Complexity analyses show two distinct types of nonlinear dynamics in short heart period variability recordings

Nonlinear Dynamics of Heart Rate Variability after Acutely Induced Myocardial Ischemia by Percutaneous Transluminal Coronary Angioplasty

Several heart rate variability (HRV) characteristics of patients with myocardial ischemia are associated with a higher mortality risk. However, the immediate effect of acute ischemia on the HRV nonlinear dynamical behavior is unknown. The objective of this work is to explore the presence of nonlinearity through surrogate data testing and describe the dynamical behavior of HRV in acutely induced ischemia by percutaneous transluminal coronary angioplasty (PTCA) with linear and recurrence quantification analysis (RQA). Short-term electrocardiographic recordings from 68 patients before and after being treated with elective PTCA were selected from a publicly available database. The presence of nonlinear behavior was confirmed by determinism and laminarity in a relevant proportion of HRV time series, in up to 29.4% during baseline conditions and 30.9% after PTCA without statistical difference between these scenarios. After PTCA, the mean value and standard deviation of HRV time series decreased, while determinism and laminarity values increased. Here, the diminishment in overall variability caused by PTCA is not accompanied by a change in nonlinearity detection. Therefore, the presence of nonlinear behavior in HRV time series is not necessarily in agreement with the change of traditional and RQA measures.

Recurrence Quantitative Analysis of Wavelet-Based Surrogate Data for Nonlinearity Testing in Heart Rate Variability

Exploring the presence of nonlinearity through surrogate data testing provides insights into the nature of physical and biological systems like those obtained from heart rate variability (HRV). Short-term HRV time series are of great clinical interest to study autonomic impairments manifested in chronic diseases such as the end stage renal disease (ESRD) and the response of patients to treatment with hemodialysis (HD). In contrast to Iterative Amplitude Adjusted Fourier Transform (IAAFT), the Pinned Wavelet Iterative Amplitude Adjusted Fourier Transform (PWIAAFT) surrogates preserve nonstationary behavior in time series, a common characteristic of HRV. We aimed to test synthetic data and HRV time series for the existence of nonlinearity. Recurrence Quantitative Analysis (RQA) indices were used as discriminative statistics in IAAFT and PWIAAFT surrogates of linear stationary and nonstationary processes. HRV time series of healthy subjects and 29 ESRD patients before and after HD were tested in this setting during an active standing test. Contrary to PWIAAFT, linear nonstationary time series may be erroneously regarded as nonlinear according to the IAAFT surrogates. Here, a lower proportion of HRV time series was classified as nonlinear with PWIAAFT, compared to IAAFT, confirming that the nonstationarity condition influences the testing of nonlinear behavior in HRV. A contribution of nonlinearity was found in the HRV data of healthy individuals. A lower proportion of nonlinear time series was also found in ESRD patients, but statistical significance was not found. Although this proportion tends to be lower in ESRD patients, as much as 60% of time series proved to be nonlinear in healthy subjects. Given the important contribution of nonlinearity in HRV data, a nonlinear point of view is required to achieve a broader understanding of cardiovascular physiology.

Bispectral Analysis of Heart Rate Variability to Characterize and Help Diagnose Pediatric Sleep Apnea

Pediatric obstructive sleep apnea (OSA) is a breathing disorder that alters heart rate variability (HRV) dynamics during sleep. HRV in children is commonly assessed through conventional spectral analysis. However, bispectral analysis provides both linearity and stationarity information and has not been applied to the assessment of HRV in pediatric OSA. Here, this work aimed to assess HRV using bispectral analysis in children with OSA for signal characterization and diagnostic purposes in two large pediatric databases (0-13 years). The first database (training set) was composed of 981 overnight ECG recordings obtained during polysomnography. The second database (test set) was a subset of the Childhood Adenotonsillectomy Trial database (757 children). We characterized three bispectral regions based on the classic HRV frequency ranges (very low frequency: 0-0.04 Hz; low frequency: 0.04-0.15 Hz; and high frequency: 0.15-0.40 Hz), as well as three OSA-specific frequency ranges obtained in recent studies (BW1: 0.001-0.005 Hz; BW2: 0.028-0.074 Hz; BWRes: a subject-adaptive respiratory region). In each region, up to 14 bispectral features were computed. The fast correlation-based filter was applied to the features obtained from the classic and OSA-specific regions, showing complementary information regarding OSA alterations in HRV. This information was then used to train multi-layer perceptron (MLP) neural networks aimed at automatically detecting pediatric OSA using three clinically defined severity classifiers. Both classic and OSA-specific MLP models showed high and similar accuracy (Acc) and areas under the receiver operating characteristic curve (AUCs) for moderate (classic regions: Acc = 81.0%, AUC = 0.774; OSA-specific regions: Acc = 81.0%, AUC = 0.791) and severe (classic regions: Acc = 91.7%, AUC = 0.847; OSA-specific regions: Acc = 89.3%, AUC = 0.841) OSA levels. Thus, the current findings highlight the usefulness of bispectral analysis on HRV to characterize and diagnose pediatric OSA.

