Investigating the mechanisms of cardiovascular and cerebrovascular regulation in orthostatic syncope through an information decomposition strategy

A Method to Assess Granger Causality, Isolation and Autonomy in the Time and Frequency Domains: Theory and Application to Cerebrovascular Variability

OBJECTIVE

Concepts of Granger causality (GC) and Granger autonomy (GA) are central to assess the dynamics of coupled physiologic processes. While causality measures have been already proposed and applied in time and frequency domains, measures quantifying self-dependencies are still limited to the time-domain formulation and lack of clear spectral representation.

METHODS

We embed into the linear parametric framework for computing GC from a driver X to a target process Y a measure of Granger Isolation (GI) quantifying the part of the dynamics of Y not originating from X, and a new spectral measure of GA assessing frequency-specific patterns of self-dependencies in Y. The measures are illustrated in theoretical simulations and applied to time series of arterial pressure and cerebral blood flow obtained in syncope subjects and healthy controls.

RESULTS

Simulations show that GI is complementary to GC but not trivially related to it, while GA reflects the regularity of the internal dynamics of the target process. In the application to cerebrovascular interactions, spectral GA quantified the physiological response to postural stress of slow cerebral blood flow oscillations, while spectral GC and GI detected an altered response to orthostasis in syncope subjects, likely related to impaired cerebral autoregulation.

CONCLUSION AND SIGNIFICANCE

The new spectral measures of GI and GA are useful complements to GC for the analysis of interacting oscillatory processes, and detect pathophysiological responses to postural stress which cannot be traced in the time domain. The thorough assessment of causality, isolation and autonomy opens new perspectives for the analysis of coupled processes in both physiological and clinical investigations.

A method to assess linear self-predictability of physiologic processes in the frequency domain: application to beat-to-beat variability of arterial compliance

The concept of self-predictability plays a key role for the analysis of the self-driven dynamics of physiological processes displaying richness of oscillatory rhythms. While time domain measures of self-predictability, as well as time-varying and local extensions, have already been proposed and largely applied in different contexts, they still lack a clear spectral description, which would be significantly useful for the interpretation of the frequency-specific content of the investigated processes. Herein, we propose a novel approach to characterize the linear self-predictability (LSP) of Gaussian processes in the frequency domain. The LSP spectral functions are related to the peaks of the power spectral density (PSD) of the investigated process, which is represented as the sum of different oscillatory components with specific frequency through the method of spectral decomposition. Remarkably, each of the LSP profiles is linked to a specific oscillation of the process, and it returns frequency-specific measures when integrated along spectral bands of physiological interest, as well as a time domain self-predictability measure with a clear meaning in the field of information theory, corresponding to the well-known information storage, when integrated along the whole frequency axis. The proposed measure is first illustrated in a theoretical simulation, showing that it clearly reflects the degree and frequency-specific location of predictability patterns of the analyzed process in both time and frequency domains. Then, it is applied to beat-to-beat time series of arterial compliance obtained in young healthy subjects. The results evidence that the spectral decomposition strategy applied to both the PSD and the spectral LSP of compliance identifies physiological responses to postural stress of low and high frequency oscillations of the process which cannot be traced in the time domain only, highlighting the importance of computing frequency-specific measures of self-predictability in any oscillatory physiologic process.

Gradients of O-information highlight synergy and redundancy in physiological applications

The study of high order dependencies in complex systems has recently led to the introduction of statistical synergy, a novel quantity corresponding to a form of emergence in which patterns at large scales are not traceable from lower scales. As a consequence, several works in the last years dealt with the synergy and its counterpart, the redundancy. In particular, the O-information is a signed metric that measures the balance between redundant and synergistic statistical dependencies. In spite of its growing use, this metric does not provide insight about the role played by low-order scales in the formation of high order effects. To fill this gap, the framework for the computation of the O-information has been recently expanded introducing the so-called gradients of this metric, which measure the irreducible contribution of a variable (or a group of variables) to the high order informational circuits of a system. Here, we review the theory behind the O-information and its gradients and present the potential of these concepts in the field of network physiology, showing two new applications relevant to brain functional connectivity probed via functional resonance imaging and physiological interactions among the variability of heart rate, arterial pressure, respiration and cerebral blood flow.

