Prediction of short cardiovascular variability signals based on conditional distribution

Application of Multiscale Sample Entropy in Assessing Effects of Exercise Training on Skin Blood Flow Oscillations in People with Spinal Cord Injury

Spinal cord injury (SCI) causes a disruption of autonomic nervous regulation to the cardiovascular system, leading to various cardiovascular and microvascular diseases. Exercise training is an effective intervention for reducing risk for microvascular diseases in healthy people. However, the effectiveness of exercise training on improving microvascular function in people with SCI is largely unknown. The purpose of this study was to compare blood flow oscillations in people with spinal cord injury and different physical activity levels to determine if such a lifestyle might influence skin blood flow. A total of 37 participants were recruited for this study, including 12 athletes with SCI (ASCI), 9 participants with SCI and a sedentary lifestyle (SSCI), and 16 healthy able-bodied controls (AB). Sacral skin blood flow (SBF) in response to local heating at 42 °C for 50 min was measured using laser Doppler flowmetry. The degree of the regularity of blood flow oscillations (BFOs) was quantified using a multiscale entropy approach. The results showed that BFO was significantly more irregular in ASCI and AB compared to SSCI during the maximal vasodilation period. Our results also demonstrate that the difference in the regularity of BFOs between original SBF signal and phase-randomized surrogate time series was larger in ASCI and AB compared to SSCI. Our findings indicate that SCI causes a loss of complexity of BFOs and exercise training may improve complexity in people with SCI. This study demonstrates that multiscale entropy is a sensitive method for detecting differences between different categories of people with SCI and might be able to detect effects of exercise training related to skin blood flow.

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.

Comparing Cross-Sample Entropy and K-Nearest-Neighbor Cross-Predictability Approaches for the Evaluation of Cardiorespiratory and Cerebrovascular Dynamic Interactions

Quantification of the cardiorespiratory and cerebrovascular couplings is a relevant clinical issue given that their changes are considered signs of pathological status. The inherent nonlinearity of mechanisms underlying cardiorespiratory and cerebrovascular links requires nonlinear tools for their reliable evaluation. In the present study we compare two nonlinear methods for the assessment of coupling strength between two time series, namely cross-sample entropy (CSampEn) and k-nearest-neighbor cross-predictability (KNNCP). CSampEn uses a strategy that fixes the pattern length, while KNNCP optimizes the pattern length to maximize cross-predictability. CSampEn and KNNCP were applied to the beat-to-beat series of heart period (HP) and respiration (R) during a controlled breathing protocol with the aim at assessing cardiorespiratory coupling and to the beat-to-beat series of mean cerebral blood flow (MCBF) and mean arterial pressure (MAP) during an orthostatic stressor with the aim at evaluating cerebrovascular coupling. Although both the methods have the possibility to quantify the degree of HP-R and MCBF-MAP association, they exhibited different statistical power and even diverse trends in response to the considered physiological challenges. CSampEn and KNNCP are not interchangeable and should be utilized in association more than in alternative for the quantification of the HP-R and MCBF-MAP coupling strength. Clinical Relevance - This study proves that cross-entropy and cross-predictability might lead to different conclusions about cardiorespiratory and cerebrovascular couplings.

Heart rate variability as a biomarker in patients with Chronic Chagas Cardiomyopathy with or without concomitant digestive involvement and its relationship with the Rassi score

Background

Dysautonomia plays an ancillary role in the pathogenesis of Chronic Chagas Cardiomyopathy (CCC), but is the key factor causing digestive organic involvement. We investigated the ability of heart rate variability (HRV) for death risk stratification in CCC and compared alterations of HRV in patients with isolated CCC and in those with the mixed form (CCC + digestive involvement). Thirty-one patients with CCC were classified into three risk groups (low, intermediate and high) according to their Rassi score. A single-lead ECG was recorded for a period of 10–20 min, RR series were generated and 31 HRV indices were calculated. The HRV was compared among the three risk groups and regarding the associated digestive involvement. Four machine learning models were created to predict the risk class of patients.

Results

Phase entropy is decreased and the percentage of inflection points is increased in patients from the high-, compared to the low-risk group. Fourteen patients had the mixed form, showing decreased triangular interpolation of the RR histogram and absolute power at the low-frequency band. The best predictive risk model was obtained by the support vector machine algorithm (overall F1-score of 0.61).

Conclusions

The mixed form of Chagas' disease showed a decrease in the slow HRV components. The worst prognosis in CCC is associated with increased heart rate fragmentation. The combination of HRV indices enhanced the accuracy of risk stratification. In patients with the mixed form of Chagas disease, a higher degree of sympathetic autonomic denervation may be associated with parasympathetic impairment.

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.

Associations between Cardiovascular Signal Entropy and Cognitive Performance over Eight Years

In this study, the relationship between non-invasively measured cardiovascular signal entropy and global cognitive performance was explored in a sample of community-dwelling older adults from The Irish Longitudinal Study on Ageing (TILDA), both cross-sectionally at baseline (n = 4525; mean (SD) age: 61.9 (8.4) years; 54.1% female) and longitudinally. We hypothesised that signal disorder in the cardiovascular system, as quantified by short-length signal entropy during rest, could provide a marker for cognitive function. Global cognitive function was assessed via Mini Mental State Examination (MMSE) across five longitudinal waves (8 year period; n = 4316; mean (SD) age: 61.9 (8.4) years; 54.4% female) and the Montreal Cognitive Assessment (MOCA) across two longitudinal waves (4 year period; n = 3600; mean (SD) age: 61.7 (8.2) years; 54.1% female). Blood pressure (BP) was continuously monitored during supine rest at baseline, and sample entropy values were calculated for one-minute and five-minute sections of this data, both for time-series data interpolated at 5 Hz and beat-to-beat data. Results revealed significant associations between BP signal entropy and cognitive performance, both cross-sectionally and longitudinally. Results also suggested that as regards associations with cognitive performance, the entropy analysis approach used herein potentially outperformed more traditional cardiovascular measures such as resting heart rate and heart rate variability. The quantification of entropy in short-length BP signals could provide a clinically useful marker of the cardiovascular dysregulations that potentially underlie cognitive decline.

