Short-term forecasting of life-threatening cardiac arrhythmias based on symbolic dynamics and finite-time growth rates

Power spectral estimate for discrete data

The identification of cycles in periodic signals is a ubiquitous problem in time series analysis. Many real-world datasets only record a signal as a series of discrete events or symbols. In some cases, only a sequence of (non-equidistant) times can be assessed. Many of these signals are furthermore corrupted by noise and offer a limited number of samples, e.g., cardiac signals, astronomical light curves, stock market data, or extreme weather events. We propose a novel method that provides a power spectral estimate for discrete data. The edit distance is a distance measure that allows us to quantify similarities between non-equidistant event sequences of unequal lengths. However, its potential to quantify the frequency content of discrete signals has so far remained unexplored. We define a measure of serial dependence based on the edit distance, which can be transformed into a power spectral estimate (EDSPEC), analogous to the Wiener-Khinchin theorem for continuous signals. The proposed method is applied to a variety of discrete paradigmatic signals representing random, correlated, chaotic, and periodic occurrences of events. It is effective at detecting periodic cycles even in the presence of noise and for short event series. Finally, we apply the EDSPEC method to a novel catalog of European atmospheric rivers (ARs). ARs are narrow filaments of extensive water vapor transport in the lower troposphere and can cause hazardous extreme precipitation events. Using the EDSPEC method, we conduct the first spectral analysis of European ARs, uncovering seasonal and multi-annual cycles along different spatial domains. The proposed method opens new research avenues in studying of periodic discrete signals in complex real-world systems.

Heart Rate Estimation from Incomplete Electrocardiography Signals

As one of the most remarkable indicators of physiological health, heart rate (HR) has become an unfailing investigation for researchers. Unlike many existing methods, this article proposes an approach to implement short-time HR estimation from electrocardiography in time series missing patterns. Benefiting from the rapid development of deep learning, we adopted a bidirectional long short-term memory model (Bi-LSTM) and temporal convolution network (TCN) to recover complete heartbeat signals from those with durations are less than one cardiac cycle, and the estimated HR from recovered segment combining the input and the predicted output. We also compared the performance of Bi-LSTM and TCN in PhysioNet dataset. Validating the method over a resting heart rate range of 60−120 bpm in the database without significant arrhythmias and a corresponding range of 30−150 bpm in the database with arrhythmias, we found that networks provide an estimated approach for incomplete signals in a fixed format. These results are consistent with real heartbeats in the normal heartbeat dataset (γ > 0.7, RMSE < 10) and in the arrhythmia database (γ > 0.6, RMSE < 30), verifying that HR could be estimated by models in advance. We also discussed the short-time limits for the predictive model. It could be used for physiological purposes such as mobile sensing in time-constrained scenarios, and providing useful insights for better time series analyses in missing data patterns.

Heart rate variability in different sleep stages is associated with metabolic function and glycemic control in type 2 diabetes mellitus

Introduction: Autonomic nervous system (ANS) plays an important role in the exchange of metabolic information between organs and regulation on peripheral metabolism with obvious circadian rhythm in a healthy state. Sleep, a vital brain phenomenon, significantly affects both ANS and metabolic function. Objectives: This study investigated the relationships among sleep, ANS and metabolic function in type 2 diabetes mellitus (T2DM), to support the evaluation of ANS function through heart rate variability (HRV) metrics, and the determination of the correlated underlying autonomic pathways, and help optimize the early prevention, post-diagnosis and management of T2DM and its complications. Materials and methods: A total of 64 volunteered inpatients with T2DM took part in this study. 24-h electrocardiogram (ECG), clinical indicators of metabolic function, sleep quality and sleep staging results of T2DM patients were monitored. Results: The associations between sleep quality, 24-h/awake/sleep/sleep staging HRV and clinical indicators of metabolic function were analyzed. Significant correlations were found between sleep quality and metabolic function (|r| = 0.386 ± 0.062, p < 0.05); HRV derived ANS function showed strengthened correlations with metabolic function during sleep period (|r| = 0.474 ± 0.100, p < 0.05); HRV metrics during sleep stages coupled more tightly with clinical indicators of metabolic function [in unstable sleep: |r| = 0.453 ± 0.095, p < 0.05; in stable sleep: |r| = 0.463 ± 0.100, p < 0.05; in rapid eye movement (REM) sleep: |r| = 0.453 ± 0.082, p < 0.05], and showed significant associations with glycemic control in non-linear analysis [fasting blood glucose within 24 h of admission (admission FBG), |r| = 0.420 ± 0.064, p < 0.05; glycated hemoglobin (HbA1c), |r| = 0.417 ± 0.016, p < 0.05]. Conclusions: HRV metrics during sleep period play more distinct role than during awake period in investigating ANS dysfunction and metabolism in T2DM patients, and sleep rhythm based HRV analysis should perform better in ANS and metabolic function assessment, especially for glycemic control in non-linear analysis among T2DM patients.

Circadian stage-dependent and stimulation duration effects of transcutaneous auricular vagus nerve stimulation on heart rate variability

Transcutaneous auricular vagus nerve stimulation (taVNS) can improve autonomic nerve function and is currently undergoing extensive clinical research; however, its efficacy heterogeneity has caused great controversy. Heart rate variability (HRV), a biomarker reflecting autonomic function, exhibits a time-varying pattern with circadian rhythms, which may be the main reason for the inconsistent stimulation effects. To test this conjecture, we performed isochronous acute stimulation experiments at intervals of 12 h. The results showed that HRV indicators representing vagal nerve activity significantly increased when stimulation was performed in the morning, and the enhancement of high frequency continued into the recovery period. However, the evening stimulation did not yield similar results. In addition, we found that improvements in the measures of autonomic balance were more pronounced in the presence of lower vagal activity. By increasing the stimulation duration, we also found that the effect of taVNS on HRV was not regulated by duration; in other words, HRV changes only had the best effect at the beginning of stimulation. These studies allowed us to determine the optimal stimulation phase and duration and potentially screen the optimal candidates for taVNS.

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.

