Exploring directionality in spontaneous heart period and systolic pressure variability interactions in humans: implications in the evaluation of baroreflex gain

A framework for assessing frequency domain causality in physiological time series with instantaneous effects

We present an approach for the quantification of directional relations in multiple time series exhibiting significant zero-lag interactions. To overcome the limitations of the traditional multivariate autoregressive (MVAR) modelling of multiple series, we introduce an extended MVAR (eMVAR) framework allowing either exclusive consideration of time-lagged effects according to the classic notion of Granger causality, or consideration of combined instantaneous and lagged effects according to an extended causality definition. The spectral representation of the eMVAR model is exploited to derive novel frequency domain causality measures that generalize to the case of instantaneous effects the known directed coherence (DC) and partial DC measures. The new measures are illustrated in theoretical examples showing that they reduce to the known measures in the absence of instantaneous causality, and describe peculiar aspects of directional interaction among multiple series when instantaneous causality is non-negligible. Then, the issue of estimating eMVAR models from time-series data is faced, proposing two approaches for model identification and discussing problems related to the underlying model assumptions. Finally, applications of the framework on cardiovascular variability series and multichannel EEG recordings are presented, showing how it allows one to highlight patterns of frequency domain causality consistent with well-interpretable physiological interaction mechanisms.

Effects of propofol anesthesia induction on the relationship between arterial blood pressure and heart rate

This paper presents the analysis of autonomic nervous system (ANS) control of heart rate (HR) and of cardiac baroreflex sensitivity (BRS) in patients undergoing general anesthesia for major surgery through spectral analysis techniques and with the Granger causality approach that take into account the causal relationships between HR and arterial blood pressure (ABP) variability. Propofol produced a general decrease in ABP due to its vasodilatory effects, a reduction in BRS, while HR remained unaltered with respect to baseline values before induction of anesthesia. The bivariate model suggests that the feedback pathway of cardiac baroreflex could be blunted by propofol induced anesthesia and that the feedforward pathway could be unaffected by anesthesia.

Measuring postural-related changes of spontaneous baroreflex sensitivity after repeated long-duration diving: frequency domain approaches

Sustained water immersion is thought to modulate orthostatic tolerance to an extent dependent on the duration and repetition over consecutive days of the diving sessions. We tested this hypothesis investigating in ten healthy subjects the potential changes in the cardiovascular response to head-up tilt induced by single and multiple resting air dives. Parametric cross-spectral analysis of spontaneous RR interval and systolic arterial pressure variability was performed in three experimental sessions: before diving (BD), after single 6-hour dive (ASD), and after multiple 6-hour dives (AMD, 5 consecutive days with 18-hour surface interval). From this analysis, baroreflex sensitivity (BRS) was computed as spectral power ratio (αBRS), non-causal transfer function gain (tfBRS) and causal transfer function gain (γBRS) evaluated at low frequency (0.04-0.14Hz) in the supine position (su) as well as in the standing upright position in the early tilt (et) and late tilt (lt) epochs. We found that, while αBRS decreased significantly in et and lt compared to su during all sessions, tfBRS and γBRS decreased during ASD and AMD but not during BD; moreover γBRS evidenced a progressive decrease from BD to ASD and to AMD in both et and lt epochs. These results indicate the necessity of following a causal approach for the estimation of BRS in the frequency domain, and suggest a progressive impairment of the baroreflex response to postural stress after single and multiple dives, which may reflect symptoms of increasing orthostatic intolerance.