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.

Early Detection of Sudden Cardiac Death by Using Ensemble Empirical Mode Decomposition-Based Entropy and Classical Linear Features From Heart Rate Variability Signals

Sudden cardiac death (SCD), which can deprive a person of life within minutes, is a destructive heart abnormality. Thus, providing early warning information for patients at risk of SCD, especially those outside hospitals, is essential. In this study, we investigated the performances of ensemble empirical mode decomposition (EEMD)-based entropy features on SCD identification. EEMD-based entropy features were obtained by using the following technology: (1) EEMD was performed on HRV beats to decompose them into intrinsic mode functions (IMFs), (2) five entropy parameters, namely Rényi entropy (RenEn), fuzzy entropy (FuEn), dispersion Entropy (DisEn), improved multiscale permutation entropy (IMPE), and Renyi distribution entropy(RdisEn), were computed from the first four IMFs obtained, which were named EEMD-based entropy features. Additionally, an automated scheme combining EEMD-based entropy and classical linear (time and frequency domains) features was proposed with the intention of detecting SCD early by analyzing 14 min (at seven successive intervals of 2 min) heart rate variability (HRV) in signals from a normal population and subjects at risk of SCD. Firstly, EEMD-based entropy and classical linear measurements were extracted from HRV beats, and then the integrated measurements were ranked by various methodologies, i.e., t-test, entropy, receiver-operating characteristics (ROC), Wilcoxon, and Bhattacharyya. Finally, these ranked features were fed into a k-Nearest Neighbor algorithm for classification. Compared with several state-of-the-art methods, the proposed scheme firstly predicted subjects at risk of SCD up to 14 min earlier with an accuracy of 96.1%, a sensitivity of 97.5%, and a specificity of 94.4% 14 min before SCD onset. The simulation results exhibited that EEMD-based entropy estimators showed significant difference between SCD patients and normal individuals and outperformed the classical linear estimators in SCD detection, the EEMD-based FuEn and IMPE indexes were particularly useful assessments for identification of patients at risk of SCD and can be used as novel indices to reveal the disorders of rhythm variations of the autonomic nervous system when affected by SCD.

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.

Short-term multiscale complexity analysis of cardiovascular variability improves low cardiac output syndrome risk stratification after coronary artery bypass grafting

BACKGROUND

Low cardiac output syndrome (LCOS) is a myocardial dysfunction leading to systemic hypoperfusion, favored by particular conditions of the autonomic nervous system. LCOS is one of the adverse events that might occur after cardiac surgery.

OBJECTIVE

The aim is to test the hypothesis that short-term multiscale complexity (MSC) analysis of heart period (HP) and systolic arterial pressure (SAP) variability series in the frequency bands typical of cardiovascular control could be fruitfully exploited in identifying subjects at risk of developing LCOS after coronary artery bypass graft (CABG).

APPROACH

HP and SAP beat-to-beat series were derived from electrocardiogram (ECG) and invasive arterial pressure (AP) signal acquired in 128 patients scheduled for CABG before (PRE) and after (POST) the induction of general anesthesia with propofol and remifentanil. Subjects were labeled as LCOS (n  =  14) and noLCOS (n  =  114) according to the LCOS development. MSC markers were calculated as the complement to 1 of the modulus of the average position of the poles dropping in the low-frequency (LF, 0.04-0.15 Hz) and high-frequency (HF, 0.15-0.5 Hz) bands as derived from the autoregressive model of HP and SAP series. Traditional time and frequency domain indexes were also calculated.

MAIN RESULTS

Traditional parameters were able to assess the depression of the cardiovascular regulation induced by general anesthesia, but showed weak performances in differentiating LCOS and noLCOS groups. Conversely, HP complexity in LF band and SAP complexity in HF band assessed during POST remained associated with LCOS even after entering a multivariate logistic regression model adjusted for clinical and demographic factors.

SIGNIFICANCE

The MSC approach can be fruitfully applied to improve risk stratification for LCOS after CABG likely because MSC markers describe the dysfunction of the sympathetic control and the impairment of the mechanical properties of the heart in the LCOS group.

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.

Conditional Self-Entropy and Conditional Joint Transfer Entropy in Heart Period Variability during Graded Postural Challenge

Self-entropy (SE) and transfer entropy (TE) are widely utilized in biomedical signal processing to assess the information stored into a system and transferred from a source to a destination respectively. The study proposes a more specific definition of the SE, namely the conditional SE (CSE), and a more flexible definition of the TE based on joint TE (JTE), namely the conditional JTE (CJTE), for the analysis of information dynamics in multivariate time series. In a protocol evoking a gradual sympathetic activation and vagal withdrawal proportional to the magnitude of the orthostatic stimulus, such as the graded head-up tilt, we extracted the beat-to-beat spontaneous variability of heart period (HP), systolic arterial pressure (SAP) and respiratory activity (R) in 19 healthy subjects and we computed SE of HP, CSE of HP given SAP and R, JTE from SAP and R to HP, CJTE from SAP and R to HP given SAP and CJTE from SAP and R to HP given R. CSE of HP given SAP and R was significantly smaller than SE of HP and increased progressively with the amplitude of the stimulus, thus suggesting that dynamics internal to HP and unrelated to SAP and R, possibly linked to sympathetic activation evoked by head-up tilt, might play a role during the orthostatic challenge. While JTE from SAP and R to HP was independent of tilt table angle, CJTE from SAP and R to HP given R and from SAP and R to HP given SAP showed opposite trends with tilt table inclination, thus suggesting that the importance of the cardiac baroreflex increases and the relevance of the cardiopulmonary pathway decreases during head-up tilt. The study demonstrates the high specificity of CSE and the high flexibility of CJTE over real data and proves that they are particularly helpful in disentangling physiological mechanisms and in assessing their different contributions to the overall cardiovascular regulation.

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.