Impairment of Cardiac Autonomic Nerve Function in Pre-school Children With Intractable Epilepsy

Objective: Intractable epilepsy and uncontrolled seizures could affect cardiac function and the autonomic nerve system with a negative impact on children's growth. The aim of this study was to investigate the variability and complexity of cardiac autonomic function in pre-school children with pediatric intractable epilepsy (PIE). Methods: Twenty four-hour Holter electrocardiograms (ECGs) from 93 patients and 46 healthy control subjects aged 3-6 years were analyzed by the methods of traditional heart rate variability (HRV), multiscale entropy (MSE), and Kurths-Wessel symbolization entropy (KWSE). Receiver operating characteristic (ROC) curve analysis was used to estimate the overall discrimination ability. Net reclassification improvement (NRI) and integrated discrimination improvement (IDI) models were also analyzed. Results: Pre-school children with PIE had significantly lower HRV measurements than healthy controls in time (Mean_RR, SDRR, RMSSD, pNN50) and frequency (VLF, LF, HF, LF/HF, TP) domains. For the MSE analysis, area 1_5 in awake state was lower, and areas 6_15 and 6_20 in sleep state were higher in PIE with a significant statistical difference. KWSE in the PIE group was also inferior to that in healthy controls. In ROC curve analysis, pNN50 had the greatest discriminatory power for PIE. Based on both NRI and IDI models, the combination of MSE indices (wake: area1_5 and sleep: area6_20) and KWSE (m = 2, τ = 1, α = 0.16) with traditional HRV measures had greater discriminatory power than any of the single HRV measures. Significance: Impaired HRV and complexity were found in pre-school children with PIE. HRV, MSE, and KWSE could discriminate patients with PIE from subjects with normal cardiac complexity. These findings suggested that the MSE and KWSE methods may be helpful for assessing and understanding heart rate dynamics in younger children with epilepsy.

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.

Nonlinear Methods Most Applied to Heart-Rate Time Series: A Review

The heart-rate dynamics are one of the most analyzed physiological interactions. Many mathematical methods were proposed to evaluate heart-rate variability. These methods have been successfully applied in research to expand knowledge concerning the cardiovascular dynamics in healthy as well as in pathological conditions. Notwithstanding, they are still far from clinical practice. In this paper, we aim to review the nonlinear methods most used to assess heart-rate dynamics. We focused on methods based on concepts of chaos, fractality, and complexity: Poincaré plot, recurrence plot analysis, fractal dimension (and the correlation dimension), detrended fluctuation analysis, Hurst exponent, Lyapunov exponent entropies (Shannon, conditional, approximate, sample entropy, and multiscale entropy), and symbolic dynamics. We present the description of the methods along with their most notable applications.

Heart Rate Variability Analysis to Predict Onset of Ventricular Tachyarrhythmias in Implantable Cardioverter Defibrillators

Implantable cardioverter defibrillators (ICDs) are commonly used in patients at high risk of sudden cardiac death (SCD) to help prevent and treat life-threatening arrhythmia. Up to 80% of cases of sudden cardiac death are caused by ventricular tachyarrhythmias (VTA) and the accurate prediction of VTA in patients with ICDs can help prevent SCD. Early prediction allows tiered and less invasive therapies to be used to help prevent VTA which are more easily tolerated by the patient and are less battery intensive. In this work, a comparative study of three types of frequency domain features (spectral, bispectrum, and Fourier-Bessel) for VTA prediction is presented based on heart rate variability (HRV) signals between one and five minutes prior to known SCD. Using Fourier-Bessel features and a standard classification approach resulted in the best performance of 87.5% accuracy, 89.3% sensitivity and 85.7% specificity. These results suggest that Fourier-Bessel features are a promising approach for SCD prediction, and that new feature development can help improve both the sensitivity and specificity of SCD prediction in ICDs.

Slope Entropy: A New Time Series Complexity Estimator Based on Both Symbolic Patterns and Amplitude Information

The development of new measures and algorithms to quantify the entropy or related concepts of a data series is a continuous effort that has brought many innovations in this regard in recent years. The ultimate goal is usually to find new methods with a higher discriminating power, more efficient, more robust to noise and artifacts, less dependent on parameters or configurations, or any other possibly desirable feature. Among all these methods, Permutation Entropy (PE) is a complexity estimator for a time series that stands out due to its many strengths, with very few weaknesses. One of these weaknesses is the PE’s disregarding of time series amplitude information. Some PE algorithm modifications have been proposed in order to introduce such information into the calculations. We propose in this paper a new method, Slope Entropy (SlopEn), that also addresses this flaw but in a different way, keeping the symbolic representation of subsequences using a novel encoding method based on the slope generated by two consecutive data samples. By means of a thorough and extensive set of comparative experiments with PE and Sample Entropy (SampEn), we demonstrate that SlopEn is a very promising method with clearly a better time series classification performance than those previous methods.

Adaptive symbolic transfer entropy and its applications in modeling for complex industrial systems

Directed coupling between variables is the foundation of studying the dynamical behavior of complex systems. We propose an adaptive symbolic transfer entropy (ASTE) method based on the principle of equal probability division. First, the adaptive kernel density method is used to obtain an accurate probability density function for an observation series. Second, the complete phase space of the system can be obtained by using the multivariable phase space reconstruction method. This provides common parameters for symbolizing a time series, including delay time and embedding dimension. Third, an optimization strategy is used to select the appropriate symbolic parameters of a time series, such as the symbol set and partition intervals, which can be used to convert the time series to a symbol sequence. Then the transfer entropy between the symbolic sequences can be carried out. Finally, the proposed method is analyzed and validated using the chaotic Lorenz system and typical complex industrial systems. The results show that the ASTE method is superior to the existing transfer entropy and symbolic transfer entropy methods in terms of measurement accuracy and noise resistance, and it can be applied to the network modeling and performance safety analysis of complex industrial systems.

