Cardiovascular Variability Signals Research Articles

Time-Frequency Analysis of Cardiovascular Variability during an Orthostatic Stress by Complete EMD.

Diverse analysis techniques have been used to comprehend the regulation by the autonomic nervous system (ANS) of the cardiovascular system when a human being faces a stressor. Recently, however, the complete ensemble empirical mode decomposition (EMD) with adaptive noise (CEEMDAN) allows analyzing nonstationary signals in a nonlinear and time- variant way. Consequently, CEEMDAN may provide a means to obtain clues about ANS regulation in health and disease. In this study, we analyze the average Hilbert-Huang spectrum (HHS) of cardiovascular variability signals by CEEMDAN during a head-up tilt test (HUTT) in 12 healthy female subjects and 18 orthostatic intolerance female patients. Beat-to-beat intervals (BBI) as well as systolic (SYS) blood pressure variability time series were analyzed. In addition, instantaneous amplitudes and frequencies of specific intrinsic mode functions (IMF) were investigated separately to define the influence of the disease on ANS regulation. Female groups demonstrated statistical differences in the high-frequency band of BBI but higher differences for the high and low-frequency bands of SYS from the mechanical transition of HUTT.Clinical Relevance- A relevant outcome of the study is the average HHS of healthy female subjects along HUTT. This HHS may be used as reference to help diagnose OI when HHS of the cardiovascular variability signals of any subject deviates from the normal course.

Basic cardiovascular variability signals: mutual directed interactions explored in the information domain

The study of short-term cardiovascular interactions is classically performed through the bivariate analysis of the interactions between the beat-to-beat variability of heart period (RR interval from the ECG) and systolic blood pressure (SBP). Recent progress in the development of multivariate time series analysis methods is making it possible to explore how directed interactions between two signals change in the context of networks including other coupled signals. Exploiting these advances, the present study aims at assessing directional cardiovascular interactions among the basic variability signals of RR, SBP and diastolic blood pressure (DBP), using an approach which allows direct comparison between bivariate and multivariate coupling measures. To this end, we compute information-theoretic measures of the strength and delay of causal interactions between RR, SBP and DBP using both bivariate and trivariate (conditioned) formulations in a group of healthy subjects in a resting state and during stress conditions induced by head-up tilt (HUT) and mental arithmetics (MA). We find that bivariate measures better quantify the overall (direct + indirect) information transferred between variables, while trivariate measures better reflect the existence and delay of directed interactions. The main physiological results are: (i) the detection during supine rest of strong interactions along the pathway RR → DBP → SBP, reflecting marked Windkessel and/or Frank–Starling effects; (ii) the finding of relatively weak baroreflex effects SBP → RR at rest; (iii) the invariance of cardiovascular interactions during MA, and the emergence of stronger and faster SBP → RR interactions, as well as of weaker RR → DBP interactions, during HUT. These findings support the importance of investigating cardiovascular interactions from a network perspective, and suggest the usefulness of directed information measures to assess physiological mechanisms and track their changes across different physiological states.

Components of arterial systolic pressure and RR-interval oscillation spectra in a case of baroreflex failure, a human open-loop model of vascular control

The baroreflex control of circulation is always operating and modulates blood pressure and heart rate oscillations. Thus, the study of cardiovascular variability in humans is performed in a closed-loop model and the physiology of post-sinoaortic denervation is completely unknown in humans. We dissected for the first time the different components of systolic arterial pressure (SAP) and RR-interval spectra in a patient with 'baroreflex failure' (due to mixed cranial nerve neuroma) who represents a human model to investigate the cardiovascular regulation in an open-loop condition. Interactions among cardiovascular variability signals and respiratory influences were described using the multivariate parametric ARXAR model with the following findings: (1) rhythms unrelated to respiration were detected only at frequencies lower than classical low frequency (LF; Slow-LF, around 0.02 Hz) both in SAP an RR spectra, (2) small high-frequency (HF) modulation is present and related with respiration at rest and in tilt (but for SAP only) and (3) the Slow-LF fluctuations detected both in SAP and RR oscillate independently as the multivariate model shows no relationships between SAP and RR, and these oscillations are not phase related. Thus, we showed that in a patient with impaired baroreflex arc integrity the Slow-LF rhythms for RR have a central origin that dictates fluctuations on RR at the same rhythm but unrelated to the oscillation of SAP (which may be related with both peripheral activity and central rhythms). The synchronization in LF band is a hallmark of integrity of baroreflex arc whose impairment unmasks lower frequency rhythms in SAP and RR whose fluctuations oscillate independently.