Toll-like receptor 9 plays a key role in the autonomic cardiac and baroreflex control of arterial pressure

The crosstalk between the immune and the autonomic nervous system may impact the cardiovascular function. Toll-like receptors are components of the innate immune system and play developmental and physiological roles. Toll-like receptor 9 (TLR9) is involved in the pathogenesis of cardiovascular diseases, such as hypertension and heart failure. Since such diseases are commonly accompanied by autonomic imbalance and lower baroreflex sensitivity, we hypothesized that TLR9 modulates cardiac autonomic and baroreflex control of arterial pressure (AP). Toll-like receptor 9 knockout (TLR9 KO) and wild-type (WT) mice were implanted with catheters into carotid artery and jugular vein and allowed to recover for 3 days. After basal recording of AP, mice received methyl-atropine or propranolol. AP and pulse interval (PI) variability were evaluated in the time and frequency domain (spectral analysis), as well as by multiscale entropy. Spontaneous baroreflex was studied by sequence technique. Behavioral and cardiovascular responses to fear-conditioning stress were also evaluated. AP was similar between groups, but TLR9 KO mice exhibited lower basal heart rate (HR). AP variability was not different, but PI variability was increased in TLR9 KO mice. The total entropy was higher in TLR9 KO mice. Moreover, baroreflex function was found higher in TLR9 KO mice. Atropine-induced tachycardia was increased in TLR9 KO mice, whereas the propranolol-induced bradycardia was similar to WT mice. TLR9 KO mice exhibit increased behavioral and decreased tachycardia responses to fear-conditioning stress. In conclusion, our findings suggest that TLR9 may negatively modulate cardiac vagal tone and baroreflex in mice.

Effect of age on complexity and causality of the cardiovascular control: comparison between model-based and model-free approaches

The proposed approach evaluates complexity of the cardiovascular control and causality among cardiovascular regulatory mechanisms from spontaneous variability of heart period (HP), systolic arterial pressure (SAP) and respiration (RESP). It relies on construction of a multivariate embedding space, optimization of the embedding dimension and a procedure allowing the selection of the components most suitable to form the multivariate embedding space. Moreover, it allows the comparison between linear model-based (MB) and nonlinear model-free (MF) techniques and between MF approaches exploiting local predictability (LP) and conditional entropy (CE). The framework was applied to study age-related modifications of complexity and causality in healthy humans in supine resting (REST) and during standing (STAND). We found that: 1) MF approaches are more efficient than the MB method when nonlinear components are present, while the reverse situation holds in presence of high dimensional embedding spaces; 2) the CE method is the least powerful in detecting age-related trends; 3) the association of HP complexity on age suggests an impairment of cardiac regulation and response to STAND; 4) the relation of SAP complexity on age indicates a gradual increase of sympathetic activity and a reduced responsiveness of vasomotor control to STAND; 5) the association from SAP to HP on age during STAND reveals a progressive inefficiency of baroreflex; 6) the reduced connection from HP to SAP with age might be linked to the progressive exploitation of Frank-Starling mechanism at REST and to the progressive increase of peripheral resistances during STAND; 7) at REST the diminished association from RESP to HP with age suggests a vagal withdrawal and a gradual uncoupling between respiratory activity and heart; 8) the weakened connection from RESP to SAP with age might be related to the progressive increase of left ventricular thickness and vascular stiffness and to the gradual decrease of respiratory sinus arrhythmia.

Children's heart rate variability as stress indicator: association with reported stress and cortisol

Stress is a complex phenomenon coordinated by two main neural systems: the hypothalamic-pituitary-adrenal system with cortisol as classical stress biomarker and the autonomic nervous system with heart rate variability (HRV) as recently suggested stress marker. To test low HRV (5 minute measurements) as stress indicator in young children (5-10 y), associations with self-reported chronic stress aspects (events, emotions and problems) (N=334) and salivary cortisol (N=293) were performed. Peer problems, anger, anxiety and sadness were associated with lower root mean square of successive differences (RMSSD) and high frequency power (i.e. lower parasympathetic activity). Anxiety and anger were also related to a higher low frequency to high frequency ratio. Using multilevel modelling, higher cortisol levels, a larger cortisol awakening response and steeper diurnal decline were also associated with these HRV patterns of lower parasympathetic activity.

CONCLUSION

Low HRV (lower parasympathetic activity) might serve as stress indicator in children.

Cardiovascular control and time domain Granger causality: insights from selective autonomic blockade

We studied causal relations among heart period (HP), systolic arterial pressure (SAP) and respiration (R) according to the definition of Granger causality in the time domain. Autonomic pharmacological challenges were used to alter the complexity of cardiovascular control. Atropine (AT), propranolol and clonidine (CL) were administered to block muscarinic receptors, β-adrenergic receptors and centrally sympathetic outflow, respectively. We found that: (i) at baseline, HP and SAP interacted in a closed loop with a dominant causal direction from HP to SAP; (ii) pharmacological blockades did not alter the bidirectional closed-loop interactions between HP and SAP, but AT reduced the dominance of the causal direction from HP to SAP; (iii) at baseline, bidirectional interactions between HP and R were frequently found; (iv) the closed-loop relation between HP and R was unmodified by the administration of drugs; (v) at baseline, unidirectional interactions from R to SAP were often found; and (vi) while AT induced frequently an uncoupling between R and SAP, CL favoured bidirectional interactions. These results prove that time domain measures of Granger causality can contribute to the description of cardiovascular control by suggesting the temporal direction of the interactions and by separating different causality schemes (e.g. closed loop versus unidirectional relations).

