description by providing new indicators for classification and diagnostic purposes. Numerous studies have documented the changes in fHRV during gestation, and fetal growth is associated with a drop in fetal heart rate and increased variability. As non-linear measures started being used, authors started to link their association with different physiological regulatory systems.

The history of non-linear methods reported to fHR summarizes 30 years. However, in the last 15 years, there has been a notable increase in their application to study fHR dynamics (see Figure 7). The main research objectives covered by this systematic review were signal processing (60 papers), hypoxia (56 papers), maturation or gestational age (53 papers), IUGR (44 papers), and fetal well-being or fetal distress (26) (see Figure 7 and Table 2). Also, in Figure 7, the evolution of papers' of the five most cited research objectives is presented per year.

Hypoxia can be caused by prolonged or profound asphyxia, an oxygen deficiency due to a pathological change in either fetal or maternal components of the placenta, when there is an exchange of carbon dioxide and oxygen by the fetus during labor. This state leads to an accumulation of carbon dioxide leading to fetal acidemia, resulting in a lower pH in the fetal blood vessels. Early detection of which babies are at risk of acidemia is crucial, as it decreases the chance of a post-diagnosis of cerebral palsy, neonatal encephalopathy, or even death (126). To relate fHR with umbilical artery pH is, therefore, of extreme importance. However, the proper definition of fetal acidemia is still not established as different authors consider different pH cutoffs. Moreover, some authors also include in the definition the value of the base excess or base deficit (127). Some authors defined as “at risk of acidemia” when pH < 7.20 (33, 47, 128–136) or pH < 7.15 (30, 121, 137–143); others define when pH < 7.1 (43, 126, 144–146) or even when pH < 7.05 (38, 44, 48, 78, 147–165). Some studies used clinical experts to identify episodes of hypoxia and asphyxia, such as, (54, 166, 167). Another challenge relate to this pathology is to collect enough data for a proper acidemia analysis since prevalence of an acidemic fetus ranges from 0.6 to 3.5% (168, 169). From the 56 papers that aim to analyze of perinatal hypoxia or asphyxia 40 papers applied entropies, 19 applied compression measures, 23 applied fractal measures, and 23 papers applied wavelets analysis.

The development of non-invasive ultrasound techniques allowed a better estimation of gestational age and, therefore, the definition of a crucial fetal outcome: small for gestational age (SGA), which corresponds to fetuses having a weight lower than the 10th percentile adjusted to gestational age. Nevertheless, healthy babies can also be considered SGA, so it is still a challenge to decide whether the small dimensions are due to physiological or pathological conditions (170). Related to SGA fetus, one of the most common pathologies is IUGR. IUGR is a metabolic dysfunction inhibiting the fetus from achieving its average size. With a prevalence of 5−8% in the general population, it can complicate 10–15% of all pregnancies (171). IUGR is the second cause of perinatal mortality, after prematurity (172), and is still an important challenge for diagnosis and management (173). From the 44 papers that aim to study IUGR, 32 papers applied entropies, 15 applied compression measures, 11 fractal and only 2 papers used wavelets.

The effect of an antepartum vs. intrapartum analysis on the complexity indices and the differences in the signal acquisition methods are important to correctly evaluate and assess fetus well-being (174, 175). Throughout pregnancy, the fetus interacts with its environment, as the mother sets the framework for the state and development of the fetus (176). In a study where the mother's breathing was controlled, Van Leeuwen et al. (176) found that the presence or absence of interaction between mother and fetus cardiac activity might be due to maternal respiration. Also, the fetal cardiac system seems to have the capability to adjust its activation rate when responding to external stimuli. Spyridou et al. (177) studied the effect of smoking in fHR and found differences with several linear and non-linear parameters (such as, mutual information, MSE, and compression). In particular, it was shown less complexity for fetus exposed, enhancing its danger. From the 26 papers that aim to study fetal well-being or fetal distress 17 papers applied entropies, 4 applied compression measures, 7 fractal, and only 3 papers used wavelets.

