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

Spectral decomposition of cerebrovascular and cardiovascular interactions in patients prone to postural syncope and healthy controls

We present a framework for the linear parametric analysis of pairwise interactions in bivariate time series in the time and frequency domains, which allows the evaluation of total, causal and instantaneous interactions and connects time- and frequency-domain measures. The framework is applied to physiological time series to investigate the cerebrovascular regulation from the variability of mean cerebral blood flow velocity (CBFV) and mean arterial pressure (MAP), and the cardiovascular regulation from the variability of heart period (HP) and systolic arterial pressure (SAP). We analyze time series acquired at rest and during the early and late phase of head-up tilt in subjects developing orthostatic syncope in response to prolonged postural stress, and in healthy controls. The spectral measures of total, causal and instantaneous coupling between HP and SAP, and between MAP and CBFV, are averaged in the low-frequency band of the spectrum to focus on specific rhythms, and over all frequencies to get time-domain measures. The analysis of cardiovascular interactions indicates that postural stress induces baroreflex involvement, and its prolongation induces baroreflex dysregulation in syncope subjects. The analysis of cerebrovascular interactions indicates that the postural stress enhances the total coupling between MAP and CBFV, and challenges cerebral autoregulation in syncope subjects, while the strong sympathetic activation elicited by prolonged postural stress in healthy controls may determine an increased coupling from CBFV to MAP during late tilt. These results document that the combination of time-domain and spectral measures allows us to obtain an integrated view of cardiovascular and cerebrovascular regulation in healthy and diseased subjects.

Time-Frequency Analysis of Cardiovascular and Cardiorespiratory Interactions During Orthostatic Stress by Extended Partial Directed Coherence

In this study, the linear method of extended partial directed coherence (ePDC) was applied to establish the temporal dynamic behavior of cardiovascular and cardiorespiratory interactions during orthostatic stress at a 70° head-up tilt (HUT) test on young age-matched healthy subjects and patients with orthostatic intolerance (OI), both male and female. Twenty 5-min windows were used to analyze the minute-wise progression of interactions from 5 min in a supine position (baseline, BL) until 18 min of the orthostatic phase (OP) without including pre-syncopal phases. Gender differences in controls were present in cardiorespiratory interactions during OP without compromised autonomic regulation. However in patients, analysis by ePDC revealed considerable dynamic alterations within cardiovascular and cardiorespiratory interactions over the temporal course during the HUT test. Considering the young female patients with OI, the information flow from heart rate to systolic blood pressure (mechanical modulation) was already increased before the tilt-up, the information flow from systolic blood pressure to heart rate (neural baroreflex) increased during OP, while the information flow from respiration to heart rate (respiratory sinus arrhythmia) decreased during the complete HUT test. Findings revealed impaired cardiovascular interactions in patients with orthostatic intolerance and confirmed the usefulness of ePDC for causality analysis.

Study of impaired cardiovascular and respiratory coupling during orthostatic stress based on joint symbolic dynamics

The present study investigates the instantaneous coupling among the cardiac, vascular, and respiratory systems, using the heart rate, respiration, and systolic and diastolic blood pressure variability in 12 healthy and 16 vasovagal syncope female subjects during a head-up tilt (HUT) testing protocol at 70° This study contributes to the coupling analysis by using a nonlinear joint symbolic dynamics (JSD) in a high-temporal resolution scheme, based on 5 min segments of the time series that are shifted every minute. For each segment, a bivariate JSD matrix was constructed to obtain global and local coupling indices in accordance to Shannon's entropy and the probability of occurrence of various bivariate words, respectively. The novel approach revealed important findings in the coupling dynamics of the systems, thus allowing the detection of group differences during the early orthostatic phase, and during the HUT test, before the occurrence of any pre-syncopal symptoms. In patients, the global indices indicated a significant decrease of cardiovascular coupling, starting at 10 min after the tilt-up, manifested by reduced baroreflex sensitivity and cardiorespiratory coupling that was initiated 8 min after the onset of the orthostatic phase (OP). A decreased autonomic control on cardiovascular-respiratory couplings was further evidenced by increased alterations of the JSD indices during the OP compared to the supine position in patients compared to controls. Furthermore, findings based on local indices demonstrated that female patients showed reductions and disengagements in cardiovascular (p < 0.001) and cardiorespiratory (p < 0.01) couplings, as early as the first 5 min and during the complete OP.

IDENTIFYING DEEP BREATH EFFECT ON CARDIOVASCULAR SIGNALS USING CONDITIONAL ENTROPY: AN INFORMATION DOMAIN APPROACH

This quantitative study identifies the coupling changes occurring among cardiac (RR), vascular (SBP) and respiratory (RESP) signals during deep breathing. The deep breathing measures the dysfunction of the parasympathetic autonomic nervous system. The traditional methods based on cross-correlation and coherence analysis lack to measure nonlinear structures and unpredictability of physiological subsystems. Therefore, information domain coupling method based on conditional entropy is proposed to detect the coupling changes. Thirty healthy volunteers were examined for 5[Formula: see text]min at normal breathing and 5[Formula: see text]min during deep breathing (6[Formula: see text]cycles/min). The reduction in respiration rate detects a significant increase in information flow from RESP to RR, RESP to SBP and SBP to RR. The increased interaction from RESP to RR and RESP to SBP at reduced respiration rate indicates the enhancement of respiratory sinus arrhythmia that results in the activation of the parasympathetic nervous system. Also, the balanced cardiovascular interaction observed on normal breathing from RR to SBP disappears, but interaction occurring in baroreflex direction (SBP to RR) increases that helps in the reduction of blood pressure during deep breathing. This detected direction of information flow helps in identifying the coupling changes occurring during parasympathetic nerve activity.