Lack of association between heart period variability asymmetry and respiratory sinus arrhythmia in healthy and chronic heart failure individuals

Temporal asymmetry is a peculiar aspect of heart period (HP) variability (HPV). HPV asymmetry (HPVA) is reduced with aging and pathology, but its origin is not fully elucidated. Given the impact of respiration on HPV resulting in the respiratory sinus arrhythmia (RSA) and the asymmetric shape of the respiratory pattern, a possible link between HPVA and RSA might be expected. In this study we tested the hypothesis that HPVA is significantly associated with RSA and asymmetry of the respiratory rhythm. We studied 42 middle-aged healthy (H) subjects, and 56 chronic heart failure (CHF) patients of whom 26 assigned to the New York Heart Association (NYHA) class II (CHF-II) and 30 to NYHA class III (CHF-III). Electrocardiogram and lung volume were monitored for 8 minutes during spontaneous breathing (SB) and controlled breathing (CB) at 15 breaths/minute. The ratio of inspiratory (INSP) to expiratory (EXP) phases, namely the I/E ratio, and RSA were calculated. HPVA was estimated as the percentage of negative HP variations, traditionally measured via the Porta’s index (PI). Departures of PI from 50% indicated HPVA and its significance was tested via surrogate data. We found that RSA increased during CB and I/E ratio was smaller than 1 in all groups and experimental conditions. In H subjects the PI was about 50% during SB and it increased significantly during CB. In both CHF-II and CHF-III groups the PI was about 50% during SB and remained unmodified during CB. The PI was uncorrelated with RSA and I/E ratio regardless of the experimental condition and group. Pooling together data of different experimental conditions did not affect conclusions. Therefore, we conclude that the HPVA cannot be explained by RSA and/or I/E ratio, thus representing a peculiar feature of the cardiac control that can be aroused in middle-aged H individuals via CB.

Maturation of the Autonomic Nervous System in Premature Infants: Estimating Development Based on Heart-Rate Variability Analysis

This study aims at investigating the development of premature infants' autonomic nervous system (ANS) based on a quantitative analysis of the heart-rate variability (HRV) with a variety of novel features. Additionally, the role of heart-rate drops, known as bradycardias, has been studied in relation to both clinical and novel sympathovagal indices. ECG data were measured for at least 3 h in 25 preterm infants (gestational age ≤32 weeks) for a total number of 74 recordings. The post-menstrual age (PMA) of each patient was estimated from the RR interval time-series by means of multivariate linear-mixed effects regression. The tachograms were segmented based on bradycardias in periods after, between and during bradycardias. For each of those epochs, a set of temporal, spectral and fractal indices were included in the regression model. The best performing model has R 2 = 0.75 and mean absolute error MAE = 1.56 weeks. Three main novelties can be reported. First, the obtained maturation models based on HRV have comparable performance to other development models. Second, the selected features for age estimation show a predominance of power and fractal features in the very-low- and low-frequency bands in explaining the infants' sympathovagal development from 27 PMA weeks until 40 PMA weeks. Third, bradycardias might disrupt the relationship between common temporal indices of the tachogram and the age of the infant and the interpretation of sympathovagal indices. This approach might provide a novel overview of post-natal autonomic maturation and an alternative development index to other electrophysiological data analysis.