When assessing fHRV, it is essential to control any factor which might confound its interpretation. Some of the most studied factors are the baby's maturation reflected in gestational age, behavioral state, and maternal condition (178). From the 53 papers that aim to study maturation or gestational age 38 papers applied entropies, 7 applied compression measures, 18 fractal and only 3 papers used wavelets. First trimester observations during pregnancy have shown a low intraindividual variation of the fHR, compared to variation between different fetuses (179). Later in pregnancy, Arduini also found this high intraindividual consistency concerning fetal behavioral states' characteristics, particularly fHR, in 2 consecutive days (180). In fact, an association between individual differences in prenatal heart rate and HRV and postnatal neural development has been reported (181). Besides these factors, Gonçalves et al. (131) and Spyridou et al. (182) noted that gender also has an effect on fHR analysis and should be considered, while Tagliaferri et al. (183) found differences on both linear and non-linear indices between different ethnic groups. Gender was also shown to influence maternal heart rate (MHR) (52). Even when twins are considered, sex differences were found both by linear and non-linear indices (184). Fetal presentation at birth has also been studied (185, 186). Reports are stating that breech fetuses have worse neurological outcomes compared to cephalic presentation ones (187, 188). Furthermore, in a study by Choi and Hoh (189), non-linear dynamic indices were able to differentiate normal pregnancies from ones with partial placental abruption with high accuracy, while linear indices were not.

The evaluation of neonatal behavior has shown more success in predicting neurodevelopment disability than neurological examination (190). Therefore, the same approach was adopted for fetal well-being assessment. These fetal behavioral states were introduced back in 1982 in studies combining the assessment of fetal body and eye movements (191). They include calm or non-eye movement sleep state (1F), active or rapid eye movement sleep state (2F), calm wakefulness state (3F), and active wakefulness state (4F). The importance of these definitions in understanding fetal physiology, interpretation of fHR monitoring, and diagnosis of pathological conditions is described with more detail elsewhere (192). There are associations between fetal behavioral states and fHR patterns. 1F is related to a stable baseline with absent or sporadic and short-lasting accelerations; 2F is associated with a stable baseline and frequent accelerations, and it is the most frequent state. 3F is rare and is usually very short in time. It also has a stable baseline but with wide variability and no accelerations. 4F shows repetitive and long-lasting accelerations with eventual returns to the baseline (193).

This field's interest is not only focused on fHR tracings classification. Features like frequency and amplitude traditionally characterize physiological signals. However, these parameters do not provide us with an insight into the regulatory processes underlying the signal dynamics, thus requiring a further extraction of more appropriate features, which has become a difficult task. These difficulties lie in the lack of a priori information on which process belongs to each component (i.e., fetal, maternal, or environmental) and the lack of knowledge on how each component behave (194). Much effort has been put into the signal acquisition and processing models because the extracted features' usability highly relies on the preprocessing steps' quality, such as artifacts removal, interpolation method, segmentation, and detrending signal (30).

In 2013, an open challenge was created, the Physionet Challenge (195), in order to promote the development of advanced signal processing techniques. Many different approaches were suggested, such as wavelet de-denoising, subspace decomposition and reconstruction, adaptive filtering and averaging, matched filtering, and entropy. Most of them followed these four steps: signal processing, maternal heartbeat detection, maternal heartbeat cancelation, fetal heartbeat detection. More information can be found in Di Maria et al. (196). These non-linear methodologies have been studied and applied to retrieve signal with the best quality possible, dismissing as much noise as possible. The preprocessing is even more important when adopting low-cost systems for signal extraction, as is the case of the fetal phonocardiography, which has a poor signal-to-noise ratio (11). From the 60 papers that aim to study signal processing 7 papers applied entropies, 1 applied compression measures, 7 fractal, and 45 papers used wavelets.

Table 2 presents the number of articles that applied each non-linear method for each research objective. Entropy, compression, and fractal measures are most used in classification papers, mainly when applied to analyze the variability of fHR in hypoxia, IUGR, and fetal distress. However, these measures are still underused in studies whose research objective is signal processing. On the other hand, wavelet analysis is most used when the research objective is signal processing (43 papers) or hypoxia (25 papers).

The number of articles probing the use of non-linear measures to assess the fHR signals analysis has been growing in the past decade. Non-linear analysis has been successfully applied in the study of fetal heart rate with several research objectives, such as fetal maturation or gestational age (197–199), fetal gender (182, 200), labor stages (201, 202), cesarean section (51, 203), preterm birth (80, 204), impact of nuchal cord on antenatal (205), fHR baseline (206), behavioral state (207, 208), IUGR (209–213), hypoxia (128, 137, 214, 215), fetal distress (216–218), maternal pathologies (219, 220), and signal processing (198, 221–224). Therefore, it is important that the scientific community is aware of the non-linear methods used depending on the research objective. Additionally, they are not yet used in clinical practice due to some critical concerns that need to be further discussed.