Detection of Nonlinearity in Cardiovascular Variability Signals using Cyclostationary Analysis

A novel approach for detection of polynomial nonlinearity in the neuro-cardiovascular system based on cyclostationary analysis is presented. Metronome breathing is employed to provide a sinusoidal input to the neuro-cardiovascular system in which Heart Rate Variability (HRV) and Blood Pressure Variation (BPV) are considered as its outputs. The presence of new harmonics of the main respiratory rate in the HRV and BPV is investigated by using the concept of (self) phase and (self) frequency coupling. It is shown that a second order polynomial nonlinear system is actually involved in producing the HRV and BPV. The strength of this nonlinearity decreases with increasing the breathing rate.

Cardiac Nociception

Cardiac Nociception

Causal transfer function analysis to describe closed loop interactions between cardiovascular and cardiorespiratory variability signals.

Although the concept of transfer function is intrinsically related to an input-output relationship, the traditional and widely used estimation method merges both feedback and feedforward interactions between the two analyzed signals. This limitation may endanger the reliability of transfer function analysis in biological systems characterized by closed loop interactions. In this study, a method for estimating the transfer function between closed loop interacting signals was proposed and validated in the field of cardiovascular and cardiorespiratory variability. The two analyzed signals x and y were described by a bivariate autoregressive model, and the causal transfer function from x to y was estimated after imposing causality by setting to zero the model coefficients representative of the reverse effects from y to x. The method was tested in simulations reproducing linear open and closed loop interactions, showing a better adherence of the causal transfer function to the theoretical curves with respect to the traditional approach in presence of non-negligible reverse effects. It was then applied in ten healthy young subjects to characterize the transfer functions from respiration to heart period (RR interval) and to systolic arterial pressure (SAP), and from SAP to RR interval. In the first two cases, the causal and non-causal transfer function estimates were comparable, indicating that respiration, acting as exogenous signal, sets an open loop relationship upon SAP and RR interval. On the contrary, causal and traditional transfer functions from SAP to RR were significantly different, suggesting the presence of a considerable influence on the opposite causal direction. Thus, the proposed causal approach seems to be appropriate for the estimation of parameters, like the gain and the phase lag from SAP to RR interval, which have a large clinical and physiological relevance.

Coupling patterns between spontaneous rhythms and respiration in cardiovascular variability signals

We performed a quantitative study of coupling patterns between respiration and spontaneous rhythms of heart rate and blood pressure variability signals by using the Recurrence Quantification Analysis (RQA). We applied RQA to both simulated and experimental data obtained in control breathing at three different frequencies (0.25, 0.20, and 0.13 Hz) from ten normal subjects. RQA succeeded in quantifying different degrees of non-linear coupling associated to several interference patterns. We found higher degrees of non-linear coupling when the respiratory frequency was close to the spontaneous Low Frequency (LF) rhythm (0.13 Hz), or almost twice the LF frequency (0.2 Hz), whereas weaker coupling was observed when the respiratory frequency was 0.25 Hz. Clinical applications of our approach should focus on new experimental protocols, featuring the stimulation of one of the two branches of the autonomic nervous system (ANS) or aimed at the analysis of pathologies linked to the ANS.

Quantifying the strength of the linear causal coupling in closed loop interacting cardiovascular variability signals.

