Baroreflex Coupling Assessed by Cross-Compression Entropy

Estimating interactions between physiological systems is an important challenge in modern biomedical research. Here, we explore a new concept for quantifying information common in two time series by cross-compressibility. Cross-compression entropy (CCE) exploits the ZIP data compression algorithm extended to bivariate data analysis. First, time series are transformed into symbol vectors. Symbols of the target time series are coded by the symbols of the source series. Uncoupled and linearly coupled surrogates were derived from cardiovascular recordings of 36 healthy controls obtained during rest to demonstrate suitability of this method for assessing physiological coupling. CCE at rest was compared to that of isometric handgrip exercise. Finally, spontaneous baroreflex interaction assessed by CCE_BRS was compared between 21 patients suffering from acute schizophrenia and 21 matched controls. The CCE_BRS of original time series was significantly higher than in uncoupled surrogates in 89% of the subjects and higher than in linearly coupled surrogates in 47% of the subjects. Handgrip exercise led to sympathetic activation and vagal inhibition accompanied by reduced baroreflex sensitivity. CCE_BRS decreased from 0.553 ± 0.030 at rest to 0.514 ± 0.035 during exercise (p < 0.001). In acute schizophrenia, heart rate, and blood pressure were elevated. Heart rate variability indicated a change of sympathovagal balance. The CCE_BRS of patients with schizophrenia was reduced compared to healthy controls (0.546 ± 0.042 vs. 0.507 ± 0.046, p < 0.01) and revealed a decrease of blood pressure influence on heart rate in patients with schizophrenia. Our results indicate that CCE is suitable for the investigation of linear and non-linear coupling in cardiovascular time series. CCE can quantify causal interactions in short, noisy and non-stationary physiological time series.

Skeletal Muscle Pump Drives Control of Cardiovascular and Postural Systems

The causal interaction between cardio-postural-musculoskeletal systems is critical in maintaining postural stability under orthostatic challenge. The absence or reduction of such interactions could lead to fainting and falls often experienced by elderly individuals. The causal relationship between systolic blood pressure (SBP), calf electromyography (EMG), and resultant center of pressure (COPr) can quantify the behavior of cardio-postural control loop. Convergent cross mapping (CCM) is a non-linear approach to establish causality, thus, expected to decipher nonlinear causal cardio-postural-musculoskeletal interactions. Data were acquired simultaneously from young participants (25 ± 2 years, n = 18) during a 10-minute sit-to-stand test. In the young population, skeletal muscle pump was found to drive blood pressure control (EMG → SBP) as well as control the postural sway (EMG → COPr) through the significantly higher causal drive in the direction towards SBP and COPr. Furthermore, the effect of aging on muscle pump activation associated with blood pressure regulation was explored. Simultaneous EMG and SBP were acquired from elderly group (69 ± 4 years, n = 14). A significant (p = 0.002) decline in EMG → SBP causality was observed in the elderly group, compared to the young group. The results highlight the potential of causality to detect alteration in blood pressure regulation with age, thus, a potential clinical utility towards detection of fall proneness.

Cardiovascular interactions assessed via conditional joint transfer entropy in patients developing atrial fibrillation after coronary artery bypass graft surgery

Assigned the universe of knowledge Ω as composed by one target and two exogenous signals, the conditional joint transfer entropy (CJTE), assessing the amount of information jointly transferred from the two sources to the target that can be uniquely linked to one of the two sources, was found useful to study cardiovascular control. We propose the assessment of CJTE from systolic arterial pressure (SAP) and respiration (R) to heart period (HP) conditioned on R (CJTESAP, R→HP|R) along the baroreflex, and from HP and R to SAP conditioned on R (CJTEHP, R→SAP|R) along the feedforward mechanical pathway, in 134 patients undergoing coronary artery bypass graft surgery before (PRE) and after (POST) the induction of general anesthesia. In this group 38 patients developed atrial fibrillation (AF) after surgery, while the remaining individuals did not (noAF, n=96). Both CJTESAP, R→HP|R and CJTEHP, R→SAP|R distinguished AF from noAF individuals in the PRE condition, suggesting an impairment of HP-SAP closed-loop regulation in AF group and the possibility to identify subjects at higher risk to develop post-surgery AF.