Systems, such as, Omniview SisPorto (225), OxSys (226), NST-Expert, which later became CAFE (227) already automatically deal with CTG assessment. All the fHR processing and analysis in these systems are based on morphological features defined by FIGO guidelines. In some, the CTG is complemented with the ST-analysis method. It has been shown that it slightly improves labor outcomes, but its use is not always possible since it requires an invasive measurement (228). However, none of these systems still integrates non-linear indices, so they can and should be optimized.

When analyzing fHR time series automated, there are two main aspects to contemplate: the signal properties and quality and the clinical characteristics that might influence the measures used. Accordingly, we found that the most studied research objectives in fHR are signal processing, hypoxia, and maturation. Furthermore, the results show that entropy is the most applied measure in fetal heart rate, followed by fractal analysis, wavelet analysis, and the least applied is compression. Although the application of entropy methods stands out, we can see that compression and wavelet analysis methods have been increasingly used in recent years. Also, highlighting the fact that entropy is the oldest method, and that is it has been extensively studied and refined when applied to much different time series (229). On the other hand, wavelets are widely used in signal processing (124, 222) dealing with the signal itself, handling problems such as noise (230) and frequency.

Routinely, the fetal heart rate monitors acquire the beat-to-beat intervals in milliseconds either from Doppler or electrocardiographic signals and then convert them to provide a sequence of instantaneous heart rates in beats per minute (bpm). However, when data is exported, it is sampled, implying an interpolation of signals (132). The sampling rate does not seem to affect many linear parameters, but differences were found when non-linear indices were considered (175). Caution must be taken when defining reference values for irregularity indices, such as entropy, as they depend on the sampling frequency, as shown in (175), where 2 vs. 4 Hz sampling was compared. It is most important not to compare computerized systems for heart rate frequency analysis that use different sampling rates (225, 231).

Several linear methods have been studied as a forecaster of fetal well-being by measuring the interaction between the fetal sympathetic and parasympathetic nervous systems and its effects on fetal cardiovascular activity (232). As the parasympathetic nervous system is more responsible for variations in short-term variability (STV), which usually assesses the beat-to-beat differences, it might be reduced in central nervous system hypoxia/ acidosis. If hypoxia is sustained and increases in severity, it leads to the loss of long-term variability (LTV) (233), resulting in a global decrease of sympathetic and parasympathetic activity. On the other hand, it has been shown that fetal hypoxia's early effects increased short and long-term variability (234). Notwithstanding, many studies verify the weakness of STV and LTV indices in identifying fetal pathologies (235). Furthermore, with fetus maturity throughout pregnancy, an increase in fetal autonomic nervous system activity and the sympathovagal balance is expected. Moreover, motor and neurological delay, as well as damage in specific brain areas with cognitive effects, also affect the STV (236). The IUGR showed a reduction in both components of the autonomic nervous system activity, which modulates heartbeat intervals receiving inputs from the heart, the lungs, and the blood vessels (204, 209, 237).

The indices presented in this review are closely related to fetal heart variability. For instance, in (199) the authors showed that the complexity indices correlate highly with abnormal STV. In (143) the authors also report correlations between the complexity indices ranging from 0.53 to 0.78. Therefore, many studies found a reduction of complexity in the fHR signal associated with hypoxia/ acidosis. However, these indices were not always able to identify fHR from IUGR fetuses (237). Contrastingly, the fractal indices are measures of long-range correlations and long-term memory of time series, therefore, applied mainly in maturation studies.

Furthermore, many of the fetal heart rate analysis methods rely upon stationarity properties like mean, variance, and correlation structure. However, it is known that these fHR properties vary in time through events like uterine contractions. One way to counter this is to select small temporal windows where this property holds. Usually, an interval of 10–20 min is considered the minimum time window to perform the analysis for tracing classification and clinical decision (231, 238). In addition, many of the described measures are parametric measures. The choice of the ideal parameter is far from established in most cases. This heterogeneity limits the possible comparison between the results of different studies. In fact, in various papers, the choice of parameters is neither discussed nor even fully described.