Prediction of Sudden Cardiac Death in Implantable Cardioverter Defibrillators: A Review and Comparative Study of Heart Rate Variability Features

Over the last four decades, implantable cardioverter defibrillators (ICDs) have been widely deployed to reduce sudden cardiac death (SCD) risk in patients with a history of life-threatening arrhythmia. By continuous monitoring of the heart rate, ICDs can use decision algorithms to distinguish normal cardiac sinus rhythm or supra-ventricular tachycardia from abnormal cardiac rhythms like ventricular tachycardia and ventricular fibrillation and deliver appropriate therapy such as an electrical stimulus. Despite the success of ICDs, more research is still needed, particularly in decision-making algorithms. Because of low specificity in practical devices, patients with ICDs still receive inappropriate shocks, which may lead to inadvertent mortality and reduction of quality of life. At the same time, higher sensitivity can lead to the use of newer tiered therapies. The purpose of this study is to review the literature on common signal features used in detection algorithms for abnormal cardiac sinus rhythm, as well as reviewing datasets used for algorithm development in previous studies. More than 50 different features to address heart rate changes before SCD have been reviewed and general methodology on this area proposed based on variety of studies on ICDs functionality. A comparative study on the prediction performance of these features, using a common database, is also presented. By combining these features with a support vector machine classifier, achieved results have compared well with other studies.

On the Relevance of Computing a Local Version of Sample Entropy in Cardiovascular Control Analysis

OBJECTIVE

Traditional definition of sample entropy (SampEn), here referred to as global SampEn (GSampEn), provides a conditional entropy estimate that blurs the local statistical properties of the time series. We hypothesized that a local version of SampEn (LSampEn) might be more powerful in the presence of determinism than GSampEn.

METHODS

LSampEn was computed by calculating the probability of the current sample conditioned on each reference pattern and averaging it over all reference patterns. The improved ability of LSampEn compared to GSampEn was demonstrated by simulating deterministic periodic, deterministic chaotic, and linear stochastic dynamics corrupted by additive noise and over real cardiovascular variability series recorded from 16 healthy subjects (max-min age range: 22-58 years) during incremental bicycle ergometer exercise.

RESULTS

We found that: i) LSampEn is more robust in describing deterministic periodic or nonlinear features in the presence of additive noise than GSampEn, ii) in association with a surrogate approach, LSampEn is more powerful in detecting nonlinear dynamics than GSampEn, iii) LSampEn and GSampEn are equivalent in the presence of stochastic linear dynamics, and iv) only LSampEn can detect the decrease of complexity of heart period variability during bicycle exercise being a likely hallmark of sympathetic activation.

CONCLUSION

LSampEn preserves the GSampEn capability in characterizing the complexity of short sequences but improves its reliability in the presence of deterministic patterns featuring sharp state transitions and nonlinear dynamics.

SIGNIFICANCE

Variations of complexity can be measured with a greater statistical power over short series using LSampEn, especially when nonlinear features are present.

Towards the identification of subjects prone to develop atrial fibrillation after coronary artery bypass graft surgery via univariate and multivariate complexity analysis of heart period variability

The assessment of cardiovascular control complexity as derived from spontaneous heart period (HP) fluctuations can be improved by exploiting a multivariate (MV) approach. This work proposes the assessment of a normalized complexity index (NCI) of HP variability according to a k-nearest-neighbor approach based on local predictability performed in a MV nonuniform embedding space. The method allows the selection of the past components of HP, systolic arterial pressure (SAP) and respiration (R) most useful for the prediction of HP fluctuations. The NCI derived from the MV approach (NCIMV) was compared to a NCI computed via the same technique applied in a univariate (UV) embedding space (NCIUV) formed exclusively by HP past samples. Indexes were computed in 130 patients undergoing coronary artery bypass graft (CABG) surgery before and after the induction of general anesthesia. Thirty-eight subjects developed atrial fibrillation (AF) after surgery, while the remaining ones did not (noAF, n=92). Both NCIUV and NCIMV could separate AF from noAF patients and revealed a larger complexity of the AF subjects. However, the statistical power of the NCIMV was superior given that the probability of type I error was smaller than that of NCIUV. The assessment of cardiac control complexity could improve risk stratification of patients at risk of developing AF after CABG surgery.

Extremes of fractional noises: A model for the timings of arrhythmic heart beats in post-infarction patients

We have analyzed symbol sequences of heart beat annotations obtained from 24-h electrocardiogram recordings of 184 post-infarction patients (from the Cardiac Arrhythmia Suppression Trial database, CAST). In the symbol sequences, each heart beat was coded as an arrhythmic or as a normal beat. The symbol sequences were analyzed with a model-based approach which relies on two-parametric peaks over the threshold (POT) model, interpreting each premature ventricular contraction (PVC) as an extreme event. For the POT model, we explored (i) the Shannon entropy which was estimated in terms of the Lempel-Ziv complexity, (ii) the shape parameter of the Weibull distribution that best fits the PVC return times, and (iii) the strength of long-range correlations quantified by detrended fluctuation analysis (DFA) for the two-dimensional parameter space. We have found that in the frame of our model the Lempel-Ziv complexity is functionally related to the shape parameter of the Weibull distribution. Thus, two complementary measures (entropy and strength of long-range correlations) are sufficient to characterize realizations of the two-parametric model. For the CAST data, we have found evidence for an intermediate strength of long-range correlations in the PVC timings, which are correlated to the age of the patient: younger post-infarction patients have higher strength of long-range correlations than older patients. The normalized Shannon entropy has values in the range 0.5<h_LZ<1.0 which indicates a high degree of randomness in the PVC timings. For the CAST and the model data, the ranges of both measures were found to be in good accordance. The correlation between the age and the persistence strength found for the CAST data could be explained as a change of model parameters.

The sensitivity of 38 heart rate variability measures to the addition of artifact in human and artificial 24-hr cardiac recordings

BACKGROUND

Artifact is common in cardiac RR interval data derived from 24-hr recordings and has a significant impact on heart rate variability (HRV) measures. However, the relative impact of progressively added artifact on a large group of commonly used HRV measures has not been assessed. This study compared the relative sensitivity of 38 commonly used HRV measures to artifact to determine which measures show the most change with increasing increments of artifact. A secondary aim was to ascertain whether short-term and long-term HRV measures, as groups, share similarities in their sensitivity to artifact.