Mechanisms of causal interaction between short-term RR interval and systolic arterial pressure oscillations during orthostatic challenge

The transition from the supine to the upright position requires a reorganization of the mechanisms of cardiovascular control that, if not properly accomplished, may lead to neurally mediated syncope. We investigated how the patterns of causality between systolic arterial pressure (SAP) and cardiac RR interval were modified by prolonged head-up tilt using a novel nonlinear approach based on corrected conditional entropy (CCE) compared with the standard approach exploiting the cross-correlation function (CCF). Measures of coupling strength and delay of the causal interactions from SAP to RR and from RR to SAP were obtained in 10 patients with recurrent, neurally mediated syncope (RNMS) and 10 healthy control (CO) subjects in the resting supine position (su) and after head-up tilting during early (et; ~2 min) and late (lt; ~15 min or before presyncope) epochs of upright posture. Main results were that 1) the coupling strength from SAP to RR increased significantly from su to et in both groups; by contrast, upon lt, the coupling strength was kept high in CO subjects and dropped to low values in RNMS patients; 2) in RNMS patients, the delay from SAP to RR was higher than in healthy controls and increased moving from et to lt. Although these trends were evident using the CCE approach, statistical significance was not attained using the CCF approach. These results indicate the necessity of dissecting causality between RR and SAP to properly assess directional mechanisms from the closed-loop cardiovascular regulation and suggest a weakened and slowed baroreflex as a major mechanism involved in the cardiovascular impairment associated to neurally mediated syncope.

Information domain analysis of the spontaneous baroreflex during pharmacological challenges

The information carried by heart period (HP) given systolic arterial pressure (SAP) changes was assessed to characterize spontaneous baroreflex (i.e. the relation linking SAP variability to HP variability): the larger the information carried by HP given SAP changes, the greater the unpredictability of HP given SAP variations, the smaller the strength of the causal coupling from SAP series to HP series. It was typified according to two parameters: i) the information carried by HP given SAP changes within the same heart cycle (i.e. 0-step-ahead information) describing immediate effects of SAP variations on HP; ii) the rate of increase of the information carried by HP given SAP changes as a function of the temporal distance, k, between the conditioning SAP pattern and future HP value (i.e. the rate of increase of k-step-ahead information with k) describing short-term effects of SAP modifications on HP. Both parameters were found under vagal control. Indeed, i) 0-step-ahead information suggested that HP and SAP variabilities were significantly coupled from SAP to HP at baseline and after the reduction of the inhibitory effect of sympathetic control on vagal influences performed through the administration of propranolol or clonidine; and ii) during vagal blockade induced by atropine or combined vagal and sympathetic blockade induced by the administration of propranolol after atropine k-step-ahead information reached a level incompatible with coupled HP and SAP dynamics regardless of k. In addition, it was found that the 0-step-ahead information at baseline and after propranolol and the rate of increase of k-step-ahead information with k at baseline could be exclusively explained in terms of linear HP-SAP interactions. Conversely, the same parameters after clonidine suggested the raise of nonlinear mechanisms probably unveiled by the central sympathetic blockade. Comparison with more traditional parameters describing the HP-SAP variability relation such as baroreflex sensitivity and squared HP-SAP coherence confirmed the complementary value of the proposed information domain analysis.

Baroreflex sensitivity estimation by the sequence method with delayed signals

OBJECTIVE

To evaluate a modified sequence method with delayed time series for baroreflex sensitivity (BRS) estimation during supine position and orthostatism in healthy human beings.

METHODS

Nineteen clinically healthy volunteers (12 men, age 28.4 ± 6.2 years old) were included. Blood pressure recordings were obtained during supine position and orthostatism (15 min each) with a Finometer. Systolic blood pressure (SBP) and inter beat intervals (IBI) measured from all heartbeats were used to estimate BRS in both positive and negative sequences, with SBP delayed between 0 and 5 heartbeats. BRS estimations were compared by ANOVA, p < 0.05 was considered significant. Optimal recording time based on fixed BRS error estimation was calculated for each time series.

RESULTS

BRS estimation was similar between positive and negative sequences in all conditions (BRS = 12.0 ± 2.0 ms/mmHg in supine position, delay 0). BRS with no delay was similar to BRS with delays between 1 and 5 heartbeats. Compared to supine position, BRS was smaller in orthostatism in all delays (BRS = 8.0 ± 2.0 ms/mmHg with delay 0). The shortest optimal recording time with delayed time series was similar in supine position and orthostatism (4.3 ± 1.7 vs. 3.74 ± 0.07 min, respectively). Estimation error was linearly correlated to IBI, regardless of the delay.