Cardiovascular and cardiorespiratory coupling analyses: a review

Recently, methods have been developed to analyse couplings in dynamic systems. In the field of medical analysis of complex cardiovascular and cardiorespiratory systems, there is growing interest in how insights may be gained into the interaction between regulatory mechanisms in healthy and diseased persons. The couplings within and between these systems can be linear or nonlinear. However, the complex mechanisms involved in cardiovascular and cardiorespiratory regulation very likely interact with each other in a nonlinear way. Recent advances in nonlinear dynamics and information theory have allowed the multivariate study of information transfer between time series. They therefore might be able to provide additional diagnostic and prognostic information in medicine and might, in particular, be able to complement traditional linear coupling analysis techniques. In this review, we describe the approaches (Granger causality, nonlinear prediction, entropy, symbolization, phase synchronization) most commonly applied to detect direct and indirect couplings between time series, especially focusing on nonlinear approaches. We will discuss their capacity to quantify direct and indirect couplings and the direction (driver-response relationship) of the considered interaction between different biological time series. We also give their basic theoretical background, their basic requirements for application, their main features and demonstrate their usefulness in different applications in the field of cardiovascular and cardiorespiratory coupling analyses.

Granger causality in cardiovascular variability series: comparison between model-based and model-free approaches

A linear model-based (MB) approach for the evaluation of Granger causality is compared to a nonlinear model-free (MF) one. The MB method is based on the identification of the coefficients of a multivariate linear regression via least-squares procedure. The MF technique is grounded on the concept of local prediction and exploits the k-nearest-neighbors approach. Both the methods optimize the multivariate embedding dimension but MF technique is more parsimonious since the number of components taken from each signal can be different. Both methods were applied to the variability series of heart period (HP), systolic arterial pressure (SAP) and respiration (R) recorded during spontaneous and controlled respiration at 15 breaths/minute (SR and RC15) in 19 healthy humans. Both MB and MF methods revealed the increase of HP predictability during RC15 and the unmodified causality from SAP to HP and from R to HP during RC15, thus suggesting that nonlinear methods are not superior to the linear ones in assessing predictability and causality in healthy humans.

Investigating the changes in heart rate asymmetry (HRA) with perturbation of parasympathetic nervous system

The heart rate asymmetry (HRA) is a disproportionate distribution of heart rate signal. The current study was designed to assess the changes in HRA in experimental conditions using Poincaré plot during parasympathetic blockade (atropine infusion) and parasympathetic enhancement (scopolamine administration). After atropine infusion, the heart rate variability in 5 out of 8 subjects was found asymmetric. In contrast, all 8 subjects were found to be asymmetric during scopolamine administration. The physiological relevance of HRA was demonstrated by showing correlation with standard frequency domain parameters during all phases of the experiment. The deviation of asymmetry index (GI ( p )) from symmetric range was further analyzed, which was maximum during scopolamine administration and minimum during atropine infusion. These findings suggest that parasympathetic block reduces the prevalence of HRA, and has significant correlation of GI ( p ) with frequency domain features of HRV analysis.

Short-term complexity indexes of heart period and systolic arterial pressure variabilities provide complementary information

It is unclear whether the complexity of the variability of the systolic arterial pressure (SAP) provides complementary information to that of the heart period (HP). The complexity of HP and SAP variabilities was assessed from short beat-to-beat recordings (i.e., 256 cardiac beats). The evaluation was made during a pharmacological protocol that induced vagal blockade with atropine or a sympathetic blockade (beta-adrenergic blockade with propranolol or central sympathetic blockade with clonidine) alone or in combination, during a graded head-up tilt, and in patients with Parkinson's disease (PD) without orthostatic hypotension undergoing orthostatic challenge. Complexity was quantified according to the mean square prediction error (MSPE) derived from univariate autoregressive (AR) and multivariate AR (MAR) models. We found that: 1) MSPEMAR did not provide additional information to that of MSPEAR; 2) SAP variability was less complex than that of HP; 3) because HP complexity was reduced by either vagal blockade or vagal withdrawal induced by head-up tilt and was unaffected by beta-adrenergic blockade, HP was under vagal control; 4) because SAP complexity was increased by central sympathetic blockade and was unmodified by either vagal blockade or vagal withdrawal induced by head-up tilt, SAP was under sympathetic control; 5) SAP complexity was increased in patients with PD; and 6) during orthostatic challenge, the complexity of both HP and SAP variabilities in patients with PD remained high, thus indicating both vagal and sympathetic impairments. Complexity indexes derived from short HP and SAP beat-to-beat series provide complementary information and are helpful in detecting early autonomic dysfunction in patients with PD well before circulatory symptoms become noticeable.

Aging reduces complexity of heart rate variability assessed by conditional entropy and symbolic analysis

Increasing age is associated with a reduction in overall heart rate variability as well as changes in complexity of physiologic dynamics. The aim of this study was to verify if the alterations in autonomic modulation of heart rate caused by the aging process could be detected by Shannon entropy (SE), conditional entropy (CE) and symbolic analysis (SA). Complexity analysis was carried out in 44 healthy subjects divided into two groups: old (n = 23, 63 ± 3 years) and young group (n = 21, 23 ± 2). It was analyzed SE, CE [complexity index (CI) and normalized CI (NCI)] and SA (0V, 1V, 2LV and 2ULV patterns) during short heart period series (200 cardiac beats) derived from ECG recordings during 15 min of rest in a supine position. The sequences characterized by three heart periods with no significant variations (0V), and that with two significant unlike variations (2ULV) reflect changes in sympathetic and vagal modulation, respectively. The unpaired t test (or Mann-Whitney rank sum test when appropriate) was used in the statistical analysis. In the aging process, the distributions of patterns (SE) remain similar to young subjects. However, the regularity is significantly different; the patterns are more repetitive in the old group (a decrease of CI and NCI). The amounts of pattern types are different: 0V is increased and 2LV and 2ULV are reduced in the old group. These differences indicate marked change of autonomic regulation. The CE and SA are feasible techniques to detect alteration in autonomic control of heart rate in the old group.

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.