The coherence function measures the amount of correlation between two signals x and y as a function of the frequency, independently of their causal relationships. Therefore, the coherence function is not useful in deciding whether an open-loop relationship between x and y is set (x acts on y, but the reverse relationship is prevented) or x and y interact in a closed loop (x affects y, and vice versa). This study proposes a method based on a bivariate autoregressive model to derive the strength of the causal coupling on both arms of a closed loop. The method exploits the definition of causal coherence. After the closed-loop identification of the model coefficients, the causal coherence is calculated by switching off separately the feedback or the feedforward path, thus opening the closed loop and fixing causality. The method was tested in simulations and applied to evaluate the degree of the causal coupling between two variables known to interact in a closed loop mainly at a low frequency (LF, around 0.1 Hz) and at a high frequency (HF, at the respiratory rate): the heart period (RR interval) and systolic arterial pressure (SAP). In dogs at control, the RR interval and the SAP are highly correlated at HF. This coupling occurs in the causal direction from the RR interval to the SAP (the mechanical path), while the coupling on the reverse causal direction (the baroreflex path) is not significant, thus pointing out the importance of the direct effects of respiration on the RR interval. Total baroreceptive denervation, by opening the closed loop at the level of the influences of SAP on RR interval, does not change these results. In elderly healthy men at rest, the RR interval and SAP are highly correlated at the LF and the HF. At the HF, a significant coupling in both causal directions is found, even though closed-loop interactions are detected in few cases. At the LF, the link on the baroreflex pathway is negligible with respect to that on the reverse mechanical one. In heart transplant recipients, in which SAP variations do not cause RR interval changes as a result of the cardiac denervation, the method correctly detects a significant coupling only on the pathway from the RR interval to the SAP.

Estimation of frequency shift in cardiovascular variability signals.

Spectral analysis of heart rate (HR) and blood pressure (BP) oscillations has traditionally concentrated on spectral power, although a shift in spectral frequency characterises the variability better than power in some cases. Experimental data were obtained from 14 healthy males in control and pharmacological blockade conditions. When parasympathetic control was reduced, LF oscillations of HR and BP tend to shift towards lower frequencies. Three parameters were compared to estimate the spectral shift within the low frequency (LF, 0.04-0.15 Hz) band in HR and BP variability: mean (fmean), median (fmed), and central frequency (fc). Parameter variance (pSTD) and sensitivity to noise were also estimated using realistic HR, systolic BP (SBP) and diastolic BP (DBP) data. fmean showed the lowest parameter variance both for an autoregressive (AR) method (SBP pSTD 3.1 vs 4.8 vs 4.7 mHz for fmean, fmed and fc, respectively; p<0.001) and an FFT method (SBP pSTD 4.7 vs 7.7 mHz for fmean and fmed, respectively; p<0.001). Furthermore, fmean was least sensitive to noise. fc showed the poorest performance being especially sensitive to noise. To analyse the spectral shift, fmean is preferred, since it performs better than fc, which has been used in most previous studies. To quantify the frequency of oscillations in cardiovascular signals, the mean frequency is recommended, with analyses across different spectral bands.

Evidence for central organization of cardiovascular rhythms.

Spectral analysis of heart rate and arterial pressure variabilities is a powerful noninvasive tool that is increasingly used to infer alterations of cardiovascular autonomic regulation in a variety of physiological and pathophysiological conditions such as hypertension, myocardial infarction, and congestive heart failure. A most important methodological issue to properly interpret the results obtained by the spectral analysis of cardiovascular variability signals is represented by the attribution of neurophysiological correlates to these spectral components. In this regard, recent application of spectral techniques to the evaluation of the oscillatory properties of sympathetic efferent activity in animals as well as in humans offers a new approach to a better understanding of the relationship between cardiovascular oscillations and autonomic regulation. The data so far collected seem to suggest the presence of a centrally organized neural code, characterized by excitatory and inhibitory neural mechanisms subserving the genesis and the regulation of cardiovascular oscillations concerning the major variables of autonomic regulation.

Reliability of transfer function estimates in cardiovascular variability analysis.

