Binary symbolic dynamics classifies heart rate variability patterns linked to autonomic modulations

A Comprehensive Review of Techniques for Processing and Analyzing Fetal Heart Rate Signals

The availability of standardized guidelines regarding the use of electronic fetal monitoring (EFM) in clinical practice has not effectively helped to solve the main drawbacks of fetal heart rate (FHR) surveillance methodology, which still presents inter- and intra-observer variability as well as uncertainty in the classification of unreassuring or risky FHR recordings. Given the clinical relevance of the interpretation of FHR traces as well as the role of FHR as a marker of fetal wellbeing autonomous nervous system development, many different approaches for computerized processing and analysis of FHR patterns have been proposed in the literature. The objective of this review is to describe the techniques, methodologies, and algorithms proposed in this field so far, reporting their main achievements and discussing the value they brought to the scientific and clinical community. The review explores the following two main approaches to the processing and analysis of FHR signals: traditional (or linear) methodologies, namely, time and frequency domain analysis, and less conventional (or nonlinear) techniques. In this scenario, the emerging role and the opportunities offered by Artificial Intelligence tools, representing the future direction of EFM, are also discussed with a specific focus on the use of Artificial Neural Networks, whose application to the analysis of accelerations in FHR signals is also examined in a case study conducted by the authors.

Symbolic Analysis of the Heart Rate Variability During the Plateau Phase Following Maximal Sprint Exercise

Cardiac autonomic control is commonly assessed via the analysis of fluctuations of the temporal distance between two consecutive R-waves (RR). Cardiac regulation assessment following high intensity physical exercise is difficult due to RR non-stationarities. The very short epoch following maximal sprint exercise when RR remains close to its lowest value, i.e., the PLATEAU, provides the opportunity to evaluate cardiac regulation from stationary RR sequences. The aim of the study is to evaluate cardiac autonomic control during PLATEAU phase following 60-m maximal sprint and compare the results to those derived from sequences featuring the same length as the PLATEAU and derived from pre-exercise and post-exercise periods. These sequences were referred to as PRE and POST sequences. RR series were recorded in 21 subjects (age: 24.9 ± 5.1 years, 15 men and six women). We applied a symbolic approach due to its ability to deal with very short RR sequences. The symbolic approach classified patterns formed by three RRs according to the sign and number of RR variations. Symbolic markers were compared to more classical time and frequency domain indexes. Comparison was extended to simulated signals to explicitly evaluate the suitability of methods to deal with short variability series. A surrogate test was applied to check the null hypothesis of random fluctuations. Over simulated data symbolic analysis was able to separate dynamics with different spectral profiles provided that the frame length was longer than 10 cardiac beats. Over real data the surrogate test indicated the presence of determinism in PRE, PLATEAU, and POST sequences. We found that the rate of patterns with two variations with unlike sign increased during PLATEAU and in POST sequences and the frequency of patterns with no variations remained unchanged during PLATEAU and decreased in POST compared to PRE sequences. Results indicated a sustained sympathetic control along with an early vagal reactivation during PLATEAU and a shift of the sympathovagal balance toward vagal predominance in POST compared to PRE sequences. Time and frequency domains markers were less powerful because they were dominated by the dramatic decrease of RR variance during PLATEAU.

Binary symbolic dynamics analysis to detect stress-associated changes of nonstationary heart rate variability

Psychological stress may have harmful physiological effects and result in deteriorating health. Acute psychological stress acts also on cardiac autonomic regulation and may lead to nonstationarities in the interbeat interval series. We address the requirement of stationary RR interval series to calculate frequency domain parameters of heart rate variability (HRV) and use binary symbolic dynamics derived from RR interval differences to overcome this obstacle. 24 healthy subjects (12 female, 20–35 years) completed the following procedure: waiting period, Trier Social Stress Test to induce acute psychological stress, recovery period. An electrocardiogram was recorded throughout the procedure and HRV parameters were calculated for nine 5-min periods. Nonstationarities in RR interval series were present in all periods. During acute stress the average RR interval and SDNN decreased compared to rest before and after the stress test. Neither low frequency oscillations (LF), high frequency oscillations (HF) nor LF/HF could unambiguously reflect changes during acute stress in comparison to rest. Pattern categories derived from binary symbolic dynamics clearly identified acute stress and accompanying alterations of cardiac autonomic regulation. Methods based on RR interval differences like binary symbolic dynamics should be preferred to overcome issues related to nonstationarities.