Concomitant evaluation of cardiovascular and cerebrovascular controls via Geweke spectral causality to assess the propensity to postural syncope

The evaluation of propensity to postural syncope necessitates the concomitant characterization of the cardiovascular and cerebrovascular controls and a method capable of disentangling closed loop relationships and decomposing causal links in the frequency domain. We applied Geweke spectral causality (GSC) to assess cardiovascular control from heart period and systolic arterial pressure variability and cerebrovascular regulation from mean arterial pressure and mean cerebral blood velocity variability in 13 control subjects and 13 individuals prone to develop orthostatic syncope. Analysis was made at rest in supine position and during head-up tilt at 60°, well before observing presyncope signs. Two different linear model structures were compared, namely bivariate autoregressive and bivariate dynamic adjustment classes. We found that (i) GSC markers did not depend on the model structure; (ii) the concomitant assessment of cardiovascular and cerebrovascular controls was useful for a deeper comprehension of postural disturbances; (iii) orthostatic syncope appeared to be favored by the loss of a coordinated behavior between the baroreflex feedback and mechanical feedforward pathway in the frequency band typical of the baroreflex functioning during the postural challenge, and by a weak cerebral autoregulation as revealed by the increased strength of the pressure-to-flow link in the respiratory band. GSC applied to spontaneous cardiovascular and cerebrovascular oscillations is a promising tool for describing and monitoring disturbances associated with posture modification.

Cardioautonomic lability assessed by heart rate variability changes in Royal Canadian Mounted Police cadets during the cadet training program

Objective

The current study examined variations in cardioautonomic lability during the Royal Canadian Mounted Police (RCMP) Cadet Training Program (CTP) between cadets starting their training who did or did not screen positive for one or more mental health disorders (i.e., posttraumatic stress disorder [PTSD], major depressive disorder [MDD], social anxiety disorder [SAD], generalized anxiety disorder [GAD], panic disorder [PD], alcohol use disorder [AUD]).

Methods

Electrocardiogram (ECG) signals integrated into Hexoskin garments were used to record ECG and heart rate Over the 26-week CTP. There were 31 heart rate variability (HRV) parameters calculated using Kubios Premium HRV analysis software. Mann-Whitney U-tests were used to perform groupwise comparisons of participant raw values and HRV during the CTP.

Results

A total of 157 cadets (79% male) were screened for any mental disorder using self-report surveys and then grouped by positive and negative screening. Analyses indicated a statistically significant (p < 0.05) decrease in low frequency (LF): High Frequency (HF) variability during CTP, but only for cadets who endorsed clinically significant anxiety symptoms on the GAD-7 at the start of their training. There were no other statistically significant groupwise differences.

Conclusion

The results indicate the participants have excellent cardiac health overall and suggest potentially important differences between groups, such that cadets who endorsed clinically significant anxiety symptoms on the GAD-7 showed less variability in the LF:HF ratio over the course of the CTP. The relatively lower variability suggests decreased parasympathetic tone in those without clinically significant anxiety symptoms. The results also have important implications for future investigations of cardioautonomic dysfunction and chronic hypothalamic pituitary adrenal (HPA) axis deviations in policing populations with anxiety disorders; specifically, cardioautonomic inflexibility related to cardiovascular morbidity and mortality. In any case, the current results provide an important baseline for future cardiac research with cadets and serving officers.