Changes in heart rate dynamics of patients with schizophrenia treated with risperidone

Neurocardiac dysregulation has been reported in schizophrenia. Indices of heart rate variability (HRV) are useful in assessing the status of cardiac autonomic regulation. We explored within-subject changes in HRV indices in acutely ill patients with schizophrenia treated with risperidone. Sixteen medication-naïve or medication-free patients with DSM-IV schizophrenia completed electrocardiogram (ECG) assessments at baseline and after six weeks of treatment with risperidone. Indices of HRV were extracted from 5-min resting ECG recordings and compared to those obtained from control subjects matched for age and gender. Psychiatric and drug-induced extrapyramidal symptoms were assessed by the Positive and Negative Syndrome Scale (PANSS) and the Drug-Induced Extrapyramidal Symptoms Scale (DIEPSS). In comparison with matched controls, patients with acute schizophrenia showed lower values of time-domain measures, lower high-frequency power (HF) and a higher ratio of low to high frequency (LF/HF). In the within-subject analyses, a significant decrease in LF/HF was associated with risperidone treatment. In addition, LF/HF, which initially co-clustered with clinical variables, congregated with other HRV measures after the six-week risperidone treatment. These results indicate that, in the therapeutic process, risperidone treatment may exert a beneficial influence on the sympathovagal imbalance in acute schizophrenia.

Symbolic dynamic analysis of relations between cardiac and breathing cycles in patients on weaning trials

Traditional time-domain techniques of data analysis are often not sufficient to characterize the complex dynamics of the cardiorespiratory interdependencies during the weaning trials. In this paper, the interactions between the heart rate (HR) and the breathing rate (BR) were studied using joint symbolic dynamic analysis. A total of 133 patients on weaning trials from mechanical ventilation were analyzed: 94 patients with successful weaning (group S) and 39 patients that failed to maintain spontaneous breathing (group F). The word distribution matrix enabled a coarse-grained quantitative assessment of short-term nonlinear analysis of the cardiorespiratory interactions. The histogram of the occurrence probability of the cardiorespiratory words presented a higher homogeneity in group F than in group S, measured with a higher number of forbidden words in group S as well as a higher number of words whose probability of occurrence is higher than a probability threshold in group S. The discriminant analysis revealed the best results when applying symbolic dynamic variables. Therefore, we hypothesize that joint symbolic dynamic analysis provides enhanced information about different interactions between HR and BR, when comparing patients with successful weaning and patients that failed to maintain spontaneous breathing in the weaning procedure.

Differential pattern of heart rate variability in patients with schizophrenia

The cardiac autonomic dysfunction has been reported in patients with schizophrenia. Heart rate variability (HRV) provides non-invasive indices of cardiac autonomic modulation. This study examined whether patients with schizophrenia may show a distinctive pattern of HRV compared to healthy controls. Nine measures of time, frequency and complexity domains were extracted from 5-min resting evaluation of HRV in 30 unmedicated patients with schizophrenia and 30 age- and gender-matched controls. In addition to inferential statistics, a hierarchical clustering (HC) was used to examine difference in the interrelationships among HRV measures between the two groups. Multivariate analysis of variance revealed a significant group effect. Significantly lower sample entropy (SampEn) and a trend towards a higher ratio of low- to high frequency (LF/HF) were observed in the schizophrenia group. In the results of HC using Ward's method, SampEn co-clustered with LF/HF ratio in patients with schizophrenia compared to the separation of LF/HF ratio in healthy controls. In concert with decreased parasympathetic activity, low complexity of heart rate dynamics may reduce adaptability of cardiovascular system to changes in internal or external environment, thus increasing the risk of cardiovascular events. Diverse HRV measures combined in a multivariate fashion appear to be useful in understanding the pattern of neurocardiac modulation in patients with schizophrenia.

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.

Assessing causality in normal and impaired short-term cardiovascular regulation via nonlinear prediction methods

We investigated the ability of mutual nonlinear prediction methods to assess causal interactions in short-term cardiovascular variability during normal and impaired conditions. Directional interactions between heart period (RR interval of the ECG) and systolic arterial pressure (SAP) short-term variability series were quantified as the cross-predictability (CP) of one series given the other, and as the predictability improvement (PI) yielded by the inclusion of samples of one series into the prediction of the other series. Nonlinear prediction was performed through global approximation (GA), approximation with locally constant models (LA0) and approximation with locally linear models (LA1) of the nonlinear function linking the samples of the two series, on patients with neurally mediated syncope and control subjects. Causality measures were evaluated in the two directions (from SAP to RR and from RR to SAP) in the supine (SU) position, in the upright position after head-up tilt (early tilt, ET) and after prolonged upright posture (late tilt, LT). While the trends for the GA, LA0 and LA1 methods were substantially superimposable, PI elicited better than CP the prevalence of causal coupling from RR to SAP during SU. Both CP and PI noted a marked decrease in coupling in both causal directions in syncope subjects during LT, documenting the impairment of cardiovascular regulation in the minutes just preceding syncope.

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.

Time-varying surrogate data to assess nonlinearity in nonstationary time series: application to heart rate variability

We propose a method to extend to time-varying (TV) systems the procedure for generating typical surrogate time series, in order to test the presence of nonlinear dynamics in potentially nonstationary signals. The method is based on fitting a TV autoregressive (AR) model to the original series and then regressing the model coefficients with random replacements of the model residuals to generate TV AR surrogate series. The proposed surrogate series were used in combination with a TV sample entropy (SE) discriminating statistic to assess nonlinearity in both simulated and experimental time series, in comparison with traditional time-invariant (TIV) surrogates combined with the TIV SE discriminating statistic. Analysis of simulated time series showed that using TIV surrogates, linear nonstationary time series may be erroneously regarded as nonlinear and weak TV nonlinearities may remain unrevealed, while the use of TV AR surrogates markedly increases the probability of a correct interpretation. Application to short (500 beats) heart rate variability (HRV) time series recorded at rest (R), after head-up tilt (T), and during paced breathing (PB) showed: 1) modifications of the SE statistic that were well interpretable with the known cardiovascular physiology; 2) significant contribution of nonlinear dynamics to HRV in all conditions, with significant increase during PB at 0.2 Hz respiration rate; and 3) a disagreement between TV AR surrogates and TIV surrogates in about a quarter of the series, suggesting that nonstationarity may affect HRV recordings and bias the outcome of the traditional surrogate-based nonlinearity test.