CONCLUSION

BRS estimation with sequence method improves with delayed time series, during supine position and orthostatism. Reduced BRS estimation error and recording time from this method could benefit studies with large populations or patients with low tolerance to orthostatism.

Autonomic mediation of the interdependence between variability signals of heart rate and blood pressure in the lizard Gallotia galloti

Autonomic nervous system (ANS) involvement in the mediation of the synchronization between beat-to-beat RR interval variability (RRIV) and systolic blood pressure variability (SBPV) signals of the lizard Gallotia galloti (Oudart, 1839) was investigated through linear and nonlinear time series analysis methods in a pharmacological blockade context. The ANS blockers used were atropine, prazosin, and propranolol. The interdependence between the signals was quantified by means of the magnitude-squared coherence (MSC), which measures amplitude and phase linear synchronization; the phase lag index (PLI), which evaluates the phase synchronization; and the index L, which quantifies the generalized linear and nonlinear synchronization. Atropine decreased the PLI in the low-frequency (LF: 0.01–0.05 Hz) range; prazosin decreased the MSC in the medium-frequency (MF: 0.06–0.15 Hz) range; and propranolol did not alter any of the interdependence measures. It is suggested that (i) the cholinoceptor activity mediates the phase cardiovascular synchronization in the LF range; (ii) the α1-adrenoceptor activity mediates the amplitude and phase linear cardiovascular synchronization in the MF range; and (iii) the β-adrenoceptor activity plays no role in mediating any dynamics of cardiovascular synchronization in the studied frequency range. When comparing these results with those in mammals, a lesser overall autonomic involvement in the mediation of the studied cardiovascular interdependences is seen in reptiles.

Measuring connectivity in linear multivariate processes: definitions, interpretation, and practical analysis

This tutorial paper introduces a common framework for the evaluation of widely used frequency-domain measures of coupling (coherence, partial coherence) and causality (directed coherence, partial directed coherence) from the parametric representation of linear multivariate (MV) processes. After providing a comprehensive time-domain definition of the various forms of connectivity observed in MV processes, we particularize them to MV autoregressive (MVAR) processes and derive the corresponding frequency-domain measures. Then, we discuss the theoretical interpretation of these MVAR-based connectivity measures, showing that each of them reflects a specific time-domain connectivity definition and how this results in the description of peculiar aspects of the information transfer in MV processes. Furthermore, issues related to the practical utilization of these measures on real-time series are pointed out, including MVAR model estimation and significance assessment. Finally, limitations and pitfalls arising from model mis-specification are discussed, indicating possible solutions and providing practical recommendations for a safe computation of the connectivity measures. An example of estimation of the presented measures from multiple EEG signals recorded during a combined visuomotor task is also reported, showing how evaluation of coupling and causality in the frequency domain may help describing specific neurophysiological mechanisms.

Assessment of the dynamic interactions between heart rate and arterial pressure by the cross time-frequency analysis