Dependency Structures in Differentially Coded Cardiovascular Time Series

Objectives. This paper analyses temporal dependency in the time series recorded from aging rats, the healthy ones and those with early developed hypertension. The aim is to explore effects of age and hypertension on mutual sample relationship along the time axis. Methods. A copula method is applied to raw and to differentially coded signals. The latter ones were additionally binary encoded for a joint conditional entropy application. The signals were recorded from freely moving male Wistar rats and from spontaneous hypertensive rats, aged 3 months and 12 months. Results. The highest level of comonotonic behavior of pulse interval with respect to systolic blood pressure is observed at time lags τ = 0, 3, and 4, while a strong counter-monotonic behavior occurs at time lags τ = 1 and 2. Conclusion. Dynamic range of aging rats is considerably reduced in hypertensive groups. Conditional entropy of systolic blood pressure signal, compared to unconditional, shows an increased level of discrepancy, except for a time lag 1, where the equality is preserved in spite of the memory of differential coder. The antiparallel streams play an important role at single beat time lag.

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

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

Wiener-Granger causality in QT-HP variability interactions

The study exploits a Wiener-Granger causality (WGC) approach in the time domain to assess directionality of the dynamical interactions between QT interval and heart period (HP) during a graded head-up tilt protocol challenging the cardiovascular control as a function of the tilt table inclination. QT interval and HP are approximated from the surface ECG as the temporal distance between the R-wave apex and T-wave offset and between two consecutive R-wave peaks respectively. The adopted WGC approach accounts for the confounding effect of respiration (RESP) affecting both QT and HP. Causality ratios (CRs) from HP to QT given RESP (CRHP→QT|RESP) and from QT to HP given RESP (CRQT→HP|RESP) were computed and their significance was tested via F-test. We found that, regardless of the tilt table angle, CRHP→QT|RESP is significant, while CRQT→HP|RESP is negligible. CRHP→QT|RESP showed a trend towards a decrease with tilt table angle. These findings suggested that the causal direction from HP over QT is dominant compared to the reverse one and sympathetic activation induced a QT-HP uncoupling.

Development of Causal Interactions Between Systolic Blood Pressure and Inter-Beat Intervals in Adolescents

Systolic blood pressure (SBP) changes control the cardiac inter-beat intervals (IBI) duration via baroreflex. Conversely, SBP is influenced by IBI via non-baroreflex mechanisms. Both causal pathways (feedback – baroreflex and feedforward – non-baroreflex) form a closed loop of the SBP – IBI interaction. The aim of this study was to assess the age-related changes in the IBI – SBP interaction. We have non-invasively recorded resting beat-to-beat SBP and IBI in 335 healthy subjects of different age, ranging from 11 to 23 years. Using a linear autoregressive bivariate model we obtained gain (GainSBP,IBI, used traditionally as baroreflex sensitivity) and coherence (CohSBP,IBI) of the SBP–IBI interaction and causal gain and coherence in baroreflex (GainSBPIBI, CohSBPIBI) and coherence in non-baroreflex (CohIBISBP) directions separately. A non-linear approach was used for causal coupling indices evaluation (CSBPIBI, CIBISBP) quantifying the amount of information transferred between signals. We performed a correlation to age analysis of all measures. CohIBISBP and CIBISBP were higher than CohSBPIBI and CSBPIBI, respectively. GainSBP,IBI increased and CohSBPIBI decreased with age. The coupling indices did not correlate with age. We conclude that the feedforward influence dominated at rest. The increase of GainSBP,IBI with age was not found in the closed loop model. A decrease of CohSBPIBI could be related to a change in the cardiovascular control system complexity during maturation.