Temporal asymmetries of short-term heart period variability are linked to autonomic regulation

We exploit time reversibility analysis, checking the invariance of statistical features of a series after time reversal, to detect temporal asymmetries of short-term heart period variability series. Reversibility indexes were extracted from 22 healthy fetuses between 16th to 40th wk of gestation and from 17 healthy humans (aged 21 to 54, median = 28) during graded head-up tilt with table inclination angles randomly selected inside the set {15, 30, 45, 60, 75, 90}. Irreversibility analysis showed that nonlinear dynamics observed in short-term heart period variability are mostly due to asymmetric patterns characterized by bradycardic runs shorter than tachycardic ones. These temporal asymmetries were 1) more likely over short temporal scales than over longer, dominant ones; 2) more frequent during the late period of pregnancy (from 25th to 40th week of gestation); 3) significantly present in healthy humans at rest in supine position; 4) more numerous during 75 and 90° head-up tilt. Results suggest that asymmetric patterns observable in short-term heart period variability might be the result of a fully developed autonomic regulation and that an important shift of the sympathovagal balance toward sympathetic predominance (and vagal withdrawal) can increase their presence.

Nonlinear coupling is absent in acute myocardial patients but not healthy subjects

We investigated whether autonomic nervous system imbalance imposed by pharmacological blockades and associated with acute myocardial infarction (AMI) is manifested as modifications of the nonlinear interactions in heart rate variability signal using a statistically based bispectrum method. The statistically based bispectrum method is an ideal approach for identifying nonlinear couplings in a system and overcomes the previous limitation of determining in an ad hoc way the presence of such interactions. Using the improved bispectrum method, we found significant nonlinear interactions in healthy young subjects, which were abolished by the administration of atropine but were still present after propranolol administration. The complete decoupling of nonlinear interactions was obtained with double pharmacological blockades. Nonlinear couplings were found to be the strongest for healthy young subjects followed by degradation with old age and a complete absence of such couplings for the old age-matched AMI subjects. Our results suggest that the presence of nonlinear couplings is largely driven by the parasympathetic nervous system regulation and that the often-reported autonomic nervous system imbalance seen in AMI subjects is manifested as the absence of nonlinear interactions between the sympathetic and parasympathetic nervous regulations.

Assessment of Granger causality by nonlinear model identification: application to short-term cardiovascular variability

A method for assessing Granger causal relationships in bivariate time series, based on nonlinear autoregressive (NAR) and nonlinear autoregressive exogenous (NARX) models is presented. The method evaluates bilateral interactions between two time series by quantifying the predictability improvement (PI) of the output time series when the dynamics associated with the input time series are included, i.e., moving from NAR to NARX prediction. The NARX model identification was performed by the optimal parameter search (OPS) algorithm, and its results were compared to the least-squares method to determine the most appropriate method to be used for experimental data. The statistical significance of the PI was assessed using a surrogate data technique. The proposed method was tested with simulation examples involving short realizations of linear stochastic processes and nonlinear deterministic signals in which either unidirectional or bidirectional coupling and varying strengths of interactions were imposed. It was found that the OPS-based NARX model was accurate and sensitive in detecting imposed Granger causality conditions. In addition, the OPS-based NARX model was more accurate than the least squares method. Application to the systolic blood pressure and heart rate variability signals demonstrated the feasibility of the method. In particular, we found a bilateral causal relationship between the two signals as evidenced by the significant reduction in the PI values with the NARX model prediction compared to the NAR model prediction, which was also confirmed by the surrogate data analysis. Furthermore, we found significant reduction in the complexity of the dynamics of the two causal pathways of the two signals as the body position was changed from the supine to upright. The proposed is a general method, thus, it can be applied to a wide variety of physiological signals to better understand causality and coupling that may be different between normal and diseased conditions.

Conditions of autonomic reciprocal interplay versus autonomic co-activation: Effects on non-linear heart rate dynamics

The present study was aimed at investigating the autonomic nervous system influences on the fractal organization of human heart rate during sympathovagal interactions, with special emphasize on the short-term fractal organization in heart rate variability (HRV), as assessed by the scaling exponent (alpha(1)) of the detrended fluctuation analysis. Linear and non-linear HRV analyses were used to study the sympathetic and vagal modulation of heart rate in ten healthy men (mean +/- SEM; age 26 +/- 1 years) during conditions of 1) increased sympathetic activity and vagal withdrawal (head-up tilt), 2) decreased sympathetic activity and increased vagal outflow (thermoneutral upright head-out water immersion, WIn), and 3) simultaneous activation of the two arms of the autonomic nervous activity (upright head-out immersion in cold water, WIc). Hemodynamic and linear HRV results were consistent with previous reports during similar physiological conditions. alpha(1) increased significantly during head-up tilt (from 0.71 +/- 0.13 supine to 0.90 +/- 0.15 upright) and WIn (0.86 +/- 0.10) and was significantly decreased during WIc (0.61 +/- 0.15). Thus, alpha(1) increased when the cardiac autonomic interplay was altered in a reciprocal fashion, whatever the direction of the balance change. Conversely, alpha(1) decreased during the concomitant activation of both vagal and sympathetic activities. The results of linear analysis were necessary to precisely define the direction of change in autonomic control revealed by an increase in alpha(1), while the direction of change in alpha(1) indicated whether an increased vagal activity is coupled with a decreased or increased sympathetic activation. Using both linear and non-linear analysis of HRV may increase the understanding of changes in cardiac autonomic status.

Assessing nonlinear properties of heart rate variability from short-term recordings: are these measurements reliable?

Several parameters assessing nonlinear properties of heart rate variability (HRV) from short-term (<10 min) laboratory recordings have been proposed so far, but their reliability is unknown. In this study, we addressed this issue analysing a comprehensive set of these indices. In 42 healthy subjects (mean age (min-max): 38 (26-56) years, 21 men) we recorded 5 min of supine ECG in two consecutive days. From RR intervals we computed 11 nonlinear HRV indices, representative of symbolic dynamics, entropy, fractality, predictability, empirical mode decomposition and Poincaré plot families. Absolute reliability was assessed by the 95% limits of random variation and relative reliability was assessed computing the intraclass correlation coefficient (ICC). We found marked differences in the reliability of short-term nonlinear indices of HRV. In the majority of indices, changes in test-retest measurements ranged between about -30% and +50%, indicating good absolute reliability while in the others the change was <-60% and >140%. Relative reliability was substantial (0.6 < ICC < 0.8) in half of the indices, moderate in one and poor in the remaining. Compared to classical linear indices, nonlinear HRV parameters seem more suitable for individual test-retest evaluations but, due to a reduced ICC, they need increased sample size in comparative studies involving two groups of subjects.