In this study, a framework for the characterization of the dynamic interactions between RR variability (RRV) and systolic arterial pressure variability (SAPV) is proposed. The methodology accounts for the intrinsic non-stationarity of the cardiovascular system and includes the assessment of both the strength and the prevalent direction of local coupling. The smoothed pseudo-Wigner-Ville distribution (SPWVD) is used to estimate the time-frequency (TF) power, coherence, and phase-difference spectra with fine TF resolution. The interactions between the signals are quantified by time-varying indices, including the local coupling, phase differences, time delay, and baroreflex sensitivity (BRS). Every index is extracted from a specific TF region, localized by combining information from the different spectra. In 14 healthy subjects, a head-up tilt provoked an abrupt decrease in the cardiovascular coupling; a rapid change in the phase difference (from 0.37 ± 0.23 to -0.27 ± 0.22 rad) and time delay (from 0.26 ± 0.14 to -0.16 ± 0.16 s) in the high-frequency band; and a decrease in the BRS (from 23.72 ± 7.66 to 6.92 ± 2.51 ms mmHg(-1)). In the low-frequency range, during a head-up tilt, restoration of the baseline level of cardiovascular coupling took about 2 min and SAPV preceded RRV by about 0.85 s during the whole test. The analysis of the Eurobavar data set, which includes subjects with intact as well as impaired baroreflex, showed that the presented methodology represents an improved TF generalization of traditional time-invariant methodologies and can reveal dysfunctions in subjects with baroreflex impairment. Additionally, the results also suggest the use of non-stationary signal-processing techniques to analyze signals recorded under conditions that are usually supposed to be stationary.

Information domain approach to the investigation of cardio-vascular, cardio-pulmonary, and vasculo-pulmonary causal couplings

The physiological mechanisms related to cardio-vascular (CV), cardio-pulmonary (CP), and vasculo-pulmonary (VP) regulation may be probed through multivariate time series analysis tools. This study applied an information domain approach for the evaluation of non-linear causality to the beat-to-beat variability series of heart period (t), systolic arterial pressure (s), and respiration (r) measured during tilt testing and paced breathing (PB) protocols. The approach quantifies the causal coupling from the series i to the series j (C_ij) as the amount of information flowing from i to j. A measure of directionality is also obtained as the difference between two reciprocal causal couplings (D_i,j = C_ij − C_ji). Significant causal coupling and directionality were detected respectively when the median of C_ij over subjects was positive (C_ij > 0), and when D_i,j was statistically different from zero (D_i,j > 0 or D_i,j < 0). The method was applied on t, s, and r series measured in 15 healthy subjects (22–32 years, 8 males) in the supine (su) and upright (up) positions, and in further 15 subjects (21–29 years, 7 males) during spontaneous (sp) and paced (pa) breathing. In the control condition (su, sp), a significant causal coupling was observed for C_rs, C_rt, C_st, and C_ts, and significant directionality was present only from r to t (D_r,t > 0). During head-up tilt (up, sp), C_rs was preserved, C_rt decreased to zero median, and C_st and C_ts increased significantly; directionality vanished between r and t (D_r,t = 0) and raised from s to t (D_s,t > 0). During PB (su, pa), C_rs increased significantly, C_rt and C_ts were preserved, and C_st decreased to zero median; directionality was preserved from r to t (D_r,t > 0), and raised from r to s (D_r,s > 0). These results suggest that the approach may reflect modifications of CV, CP, and VP mechanisms consequent to altered physiological conditions, such as the baroreflex engagement and the dampening of respiratory sinus arrhythmia induced by tilt, or the respiratory driving on arterial pressure induced by PB. Thus, it could be suggested as a tool for the non-invasive monitoring of CV and cardiorespiratory control systems in normal and impaired conditions.

Mathematical modeling of cardiovascular coupling: Central autonomic commands and baroreflex control

The cross-correlation function (CCF) yields the correlation coefficient between spontaneous fluctuations of heart period and blood pressure as a function of the time shift between these variables. Two CCF patterns occur in humans: I) positive correlation between heart period and previous pressure values; II) negative correlation between heart period and subsequent pressure values. These patterns may result from the baroreflex and central autonomic commands (CAC), respectively. The aim of this study was to test this interpretation with a non-linear mathematical model of the human cardiovascular system. CAC were modeled as either phasic changes or random fluctuations of vagal and sympathetic activities with opposite sign. CCF pattern I resulted from baroreflex buffering of blood pressure changes elicited by vascular resistance fluctuations. When cardiac baroreflex control was absent or outweighed by CAC to the heart, simulations resulted in CCF pattern II only. In intermediate conditions when cardiac baroreflex interacted with CAC to the heart, CCF patterns I and II coexisted because the coupling between heart period and blood pressure varied with time. CAC to the heart decreased in magnitude the correlation coefficient and lengthened the time shift of CCF pattern I, thus apparently slowing and blunting baroreflex effects. Conversely, the baroreflex decreased in magnitude the correlation coefficient of CCF pattern II, thus blunting CAC effects. These results provide theoretical evidence in favor of application of the CCF analysis to investigate the balance between central autonomic and baroreflex cardiac control.