Statistical Approaches to Characterize Functional Connectivity in Brain and Physiologic Networks on a Single-Subject Basis

The trend toward personalized medicine necessitates drawing conclusions from descriptive indexes of physiopathological states estimated from individual recordings of biomedical signals, using statistical analyses that focus on subject-specific differences between experimental conditions. In this context, the present work introduces an approach to assess functional connectivity in brain and physiologic networks by pairwise information-theoretic measures of coupling between signals, whose significance and variations between conditions are statistically validated on a single-subject basis through the use of surrogate and bootstrap data analyses. The approach is illustrated on single-subject recordings of (i) resting-state functional magnetic resonance imaging (rest-fMRI) signals acquired in a pediatric patient with hepatic encephalography associated to a portosystemic shunt and undergoing liver vascular shunt correction, and of (ii) cardiovascular and cerebrovascular time series acquired at rest and during head-up tilt in a subject suffering from orthostatic intolerance.

On the Different Abilities of Cross-Sample Entropy and K-Nearest-Neighbor Cross-Unpredictability in Assessing Dynamic Cardiorespiratory and Cerebrovascular Interactions

Nonlinear markers of coupling strength are often utilized to typify cardiorespiratory and cerebrovascular regulations. The computation of these indices requires techniques describing nonlinear interactions between respiration (R) and heart period (HP) and between mean arterial pressure (MAP) and mean cerebral blood velocity (MCBv). We compared two model-free methods for the assessment of dynamic HP-R and MCBv-MAP interactions, namely the cross-sample entropy (CSampEn) and k-nearest-neighbor cross-unpredictability (KNNCUP). Comparison was carried out first over simulations generated by linear and nonlinear unidirectional causal, bidirectional linear causal, and lag-zero linear noncausal models, and then over experimental data acquired from 19 subjects at supine rest during spontaneous breathing and controlled respiration at 10, 15, and 20 breaths·minute-1 as well as from 13 subjects at supine rest and during 60° head-up tilt. Linear markers were computed for comparison. We found that: (i) over simulations, CSampEn and KNNCUP exhibit different abilities in evaluating coupling strength; (ii) KNNCUP is more reliable than CSampEn when interactions occur according to a causal structure, while performances are similar in noncausal models; (iii) in healthy subjects, KNNCUP is more powerful in characterizing cardiorespiratory and cerebrovascular variability interactions than CSampEn and linear markers. We recommend KNNCUP for quantifying cardiorespiratory and cerebrovascular coupling.

The reciprocal relationship between cardiac baroreceptor sensitivity and cerebral autoregulation during simulated hemorrhage in humans

A reciprocal relationship between the baroreflex and cerebral autoregulation (CA) has been demonstrated at rest and in response to acute hypotension. We hypothesized that the reciprocal relationship between cardiac baroreflex sensitivity (BRS) and CA would be maintained during sustained central hypovolemia induced by lower body negative pressure (LBNP), and that the strength of this relationship would be greater in subjects with higher tolerance to this stress. Healthy young adults (n = 51; 23F/28M) completed a LBNP protocol to presyncope. Subjects were classified as high tolerant (HT; completion of -60 mmHg LBNP stage, ≥20-min) or low tolerant (LT; did not complete -60 mmHg LBNP stage, <20-min). R-R intervals (RRI), systolic arterial pressure (SAP), mean arterial pressure (MAP), and middle cerebral artery velocity (MCAv) were measured continuously. Cardiac BRS was calculated in the time domain (ΔHR/ΔSAP) and frequency domain (RRI-SAP low frequency (LF) transfer function gain), and CA was calculated in the time domain (ΔMCAv/ΔMAP) and frequency domain (MAP-mean MCAv LF transfer function gain). There was a moderate relationship between cardiac BRS and CA for the group of 51 subjects in both the time (R = -0.54, P < 0.0001) and frequency (R = 0.61, P < 0.001) domains; there was a stronger relationship in the HT group (R = 0.73) compared to the LT group (R = 0.31) in the frequency domain (P = 0.08), but no difference between groups in the time domain (HT: R = -0.73 vs. LT: R = -0.63; P = 0.27). These findings suggest that an interaction between BRS and CA may be an important compensatory mechanism that contributes to tolerance to simulated hemorrhage in young healthy adults.

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.