Disentangling cardiovascular control mechanisms during head-down tilt via joint transfer entropy and self-entropy decompositions

A full decomposition of the predictive entropy (PE) of the spontaneous variations of the heart period (HP) given systolic arterial pressure (SAP) and respiration (R) is proposed. The PE of HP is decomposed into the joint transfer entropy (JTE) from SAP and R to HP and self-entropy (SE) of HP. The SE is the sum of three terms quantifying the synergistic/redundant contributions of HP and SAP, when taken individually and jointly, to SE and one term conditioned on HP and SAP denoted as the conditional SE (CSE) of HP given SAP and R. The JTE from SAP and R to HP is the sum of two terms attributable to SAP or R plus an extra term describing the redundant/synergistic contribution to the JTE. All quantities were computed during cardiopulmonary loading induced by −25° head-down tilt (HDT) via a multivariate linear regression approach. We found that: (i) the PE of HP decreases during HDT; (ii) the decrease of PE is attributable to a lessening of SE of HP, while the JTE from SAP and R to HP remains constant; (iii) the SE of HP is dominant over the JTE from SAP and R to HP and the CSE of HP given SAP and R is prevailing over the SE of HP due to SAP and R both in supine position and during HDT; (iv) all terms of the decompositions of JTE from SAP and R to HP and SE of HP due to SAP and R were not affected by HDT; (v) the decrease of the SE of HP during HDT was attributed to the reduction of the CSE of HP given SAP and R; (vi) redundancy of SAP and R is prevailing over synergy in the information transferred into HP both in supine position and during HDT, while in the HP information storage synergy and redundancy are more balanced. The approach suggests that the larger complexity of the cardiac control during HDT is unrelated to the baroreflex control and cardiopulmonary reflexes and may be related to central commands and/or modifications of the dynamical properties of the sinus node.

General anesthesia reduces the information exchange between heart and circulation

The study demonstrates the ability of an information-theoretic measure, such as the transfer entropy (TE), in detecting the depression of the cardiac baroreflex control and circulatory-cardio mechanical feedforward link during propofol-induced general anesthesia. TE was computed from spontaneous variability of heart period (HP) and systolic arterial pressure (SAP) in patients undergoing coronary artery bypass graft (CABG). TE from SAP to HP and from HP to SAP were evaluated by accounting for the confounding effect of respiration (R) affecting both HP and SAP (i.e. TESAP→HP|R and TEHP→SAP|R respectively). Both TESAP→HP|R and TEHP→SAP|R decreased during general anesthesia, thus suggesting that the strength of the causal relation diminished over both arms of the closed loop HP-SAP control. The squared coherence function between HP and SAP confirmed the decreased HP-SAP coupling during general anesthesia, even though it could not distinguish directionality.

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

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

Cardiovascular control in women with fibromyalgia syndrome: do causal methods provide nonredundant information compared with more traditional approaches?

The cardiovascular autonomic control and the baroreflex sensitivity (BRS) have been widely studied in fibromyalgia syndrome (FMS) patients through the computation of linear indices of spontaneous heart period (HP) and systolic arterial pressure (SAP) variabilities. However, there are many methodological difficulties regarding the quantification of BRS by the traditional indices especially in relation to the issue of causality. This difficulty has been directly tackled via a model-based approach describing the closed-loop HP-SAP interactions and the exogenous influences of respiration. Therefore, we aimed to assess whether the BRS assessed by the model-based causal closed-loop approach during supine and active standing in patients with FMS could provide complementary information to those obtained by traditional indices based on time and frequency domains. The findings of this study revealed that, at difference with the traditional methods to quantify BRS, the causality analysis applied to the HP, SAP, and respiratory series, through the model-based closed-loop approach, detected lower BRS in supine position, as well as a blunted response to the orthostatic stimulus in patients with FMS compared with healthy control subjects. Also, the strength of the causal relation from SAP to HP (i.e., along the cardiac baroreflex) increased during the active standing only in the control subjects. The model-based closed-loop approach proved to provide important complementary information about the cardiovascular autonomic control in patients with FMS.

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.