METHODS

Up to 10% of artifact was added to 20 artificial RR (ARR) files and 20 human cardiac recordings, which had been assessed for artifact by a cardiac technician. The added artifact simulated deletion of RR intervals and insertion of individual short RR intervals. Thirty-eight HRV measures were calculated for each file. Regression analysis was used to rank the HRV measures according to their sensitivity to artifact as determined by the magnitude of slope.

RESULTS

RMSSD, SDANN, SDNN, RR triangular index and TINN, normalized power and relative power linear measures, and most nonlinear methods examined are most robust to artifact.

CONCLUSION

Short-term time domain HRV measures are more sensitive to added artifact than long-term measures. Absolute power frequency domain measures across all frequency bands are more sensitive than normalized and relative frequency domain measures. Most nonlinear HRV measures assessed were relatively robust to added artifact, with Poincare plot SD1 being most sensitive.

Are Nonlinear Model-Free Conditional Entropy Approaches for the Assessment of Cardiac Control Complexity Superior to the Linear Model-Based One?

OBJECTIVE

We test the hypothesis that the linear model-based (MB) approach for the estimation of conditional entropy (CE) can be utilized to assess the complexity of the cardiac control in healthy individuals.

METHODS

An MB estimate of CE was tested in an experimental protocol (i.e., the graded head-up tilt) known to produce a gradual decrease of cardiac control complexity as a result of the progressive vagal withdrawal and concomitant sympathetic activation. The MB approach was compared with traditionally exploited nonlinear model-free (MF) techniques such as corrected approximate entropy, sample entropy, corrected CE, two k -nearest-neighbor CE procedures and permutation CE. Electrocardiogram was recorded in 17 healthy subjects at rest in supine position and during head-up tilt with table angles of 15°, 30°, 45°, 60°, and 75°. Heart period (HP) was derived as the temporal distance between two consecutive R-wave peaks and analysis was carried out over stationary sequences of 256 successive HPs.

RESULTS

The performance of the MB method in following the progressive decrease of HP complexity with tilt table angles was in line with those of MF approaches and the MB index was remarkably correlated with the MF ones.

CONCLUSION

The MB approach can be utilized to monitor the changes of the complexity of the cardiac control, thus speeding up dramatically the CE calculation.

SIGNIFICANCE

The remarkable performance of the MB approach challenges the notion, generally assumed in cardiac control complexity analysis based on CE, about the need of MF techniques and could allow real-time applications.

Cardiovascular coupling during graded postural challenge: comparison between linear tools and joint symbolic analysis

Background

A joint symbolic analysis (JSA) is applied to assess the strength of the cardiovascular coupling from spontaneous beat-to-beat variability of the heart period (HP) and the systolic arterial pressure (SAP) during an experimental protocol inducing a gradual baroreflex unloading evoked by postural change (i.e. graded head-up tilt).

Method:

The adopted JSA can quantify the degree of association between the HP and SAP variabilities as a function of the time scale of the HP and SAP patterns. Traditional linear tools assessing the HP-SAP coupling strength, such as squared correlation coefficient, squared coherence function, and percentage of baroreflex sequences, were computed as well for comparison.

Results:

We found that: i) JSA indicated that the strength of the cardiovascular coupling at slow temporal scales gradually increased with the magnitude of the orthostatic challenge, while that at fast temporal scales gradually decreased; ii) the squared correlation coefficient and percentage of baroreflex sequences did not detect this behavior; iii) even though squared coherence function could measure the magnitude of the HP-SAP coupling as a function of the time scale, it was less powerful than JSA owing to the larger dispersion of the frequency domain indexes.

Conclusion:

Due to its peculiar features and high statistical power, JSA deserves applications to pathological groups in which the link between HP and SAP variabilities is lost or decreased due to the overall depression or impairment of the cardiovascular control.

Nonlinear effects of respiration on the crosstalk between cardiovascular and cerebrovascular control systems

Cardiovascular and cerebrovascular regulatory systems are vital control mechanisms responsible for guaranteeing homeostasis and are affected by respiration. This work proposes the investigation of cardiovascular and cerebrovascular control systems and the nonlinear influences of respiration on both regulations through joint symbolic analysis (JSA), conditioned or unconditioned on respiration. Interactions between cardiovascular and cerebrovascular regulatory systems were evaluated as well by performing correlation analysis between JSA indexes describing the two control systems. Heart period, systolic and mean arterial pressure, mean cerebral blood flow velocity and respiration were acquired on a beat-to-beat basis in 13 subjects experiencing recurrent syncope episodes (SYNC) and 13 healthy individuals (non-SYNC) in supine resting condition and during head-up tilt test at 60° (TILT). Results showed that JSA distinguished conditions and groups, whereas time domain parameters detected only the effect of TILT. Respiration affected cardiovascular and cerebrovascular regulatory systems in a nonlinear way and was able to modulate the interactions between the two control systems with different outcome in non-SYNC and SYNC groups, thus suggesting that the analysis of the impact of respiration on cardiovascular and cerebrovascular regulatory systems might improve our understanding of the mechanisms underpinning the development of postural-related syncope.

Predicting the risk of sudden cardiac death

Sudden cardiac death (SCD) is the result of a change of cardiac activity from normal (typically sinus) rhythm to a rhythm that does not pump adequate blood to the brain. The most common rhythms leading to SCD are ventricular tachycardia (VT) or ventricular fibrillation (VF). These result from an accelerated ventricular pacemaker or ventricular reentrant waves. Despite significant efforts to develop accurate predictors for the risk of SCD, current methods for risk stratification still need to be improved. In this article we briefly review current approaches to risk stratification. Then we discuss the mathematical basis for dynamical transitions (called bifurcations) that may lead to VT and VF. One mechanism for transition to VT or VF involves a perturbation by a premature ventricular complex (PVC) during sinus rhythm. We describe the main mechanisms of PVCs (reentry, independent pacemakers and abnormal depolarizations). An emerging approach to risk stratification for SCD involves the development of individualized dynamical models of a patient based on measured anatomy and physiology. Careful analysis and modelling of dynamics of ventricular arrhythmia on an individual basis will be essential in order to improve risk stratification for SCD and to lay a foundation for personalized (precision) medicine in cardiology.