Assessment of the classification capability of prediction and approximation methods for HRV analysis

The goal of this paper is to examine the classification capabilities of various prediction and approximation methods and suggest which are most likely to be suitable for the clinical setting. Various prediction and approximation methods are applied in order to detect and extract those which provide the better differentiation between control and patient data, as well as members of different age groups. The prediction methods are local linear prediction, local exponential prediction, the delay times method, autoregressive prediction and neural networks. Approximation is computed with local linear approximation, least squares approximation, neural networks and the wavelet transform. These methods are chosen since each has a different physical basis and thus extracts and uses time series information in a different way.

An integrated approach based on uniform quantization for the evaluation of complexity of short-term heart period variability: Application to 24 h Holter recordings in healthy and heart failure humans

We propose an integrated approach based on uniform quantization over a small number of levels for the evaluation and characterization of complexity of a process. This approach integrates information-domain analysis based on entropy rate, local nonlinear prediction, and pattern classification based on symbolic analysis. Normalized and non-normalized indexes quantifying complexity over short data sequences ( approximately 300 samples) are derived. This approach provides a rule for deciding the optimal length of the patterns that may be worth considering and some suggestions about possible strategies to group patterns into a smaller number of families. The approach is applied to 24 h Holter recordings of heart period variability derived from 12 normal (NO) subjects and 13 heart failure (HF) patients. We found that: (i) in NO subjects the normalized indexes suggest a larger complexity during the nighttime than during the daytime; (ii) this difference may be lost if non-normalized indexes are utilized; (iii) the circadian pattern in the normalized indexes is lost in HF patients; (iv) in HF patients the loss of the day-night variation in the normalized indexes is related to a tendency of complexity to increase during the daytime and to decrease during the nighttime; (v) the most likely length L of the most informative patterns ranges from 2 to 4; (vi) in NO subjects classification of patterns with L=3 indicates that stable patterns (i.e., those with no variations) are more present during the daytime, while highly variable patterns (i.e., those with two unlike variations) are more frequent during the nighttime; (vii) during the daytime in HF patients, the percentage of highly variable patterns increases with respect to NO subjects, while during the nighttime, the percentage of patterns with one or two like variations decreases.

Complexity and nonlinearity in short-term heart period variability: comparison of methods based on local nonlinear prediction

This paper evaluates the paradigm that proposes to quantify short-term complexity and detect nonlinear dynamics by exploiting local nonlinear prediction. Local nonlinear prediction methods are classified according to how they judge similarity among patterns of L samples (i.e., according to different definitions of the cells utilized to discretize the phase space) and examined in connection with different types of surrogate data: 1) phase-randomized or Fourier transform based, FT; 2) amplitude-adjusted FT, AAFT; 3) iteratively-refined AAFT, IAAFT, preserving distribution IAAFT-1; 4) IAAFT preserving power spectrum, IAAFT-2. The methods were applied on ad-hoc simulations and on a large database of short heart period variability series (approximately 300 cardiac beats) recorded in healthy young subjects during experimental conditions inducing a sympathetic activation (head-up tilt, infusion of nitroprusside, or handgrip), a parasympathetic activation (low dose administration of atropine or infusion of phenylephrine), a complete parasympathetic blockade (high dose administration of atropine), or during controlled respiration at different breathing rates. As to complexity analysis we found that: 1) although complexity indexes derived from different methods were different in terms of absolute values, changes due to experimental conditions were consistently detected; 2) complexity was significantly decreased by all the experimental conditions provoking a sympathetic activation and by controlled respiration at slow breathing rates. As to detection of nonlinearities we found that: 1) IAAFT-1 and IAAFT-2 surrogates performed similarly in all protocols; 2) FT and IAAFT surrogates detected about the same percentage of nonlinear dynamics in all protocols; 3) AAFT surrogates were inappropriate with all the methods and should be dismissed in future applications; 4) methods based on overlapping cells with variable size were characterized by a larger rate of false detections of nonlinear dynamics; 5) short-term heart period variability at rest was mostly linear; 6) controlled respiration at slow breathing rates increased nonlinear components, while the separate activation of the two branches of the autonomic nervous system (i.e., sympathetic or parasympathetic) was ineffective at this regard.

Assessment of cardiac autonomic modulation during graded head-up tilt by symbolic analysis of heart rate variability

Two symbolic indexes, the percentage of sequences characterized by three heart periods with no significant variations (0V%) and that with two significant unlike variations (2UV%), have been found to reflect changes in sympathetic and vagal modulations, respectively. We tested the hypothesis that symbolic indexes may track the gradual shift of the cardiac autonomic modulation during an incremental head-up tilt test. Symbolic analysis was carried out over heart period variability series (250 cardiac beats) derived from ECG recordings during a graded head-up tilt test (0, 15, 30, 45, 60, 75, and 90 degrees ) in 17 healthy subjects. The percentage of subjects showing a significant linear correlation (Spearman rank-order correlation) with tilt angles was utilized to evaluate the performance of symbolic analysis. Spectral analysis was carried out for comparison over the same series. 0V% progressively increased with tilt angles, whereas 2UV% gradually decreased. The decline of 2UV% was greater than the increase of 0V% at low tilt angles. Linear correlation with tilt angles was exhibited in a greater percentage of subjects for 0V% and 2UV% than for any spectral index. Our findings suggest that symbolic analysis performed better than spectral analysis and, thus, is a suitable methodology for assessment of the subtle changes of cardiac autonomic modulation induced by a graded head-up tilt test. Moreover, symbolic analysis indicates that the changes of cardiac sympathetic and vagal modulations observed during this protocol were reciprocal but characterized by different absolute magnitudes.