Evaluation of the impact of surgical aortic valve replacement on short-term cardiovascular and cerebrovascular controls through spontaneous variability analysis

We assessed the effect of surgical aortic valve replacement (SAVR) on cardiovascular and cerebrovascular controls via spontaneous variability analyses of heart period, approximated as the temporal distance between two consecutive R-wave peaks on the electrocardiogram (RR), systolic, diastolic and mean arterial pressure (SAP, DAP and MAP) and mean cerebral blood flow (MCBF). Powers in specific frequency bands, complexity, presence of nonlinear dynamics and markers of cardiac baroreflex and cerebral autoregulation were calculated. Variability series were acquired before (PRE) and after (POST) SAVR in 11 patients (age: 76±5 yrs, 7 males) at supine resting and during active standing. Parametric spectral analysis was performed based on the autoregressive model. Complexity was assessed via a local nonlinear prediction approach exploiting the k-nearest-neighbor strategy. The presence of nonlinear dynamics was checked by comparing the complexity marker computed over the original series with the distribution of the same index assessed over a set of surrogates preserving distribution and power spectral density of the original series. Cardiac baroreflex and cerebral autoregulation were estimated by assessing the transfer function from SAP to RR and from MAP to MCBF and squared coherence function via the bivariate autoregressive approach. We found that: i) orthostatic challenge had no effect on cardiovascular and cerebrovascular control markers in PRE; ii) RR variance was significantly reduced in POST; iii) complexity of SAP, DAP and MAP variabilities increased in POST with a greater likelihood of observing nonlinear dynamics over SAP compared to PRE at supine resting; iv) the amplitude of MCBF variations and MCBF complexity in POST remained similar to PRE; v) cardiac baroreflex sensitivity decreased in POST, while cerebrovascular autoregulation was preserved. SAVR induces important changes of cardiac and vascular autonomic controls and baroreflex regulation in patients exhibiting poor reactivity of cardiovascular regulatory mechanisms, while cerebrovascular autoregulation seems to be less affected.

Complexity and Nonlinearities of Short-Term Cardiovascular and Cerebrovascular Controls after Surgical Aortic Valve Replacement

We assessed the effect of surgical aortic valve replacement (SAVR) on cardiovascular and cerebrovascular controls with particular attention to their complexity and presence of nonlinear behaviors via the analysis of spontaneous variability of heart period (HP), systolic and diastolic arterial pressure (SAP and DAP) and mean cerebral blood flow (MCBF). Variability series were acquired before (PRE) and after (POST) SAVR in 12 patients (age: 76±4.7 yrs, 7 males) at rest in supine position and during active standing. Complexity was assessed via a local nonlinear prediction approach exploiting the k-nearest neighbor strategy. The presence of nonlinear dynamics was checked by comparing the complexity marker computed over the original series with the distribution of values assessed over 100 surrogates preserving distribution and power spectral density of the original series but with random phases. We found that: i) HP variance was significantly reduced in POST; ii) the complexity of SAP and DAP variabilities increased in POST with a greater likelihood of observing nonlinear dynamics over SAP compared to PRE at supine rest; iii) the amplitude of MCBF fluctuations and its complexity in POST remained similar to PRE. SAVR induces important changes of the cardiac and vascular autonomic controls, while cerebrovascular regulation seems to be less affected.

Comparison of methods for the assessment of nonlinearity in short-term heart rate variability under different physiopathological states