Factors like fetus maturation, behavioral states, and maternal conditions are critical for a good assessment of the fetus and fully understanding their influence in the fHRV is no easy task. Incorporating such variables in predictive models for fetal evaluation will elucidate the importance of individual fHRV and increase its accuracy (178). Maternal psychological conditions such as stress and anxiety influence fHR and maternal hormones transferred via placenta or changes in the oxygen and nutrition supply for the fetus (239, 240). As seen in some results, gender is also a factor that should be taken into consideration. Even when twins are considered, sex differences were found both by linear and non-linear indices (184). Although Park et al. (185) found no significant differences between fetuses with different fetal presentation using spectral and complexity measures such as Lempel-Ziv complexity, ApEn, SampEn, and CD. Gonçalves et al. (186) found differences not only using linear indices but also with non-linear and spectral ones. This example of contrasting results reflects the difficulty and complexity of the fetal assessment. In this case, and according to the authors, the discrepancy might have resulted from different inclusion criteria, conditions for fHR recording, the occurrence of maternal fasting, time interval between acquisition and delivery, and equipment used. Moreover, an interesting study comparing uterine contraction influence on fHRV features between acidemic and non-acidemic fetuses suggested that separating contractions from rest periods improves fHRV analysis in detecting asphyxia during labor (151).

Having as a premise that humans are a result of self-organization and adaptation process and that ontogenetic development reflects phylogenetic development and indices of developmental biology may be helpful in fetal maturation assessment. Many studies addressed here found HRV changes, such as variability increase and pattern formation (204). These universal developmental features deliver appropriate measures of fetal maturation. Therefore, it seems only natural that these self-organization and adaptation features might better understand and identify developmental disorders (241). In fact, attention-deficit hyperactivity disorders in teenage boys were associated with antenatal maternal anxiety (242), which might influence fetal humoral development and autonomic control reproduced in heart rate patterns. This phenomenon, resulting from adverse influences on the fetus explained by epigenetic mechanisms, is called “fetal programming.” Therefore, early identification of fetal developmental disorders is essential as they may not be wholly compensated for later postnatal therapies (243). Many different approaches to fHR processing and analysis have been studied. They range from simple feature extraction methods to more sophisticated classification programs and joining research centers from different countries for joint projects, as the Digi-Newb project (244). Usage of continuous non-invasive evaluation, such as the usage of wearables, have been discussed (27, 245) and will contribute to the patient's care improvement since it will improve data gathering, reducing costs of fetal monitoring. Insurgent approaches are opening new windows on the continuous monitoring of fetal development. A single index cannot retrieve all the information from pathophysiological processes in the fetus's development, so approaches considering both linear and non-linear measures, through multivariate analysis, can improve the assessment of both fetal and maternal well-being.

In (35, 246), time, spectral and complexity indices were used as parameters to discriminate fetuses who were or not in a distressed state. Ferrario et al. (247) conclude that compression quantifies the rate of new patterns arising as the signal evolves, whereas entropy quantifies the recurrence of repetitive patterns. This idea of complementary of different indices is also supported in other papers (130, 145, 167, 247). It seems only logical for such a complex/chaotic system to be evaluated using a multiparameteric approach through advanced classification techniques capable of discriminating fetuses in distress in non-linear regions of a multidimensional space (30). With this approach, Signorini (248) was able to classify IUGR fetuses with accuracy, sensitivity, and specificity above 90%.

Mapping from feature space captured from the fHR signal to the space of decision or diagnosis, many machine learning, and deep learning techniques has been applied. Some examples are: support vector machines (38, 150, 152, 249, 250), conventional methods like k-nearest neighbors (250, 251), a hybrid approach using grammatical evolution (146, 252), artificial neural networks (134), and random forests (49, 253, 254). Cömert and Kocamaz (166) introduced a novel software for comprehensive CTG signals analysis, named CTG Open Access Software (CTG-OAS). This software embeds machine learning tools, such as preprocessing, feature extraction, feature selection, and classification. Fergus et al. (51) demonstrated, using deep learning tools, that machine learning significantly improves the efficiency of detecting cesarean section and vaginal deliveries, compared with the usual visual assessment. In this paper, impressive results were achieved, with both sensitivity and specificity over 90%. One problem of comparing these classification approaches is the apriori definition of the classes. For example, as said before, the definition of acidemia based on the umbilical cord artery's pH varies greatly between studies. Karvelis et al. (255) proposed a classification approach based on weighted voting of clinical annotations. These weights are estimated by using a latent class model with three or four latent classes. Moreover, as these learning techniques depend on the signal and the linear and non-linear measures computed, all the previously referred concerns must be contemplated meticulously. Therefore, the machine and deep learning techniques are particularly resourceful when the measures are thoroughly probed and understood. In this systematic review were found several other articles with machine learning and deep learning techniques. However, the description of these techniques is not the focus of this paper. Future work that analyzes in detail the machine learning and deep learning techniques that apply measures based on fHR dynamics should be considered.