Extended causal modeling to assess Partial Directed Coherence in multiple time series with significant instantaneous interactions

The Partial Directed Coherence (PDC) and its generalized formulation (gPDC) are popular tools for investigating, in the frequency domain, the concept of Granger causality among multivariate (MV) time series. PDC and gPDC are formalized in terms of the coefficients of an MV autoregressive (MVAR) model which describes only the lagged effects among the time series and forsakes instantaneous effects. However, instantaneous effects are known to affect linear parametric modeling, and are likely to occur in experimental time series. In this study, we investigate the impact on the assessment of frequency domain causality of excluding instantaneous effects from the model underlying PDC evaluation. Moreover, we propose the utilization of an extended MVAR model including both instantaneous and lagged effects. This model is used to assess PDC either in accordance with the definition of Granger causality when considering only lagged effects (iPDC), or with an extended form of causality, when we consider both instantaneous and lagged effects (ePDC). The approach is first evaluated on three theoretical examples of MVAR processes, which show that the presence of instantaneous correlations may produce misleading profiles of PDC and gPDC, while ePDC and iPDC derived from the extended model provide here a correct interpretation of extended and lagged causality. It is then applied to representative examples of cardiorespiratory and EEG MV time series. They suggest that ePDC and iPDC are better interpretable than PDC and gPDC in terms of the known cardiovascular and neural physiologies.

Short-term couplings of the cardiovascular system in pregnant women suffering from pre-eclampsia

Pre-eclampsia (PE), a serious pregnancy-specific disorder, causes significant neonatal and maternal morbidity and mortality. Recent studies showed that cardiovascular variability parameters as well as the baroreflex sensitivity remarkably improve its early diagnosis. For a better understanding of the dynamical changes caused by PE, in this study the coupling between respiration, systolic and diastolic blood pressure, and heart rate is investigated. Thirteen datasets of healthy pregnant women and 10 of subjects suffering from PE are included. Nonlinear additive autoregressive models with external input are used for a model-based coupling analysis following the idea of Granger causality. To overcome the problem of misdetections of standard methods in systems with a dominant driver, a heuristic ensemble approach is used here. A coupling is assumed to be real when existent in more than 80 per cent of the ensemble members, and otherwise denoted as artefacts. As the main result, we found that the coupling structure between heart rate, systolic blood pressure, diastolic blood pressure and respiration for healthy subjects and PE patients is the same and reliable. As a pathological mechanism, however, a significant increased respiratory influence on the diastolic blood pressure could be found for PE patients (p=0.003). Moreover, the nonlinear form of the respiratory influence on the heart rate is significantly different between the two groups (p=0.002). Interestingly, the influence of systolic blood pressure on the heart rate is not selected, which indicates that the baroreflex sensitivity estimation strongly demands the consideration of causal relationships between heart rate, blood pressure and respiration. Finally, our results point to a potential role of respiration for understanding the pathogenesis of PE.

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.

Baroreflex contribution to blood pressure and heart rate oscillations: time scales, time-variant characteristics and nonlinearities

The aim of this paper is to highlight the aspects of the baroreflex control of the cardiovascular system that could be relevant to the analysis and modelling of cardiovascular oscillations and regulation. In particular, complex and/or controversial issues of the baroreflex control are addressed on the basis of results obtained in previous studies by others as well as by our group. Attention has been focused on time-variant and nonlinear characteristics of the baroreflex function and on the influence of this physiological mechanism on different frequency regions of blood pressure and heart rate spectra.