An easy-to-use technique to characterize cardiodynamics from first-return maps on ΔRR-intervals

Heart rate variability analysis using 24-h Holter monitoring is frequently performed to assess the cardiovascular status of a patient. The present retrospective study is based on the beat-to-beat interval variations or ΔRR, which offer a better view of the underlying structures governing the cardiodynamics than the common RR-intervals. By investigating data for three groups of adults (with normal sinus rhythm, congestive heart failure, and atrial fibrillation, respectively), we showed that the first-return maps built on ΔRR can be classified according to three structures: (i) a moderate central disk, (ii) a reduced central disk with well-defined segments, and (iii) a large triangular shape. These three very different structures can be distinguished by computing a Shannon entropy based on a symbolic dynamics and an asymmetry coefficient, here introduced to quantify the balance between accelerations and decelerations in the cardiac rhythm. The probability P111111 of successive heart beats without large beat-to-beat fluctuations allows to assess the regularity of the cardiodynamics. A characteristic time scale, corresponding to the partition inducing the largest Shannon entropy, was also introduced to quantify the ability of the heart to modulate its rhythm: it was significantly different for the three structures of first-return maps. A blind validation was performed to validate the technique.

Univariate and bivariate symbolic analyses of cardiovascular variability differentiate general anesthesia procedures

General anesthesia attenuates autonomic function and baroreflex control. This side effect should be prevented as much as possible because it limits the subject's ability in responding to physiological challenges during surgery (e.g. arterial pressure and ventricular contractility drops). This study is designed to rank two of the most commonly exploited general anesthesia treatments, i.e. intravenous anesthesia (IA) based on a propofol-opioid combination and volatile anesthesia (VA) based on a sevoflurane-opioid combination, according to their ability to maintain autonomic nervous system activity and baroreflex control. Univariate and bivariate symbolic techniques were applied to spontaneous heart period (HP) and systolic arterial pressure (SAP) variability series recorded during IA and VA procedures in 19 and 18 patients undergoing elective intracranial neurosurgery. Traditional linear univariate and bivariate frequency domain markers of the autonomic nervous system state and baroreflex control were evaluated as well. We found that: (i) univariate symbolic analysis of HP series suggests a better preservation of vagal modulation in VA than in IA; (ii) bivariate symbolic markers assessing the degree of HP-SAP association differentiate IA from VA, while baroreflex sensitivity and squared coherence function cannot; (iii) bivariate symbolic analysis indicates a better preservation of the HP-SAP association at slow frequencies in IA than in VA, thus suggesting a more active baroreflex control in IA. We conclude that symbolic indexes can be fruitfully exploited to rank general anesthesia treatments, and their performance appears to be superior to that of more traditional linear markers.

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

Two diverse complexity metrics quantifying time irreversibility and local prediction, in connection with a surrogate data approach, were utilized to detect nonlinear dynamics in short heart period (HP) variability series recorded in fetuses, as a function of the gestational period, and in healthy humans, as a function of the magnitude of the orthostatic challenge. The metrics indicated the presence of two distinct types of nonlinear HP dynamics characterized by diverse ranges of time scales. These findings stress the need to render more specific the analysis of nonlinear components of HP dynamics by accounting for different temporal scales.

Conditional symbolic analysis detects nonlinear influences of respiration on cardiovascular control in humans

We propose a symbolic analysis framework for the quantitative characterization of complex dynamical systems. It allows the description of the time course of a single variable, the assessment of joint interactions and an analysis triggered by a conditioning input. The framework was applied to spontaneous variability of heart period (HP), systolic arterial pressure (SAP) and integrated muscle sympathetic nerve activity (MSNA) with the aim of characterizing cardiovascular control and nonlinear influences of respiration at rest in supine position, during orthostatic challenge induced by 80° head-up tilt (TILT) and about 3 min before evoked pre-syncope signs (PRESY). The approach detected (i) the exaggerated sympathetic modulation and vagal withdrawal from HP variability and the increased presence of fast MSNA variability components during PRESY compared with TILT; (ii) the increase of the SAP-HP coordination occurring at slow temporal scales and a decrease of that occurring at faster time scales during PRESY compared with TILT; (iii) the reduction of the coordination between fast MSNA and SAP patterns during TILT and PRESY; (iv) the nonlinear influences of respiration leading to an increased likelihood to observe the abovementioned findings during expiration compared with inspiration one. The framework provided simple, quantitative indexes able to distinguish experimental conditions characterized by different states of the autonomic nervous system and to detect the early signs of a life threatening situation such as postural syncope.

Inference of human affective states from psychophysiological measurements extracted under ecologically valid conditions

Compared to standard laboratory protocols, the measurement of psychophysiological signals in real world experiments poses technical and methodological challenges due to external factors that cannot be directly controlled. To address this problem, we propose a hybrid approach based on an immersive and human accessible space called the eXperience Induction Machine (XIM), that incorporates the advantages of a laboratory within a life-like setting. The XIM integrates unobtrusive wearable sensors for the acquisition of psychophysiological signals suitable for ambulatory emotion research. In this paper, we present results from two different studies conducted to validate the XIM as a general-purpose sensing infrastructure for the study of human affective states under ecologically valid conditions. In the first investigation, we recorded and classified signals from subjects exposed to pictorial stimuli corresponding to a range of arousal levels, while they were free to walk and gesticulate. In the second study, we designed an experiment that follows the classical conditioning paradigm, a well-known procedure in the behavioral sciences, with the additional feature that participants were free to move in the physical space, as opposed to similar studies measuring physiological signals in constrained laboratory settings. Our results indicate that, by using our sensing infrastructure, it is indeed possible to infer human event-elicited affective states through measurements of psychophysiological signals under ecological conditions.