The non-linear methods described in this review are entropy (Shannon, approximate, sample, and multiscale), compression, fractal analysis (fractal dimension, Hurst exponent, detrended fluctuation analysis, and multifractal detrended fluctuation analysis), and wavelet analysis. Other non-linear methods were found in our review, such as Poincaré plot (217), symbolic dynamics (256), phase rectified signal average (210, 211, 257, 258), Lyapunov exponents (259), and recurrence plot analysis (137). In the recent years, Phase Rectified Signal Averaging and derived parameters have been largely applied in fHR analysis to face the problem of accelerations and deceleration which are characteristic of the fHR signal.

Due to the high heterogeneity of study designs, data acquisition methods, aims of the studies, signal processing techniques, and measures (and parameters) used, no meta-analysis was possible to be performed.

This systematic review confirmed the importance of non-linear fetal monitoring measures to analyze the fetus' well-being and pathologies' prediction. The methods probed successfully diagnose pathologies, and new techniques are being proposed and explored to improve that prediction. However, the contradictory results of some of the findings due to the characteristic of the signal, or the sensibility of the measures to some clinical factors, such as fetus sex and gestational age, revealed that the use of these findings in clinical practice is far from reality. These results inhibit the reach for a gold standard or the creation of a decision support system. This review determined the significance of creating several small meta-analyses that might focus on a specific research aim. Additionally, a sizeable multicentric study that can assess the multitude of perspectives involved in the fHR signal analysis is imperative.

Non-linear measures based on the concepts of chaos, fractality, and complexity gained space in the analysis of fetal heart rate. Good results were achieved in signal processing, in the analysis of fetal well-being, and in diagnosing and predicting pathologies. This systematic review of the non-linear methods (entropy, data compression, fractal analysis, and wavelet analysis) applied to fetal heart rate dynamics includes 270 papers. The application of non-linear methods in the fHR analysis is around 30 years old. However, its application has significantly increased in the last 15 years. This review's main contributions are a detailed description of the non-linear methods most applied in the fHR papers and a discussion of the research objectives. Signal processing, hypoxia, and maturation lead the research objectives of papers that use non-linear analysis in fHR. We found that entropy has been the most used method in classification analysis. Despite, in signal processing, the most used method is wavelet analysis. Machine learning and deep learning techniques should also be analyzed with results in the study of fHR dynamics using linear and non-linear measures. The multitude of conditioning involved in the analysis and classification of the fHR, from the signal characteristics to the effect of some clinical factors in the measures, limits the use of the non-linear measures in clinical practice and difficult the creation of a decision support system. Future studies should focus on a research question and perform a meta-analysis, probing the indices' performance.

The original contributions presented in the study are included in the article/supplementary material, further inquiries can be directed to the corresponding author/s.

JM-S, LA, CC-S, and AT conducted the preliminary literature review by establishing the search method and keywords. MR, JM-S, and AT determined the eligibility, summarized the findings from each study, and compiled them in tables. LC, CC-S, and TH analyzed the disagreements between reviewers. MR, JM-S, LC, AT, and TH writing and editing of the manuscript. CC-S, LA, AT, and TH supervision. All authors revised the paper critically for important intellectual content, made substantial contributions to the conception and design of the article, and agreed to the published version of the manuscript.

The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.

All claims expressed in this article are solely those of the authors and do not necessarily represent those of their affiliated organizations, or those of the publisher, the editors and the reviewers. Any product that may be evaluated in this article, or claim that may be made by its manufacturer, is not guaranteed or endorsed by the publisher.