Cardiorespiratory interactions in patients with atrial flutter

Respiratory sinus arrhythmia (RSA) is generally known as the autonomically mediated modulation of the sinus node pacemaker frequency in synchrony with respiration. Cardiorespiratory interactions have been largely investigated during sinus rhythm, whereas little is known about interactions during reentrant arrhythmias. In this study, cardiorespiratory interactions at the atrial and ventricular level were investigated during atrial flutter (AFL), a supraventricular arrhythmia based on a reentry, by using cross-spectral analysis and computer modeling. The coherence and phase between respiration and atrial (γ[Formula: see text], φAA) and ventricular (γ[Formula: see text], φRR) interval series were estimated in 20 patients with typical AFL (68.0 ± 8.8 yr) and some degree of atrioventricular (AV) conduction block. In all patients, atrial intervals displayed oscillations strongly coupled and in phase with respiration (γ[Formula: see text]= 0.97 ± 0.05, φAA = 0.71 ± 0.31 rad), corresponding to a paradoxical lengthening of intervals during inspiration. The modulation pattern was frequency independent, with in-phase oscillations and short time delays (0.40 ± 0.15 s) for respiratory frequencies in the range 0.1–0.4 Hz. Ventricular patterns were affected by AV conduction type. In patients with fixed AV conduction, ventricular intervals displayed oscillations strongly coupled (γ[Formula: see text]= 0.97 ± 0.03) and in phase with respiration (φRR = 1.08 ± 0.80 rad). Differently, in patients with variable AV conduction, respiratory oscillations were secondary to Wencheback rhythmicity, resulting in a decreased level of coupling (γ[Formula: see text]= 0.50 ± 0.21). Simulations with a simplified model of AV conduction showed ventricular patterns to originate from the combination of a respiratory modulated atrial input with the functional properties of the AV node. The paradoxical frequency-independent modulation pattern of atrial interval, the short time delays, and the complexity of ventricular rhythm characterize respiratory arrhythmia during AFL and distinguish it from normal RSA. These peculiar features can be explained by assuming a direct mechanical action of respiration on AFL reentrant circuit.

Mutual nonlinear prediction as a tool to evaluate coupling strength and directionality in bivariate time series: comparison among different strategies based on k nearest neighbors

We compare the different existing strategies of mutual nonlinear prediction regarding their ability to assess the coupling strength and directionality of the interactions in bivariate time series. Under the common framework of k -nearest neighbor local linear prediction, we test three approaches based on cross prediction, mixed prediction, and predictability improvement. The measures of interdependence provided by these approaches are first evaluated on short realizations of bivariate time series generated by coupled Henon models, investigating also the effects of noise. The usefulness of the three mutual nonlinear prediction schemes is then assessed in a common physiological application during known conditions of interaction-i.e., the analysis of the interdependence between heart rate and arterial pressure variability in healthy humans during supine resting and passive head-up tilting. Based on both simulation results and physiological interpretability of cardiovascular results, we conclude that cross prediction is valuable to quantify the coupling strength and predictability improvement to elicit directionality of the interactions in short and noisy bivariate time series.

Heart rate and blood pressure variability and baroreflex sensitivity in patients with anorexia nervosa

OBJECTIVE

Anorexia nervosa (AN) is considered to have a significant risk for sudden death because of cardiac complications, and abnormalities of the autonomic nervous system might be a cause of cardiac dysfunction. The aim of this study was to investigate autonomic nervous system function in AN patients by analyzing heart rate variability (HRV), blood pressure variability (BPV), and baroreflex sensitivity (BRS).