Comparison of fetal heart rate variability by symbolic dynamics at the third trimester of pregnancy and low-risk parturition

Fetal heart rate variability (fHRV) is an essential source of information to monitor fetal well-being during pregnancy. This study aimed to apply a nonlinear approach, known as symbolic dynamics (SD), for comparing human fHRV in the third trimester of pregnancy during active fetal state (TT) and active labor at term (P). We performed a longitudinal, prospective, descriptive, and comparative study composed of 42 longitudinal recordings of 5-minutes of fetal heartbeat interval series. Recordings were collected from 21 low-risk, healthy, pregnant women attending the Maternal and Child Research Center (CIMIGen), Mexico City. We calculated relevant linear parameters of fHRV between TT and P stages, such as the percentage of differences between adjacent RR intervals >5 ms (PRR5, related to vagal modulations) and other SD parameters such as the percentage of no variations between three successive symbols (%0V, reflects sympathetic modulations) and the probability of low variability with a threshold of 4 ms (POLVAR4, associated with a low variability). We identified statistical differences for PRR5 between TT and P (37.13% [28.47-47.60%] vs. 28.84% [19.36-36.76%], p = 0.03), respectively. Also, for 0V% (65.66% [59.01-71.80%] vs. 71.14% [65.94-75.87%], p = 0.03) and for POLVAR4 values (0.06 [0.04-0.11] vs. 0.15 [0.09-0.24], p = 0.002), respectively. Our results indicate that during parturition, the short-term fetal fHRV is decreased, showing a decreased vagal modulations and higher adrenergic response of the heart. These autonomic modifications may result from the fetal response to the stressful inflammatory challenge of labor. We thus confirmed that the analysis of the SD applied to fHRV time series could be a potential clinical biomarker to differentiate the fetal autonomic cardiac condition at different stages of pregnancy.

Monitoring fetal maturation-objectives, techniques and indices of autonomic function

Monitoring the fetal behavior does not only have implications for acute care but also for identifying developmental disturbances that burden the entire later life. The concept, of 'fetal programming', also known as 'developmental origins of adult disease hypothesis', e.g. applies for cardiovascular, metabolic, hyperkinetic, cognitive disorders. Since the autonomic nervous system is involved in all of those systems, cardiac autonomic control may provide relevant functional diagnostic and prognostic information. The fetal heart rate patterns (HRP) are one of the few functional signals in the prenatal period that relate to autonomic control and, therefore, is predestinated for its evaluation. The development of sensitive markers of fetal maturation and its disturbances requires the consideration of physiological fundamentals, recording technology and HRP parameters of autonomic control. Based on the ESGCO2016 special session on monitoring the fetal maturation we herein report the most recent results on: (i) functional fetal autonomic brain age score (fABAS), Recurrence Quantitative Analysis and Binary Symbolic Dynamics of complex HRP resolve specific maturation periods, (ii) magnetocardiography (MCG) based fABAS was validated for cardiotocography (CTG), (iii) 30 min recordings are sufficient for obtaining episodes of high variability, important for intrauterine growth restriction (IUGR) detection in handheld Doppler, (iv) novel parameters from PRSA to identify Intra IUGR fetuses, (v) evaluation of fetal electrocardiographic (ECG) recordings, (vi) correlation between maternal and fetal HRV is disturbed in pre-eclampsia. The reported novel developments significantly extend the possibilities for the established CTG methodology. Novel HRP indices improve the accuracy of assessment due to their more appropriate consideration of complex autonomic processes across the recording technologies (CTG, handheld Doppler, MCG, ECG). The ultimate objective is their dissemination into routine practice and studies of fetal developmental disturbances with implications for programming of adult diseases.

Heart rate variability in shift workers: responses to orthostatism and relationships with anthropometry, body composition, and blood pressure

In order to investigate the response of heart rate variability (HRV) components to postural change and their association with cardiovascular risk factors in shift workers, a cross-sectional study with 438 Brazilian males rotating shift workers was done. Anthropometric, body composition, and clinical measures were collected. Electrocardiogram was recorded for 3 minutes, in the supine and orthostatic position, and HRV components were extracted. Descriptive analyses showed that mean values of body mass index, waist circumference (WC), waist-to-height ratio, visceral fat area (VFA), and blood pressure (BP) were higher than the reference values. In the regression model, age, WC, VFA, and systolic BP showed negative association with HRV components. These findings suggest the need for determining effective strategies for the evaluation and promotion of health among shift workers focused on the altered variables.