Exploring metrics for the characterization of the cerebral autoregulation during head-up tilt and propofol general anesthesia

Techniques grounded on the simultaneous utilization of Tiecks' second order differential equations and spontaneous variability of mean arterial pressure (MAP) and mean cerebral blood flow velocity (MCBFV), recorded from middle cerebral arteries through a transcranial Doppler device, provide a characterization of cerebral autoregulation (CA) via the autoregulation index (ARI). These methods exploit two metrics for comparing the measured MCBFV series with the version predicted by Tiecks' model: normalized mean square prediction error (NMSPE) and normalized correlation ρ. The aim of this study is to assess the two metrics for ARI computation in 13 healthy subjects (age: 27 ± 8 yrs., 5 males) at rest in supine position (REST) and during 60° head-up tilt (HUT) and in 19 patients (age: 64 ± 8 yrs., all males), scheduled for coronary artery bypass grafting, before (PRE) and after (POST) propofol general anesthesia induction. Analyses were carried out over the original MAP and MCBFV pairs and surrogate unmatched couples built individually via time-shifting procedure. We found that: i) NMSPE and ρ metrics exhibited similar performances in passing individual surrogate test; ii) the two metrics could lead to different ARI estimates; iii) CA was not different during HUT or POST compared to baseline and this conclusion held regardless of the technique and metric for ARI estimation. Results suggest a limited impact of the sympathetic control on CA.

Pairwise and higher-order measures of brain-heart interactions in children with temporal lobe epilepsy

OBJECTIVE

While it is well-known that epilepsy has a clear impact on the activity of both the central nervous system (CNS) and the autonomic nervous system (ANS), its role on the complex interplay between CNS and ANS has not been fully elucidated yet. In this work, pairwise and higher-order predictability measures based on the concepts of Granger causality (GC) and Partial Information Decomposition (PID) were applied on time series of electroencephalographic (EEG) brain wave amplitude and heart rate variability (HRV) in order to investigate directed brain-heart interactions associated with the occurrence of focal epilepsy.

APPROACH

HRV and the envelopes of δ and α EEG activity recorded from ipsilateral (ipsi-EEG) and contralateral (contra-EEG) scalp regions were analyzed in 18 children suffering from temporal lobe epilepsy monitored during pre-ictal, ictal and post-ictal periods. After linear parametric model identification, we compared pairwise GC measures computed between HRV and a single EEG component with PID measures quantifying the unique, redundant and synergistic information transferred from ipsi-EEG and contra-EEG to HRV.

MAIN RESULTS

The analysis of GC revealed a dominance of the information transfer from EEG to HRV and negligible transfer from HRV to EEG, suggesting that CNS activities drive the ANS modulation of the heart rhythm, but did not evidence clear differences between δ and α rhythms, ipsi-EEG and contra-EEG, or pre- and post-ictal periods. On the contrary, PID revealed that epileptic seizures induce a reorganization of the interactions from brain to heart, as the unique predictability of HRV originated from the ipsi-EEG for the δ waves and from the contra-EEG for the α waves in the pre-ictal phase, while these patterns were reversed after the seizure.

SIGNIFICANCE

These results highlight the importance of considering higher-order interactions elicited by PID for the study of the neuro-autonomic effects of focal epilepsy, and may have neurophysiological and clinical implications.

Information Dynamics of Electric Field Intensity before and during the COVID-19 Pandemic