METHODS

The subjects were 32 AN patients without other psychiatric comorbidities and 37 healthy controls. Beat-to-beat R-R interval and systolic blood pressure recorded in the supine position were analyzed using power spectral analysis and cross-spectrum analysis to quantify the frequency domain properties of HRV, BPV, and BRS. In addition, detrended fluctuation analysis was used to quantify the fractal correlation properties from the scaling exponent alpha1 of HRV.

RESULTS

High frequency power and total power of HRV and BRS were significantly higher in AN patients and low frequency power of BPV, low frequency/High frequency ratio of HRV, and the scaling exponent alpha1 of HRV were significantly lower in AN patients, compared with controls.

CONCLUSIONS

These findings suggest that AN patients have reduced cardiovascular sympathetic nervous responsiveness, increased parasympathetic nervous responsiveness, and increased complexity of the interbeat interval time series compared with healthy controls. Regarding the relationship to prognosis of AN, the study showed conflicting results, and further prospective studies are needed to determine if these results are related to high mortality in AN patients.

Reducing the effect of respiration in baroreflex sensitivity estimation with adaptive filtering

Cardiac baroreflex is described by baroreflex sensitivity (BRS) from blood pressure and heart rate interval (RRi) fluctuations. However, respiration affects both blood pressure and RRi via mechanisms that are not necessarily of baroreflex origin. To separate the effects of baroreflex and respiration, metronome-guided breathing in a high frequency band (HF, 0.25-0.4 Hz) and a low frequency spectral band (LF, 0.04-0.15 Hz) have therefore been commonly used for BRS estimation. The controlled breathing may, however, change the natural functioning of the autonomic system and interfere BRS estimates. To enable usage of spontaneous breathing, we propose an adaptive LMS-based filter for removing the respiration effect from the BRS estimates. ECG, continuous blood pressure and respiration were measured during 5 min spontaneous and 5 min controlled breathing at 0.25 Hz in healthy males (n = 24, 33+/-7 years). BRS was calculated with spectral methods from the LF band with and without filtering. In those subjects whose spontaneous breathing rate was <0.15 Hz, the BRS(LF) values were overestimated, whereas the adaptive filtering reduced the bias significantly. As a conclusion, the adaptive filter reduces the distorting effect of respiration on BRS values, which enables more accurate estimation of BRS and the usage of spontaneous breathing as a measurement protocol.

Sleep-dependent changes in the coupling between heart period and blood pressure in human subjects

We investigated whether in human subjects, the pattern of coupling between the spontaneous fluctuations of heart period (HP) and those of systolic blood pressure (SBP) differs among wake-sleep states. Polysomnographic recordings and finger blood pressure measurements were performed for 48 h in 15 nonobese adults without sleep-disordered breathing. The cross-correlation function (CCF) between the fluctuations of HP and SBP at frequencies <0.15 Hz was computed during quiet wakefulness (QW), light (stages 1 and 2) and deep (stages 3 and 4) nonrapid-eye-movement sleep (NREMS), and rapid-eye-movement sleep (REMS). A positive correlation between HP and the previous SBP values, which is the expected result of baroreflex feedback control, was observed in the sleep states but not in QW. In deep NREMS, the maximum CCF value was significantly higher than in any other state, suggesting the greatest baroreflex contribution to the coupling between HP and SBP. A negative correlation between HP and the subsequent SBP values was also observed in each state, consistent with the mechanical feed-forward action of HP on SBP and with central autonomic commands. The contribution of these mechanisms to the coupling between HP and SBP, estimated from the minimum CCF value, was significantly lower in deep NREMS than either in light NREMS or QW. These results indicate that the pattern of coupling between HP and SBP at low frequencies differs among wake-sleep states in human subjects, with deep NREMS entailing the highest feedback contribution of the baroreflex and a low effectiveness of feed-forward mechanisms.

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.