Different approaches of symbolic dynamics to quantify heart rate complexity

The analysis of symbolic dynamics applied to physiological time series is able to retrieve information about dynamical properties of the underlying system that cannot be gained with standard methods like e.g. spectral analysis. Different approaches for the transformation of the original time series to the symbolic time series have been proposed. Yet the differences between the approaches are unknown. In this study three different transformation methods are investigated: (1) symbolization according to the deviation from the average time series, (2) symbolization according to several equidistant levels between the minimum and maximum of the time series, (3) binary symbolization of the first derivative of the time series. Each method was applied to the cardiac interbeat interval series RR(i) and its difference ΔRR(I) of 17 healthy subjects obtained during head-up tilt testing. The symbolic dynamics of each method is analyzed by means of the occurrence of short sequences ('words') of length 3. The occurrence of words is grouped according to words without variations of the symbols (0V%), words with one variation (1V%), two like variations (2LV%) and two unlike variations (2UV%). Linear regression analysis showed that for method 1 0V%, 1V%, 2LV% and 2UV% changed with increasing tilt angle. For method 2 0V%, 2LV% and 2UV% changed with increasing tilt angle and method 3 showed changes for 0V% and 1V%. In conclusion, all methods are capable of reflecting changes of the cardiac autonomic nervous system during head-up tilt. All methods show that even the analysis of very short symbolic sequences is capable of tracking changes of the cardiac autonomic regulation during head-up tilt testing.

Formation of functional associations across time scales in the fetal autonomic control system--a multifractal analysis

During fetal development, different control systems mediated by the autonomic nervous system form functional connections over a wide range of time scales. Using multiscale multifractal analysis (MMA) of fetal heart rate variability (HRV), we describe fundamental relationships in the developing scale-wide adjustments within fetal behavior states as well as across state changes. MMA yields the local Hurst exponent surface h(q,s) with q as the multifractal parameter and s as the scale. In 30-minute recordings of healthy fetuses between 24 and 36weeks of gestation (n=25 in quiet sleep, n=29 in active sleep, n=30 changing sleep state) we investigated the dependency of h(q,s) on gestation age. In univariate models, we found a decreasing persistence for short scales and small amplitudes in the quiet (s1=39, q1=-0.7, R(2)=0.52) and in the active (s1=69, q1=-1.4, R(2)=0.23) sleep in contrast to an increasing persistency for long scales and large amplitudes (s1=147, q1=2.4, R(2)=0.29) in the mixed state. Bivariate models (additional scales considered) presented increased coefficients of determination R(2)=0.56, 0.4, and 0.43, respectively. Persistency increasing with age in connection with the sleep state changes (independent of the age related short range dependencies within the separate homogeneous sleep states) is reported here for the first time. The MMA indices obtained for the fetal HRV represent characteristics of the maturating scale-wide cardiovascular control in the context of the evolving sleep state dynamics, which have so far not been considered. They should be incorporated in the search for HRV indices for prenatal diagnosis of developmental disorders and risk assessment.

Symbolic transformations of heart rate variability preserve information about cardiac autonomic control

Traditional measures of heart rate variability (HRV) in the time or frequency domain (e.g. standard deviation of normal-to-normal intervals, SDNN, or the high frequency component of spectral analysis, HF) may be used to track vagal and sympathetic modulation directed to the sinus node. In this study, we assess the ability of symbolic analysis to monitor cardiac autonomic regulation during two autonomic challenges (phenylephrine and nitroprusside; low and high dose of atropine). To assess the effect of the coarse graining procedure, symbolic series obtained from four different transformations over the original series and the series of successive differences of the original values. The analysis focused on patterns of length 3 and exploited a redundancy reduction strategy to group patterns into a small number of families. It turns out that each symbolic series created by the four transformations still contained sufficient dynamical features to quantify differences of cardiovascular changes during the pharmacological challenges. The symbolic series created by transformations of the beat-to-beat interview, i.e RR interval series, showed that patterns without variations (0V) appear more often during a high dose of atropine compared to rest or to a low dose of atropine. Furthermore, patterns with two unlike variations (2UV) appear more often during a low dose of atropine and less often during a high dose of atropine. Differences of nitroprusside and phenylephrine could also be assessed by patterns with these variations. In conclusion, the changes of cardiovascular regulation during pharmacological challenges can be assessed by the analysis of symbolic dynamics derived from the RR interval series independently of the specific symbolic transformation.

Strategies of symbolization in cardiovascular time series to test individual gestational development in the fetus

The analysis of symbolic dynamics applied to physiological time series retrieves dynamical properties of the underlying regulation which are robust against the symbolic transformation. In this study, three different transformations to produce a symbolic series were applied to fetal RR interval series to test whether they reflect individual changes of fetal heart rate variability in the course of pregnancy. Each transformation was applied to 215 heartbeat datasets obtained from 11 fetuses during the second and the third trimester of pregnancy (at least 10 datasets per fetus, median 17). In the symbolic series, the occurrence of symbolic sequences of length 3 was categorized according to the amount of variations in the sequence: no variation of the symbols, one variation, two variations. Linear regression with respect to gestational age showed that the individual course during pregnancy performed best using a binary transformation reflecting whether the RR interval differences are below or above a threshold. The median goodness of fit of the individual regression lines was 0.73 and also the variability among the individual slopes was low. Other transformations to symbolic dynamics performed worse but were still able to reflect the individual progress of fetal cardiovascular regulation.