Morning surge of ventricular arrhythmias in a new arrhythmogenic canine model of chronic heart failure is associated with attenuation of time-of-day dependence of heart rate and autonomic adaptation, and reduced cardiac chaos

Patients with chronic heart failure (CHF) exhibit a morning surge in ventricular arrhythmias, but the underlying cause remains unknown. The aim of this study was to determine if heart rate dynamics, autonomic input (assessed by heart rate variability (HRV)) and nonlinear dynamics as well as their abnormal time-of-day-dependent oscillations in a newly developed arrhythmogenic canine heart failure model are associated with a morning surge in ventricular arrhythmias. CHF was induced in dogs by aortic insufficiency & aortic constriction, and assessed by echocardiography. Holter monitoring was performed to study time-of-day-dependent variation in ventricular arrhythmias (PVCs, VT), traditional HRV measures, and nonlinear dynamics (including detrended fluctuations analysis α1 and α2 (DFAα1 & DFAα2), correlation dimension (CD), and Shannon entropy (SE)) at baseline, as well as 240 days (240 d) and 720 days (720 d) following CHF induction. LV fractional shortening was decreased at both 240 d and 720 d. Both PVCs and VT increased with CHF duration and showed a morning rise (2.5-fold & 1.8-fold increase at 6 AM-noon vs midnight-6 AM) during CHF. The morning rise in HR at baseline was significantly attenuated by 52% with development of CHF (at both 240 d & 720 d). Morning rise in the ratio of low frequency to high frequency (LF/HF) HRV at baseline was markedly attenuated with CHF. DFAα1, DFAα2, CD and SE all decreased with CHF by 31, 17, 34 and 7%, respectively. Time-of-day-dependent variations in LF/HF, CD, DFA α1 and SE, observed at baseline, were lost during CHF. Thus in this new arrhythmogenic canine CHF model, attenuated morning HR rise, blunted autonomic oscillation, decreased cardiac chaos and complexity of heart rate, as well as aberrant time-of-day-dependent variations in many of these parameters were associated with a morning surge of ventricular arrhythmias.

Entropy-based complexity of the cardiovascular control in Parkinson disease: comparison between binning and k-nearest-neighbor approaches

Entropy-based approaches are frequently used to quantify complexity of short-term cardiovascular control from spontaneous beat-to-beat variability of heart period (HP) and systolic arterial pressure (SAP). Among these tools the ones optimizing a critical parameter such as the pattern length are receiving more and more attention. This study compares two entropy-based techniques for the quantification of complexity making use of completely different strategies to optimize the pattern length. Comparison was carried out over HP and SAP variability series recorded from 12 Parkinson's disease (PD) patients without orthostatic hypotension or symptoms of orthostatic intolerance and 12 age-matched healthy control (HC) subjects. Regardless of the method, complexity of cardiovascular control increased in PD group, thus suggesting the early impairment of cardiovascular function.

Cardiovascular and cardiorespiratory coupling in unmedicated schizophrenic patients in comparison to healthy subjects

Schizophrenia is associated with a cardiac autonomic dysregulation which is characterized by a decreased vagal modulation. Nevertheless, there are less information about the interrelationships of the cardiovascular and respiratory systems in schizophrenia.

Multipole analysis of heart rate variability as a predictor of imminent ventricular arrhythmias in ICD patients

BACKGROUND

Contemporary implantable cardiac defibrillators (ICD) enable storage of multiple, preepisode R-R recordings in patients who suffered from ventricular tachyarrhythmia (VTA). Timely prediction of VTA, using heart rate variability (HRV) analysis techniques, may facilitate the implementation of preventive and therapeutic strategies.

AIM

To evaluate the novel multipole method of the HRV analysis in prediction of imminent VTAs in ICD patients.

METHODS

We screened patients from the Biotronik HAWAI Registry (Heart Rate Analysis with Automated ICDs). A total of 28 patients from the HAWAI registries (phase I and II), having medical records, who had experienced documented, verified VTA during the 2-year follow-up, were included in our analysis. HRV during preepisode recordings of 4,500 R-R intervals were analyzed using the Dyx parameter and compared to HRV of similar length recordings from the same patients that were not followed by arrhythmia.

RESULTS

Our study population consisted mainly of men 25 of 28 (89%), average age of 64.8 ± 9.4 years, 92% with coronary artery disease. HRV during 64 preevent recordings (2.3 events per patient on average) was analyzed and compared with 60 control recordings. The multipole method of HRV analysis showed 50% sensitivity and 91.6% specificity for prediction of ventricular tachycardia/ventricular fibrillation in the study population, with 84.5% positive predictive value. No statistically significant correlation was found between various clinical parameters and the sensitivity of imminent VTA predetection in our patients.

CONCLUSION

The multipole method of HRV analysis emerges as a highly specific, possible predictor of imminent VTA, providing an early warning allowing to prepare for an arrhythmic episode.

Ischemic risk stratification by means of multivariate analysis of the heart rate variability

In this work, a univariate and multivariate statistical analysis of indexes derived from heart rate variability (HRV) was conducted to stratify patients with ischemic dilated cardiomyopathy (IDC) in cardiac risk groups. Indexes conditional entropy, refined multiscale entropy (RMSE), detrended fluctuation analysis, time and frequency analysis, were applied to the RR interval series (beat-to-beat series), for single and multiscale complexity analysis of the HRV in IDC patients. Also, clinical parameters were considered. Two different end-points after a follow-up of three years were considered: (i) analysis A, with 151 survivor patients as a low risk group and 13 patients that suffered sudden cardiac death as a high risk group; (ii) analysis B, with 192 survivor patients as a low risk group and 30 patients that suffered cardiac mortality as a high risk group. A univariate and multivariate linear discriminant analysis was used as a statistical technique for classifying patients in risk groups. Sensitivity (Sen) and specificity (Spe) were calculated as diagnostic criteria in order to evaluate the performance of the indexes and their linear combinations. Sen and Spe values of 80.0% and 72.9%, respectively, were obtained during daytime by combining one clinical parameter and one index from RMSE, and during nighttime Sen = 80% and Spe = 73.4% were attained by combining one clinical factor and two indexes from RMSE. In particular, relatively long time scales were more relevant for classifying patients into risk groups during nighttime, while during daytime shorter scales performed better. The results suggest that the left atrial size, indexed to body surface and RMSE indexes are those that allow enhanced classification of ischemic patients in their respective risk groups, confirming that a single measurement is not enough to fully characterize ischemic risk patients and the clinical relevance of HRV complexity measures.

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.