This work investigates the temporal statistical structure of time series of electric field (EF) intensity recorded with the aim of exploring the dynamical patterns associated with periods with different human activity in urban areas. The analyzed time series were obtained from a sensor of the EMF RATEL monitoring system installed in the campus area of the University of Novi Sad, Serbia. The sensor performs wideband cumulative EF intensity monitoring of all active commercial EF sources, thus including those linked to human utilization of wireless communication systems. Monitoring was performed continuously during the years 2019 and 2020, allowing us to investigate the effects on the patterns of EF intensity of varying conditions of human mobility, including regular teaching and exam activity within the campus, as well as limitations to mobility related to the COVID-19 pandemic. Time series analysis was performed using both simple statistics (mean and variance) and combining the information-theoretic measure of information storage (IS) with the method of surrogate data to quantify the regularity of EF dynamic patterns and detect the presence of nonlinear dynamics. Moreover, to assess the possible coexistence of dynamic behaviors across multiple temporal scales, IS analysis was performed over consecutive observation windows lasting one day, week, month, and year, respectively coarse grained at time scales of 6 min, 30 min, 2 h, and 1 day. Our results document that the EF intensity patterns of variability are modulated by the movement of people at daily, weekly, and monthly scales, and are blunted during periods of restricted mobility related to the COVID-19 pandemic. Mobility restrictions also affected significantly the regularity of the EF intensity time series, resulting in lower values of IS observed simultaneously with a loss of nonlinear dynamics. Thus, our analysis can be useful to investigate changes in the global patterns of human mobility both during pandemics or other types of events, and from this perspective may serve to implement strategies for safety assessment and for optimizing the design of networks of EF sensors.

Relationship Between Baroreflex and Cerebral Autoregulation in Patients With Cerebral Vasospasm After Aneurysmal Subarachnoid Hemorrhage

Introduction: Common consequences following aneurysmal subarachnoid hemorrhage (aSAH) are cerebral vasospasm (CV), impaired cerebral autoregulation (CA), and disturbance in the autonomic nervous system, as indicated by lower baroreflex sensitivity (BRS). The compensatory interaction between BRS and CA has been shown in healthy volunteers and stable pathological conditions such as carotid atherosclerosis. The aim of this study was to investigate whether the inverse correlation between BRS and CA would be lost in patients after aSAH during vasospasm. A secondary objective was to analyze the time-trend of BRS after aSAH.

Materials and Methods: Retrospective analysis of prospectively collected data was performed at the Neuro-Critical Care Unit of Addenbrooke's Hospital (Cambridge, UK) between June 2010 and January 2012. The cerebral blood flow velocity (CBFV) was measured in the middle cerebral artery using transcranial Doppler ultrasonography (TCD). The arterial blood pressure (ABP) was monitored invasively through an arterial line. CA was quantified by the correlation coefficient (Mxa) between slow oscillations in ABP and CBFV. BRS was calculated using the sequential cross-correlation method using the ABP signal.

Results: A total of 73 patients with aSAH were included. The age [median (lower-upper quartile)] was 58 (50–67). WFNS scale was 2 (1–4) and the modified Fisher scale was 3 (1–3). In the total group, 31 patients (42%) had a CV and 42 (58%) had no CV. ABP and CBFV were higher in patients with CV during vasospasm compared to patients without CV (p = 0.001 and p < 0.001). There was no significant correlation between Mxa and BRS in patients with CV, neither during nor before vasospasm. In patients without CV, a significant, although moderate correlation was found between BRS and Mxa (r_S = 0.31; p = 0.040), with higher BRS being associated with worse CA. Multiple linear regression analysis showed a significant worsening of BRS after aSAH in patients with CV (R_p = −0.42; p < 0.001).

Conclusions: Inverse compensatory correlation between BRS and CA was lost in patients who developed CV after aSAH, both before and during vasospasm. The impact of these findings on the prognosis of aSAH should be investigated in larger studies.

Monitoring the Evolution of Asynchrony between Mean Arterial Pressure and Mean Cerebral Blood Flow via Cross-Entropy Methods

Cerebrovascular control is carried out by multiple nonlinear mechanisms imposing a certain degree of coupling between mean arterial pressure (MAP) and mean cerebral blood flow (MCBF). We explored the ability of two nonlinear tools in the information domain, namely cross-approximate entropy (CApEn) and cross-sample entropy (CSampEn), to assess the degree of asynchrony between the spontaneous fluctuations of MAP and MCBF. CApEn and CSampEn were computed as a function of the translation time. The analysis was carried out in 23 subjects undergoing recordings at rest in supine position (REST) and during active standing (STAND), before and after surgical aortic valve replacement (SAVR). We found that at REST the degree of asynchrony raised, and the rate of increase in asynchrony with the translation time decreased after SAVR. These results are likely the consequence of the limited variability of MAP observed after surgery at REST, more than the consequence of a modified cerebrovascular control, given that the observed differences disappeared during STAND. CApEn and CSampEn can be utilized fruitfully in the context of the evaluation of cerebrovascular control via the noninvasive acquisition of the spontaneous MAP and MCBF variability.