Nonlinear indices of heart rate variability in chronic heart failure patients: redundancy and comparative clinical value

AIMS

We aimed to assess the mutual interrelationships and to compare the prognostic value of a comprehensive set of nonlinear indices of heart rate variability (HRV) in a population of chronic heart failure (CHF) patients.

METHODS AND RESULTS

Twenty nonlinear HRV indices, representative of symbolic dynamics, entropy, fractality-multifractality, predictability, empirical mode decomposition, and Poincaré plot families, were computed from 24-hour Holter recordings in 200 stable CHF patients in sinus rhythm (median age [interquartile range]: 54 [47-58] years, LVEF: 23 [19-28]%, NYHA class II-III: 88%). End point for survival analysis (Cox model) was cardiac death or urgent transplantation. Homogeneous variables were grouped by cluster analysis, and in each cluster redundant variables were discarded. A prognostic model including only known clinical and functional risk factors was built and the ability of each selected HRV variable to add prognostic information to this model assessed. Bootstrap resampling was used to test the models stability. Four nonlinear variables showed a correlation >0.90 with classical linear ones and were discarded. Correlations >0.80 were found between several nonlinear variables. Twelve clusters were obtained and from each cluster a candidate predictor was selected. Only two variables (from empirical mode decomposition and symbolic dynamics families) added prognostic information to the clinical model.

CONCLUSION

This exploratory study provides evidence that, despite some redundancies in the informative content of nonlinear indices and strong differences in their prognostic power, quantification of nonlinear properties of HRV provides independent information in risk stratification of CHF patients.

Clinical correlates of non-linear indices of heart rate variability in chronic heart failure patients

We assessed the clinical correlates of a comprehensive set of non-linear heart rate variability (HRV) indices computed from 24-h Holter recordings for 200 stable chronic heart failure (CHF) patients [median age (lower quartile, upper quartile) 54 (47, 58) years, LVEF 23% (19%, 28%)]. A total of 19 non-linear indices belonging to six major families, namely symbolic dynamics, entropy, empirical mode decomposition, fractality-multifractality, unpredictability and Poincaré plots, were considered. Most indices showed a significant association with ejection fraction and with the severity of symptoms, while only two (one each from the fractality and Poincaré plot families) showed an association with aetiology. Only one symbolic dynamics variable was associated with the presence of non-sustained ventricular tachycardia and two symbolic dynamics variables were associated with the rate of ventricular ectopic events. Our results demonstrate the existence of selective links between non-linear indexes of HRV and the clinical status and functional impairment of CHF patients. This indicates that further studies should be designed to investigate the physiopathological mechanisms involved in such links.

Role of the autonomic nervous system in generating non-linear dynamics in short-term heart period variability

We evaluated the role played by the autonomic nervous system in producing non-linear dynamics in short heart period variability (HPV) series recorded in healthy young humans. Non-linear dynamics are detected using an index of predictability based on a local non-linear predictor and a surrogate data approach. Different types of surrogates are utilized: (i) phase-randomized Fourier-transform based (FT) data; (ii) amplitude-adjusted FT (AAFT) data; and (iii) iteratively refined AAFT (IAAFT) data of two types (IAAFT-1 and IAAFT-2). The approach was applied to experimental protocols activating or blocking the sympathetic or parasympathetic branches of the autonomic nervous system or periodically perturbing cardiovascular control via paced respiration at different breathing rates. We found that short-term HPV was mostly linear at rest. Experimental protocols activating the sympathetic or parasympathetic nervous system did not produce non-linear dynamics. In contrast, paced respiration, especially at slow breathing rates, elicited significantly non-linear dynamics. Therefore, in short-term HPV ( approximately 300 beats) the use of non-linear models is not supported by the data, except under conditions whereby the subject is constrained to a slow respiratory rate.

Bivariate nonlinear prediction to quantify the strength of complex dynamical interactions in short-term cardiovascular variability

A nonlinear prediction method for investigating the dynamic interdependence between short length time series is presented. The method is a generalization to bivariate prediction of the univariate approach based on nearest neighbor local linear approximation. Given the input and output series x and y, the relationship between a pattern of samples of x and a synchronous sample of y was approximated with a linear polynomial whose coefficients were estimated from an equation system including the nearest neighbor patterns in x and the corresponding samples in y. To avoid overfitting and waste of data, the training and testing stages of the prediction were designed through a specific out-of-sample cross validation. The robustness of the method was assessed on short realizations of simulated processes interacting either linearly or nonlinearly. The predictor was then used to characterize the dynamical interaction between the short-term spontaneous fluctuations of heart period (RR interval) and systolic arterial pressure (SAP) in healthy young subjects. In the supine position, the predictability of RR given SAP was low and influenced by nonlinear dynamics. After head-up tilt the predictability increased significantly and was mostly due to linear dynamics. These findings were related to the larger involvement of the baroreflex regulation from SAP to RR in upright than in supine humans, and to the simplification of the RR-SAP coupling occurring with the tilt-induced alteration of the neural regulation of the cardiovascular rhythms.

Autonomic information flow improves prognostic impact of task force HRV monitoring

Heart rate variability (HRV) represents the cardiovascular control mediated by the autonomic nervous system and other mechanisms. In the established task force HRV monitoring different cardiovascular control mechanisms can approximately be identified at typical frequencies of heart rate oscillations by power spectral analysis. HRV measures assessing complex and fractal behavior partly improved clinical risk stratification. However, their relationship to (patho-)physiology is not sufficiently explored. Objective of the present work is the introduction of complexity measures of different physiologically relevant time scales. This is achieved by a new concept of the autonomic information flow (AIF) analysis which was designed according to task force HRV. First applications show that different time scales of AIF improve the risk stratification of patients with multiple organ dysfunction syndrome and cardiac arrest patients in comparison to standard HRV. Each group's significant time scales correspond to their respective pathomechanisms.