Model-free causality analysis of cardiovascular variability detects the amelioration of autonomic control in Parkinson's disease patients undergoing mechanical stimulation

We tested the hypothesis that causality analysis, applied to the spontaneous beat-to-beat variability of heart period (HP) and systolic arterial pressure (SAP), can identify the improvement of autonomic control linked to plantar mechanical stimulation in patients with Parkinson's disease (PD). A causality index, measuring the strength of the association from SAP to HP variability, and derived according to the Granger paradigm (i.e. SAP causes HP if the inclusion of SAP into the set of signals utilized to describe cardiovascular interactions improves the prediction of HP series), was calculated using both linear model-based (MB) and nonlinear model-free (MF) approaches. Univariate HP and SAP variability indices in time and frequency domains, and bivariate descriptors of the HP-SAP variability interactions were computed as well. We studied ten PD patients (age range: 57-78 years; Hoehn-Yahr scale: 2-3; six males, four females) without orthostatic hypotension or symptoms of orthostatic intolerance and 'on-time' according to their habitual pharmacological treatment. PD patients underwent recordings at rest in a supine position and during a head-up tilt before, and 24 h after, mechanical stimulation was applied to the plantar surface of both feet. The MF causality analysis indicated a greater involvement of baroreflex in regulating HP-SAP variability interactions after mechanical stimulation. Remarkably, MB causality and more traditional univariate or bivariate techniques could not detect changes in cardiovascular regulation after mechanical stimulation, thus stressing the importance of accounting for nonlinear dynamics in PD patients. Due to the higher statistical power of MF causality we suggest its exploitation to monitor the baroreflex control improvement in PD patients, and we encourage the clinical application of the Granger causality approach to evaluate the modification of the autonomic control in relation to the application of a pharmacological treatment, a rehabilitation procedure or external intervention.

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

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

Decomposing the transfer entropy to quantify lag-specific Granger causality in cardiovascular variability

We present a modification of the well known transfer entropy (TE) which makes it able to detect, besides the direction and strength of the information transfer between coupled processes, its exact timing. The approach follows a decomposition strategy which identifies--according to a lag-specific formulation of the concept of Granger causality--the set of time delays carrying significant information, and then assigns to each of these delays an amount of information transfer such that the total contribution yields the overall TE. We propose also a procedure for the practical estimation from time series data of the relevant delays and lag-specific TE in both bivariate and multivariate settings. The proposed approach is tested in simulations and in real cardiovascular time series, showing the feasibility of lag-specific TE estimation, the ability to reflect expected mechanisms of cardiovascular regulation, and the necessity of using the multivariate TE to properly assess time-lagged information transfer in the presence of multiple interacting systems.

Model-based causal closed-loop approach to the estimate of baroreflex sensitivity during propofol anesthesia in patients undergoing coronary artery bypass graft

Cardiac baroreflex is a fundamental component of the cardiovascular control. The continuous assessment of baroreflex sensitivity (BRS) from spontaneous heart period (HP) and systolic arterial pressure (SAP) variations during general anesthesia provides relevant information about cardiovascular regulation in physiological conditions. Unfortunately, several difficulties including unknown HP-SAP causal relations, negligible SAP changes, small BRS values, and confounding influences due to mechanical ventilation prevent BRS monitoring from HP and SAP variabilities during general anesthesia. We applied a model-based causal closed-loop approach aiming at BRS assessment during propofol anesthesia in 34 patients undergoing coronary artery bypass graft (CABG) surgery. We found the following: 1) traditional time and frequency domain approaches (i.e., baroreflex sequence, cross-correlation, spectral, and transfer function techniques) exhibited irremediable methodological limitations preventing the assessment of the BRS decrease during propofol anesthesia; 2) Granger causality approach proved that the methodological caveats were linked to the decreased presence of bidirectional closed-loop HP-SAP interactions and to the increased incidence of the HP-SAP uncoupling; 3) our model-based closed-loop approach detected the significant BRS decrease during propofol anesthesia as a likely result of accounting for the influences of mechanical ventilation and causal HP-SAP interactions; and 4) the model-based closed-loop approach found also a diminished gain of the relation from HP to SAP linked to vasodilatation and reduced ventricular contractility during propofol anesthesia. The proposed model-based causal closed-loop approach is more effective than traditional approaches in monitoring cardiovascular control during propofol anesthesia and indicates an overall depression of the HP-SAP closed-loop regulation.