Categorizing the Role of Respiration in Cardiovascular and Cerebrovascular Variability Interactions

OBJECTIVE

Respiration disturbs cardiovascular and cerebrovascular controls but its role is not fully elucidated.

METHODS

Respiration can be classified as a confounder if its observation reduces the strength of the causal relationship from source to target. Respiration is a suppressor if the opposite situation holds. We prove that a confounding/suppression (C/S) test can be accomplished by evaluating the sign of net redundancy/synergy balance in the predictability framework based on multivariate autoregressive modelling. In addition, we suggest that, under the hypothesis of Gaussian processes, the C/S test can be given in the transfer entropy decomposition framework as well. Experimental protocols: We applied the C/S test to variability series of respiratory movements, heart period, systolic arterial pressure, mean arterial pressure, and mean cerebral blood flow recorded in 17 pathological individuals (age: 648 yrs; 17 males) before and after induction of propofol-based general anesthesia prior to coronary artery bypass grafting, and in 13 healthy subjects (age: 278 yrs; 5 males) at rest in supine position and during head-up tilt with a table inclination of 60.

RESULTS

Respiration behaved systematically as a confounder for cardiovascular and cerebrovascular controls. In addition, its role was affected by propofol-based general anesthesia but not by a postural stimulus of limited intensity.

CONCLUSION

The C/S test can be fruitfully exploited to categorize the role of respiration over causal variability interactions.

SIGNIFICANCE

The application of the C/S test could favor the comprehension of the role of respiration in cardiovascular and cerebrovascular regulations.

Respiration is a Confounder of the Closed Loop Relationship Between Mean Arterial Pressure and Mean Cerebral Blood Flow

This study tested the hypothesis that respiration (RESP) is a confounder or suppressor of the closed loop relationship responsible for the cerebrovascular dynamical interactions as assessed from spontaneous variability of mean arterial pressure (MAP) and mean cerebral blood flow (MCBF). The evaluation was carried out in the information domain via transfer entropy (TE) estimated through a linear model-based approach comparing TE markers computed solely over MAP and MCBF series with TE indexes accounting for the eventual action of RESP over MAP and MCBF. We considered 11 patients (age: 76±5 yrs, 7 males) undergoing surgical aortic valve replacement (SAVR) at supine resting (REST) and during active standing (STAND) before and after SAVR surgery. The decrease of the predictive ability of MCBF to MAP when accounting for RESP compared to the one assessed when disregarding RESP suggested that RESP is a confounder of the link from MCBF to MAP along the Cushing reflex instead of being a suppressor. This result was more evident in POST when autonomic control was dramatically depressed and in an unchallenged condition such as REST. RESP did not affect significantly the link from MAP to MCBF along the pressure-to-flow relationship. Clarification of the type of RESP influence on the MAP-MCBF closed loop relationship could favor a deeper characterization of cerebrovascular interactions and the comprehension of cerebral autoregulation mechanisms.Clinical Relevance- This study suggests that respiration is a confounder of the closed loop relationship between MAP and MCBF, especially of the flow-to-pressure causal link. This result might open new possibilities in elucidating the mechanisms of cerebral autoregulation in healthy and pathological populations.