Transfer function (TF) analysis is a widely diffused technique in the assessment of the relationship between short-term cardiovascular variability signals, particularly blood pressure, heart rate and respiration. To guarantee the reliability of the estimates, a conventional threshold of 0.5 on the magnitude squared coherence (MSC) is commonly used, although (i) other analysis parameters play a role and (ii) lower values of MSC are frequently unavoidable in physiological systems. In this study, computer simulations are performed to assess the dependency of the bias and standard deviation (SD) of TF estimates on record length (RL), spectral window bandwidth (Bw) and MSC; to evaluate the accuracy of theoretical expressions for the computation of the confidence interval (CI) of the estimates; and to assess, in some representative situations, how faithfully observed TF shapes reproduce the underlying true functions in conditions of very low MSC. The accuracy of TF estimates increases non-linearly with increasing RL, and the benefit over 7 min is small. Using this RL, the relative bias for the TF modulus is < 10% for MSC > 0.2. Estimates of TF phase are unbiased. The SD of both the modulus and phase increases linearly as the MSC decrease to 0.4 and then, for lower MSC, increases markedly with nonlinear behaviour. Bw= 0.03Hz appears to be most suitable to reduce the error, preserving spectral resolution. CIs for the TF phase are highly reliable, whereas those for the modulus tend to be slightly narrower than the nominal value at high coherence values. Major features of the TF shape appear to be preserved in simulations with very low MSC. The major problem in TF estimation is the sharp increase in the variability of the measurements as the coherence decreases towards the lowest values. The combination of RL > or = 420s and Bw= 0.03Hz should be suggested in short-term cardiovascular variability studies. Although basic features of the true TF can be recovered even when the MSC is < 0.5, much greater values can be necessary when accurate point estimates are needed. Theoretical expressions for the computation of confidence intervals of the TF are adequate for practical purposes.

Information domain analysis of cardiovascular variability signals: evaluation of regularity, synchronisation and co-ordination.

A unifying general approach to measure regularity, synchronisation and co-ordination is proposed. This approach is based on conditional entropy and is specifically designed to deal with a small amount of data (a few hundred samples). Quantitative and reliable indexes of regularity, synchronisation and co-ordination (ranging from 0 to 1) are derived in a domain (i.e. the information domain) different from time and frequency domains. The method is applied to evaluate regularity, synchronisation and co-ordination among cardiovascular beat-to-beat variability signals during sympathetic activation induced by head-up tilt (T), during the perturbing action produced by controlled respiration at 10, 15 and 20 breaths/min (CR10, CR15 and CR20), and after peripheral muscarinic blockade provoked by the administration of low and high doses of atropine (LD and HD). It is found that: (1) regularity of the RR interval series is around 0.209; (2) this increases during T, CR10 and HD; (3) the systolic arterial pressure (SAP) series is more regular (0.406) and its regularity is not affected by the specified experimental conditions; (4) the muscle sympathetic (MS) series is a complex signal (0.093) and its regularity is not influenced by HD and LD; (5) the RR interval and SAP series are significantly, though weakly, synchronised (0.093) and their coupling increases during T, CR10 and CR15; (6) the RR interval and respiration are coupled (0.152) and their coupling increases during CR10; (7) SAP and respiration are significantly synchronised (0.108) and synchronisation increases during CR10; (8) MS and respiration are uncoupled and become coupled (0.119) after HD; (9) the RR interval, SAP and respiration are significantly co-ordinated (0.118) and co-ordination increases during CR10 and CR15; (10) during HD the co-ordination among SAP, MS and the respiratory signal is larger than that among the RR interval, SAP, MS and the respiratory signal, thus indicating that the RR interval contributes towards reducing co-ordination.

Prediction of short cardiovascular variability signals based on conditional distribution.