Predicting cardiac autonomic neuropathy category for diabetic data with missing values

Cardiovascular autonomic neuropathy (CAN) is a serious and well known complication of diabetes. Previous articles circumvented the problem of missing values in CAN data by deleting all records and fields with missing values and applying classifiers trained on different sets of features that were complete. Most of them also added alternative features to compensate for the deleted ones. Here we introduce and investigate a new method for classifying CAN data with missing values. In contrast to all previous papers, our new method does not delete attributes with missing values, does not use classifiers, and does not add features. Instead it is based on regression and meta-regression combined with the Ewing formula for identifying the classes of CAN. This is the first article using the Ewing formula and regression to classify CAN. We carried out extensive experiments to determine the best combination of regression and meta-regression techniques for classifying CAN data with missing values. The best outcomes have been obtained by the additive regression meta-learner based on M5Rules and combined with the Ewing formula. It has achieved the best accuracy of 99.78% for two classes of CAN, and 98.98% for three classes of CAN. These outcomes are substantially better than previous results obtained in the literature by deleting all missing attributes and applying traditional classifiers to different sets of features without regression. Another advantage of our method is that it does not require practitioners to perform more tests collecting additional alternative features.

Symbolic patterns of heart rate dynamics reflect cardiac autonomic changes during childhood and adolescence

Symbolic dynamics derived from heart rate variability (HRV) is able to reflect changes of cardiac autonomic modulations in healthy subjects. It has been shown that linear measures of HRV in children and adolescents monotonically increase or decrease (depending on the measure) with age whereas non-linear measures show a local extreme value at the age of 7 to 9 years. In this study, the age-related variations of dynamical features of the R-R interval series during childhood and adolescence were addressed. In particular, the binary symbolic dynamics reflecting the sequence of acceleration (='1') and deceleration (='0') of heart rate was examined. The R-R interval series of 409 healthy children and adolescents (age range: 1 to 22 years, 220 females) was analyzed with respect to the regularity of binary patterns of length 8 using Approximate Entropy (ApEn). Binary patterns were grouped to patterns sets according to the level of their regularity as assessed by ApEn. Pattern sets containing regular binary patterns occurred more often with increasing age whereas irregular binary patterns occurred less often. Specific regular binary patterns show an unexpected behavior. They occurred fewest in the group 7 to 9 years. Furthermore, regular binary patterns occur more often during daytime whereas irregular binary patterns occur more often during nighttime. In conclusion, the analysis of binary symbolic dynamics is able to reflect age-related changes during childhood and adolescence in spite of the considerable reduction of information involved. As many binary patterns are linked to sympathetic or parasympathetic modulations of the autonomic nervous system e.g. spectral analysis of HRV may be complemented by this kind of analysis.

K-nearest-neighbor conditional entropy approach for the assessment of the short-term complexity of cardiovascular control

Complexity analysis of short-term cardiovascular control is traditionally performed using entropy-based approaches including corrective terms or strategies to cope with the loss of reliability of conditional distributions with pattern length. This study proposes a new approach aiming at the estimation of conditional entropy (CE) from short data segments (about 250 samples) based on the k-nearest-neighbor technique. The main advantages are: (i) the control of the loss of reliability of the conditional distributions with the pattern length without introducing a priori information; (ii) the assessment of complexity indexes without fixing the pattern length to an arbitrary low value. The approach, referred to as k-nearest-neighbor conditional entropy (KNNCE), was contrasted with corrected approximate entropy (CApEn), sample entropy (SampEn) and corrected CE (CCE), being the most frequently exploited approaches for entropy-based complexity analysis of short cardiovascular series. Complexity indexes were evaluated during the selective pharmacological blockade of the vagal and/or sympathetic branches of the autonomic nervous system. We found that KNNCE was more powerful than CCE in detecting the decrease of complexity of heart period variability imposed by double autonomic blockade. In addition, KNNCE provides indexes indistinguishable from those derived from CApEn and SampEn. Since this result was obtained without using strategies to correct the CE estimate and without fixing the embedding dimension to an arbitrary low value, KNNCE is potentially more valuable than CCE, CApEn and SampEn when the number of past samples most useful to reduce the uncertainty of future behaviors is high and/or variable among conditions and/or groups.