Monitoring in cardiovascular disease patients by nonlinear biomedical signal processing

Due to recent advances in technology extensive cardiovascular monitoring is widely introduced today. An essential component of cardiovascular monitoring is the analysis of several biosignals as electrocardiogram, blood pressure and other vital signs. This manuscript provides an overview about several application fields of cardiovascular monitoring with the main focus on nonlinear dynamics analysis.

Using n-gram analysis to cluster heartbeat signals

Background

Biological signals may carry specific characteristics that reflect basic dynamics of the body. In particular, heart beat signals carry specific signatures that are related to human physiologic mechanisms. In recent years, many researchers have shown that representations which used non-linear symbolic sequences can often reveal much hidden dynamic information. This kind of symbolization proved to be useful for predicting life-threatening cardiac diseases.

Methods

This paper presents an improved method called the “Adaptive Interbeat Interval Analysis (AIIA) method”. The AIIA method uses the Simple K-Means algorithm for symbolization, which offers a new way to represent subtle variations between two interbeat intervals without human intervention. After symbolization, it uses the n-gram algorithm to generate different kinds of symbolic sequences. Each symbolic sequence stands for a variation phase. Finally, the symbolic sequences are categorized by classic classifiers.

Results

In the experiments presented in this paper, AIIA method achieved 91% (3-gram, 26 clusters) accuracy in successfully classifying between the patients with Atrial Fibrillation (AF), Congestive Heart Failure (CHF) and healthy people. It also achieved 87% (3-gram, 26 clusters) accuracy in classifying the patients with apnea.

Conclusions

The two experiments presented in this paper demonstrate that AIIA method can categorize different heart diseases. Both experiments acquired the best category results when using the Bayesian Network. For future work, the concept of the AIIA method can be extended to the categorization of other physiological signals. More features can be added to improve the accuracy.

Review and classification of variability analysis techniques with clinical applications

Analysis of patterns of variation of time-series, termed variability analysis, represents a rapidly evolving discipline with increasing applications in different fields of science. In medicine and in particular critical care, efforts have focussed on evaluating the clinical utility of variability. However, the growth and complexity of techniques applicable to this field have made interpretation and understanding of variability more challenging. Our objective is to provide an updated review of variability analysis techniques suitable for clinical applications. We review more than 70 variability techniques, providing for each technique a brief description of the underlying theory and assumptions, together with a summary of clinical applications. We propose a revised classification for the domains of variability techniques, which include statistical, geometric, energetic, informational, and invariant. We discuss the process of calculation, often necessitating a mathematical transform of the time-series. Our aims are to summarize a broad literature, promote a shared vocabulary that would improve the exchange of ideas, and the analyses of the results between different studies. We conclude with challenges for the evolving science of variability analysis.

Clustering heart rate dynamics is associated with β-adrenergic receptor polymorphisms: analysis by information-based similarity index

Background

Genetic polymorphisms in the gene encoding the β-adrenergic receptors (β-AR) have a pivotal role in the functions of the autonomic nervous system. Using heart rate variability (HRV) as an indicator of autonomic function, we present a bottom-up genotype–phenotype analysis to investigate the association between β-AR gene polymorphisms and heart rate dynamics.

Methods

A total of 221 healthy Han Chinese adults (59 males and 162 females, aged 33.6±10.8 years, range 19 to 63 years) were recruited and genotyped for three common β-AR polymorphisms: β₁-AR Ser49Gly, β₂-AR Arg16Gly and β₂-AR Gln27Glu. Each subject underwent two hours of electrocardiogram monitoring at rest. We applied an information-based similarity (IBS) index to measure the pairwise dissimilarity of heart rate dynamics among study subjects.

Results

With the aid of agglomerative hierarchical cluster analysis, we categorized subjects into major clusters, which were found to have significantly different distributions of β₂-AR Arg16Gly genotype. Furthermore, the non-randomness index, a nonlinear HRV measure derived from the IBS method, was significantly lower in Arg16 homozygotes than in Gly16 carriers. The non-randomness index was negatively correlated with parasympathetic-related HRV variables and positively correlated with those HRV indices reflecting a sympathovagal shift toward sympathetic activity.

Conclusions

We demonstrate a bottom-up categorization approach combining the IBS method and hierarchical cluster analysis to detect subgroups of subjects with HRV phenotypes associated with β-AR polymorphisms. Our results provide evidence that β₂-AR polymorphisms are significantly associated with the acceleration/deceleration pattern of heart rate oscillation, reflecting the underlying mode of autonomic nervous system control.

New insight into arrhythmia onset using HRV and BPV analysis

In this paper Heart Rate Variability (HRV) and Blood Pressure Variability (BPV) were analyzed before the onset of cardiac arrhythmia in order to derive markers for short-term forecasting. The (a) coherence between systolic blood pressure (SBP) and cardiac oscillations in low-frequency (LF) and high-frequency (HF) band; (b) fluctuations of phase; (c) HRV and BPV as a LF power and HF power in frequency and time-frequency domain; (d) transfer function analysis of cardiovascular signals were analyzed. Arrhythmia was preceded by: a) lower coherence; b) increase in fluctuations of phase between signals; c) higher spectral energy associated with respiratory frequency in blood pressure signal; d) raise of sympathetic outflow to the heart; e) decreased HRV. Cardiac arrhythmia was characterized mainly by an increase in LF power of blood pressure, cardiac signal and transfer function. During self-termination of arrhythmia a larger increased in total BPV and HRV was recorded. These results suggest that important information about both neuronal cardiovascular control and risk for spontaneous arrhythmia can be provided by combined analysis of frequency, phase, and time-frequency analysis of blood pressure and cardiac oscillation.

Complexity of the short-term heart-rate variability

This work has proposed a methodology based on the concept of entropy rates to study the complexity of the short-term heart-rate variability (HRV) for improving risk stratification to predict sudden cardiac death (SCD) of patients with established ischemic-dilated cardiomyopathy (IDC). The short-term HRV was analyzed during daytime and nighttime by means of RR series. An entropy rate was calculated on the RR series, previously transformed to symbol sequences by means of an alphabet. A statistical analysis permitted to stratify high- and low-risk patients of suffering SCD, with a specificity (SP) of 95% and sensitivity (SE) of 83.3%.