A new approach measuring the predictability of a process is proposed. The predictor is defined as the median of the distribution conditioned by a sequence of L - 1 previous samples (i.e., a pattern). A function referred to as the corrected mean squared predictor error is defined to prevent the perfect adequacy to the data (i.e., the decrease to zero of the prediction error), thus avoiding to divide the whole set of data in learning and test sets. This function exhibits a minimum and this minimum is taken as a measure of predictability of the series. The use of the minimization procedure avoids to fix a priori the pattern length L. This approach permits one a reliable measure of predictability on short data sequences (around 300 samples). Moreover, this method, in connection with a surrogate data approach, is useful to detect nonlinear dynamics. The analysis indicates that, in simulated and real data, predictability and nonlinearity measures provide different information. The application of this approach to the analysis of cardiovascular variability series of the heart period (RR interval) and systolic arterial pressure (SAP) shows: 1) SAP series is more predictable than RR interval series; 2) predictability of the RR interval series is larger during tilt, during controlled respiration at 10 breaths/min (bpm) and after high-dose administration of atropine; 3) SAP series is dominated by linear correlation; 4) RR interval series exhibits nonlinear dynamics during controlled respiration at 10 bpm and after low-dose administration of atropine, while it is linear during sympathetic activation produced by tilt and after peripheral parasympathetic blockade caused by high-dose administration of atropine.

Monitoring the autonomic nervous system in the ICU through cardiovascular variability signals.

Studies the usefulness of cardiovascular variability parameters for monitoring intensive-care unit (ICU) patients, and discusses assessing ICU patient status using spectral analysis parameters. Both short-term and long-term spectral parameters were employed for the assessment of patient status in the ICU. Short-term parameters were sensitive to the airway suction (AWS) and may also be employed to monitor the response to different therapeutic interventions. Long-term parameters showed significantly increased /spl alpha/-slope values in nonsurviving patients. This result suggests that the /spl alpha/-slope value on 24-hour RR spectra obtained from the ECG signal may be a relevant prognostic index.

Application of time series spectral analysis theory: analysis of cardiovascular variability signals.

The paper focuses on the most important application problems commonly encountered in spectral analysis of short-term (less than 10 min) recordings of cardiovascular variability signals (CVSs), critically analysing the different approaches to these problems presented in the literature and suggesting practical solutions based on sound theoretical and empirical considerations. The Blackman-Tukey (BT) and Burg methods have been selected as the most representative of classical and AR spectral estimators, respectively. For realistic simulations, 'synthetic' CVSs are generated as AR processes whose parameters are estimated on corresponding time series of normal, post-myocardial infarction and congestive heart failure subjects. The problem of resolution of spectral estimates is addressed, and an empirical method is proposed for model order selection in AR estimation. The issue of the understandability and interpretability of spectral shapes is discussed. The problem of non-stationarity and removing trends is dealt with. The important issue of identification and estimation of spectral components is discussed, and the main advantages and drawbacks of spectral decomposition algorithms are critically evaluated.

Assessment of training-induced autonomic adaptations in athletes with spectral analysis of cardiovascular variability signals.

The purpose of this study was to assess the adaptive effects of endurance training on autonomic functions in athletes with spectral analysis of cardiovascular variability signals. Continuous ECG, arterial blood pressure (ABP), and respiratory signals were recorded from 15 athletes (VO2max > 55 ml/(kg.min)) and 15 nonathletes (VO2max < 45 ml/(kg.min)) in the sitting position during controlled respiration (tidal volume 700 ml and 15 cycles/min). The autonomic functions were assessed by the normalized low-frequency power (LF power: 0.06-0.14 Hz) and high-frequency power (HF power: the region of the respiratory frequency based on respiratory spectrum) obtained from the autospectra of the RR interval, systolic arterial pressure (SAP), and diastolic arterial pressure (DAP) variability signals. The spontaneous baroreflex sensitivity (BRS) was evaluated by the moduli, BRSLF and BRSHF, of the transfer function between the RR interval and SAP variability in LF and HF bands. The resting HR in athletes was significantly lower than that in nonathletes. In the case of RR interval spectra, the HF power was significantly higher in athletes than in nonathletes, whereas the LF power was significantly lower in athletes than in nonahtletes. These differences might reflect an alteration of sympathovagal interaction with a predominance of parasympathetic activity. However, there was no significant difference in the LF power of SAP and DAP autospectra, reflecting the sympathetic vascular control. The BRSLF and BRSHF were significantly higher in athletes as compared with nonathletes. These results indicate that endurance training induces autonomic imbalance (i.e., the enhanced vagal activities/the attenuated sympathetic tone), which may in part contribute to the resting bradycardia and an increase in the spontaneous BRS in athletes.