Quantitative Complexity Theory Used in the Prediction of Head-Up Tilt Testing Outcome

Background

Head-up tilt testing (HUTT), a well-established tool in the diagnosis of vasovagal syncope, is time-consuming, and every provoked vasovagal reaction may result in consolidating the reflex mechanism. Therefore, identification of parameters that could shorten the duration of HUTT and prevent fainting is desirable. Quantitative complexity theory (QCT) may provide holistic information on the cardiovascular reaction in HUTT. The aim of the present article was to evaluate the prognostic value of complexity in comparison with traditional haemodynamic parameters (HR and BP) in predicting the HUTT outcome.

Methods

Eighty-one healthy volunteers (74 men; mean age: 37.8 years) were included in this retrospective analysis of data collected within the project realized in Department of Cardiology and Internal Diseases, Military Institute of Medicine between January 2012 and October 2014. The subjects underwent HUTT, with beat-to-beat haemodynamic monitoring with a Niccomo™. The chosen haemodynamic parameters (including BP, HR, stroke volume, cardiac output, systemic vascular resistance) have been used in complexity analysis.

Results

HUTT was positive in 54 (66.7%) study participants. The values of complexity were already higher in fainting subjects than those were in nonfainting ones 300 s before HUTT termination (HUTT_end), with a significant upward trend starting 150 s before (pre)syncope. An area under the curve (AUC) over 0.700 was observed for complexity from 120 s before HUTT_end, with a sensitivity of 63% and specificity of 78% at this time point. The prognostic value of complexity was superior to that of the HR and mean arterial pressure (MAP).

Conclusions

Complexity has been shown to be a sensitive marker of cardiovascular haemodynamic response to orthostatic stress and proved to be superior over HR and BP in predicting HUTT outcomes.

Information Flow Between Heart Rhythm, Repolarization, and the Diastolic Interval Series for Healthy Individuals and LQTS1 Patients

Using information theoretic measures, relations between heart rhythm, repolarization in the tissue of the heart, and the diastolic interval time series are analyzed. These processes are a fragment of the cardiovascular physiological network. A comparison is made between the results for 84 (42 women) healthy individuals and 65 (45 women) long QT syndrome type 1 (LQTS1) patients. Self-entropy, transfer entropy, and joint transfer entropy are calculated for the three time series and their combinations. The results for self-entropy indicate the well-known result that regularity of heart rhythm for healthy individuals is larger than that of QT interval series. The flow of information depends on the direction with the flow from the heart rhythm to QT dominating. In LQTS1 patients, however, our results indicate that information flow in the opposite direction may occur-a new result. The information flow from the heart rhythm to QT dominates, which verifies the asymmetry seen by Porta et al. in the variable tilt angle experiment. The amount of new information and self-entropy for LQTS1 patients is smaller than that for healthy individuals. However, information transfers from RR to QT and from DI to QT are larger in the case of LQTS1 patients.

Quantifying the Predictability of Visual Scanpaths Using Active Information Storage

Entropy-based measures are an important tool for studying human gaze behavior under various conditions. In particular, gaze transition entropy (GTE) is a popular method to quantify the predictability of a visual scanpath as the entropy of transitions between fixations and has been shown to correlate with changes in task demand or changes in observer state. Measuring scanpath predictability is thus a promising approach to identifying viewers' cognitive states in behavioral experiments or gaze-based applications. However, GTE does not account for temporal dependencies beyond two consecutive fixations and may thus underestimate the actual predictability of the current fixation given past gaze behavior. Instead, we propose to quantify scanpath predictability by estimating the active information storage (AIS), which can account for dependencies spanning multiple fixations. AIS is calculated as the mutual information between a processes' multivariate past state and its next value. It is thus able to measure how much information a sequence of past fixations provides about the next fixation, hence covering a longer temporal horizon. Applying the proposed approach, we were able to distinguish between induced observer states based on estimated AIS, providing first evidence that AIS may be used in the inference of user states to improve human-machine interaction.

Time, frequency and information domain analysis of short-term heart rate variability before and after focal and generalized seizures in epileptic children

OBJECTIVE

In this work we explore the potential of combining standard time and frequency domain indexes with novel information measures, to characterize pre- and post-ictal heart rate variability (HRV) in epileptic children, with the aim of differentiating focal and generalized epilepsy regarding the autonomic control mechanisms.