Despite the widespread diffusion of nonlinear methods for heart rate variability (HRV) analysis, the presence and the extent to which nonlinear dynamics contribute to short-term HRV are still controversial. This work aims at testing the hypothesis that different types of nonlinearity can be observed in HRV depending on the method adopted and on the physiopathological state. Two entropy-based measures of time series complexity (normalized complexity index, NCI) and regularity (information storage, IS), and a measure quantifying deviations from linear correlations in a time series (Gaussian linear contrast, GLC), are applied to short HRV recordings obtained in young (Y) and old (O) healthy subjects and in myocardial infarction (MI) patients monitored in the resting supine position and in the upright position reached through head-up tilt. The method of surrogate data is employed to detect the presence and quantify the contribution of nonlinear dynamics to HRV. We find that the three measures differ both in their variations across groups and conditions and in the percentage and strength of nonlinear HRV dynamics. NCI and IS displayed opposite variations, suggesting more complex dynamics in O and MI compared to Y and less complex dynamics during tilt. The strength of nonlinear dynamics is reduced by tilt using all measures in Y, while only GLC detects a significant strengthening of such dynamics in MI. A large percentage of detected nonlinear dynamics is revealed only by the IS measure in the Y group at rest, with a decrease in O and MI and during T, while NCI and GLC detect lower percentages in all groups and conditions. While these results suggest that distinct dynamic structures may lie beneath short-term HRV in different physiological states and pathological conditions, the strong dependence on the measure adopted and on their implementation suggests that physiological interpretations should be provided with caution.

Cardiac baroreflex hysteresis is one of the determinants of the heart period variability asymmetry

In heart period (HP) variability (HPV) recordings the percentage of negative HP variations tends to be greater than that of positive ones and this pattern is referred to as HPV asymmetry (HPVA). HPVA has been studied in several experimental conditions in healthy and pathological populations, but its origin is unclear. The baroreflex (BR) exhibits an asymmetric behavior as well given that it reacts more importantly to positive than negative arterial pressure (AP) variations. We tested the hypothesis that the BR asymmetry (BRA) is a HPVA determinant over spontaneous fluctuations of HP and systolic AP (SAP). We studied 100 healthy subjects (age from 21 to 70 yr, 54 men) comprising 20 subjects in each age decade. Electrocardiogram and noninvasive AP were recorded for 15 min at rest in supine position (REST) and during active standing (STAND). The HPVA was evaluated via Porta's index and Guzik's index, while the BRA was assessed as the difference, and normalized difference, between BR sensitivities computed over positive and negative SAP variations via the sequence method applied to HP and SAP variability. HPVA significantly increased during STAND and decreased progressively with age. BRA was not significantly detected both at REST and during STAND. However, we found a significant positive association between BRA and HPVA markers during STAND persisting even within the age groups. This study supports the use of HPVA indexes as descriptors of BRA and identified a challenge soliciting the BR response like STAND to maximize the association between HPVA and BRA markers.

Nonlinearities of heart rate variability in animal models of impaired cardiac control: contribution of different time scales

Heart rate variability (HRV) has been extensively explored by traditional linear approaches (e.g., spectral analysis); however, several studies have pointed to the presence of nonlinear features in HRV, suggesting that linear tools might fail to account for the complexity of the HRV dynamics. Even though the prevalent notion is that HRV is nonlinear, the actual presence of nonlinear features is rarely verified. In this study, the presence of nonlinear dynamics was checked as a function of time scales in three experimental models of rats with different impairment of the cardiac control: namely, rats with heart failure (HF), spontaneously hypertensive rats (SHRs), and sinoaortic denervated (SAD) rats. Multiscale entropy (MSE) and refined MSE (RMSE) were chosen as the discriminating statistic for the surrogate test utilized to detect nonlinearity. Nonlinear dynamics is less present in HF animals at both short and long time scales compared with controls. A similar finding was found in SHR only at short time scales. SAD increased the presence of nonlinear dynamics exclusively at short time scales. Those findings suggest that a working baroreflex contributes to linearize HRV and to reduce the likelihood to observe nonlinear components of the cardiac control at short time scales. In addition, an increased sympathetic modulation seems to be a source of nonlinear dynamics at long time scales. Testing nonlinear dynamics as a function of the time scales can provide a characterization of the cardiac control complementary to more traditional markers in time, frequency, and information domains.NEW & NOTEWORTHY Although heart rate variability (HRV) dynamics is widely assumed to be nonlinear, nonlinearity tests are rarely used to check this hypothesis. By adopting multiscale entropy (MSE) and refined MSE (RMSE) as the discriminating statistic for the nonlinearity test, we show that nonlinear dynamics varies with time scale and the type of cardiac dysfunction. Moreover, as complexity metrics and nonlinearities provide complementary information, we strongly recommend using the test for nonlinearity as an additional index to characterize HRV.