Non-Linear Dynamics of Cardiovascular Variability Signals

Long-term regulation of beat-to-beat variability involves several different kinds of controls. A linear approach performed by parametric models enhances the short-term regulation of the autonomic nervous system. Some non-linear long-term regulation can be assessed by the chaotic deterministic approach applied to the beat-to-beat variability of the discrete RR-interval series, extracted from the ECG. For chaotic deterministic systems, trajectories of the state vector describe a strange attractor characterized by a fractal of dimension D. Signals are supposed to be generated by a deterministic and finite dimensional but non-linear dynamic system with trajectories in a multi-dimensional space-state. We estimated the fractal dimension through the Grassberger and Procaccia algorithm and Self-Similarity approaches of the 24-h heart-rate variability (HRV) signal in different physiological and pathological conditions such as severe heat failure, or after heart transplantation. State-space representations through Return Maps are also obtained. Differences between physiological and pathological cases have been assessed and generally a decrease in the system complexity is correlated to pathological conditions.

Power spectrum analysis of cardiovascular variability monitored by telemetry in conscious unrestrained rats

Beat-to-beat variability of arterial pressure and heart period (R-R) was studied in eight conscious freely-moving adult male rats in which telemetric recordings of arterial pressure. ECG and respiratory movements were obtained under unrestrained and unstressed conditions. The beat-to-beat time series of these signals (systolic arterial pressure, diastolic arterial pressure and R-R) were analyzed, in the frequency domain, using autoregressive spectral analysis in order to detect and quantify the rhythmic components. In basal conditions, the systolic arterial pressure variability spectrum was characterized by three major spectral components which had central frequencies respectively of 0.08 ± 0.03 Hz (very low frequency), 0.43 ± 0.02 Hz (low frequency) and 1.36 ± 0.19 Hz (high frequency). Similar rhythmic components were found in R-R signal variability. The very low frequency component included a higher percentage of total power in R-R variability spectrum (75.3%) than in systolic arterial pressure variability spectrum (58.4%). The low frequency component was more pronounced in both systolic and diastolic arterial pressure variability spectra. The high frequency component of R-R, systolic and diastolic arterial pressure was synchronous with respiration. Cross-spectral analysis revealed a high statistical coherence between R-R and arterial pressure variabilities in all the three frequency bands. An α-adrenergic blocker (phentolamine) specifically abolished the low frequency components of systolic and diastolic arterial pressure variability spectra, thus suggesting that low frequency is a marker of sympathetic modulation of vasomotor activity. The low frequency component of R-R variability spectrum was also markedly blunted. We suggest that cardiovascular variability signals, (R-R, systolic and diastolic arterial pressure) are composed almost of two main rhythms linked to respiration and vasomotor activity. These rhythms can be quantified in conscious unrestrained rats by using telemetry and spectral analysis. This approach seems to offer a new powerful tool for pharmacological studies in conscious small animals.

Cardiovascular variability signals: towards the identification of a closed-loop model of the neural control mechanisms

The authors consider parametric methods for processing cardiovascular signals and try to provide a global, although indirect evaluation of some neural regulatory activities. In particular, the variability signals of the heart rate (under the form of interval tachogram) and arterial blood pressure (systogram) together with respiratory movement signal (respirogram) are considered as inputs to a closed-loop model which describes a few aspects of the physiological interactions among the signals themselves. The identifiability of the transfer function of the model is demonstrated from the joint process black-box description of the signals. A direct identification procedure is proposed dividing the system into two dynamic adjustment models. A few suggestions are deduced on how and where the respirogram enters the model and on the genesis of the 10-s rhythm, parameters relevant to the Starling effect, Windkessel model, and the gain of baroreceptor mechanisms. The approach presented is intended also to provide a general frame for closed-loop identification in different pathophysiological conditions. >

Patterns of sympathetic neuron activity associated with Mayer waves.

Patterns of sympathetic neuron activity associated with Mayer waves.