Dynamical properties of LFPs from mice with unilateral injection of TeNT

Local field potential (LFP) recordings were performed from the visual cortex (V1) of a focal epilepsy mouse model. Epilepsy was induced by a unilateral injection of the synaptic blocker tetanus neurotoxin (TeNT). LFP signals were simultaneously recorded from V1 of both hemispheres of each animal under acute and chronic conditions (i.e. during and after the period of TeNT action). All data were analysed by using nonlinear time series methods. Suitable values of the lag time and embedding dimension for phase space reconstruction were estimated by employing well-known methods. The results showed that lag times are sensitive to the presence of TeNT. Interestingly, TeNT promoted an increase in the level of linear and nonlinear correlation of LFP signals. The values of the embedding dimension failed to show any dependence on the presence of the neurotoxin. However, a local nonlinear prediction method showed that the presence of TeNT increases the predictability, quantified by the normalized prediction error, of the neural recordings. From a neurophysiological point of view, the above results suggest that TeNT injected in one hemisphere strongly impacts the local electrical activity of the neural populations in the opposite hemisphere. We hypothesize that this could arise from a qualitative and quantitative alteration of the transmission properties of the callosal fibers.

Estimating the decomposition of predictive information in multivariate systems

In the study of complex systems from observed multivariate time series, insight into the evolution of one system may be under investigation, which can be explained by the information storage of the system and the information transfer from other interacting systems. We present a framework for the model-free estimation of information storage and information transfer computed as the terms composing the predictive information about the target of a multivariate dynamical process. The approach tackles the curse of dimensionality employing a nonuniform embedding scheme that selects progressively, among the past components of the multivariate process, only those that contribute most, in terms of conditional mutual information, to the present target process. Moreover, it computes all information-theoretic quantities using a nearest-neighbor technique designed to compensate the bias due to the different dimensionality of individual entropy terms. The resulting estimators of prediction entropy, storage entropy, transfer entropy, and partial transfer entropy are tested on simulations of coupled linear stochastic and nonlinear deterministic dynamic processes, demonstrating the superiority of the proposed approach over the traditional estimators based on uniform embedding. The framework is then applied to multivariate physiologic time series, resulting in physiologically well-interpretable information decompositions of cardiovascular and cardiorespiratory interactions during head-up tilt and of joint brain-heart dynamics during sleep.

Cardiovascular and cardiorespiratory phase synchronization in normovolemic and hypovolemic humans

We investigated whether and how cardiovascular and cardiorespiratory phase synchronization would respond to changes in hydration status and orthostatic stress. Four men and six women were tested during graded head-up tilt (HUT) in both euhydration and dehydration (DEH) conditions. Continuous R-R intervals (RRI), systolic blood pressure (SBP) and respiration were investigated in low (LF 0.04-0.15 Hz) and high (HF 0.15-0.4 Hz) frequency ranges using a phase synchronization index (λ) ranging from 0 (complete lack of interaction) to 1 (perfect interaction) and a directionality index (d), where a positive value of d reflects oscillator 1 driving oscillator 2, and a negative value reflects the opposite driving direction. Surrogate data analysis was used to exclude relationships that occurred by chance. In the LF range, respiration was not synchronized with RRI or SBP, whereas RRI and SBP were phase synchronized. In the HF range, phases among all variables were synchronized. DEH reduced λ among all variables in the HF and did not affect λ between RRI and SBP in the LF region. DEH reduced d between RRI and SBP in the LF and did not affect d among all variables in the HF region. Increasing λ and decreasing d between SBP and RRI were observed in the LF range during HUT. Decreasing λ between SBP and RRI, respiration and RRI, and decreasing d between respiration and SBP were observed in the HF range during HUT. These results show that orthostatic stress disassociated interactions among RRI, SBP and respiration, and that DEH exacerbated the disconnection.

MuTE: a MATLAB toolbox to compare established and novel estimators of the multivariate transfer entropy

A challenge for physiologists and neuroscientists is to map information transfer between components of the systems that they study at different scales, in order to derive important knowledge on structure and function from the analysis of the recorded dynamics. The components of physiological networks often interact in a nonlinear way and through mechanisms which are in general not completely known. It is then safer that the method of choice for analyzing these interactions does not rely on any model or assumption on the nature of the data and their interactions. Transfer entropy has emerged as a powerful tool to quantify directed dynamical interactions. In this paper we compare different approaches to evaluate transfer entropy, some of them already proposed, some novel, and present their implementation in a freeware MATLAB toolbox. Applications to simulated and real data are presented.

Detecting determinism with improved sensitivity in time series: rank-based nonlinear predictability score

The rank-based nonlinear predictability score was recently introduced as a test for determinism in point processes. We here adapt this measure to time series sampled from time-continuous flows. We use noisy Lorenz signals to compare this approach against a classical amplitude-based nonlinear prediction error. Both measures show an almost identical robustness against Gaussian white noise. In contrast, when the amplitude distribution of the noise has a narrower central peak and heavier tails than the normal distribution, the rank-based nonlinear predictability score outperforms the amplitude-based nonlinear prediction error. For this type of noise, the nonlinear predictability score has a higher sensitivity for deterministic structure in noisy signals. It also yields a higher statistical power in a surrogate test of the null hypothesis of linear stochastic correlated signals. We show the high relevance of this improved performance in an application to electroencephalographic (EEG) recordings from epilepsy patients. Here the nonlinear predictability score again appears of higher sensitivity to nonrandomness. Importantly, it yields an improved contrast between signals recorded from brain areas where the first ictal EEG signal changes were detected (focal EEG signals) versus signals recorded from brain areas that were not involved at seizure onset (nonfocal EEG signals).

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.

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.

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.

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.