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

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

The impact of latent confounders in directed network analysis in neuroscience

In the analysis of neuroscience data, the identification of task-related causal relationships between various areas of the brain gives insights about the network of physiological pathways that are active during the task. One increasingly used approach to identify causal connectivity uses the concept of Granger causality that exploits predictability of activity in one region by past activity in other regions of the brain. Owing to the complexity of the data, selecting components for the analysis of causality as a preprocessing step has to be performed. This includes predetermined-and often arbitrary-exclusion of information. Therefore, the system is confounded by latent sources. In this paper, the effect of latent confounders is demonstrated, and paths of influence among three components are studied. While methods for analysing Granger causality are commonly based on linear vector autoregressive models, the effects of latent confounders are expected to be present also in nonlinear systems. Therefore, all analyses are also performed for a simulated nonlinear system and discussed with regard to applications in neuroscience.

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.

Causal inference with multiple time series: principles and problems

I review the use of the concept of Granger causality for causal inference from time-series data. First, I give a theoretical justification by relating the concept to other theoretical causality measures. Second, I outline possible problems with spurious causality and approaches to tackle these problems. Finally, I sketch an identification algorithm that learns causal time-series structures in the presence of latent variables. The description of the algorithm is non-technical and thus accessible to applied scientists who are interested in adopting the method.

Classification of cardiovascular time series based on different coupling structures using recurrence networks analysis

We analyse cardiovascular time series with the aim of performing early prediction of preeclampsia (PE), a pregnancy-specific disorder causing maternal and foetal morbidity and mortality. The analysis is made using a novel approach, namely the ε-recurrence networks applied to a phase space constructed by means of the time series of the variabilities of the heart rate and the blood pressure (systolic and diastolic). All the possible coupling structures among these variables are considered for the analysis. Network measures such as average path length, mean coreness, global clustering coefficient and scale-local transitivity dimension are computed and constitute the parameters for the subsequent quadratic discriminant analysis. This allows us to predict PE with a sensitivity of 91.7 per cent and a specificity of 68.1 per cent, thus validating the use of this method for classifying healthy and preeclamptic patients.

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.

Coherence analysis overestimates the role of baroreflex in governing the interactions between heart period and systolic arterial pressure variabilities during general anesthesia

During general anesthesia positive pressure mechanical ventilation (MV) profoundly affects intrathoracic pressure and venous return, thus soliciting cardiopulmonary reflexes and modifying stroke volume. As a consequence heart period, approximated as the temporal distance between two consecutive R peaks on the ECG (RR), and systolic arterial pressure (SAP) variability series are usually highly correlated at the MV frequency (MVF) and this significant correlation is commonly taken as an indication of an active baroreflex. In this study the involvement of baroreflex was tested according to a time-domain linear Granger causality approach accounting explicitly for MV in two experimental protocols. In the first protocol volatile (VA) or intravenous (IA) anesthetic was administered in humans during pressure controlled MV (PCMV). In the second protocol IA was administered in pigs during PCMV or pressure support MV (PSMV). Causality analysis was contrasted with RR-SAP squared coherence. Significant coherence values at MVF were always found in both protocols. On the contrary, a significant causal link from SAP to RR was less frequently found in humans independently of the anesthesiological strategy and in animals during PCMV. PSMV was superior to PCMV in animals because it was able to better preserve a link from SAP to RR. During general anesthesia the involvement of baroreflex in governing RR-SAP variability interactions is largely overestimated by RR-SAP squared coherence and causality analysis can be exploited to rank anesthesiological strategies and MV modes according to the ability of preserving a working baroreflex.

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

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