Autonomic cardiovascular modulation

We validated a symbolic approach to assess autonomic modulation from pulse interval (PI) and systolic arterial pressure (SAP) series obtained from an animal model of chronic heart failure (CHF). We studied three groups of rats: controls; CHF animals; CHF animals treated with spironolactone (CHF-SP), reducing sympathetic activity in CHF. Simulations confirmed that symbolic analysis captures modifications of cardiovascular regulation in the case of fast dynamics and negligible variance. While spectral indexes did not reveal any significant difference among groups, symbolic analysis pointed out that sympathetic modulation is reduced in CHF group and restored to basal values in CHF-SP one.

Is the normal heart rate "chaotic" due to respiration?

The incidence of cardiovascular diseases increases with the growth of the human population and an aging society, leading to very high expenses in the public health system. Therefore, it is challenging to develop sophisticated methods in order to improve medical diagnostics. The question whether the normal heart rate is chaotic or not is an attempt to elucidate the underlying mechanisms of cardiovascular dynamics and therefore a highly controversial topical challenge. In this contribution we demonstrate that linear and nonlinear parameters allow us to separate completely the data sets of the three groups provided for this controversial topic in nonlinear dynamics. The question whether these time series are chaotic or not cannot be answered satisfactorily without investigating the underlying mechanisms leading to them. We give an example of the dominant influence of respiration on heart beat dynamics, which shows that observed fluctuations can be mostly explained by respiratory modulations of heart rate and blood pressure (coefficient of determination: 96%). Therefore, we recommend reformulating the following initial question: "Is the normal heart rate chaotic?" We rather ask the following: "Is the normal heart rate 'chaotic' due to respiration?"

Clinical impact of evaluation of cardiovascular control by novel methods of heart rate dynamics

Heart rate variability (HRV) has been conventionally analysed with time- and frequency-domain methods, which measure the overall magnitude of RR interval fluctuations around its mean value or the magnitude of fluctuations in some predetermined frequencies. Analysis of heart rate dynamics by novel methods, such as heart rate turbulence after ventricular premature beats, deceleration capacity of heart rate and methods based on chaos theory and nonlinear system theory, have gained recent interest. Recent observational studies have suggested that some indices describing nonlinear heart rate dynamics, such as fractal scaling exponents, heart rate turbulence and deceleration capacity, may provide useful prognostic information in various clinical settings and their reproducibility may be better than that of traditional indices. For example, the short-term fractal scaling exponent measured by the detrended fluctuation analysis method has been shown to predict fatal cardiovascular events in various populations. Similarly, heart rate turbulence and deceleration capacity have performed better than traditional HRV measures in predicting mortality in post-infarction patients. Approximate entropy, a nonlinear index of heart rate dynamics, which describes the complexity of RR interval behaviour, has provided information on the vulnerability to atrial fibrillation. There are many other nonlinear indices which also give information on the characteristics of heart rate dynamics, but their clinical usefulness is not as well established. Although the concepts of nonlinear dynamics, fractal mathematics and complexity measures of heart rate behaviour, heart rate turbulence, deceleration capacity in relation to cardiovascular physiology or various cardiovascular events are still far away from clinical medicine, they are a fruitful area for research to expand our knowledge concerning the behaviour of cardiovascular oscillations in normal healthy conditions as well as in disease states.

Assessment of cardiovascular regulation through irreversibility analysis of heart period variability: a 24 hours Holter study in healthy and chronic heart failure populations

We propose an approach based on time reversibility analysis to characterize the cardiovascular regulation and its nonlinearities as derived from 24 hours Holter recordings of heart period variability in a healthy population (n=12, age: median=43 years, range=34-55 years) and in a pathological group of age-matched chronic heart failure (CHF) patients (n=13, primarily in NYHA class II, age: median=37 years, range=33-56 years, ejection fraction: median=25%, range=13-30%). Two indices capable of detecting nonlinear irreversible dynamics according to different strategies of phase-space reconstruction (i.e. a fixed two-dimensional phase-space reconstruction and an optimal selection of the embedding dimension, respectively) are tested and compared with a more traditional nonlinear index based on local nonlinear prediction. Results showed that nonlinear dynamics owing to time irreversibility at short time scales are significantly present during daytime in healthy subjects, more frequently present in the CHF population and less frequently during night-time in both groups, thus suggesting their link with a dominant sympathetic regulation and/or with a vagal withdrawal. On the contrary, nonlinear dynamics owing to time irreversibility at longer, dominant time scales were insignificantly present in both groups. During daytime in the healthy population, irreversibility was mostly due to the presence of asymmetric patterns characterized by bradycardic runs shorter than tachycardic ones. Nonlinear dynamics produced by mechanisms different from those inducing temporal irreversibility were significantly detectable in both groups and more frequently during night-time. The present study proposes a method to distinguish different types of nonlinearities and assess their contribution over different temporal scales. Results confirm the usefulness of this method even when applied in uncontrolled experimental conditions such as those during 24 hours Holter recordings.

Depression of cardiovascular autonomic function is more pronounced after mitral valve surgery: evidence for direct trauma

The analysis of baroreflex sensitivity (BRS) and heart rate variability (HRV) leads to additional insights into patients' prognosis after cardiovascular events. The following study was performed to assess the differences in the post-operative recovery of autonomic regulation after mitral valve (MV) and aortic valve (AV) surgery with a heart-lung machine. Among the 43 consecutive male patients enrolled in a prospective study, 26 underwent isolated AV surgery and 17 isolated MV surgery. Blood pressure as well as ECG signals were recorded the day before, 24 hours after and one week after surgery. BRS was calculated according to the dual sequence method, and HRV was calculated using standard linear as well as nonlinear parameters. There were no major differences between the two groups in the pre-operative values. At 24 hours a comparable depression of HRV and BRS in both groups was observed, while at 7 days there was partial recovery in AV patients, which was absent in MV patients: p(AV versus MV)<0.001. While the response of the autonomic system to surgery is similar in AV and MV patients, there is obviously a decreased ability to recover in MV patients, probably attributed to traumatic lesions of the autonomic nervous system by opening the atria. Ongoing research is required for further clarification of the pathophysiology of this phenomenon and to establish strategies to restore autonomic function.