Multiscale entropy analysis of heart rate variability in heart failure, hypertensive, and sinoaortic-denervated rats: classical and refined approaches

The analysis of heart rate variability (HRV) by nonlinear methods has been gaining increasing interest due to their ability to quantify the complexity of cardiovascular regulation. In this study, multiscale entropy (MSE) and refined MSE (RMSE) were applied to track the complexity of HRV as a function of time scale in three pathological conscious animal models: rats with heart failure (HF), spontaneously hypertensive rats (SHR), and rats with sinoaortic denervation (SAD). Results showed that HF did not change HRV complexity, although there was a tendency to decrease the entropy in HF animals. On the other hand, SHR group was characterized by reduced complexity at long time scales, whereas SAD animals exhibited a smaller short- and long-term irregularity. We propose that short time scales (1 to 4), accounting for fast oscillations, are more related to vagal and respiratory control, whereas long time scales (5 to 20), accounting for slow oscillations, are more related to sympathetic control. The increased sympathetic modulation is probably the main reason for the lower entropy observed at high scales for both SHR and SAD groups, acting as a negative factor for the cardiovascular complexity. This study highlights the contribution of the multiscale complexity analysis of HRV for understanding the physiological mechanisms involved in cardiovascular regulation.

Self-Organization of Blood Pressure Regulation: Clinical Evidence

The pathogenesis of vasovagal syncope has remained elusive despite many efforts to identify an underlying dysfunction. Catastrophe theory explains the spontaneous occurrence of sudden events in some mathematically complex systems known as self-organized systems poised at criticality. These systems universally exhibit a power law initially described in earthquake occurrence: the Gutenberg Richter law. The magnitude plotted against the total number of earthquakes of at least this magnitude draw a straight line on log-log graph. We hypothesized that vasovagal syncope is a catastrophe occurring spontaneously in the cardiovascular system. We counted the number and magnitude (number of beats) of vasovagal reactions (simultaneous decreases in both blood pressure and heart rate on consecutive beats) in 24 patients with vasovagal symptoms during a head-up tilt test and 24 paired patients with no symptoms during the test. For each patient, we checked whether vasovagal reaction occurrence followed the Gutenberg Richter law. The occurrence followed the Gutenberg Richter law in 43 patients (correlation coefficient |r| = 0.986 ± 0.001, mean ± SEM) out of 48, with no difference between patients with and without symptoms. We demonstrated that vasovagal syncope matches a catastrophe model occurring in a self-organized cardiovascular complex system poised at criticality. This is a new vision of cardiovascular regulation and its related disorders.

Quantifying the Interactions between Maternal and Fetal Heart Rates by Transfer Entropy

Evidence of the short term relationship between maternal and fetal heart rates has been found in previous studies. However there is still limited knowledge about underlying mechanisms and patterns of the coupling throughout gestation. In this study, Transfer Entropy (TE) was used to quantify directed interactions between maternal and fetal heart rates at various time delays and gestational ages. Experimental results using maternal and fetal electrocardiograms showed significant coupling for 63 out of 65 fetuses, by statistically validating against surrogate pairs. Analysis of TE showed a decrease in transfer of information from fetus to the mother with gestational age, alongside the maturation of the fetus. On the other hand, maternal to fetal TE was significantly greater in mid (26-31 weeks) and late (32-41 weeks) gestation compared to early (16-25 weeks) gestation (Mann Whitney Wilcoxon (MWW) p<0.05). TE further increased from mid to late, for the fetuses with RMSSD of fetal heart rate being larger than 4 msec in the late gestation. This difference was not observed for the fetuses with smaller RMSSD, which could be associated with the quiet sleep state. Delay in the information transfer from mother to fetus significantly decreased (p = 0.03) from mid to late gestation, implying a decrease in fetal response time. These changes occur concomitant with the maturation of the fetal sensory and autonomic nervous systems with advancing gestational age. The effect of maternal respiratory rate derived from maternal ECG was also investigated and no significant relationship was found between breathing rate and TE at any lag. In conclusion, the application of TE with delays revealed detailed information on the fetal-maternal heart rate coupling strength and latency throughout gestation, which could provide novel clinical markers of fetal development and well-being.