Brain structures mediating cardiovascular arousal and interoceptive awareness

Different emotions are accompanied by different bodily states and it is unclear which brain structures are involved in both, the cerebral representation of the bodily change and the representation of its perception. Structures connecting bodily signals and interoceptive awareness could trigger, in a feedforward manner, behavioral responses appropriate to maintain a desired state of the cardiovascular system. The present functional magnetic resonance imaging study aimed at identifying brain structures that are mutually activated during interoceptive awareness of heartbeats and during cardiovascular arousal. Additionally, we searched for brain regions connecting interoception with feelings. During the interoceptive task (directing attention towards heartbeats in relation to an exteroceptive task) the thalamus, the insula, the medial frontal/dorsal cingulate and the inferior frontal gyrus, as well as the somatomotor cortex were activated. The conjunction of the interoceptive awareness of heartbeats and cardiovascular arousal revealed structures presumably connecting both conditions, i.e. the right thalamus, insula, somatomotor cortex, and the dorsal cingulate as well as medial frontal gyrus. Furthermore, the degree of interoceptive awareness predicted the degree of activation of both the insula and the medial frontal/dorsal cingulate gyrus. Negative feelings correlated with the BOLD response of the interoceptive awareness condition in the dorsal cingulate gyrus extending into the dorsomedial prefrontal cortex. We provide evidence that the insula, the dorsal cingulate gyrus, and the dorsomedial prefrontal cortex are specifically involved in processing cardiac sensations. The dorsal cingulate gyrus and the dorsomedial prefrontal cortex presumably represent the neural substrates of experiencing negative emotions.

A simplified two-component model of blood pressure fluctuation

We propose a simple moving-average (MA) model that uses the low-frequency (LF) component of the peroneal muscle sympathetic nerve spike rate (LF(spike rate)) and the high-frequency (HF) component of respiration (HF(Resp)) to describe the LF neurovascular fluctuations and the HF mechanical oscillations in systolic blood pressure (SBP), respectively. This method was validated by data from eight healthy subjects (23-47 yr old, 6 male, 2 female) during a graded tilt (15 degrees increments every 5 min to a 60 degrees angle). The LF component of SBP (LF(SBP)) had a strong baroreflex-mediated feedback correlation with LF(spike rate) (r = -0.69 +/- 0.05) and also a strong feedforward relation to LF(spike rate) [r = 0.58 +/- 0.03 with LF(SBP) delay (tau) = 5.625 +/- 0.15 s]. The HF components of spike rate (HF(spike rate)) and SBP (HF(SBP)) were not significantly correlated. Conversely, HF(Resp) and HF(SBP) were highly correlated (r = -0.79 +/- 0.04), whereas LF(Resp) and LF(SBP) were significantly less correlated (r = 0.45 +/- 0.08). The mean correlation coefficients between the measured and model-predicted LF(SBP) (r = 0.74 +/- 0.03) in the supine position did not change significantly during tilt. The mean correlation between the measured and model-predicted HF(SBP) was 0.89 +/- 0.02 in the supine position. R(2) values for the regression analysis of the model-predicted and measured LF and HF powers indicate that 78 and 91% of the variability in power can be explained by the linear relation of LF(spike rate) to LF(SBP) and HF(Resp) to HF(SBP). We report a simple two-component model using neural sympathetic and mechanical respiratory inputs that can explain the majority of blood pressure fluctuation at rest and during orthostatic stress in healthy subjects.

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.

Causal Cross-Spectral Analysis of Heart Rate and Blood Pressure Variability for describing the Impairment of the Cardiovascular Control in Neurally Mediated Syncope

A causal approach to the calculation of coherence and transfer function between systolic pressure (SP) and RR interval variability was applied in eight patients and eight control subjects during prolonged tilt test for investigating the impairment of cardiovascular control related to neurally mediated syncope. The causal analysis showed a depressed baroreflex regulation in resting patients, with reduced gain and increased latency from SP to RR, and a drop of the baroreflex coupling immediately before syncope. These findings, which were not elicited by traditional cross-spectral analysis, strongly suggest the use of the causal approach for the study of syncope mechanisms.