APPROACH

We analyze short-term HRV in 37 children suffering from generalized or focal epilepsy, monitored 10 s, 300 s, 600 s and 1800 s both before and after seizure episodes. Nine indexes are computed in time (mean, standard deviation of normal-to-normal intervals, root mean square of the successive differences (RMSSD)), frequency (low-to-high frequency power ratio LF/HF, normalized LF and HF power) and information (entropy, conditional entropy and self-entropy) domains. Focal and generalized epilepsy are compared through statistical analysis of the indexes and using linear discriminant analysis (LDA).

MAIN RESULTS

In children with focal epilepsy, early post-ictal phase is characterized by significant tachycardia, depressed HRV, increased LF power and LF/HF, and decreased complexity, progressively recovered across time windows after the episodes. Children with generalized seizures instead show significant tachycardia, lower RMSSD, higher LF power and LF/HF ratio before the seizure. These different behaviors are exploited by LDA analysis to separate focal and generalized epilepsy up to an accuracy of 75%. Results suggest a shift of the sympatho-vagal balance towards sympathetic dominance and vagal withdrawal, noticeable just after the termination of seizure episodes and then reverted in focal epilepsy, and persistent during inter-ictal and pre-ictal periods in generalized epilepsy.

SIGNIFICANCE

Our analysis helps in elucidating the pathophysiology of inter-ictal HRV autonomic control and the differential diagnosis of generalized and focal epilepsy. These findings may have clinical relevance since altered sympatho-vagal control can be related to a higher danger of morbidity and mortality, may reduce thresholds for life-threatening arrhythmias, and could be a biomarker of risk for sudden unexpected death in epilepsy.

Causality analysis reveals the link between cerebrovascular control and acute kidney dysfunction after coronary artery bypass grafting

BACKGROUND

Patients undergoing coronary artery bypass graft (CABG) surgery might experience postoperative complications and some of them, such as acute kidney dysfunction (AKD), are the likely consequence of hypoperfusion. We hypothesized that an impaired cerebrovascular control is a hallmark of a vascular damage that might favor AKD after CABG.

OBJECTIVE

Our aim is to characterize cerebrovascular control in CABG patients through the assessment of the relationship between mean arterial pressure (MAP) and mean cerebral blood flow velocity (MCBFV) and to check whether markers describing MCBFV-MAP dynamical interactions could identify subjects at risk to develop postoperative AKD.

APPROACH

MAP and MCBFV beat-to-beat series were extracted from invasive arterial pressure and transcranial Doppler recordings acquired simultaneously in 23 patients just before CABG after the induction of propofol general anesthesia. Subjects were divided into AKD group (n  =  9, age: 68  ±  9, 8 males) and noAKD group (n  =  14, age: 65  ±  8, 12 males) according to whether they developed postoperative AKD or not after CABG. We computed MAP and MCBFV time-domain and spectral markers as well as MCBFV-MAP cross-spectral indexes in very-low-frequency (VLF, 0.02-0.07 Hz), low-frequency (LF, 0.07-0.15 Hz) and high-frequency (HF, 0.15-0.30 Hz) bands. We also calculated model-based transfer entropy (TE) to quantify the degree of MCBFV dependence on MAP and vice versa. The null hypothesis of MCBFV-MAP uncoupling was tested via a surrogate approach associating MAP and MCBFV in different patients.

MAIN RESULTS

Time, spectral and cross-spectral markers had a limited power in separating AKD from noAKD individuals. Conversely, TE from MAP to MCBFV was significantly above the level set by surrogates only in AKD groups and significantly larger than that computed in noAKD.

SIGNIFICANCE

The reduced cerebrovascular autoregulation in AKD patients suggest a vascular impairment likely making them more at risk of hypoperfusion during CABG and AKD after CABG.

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.

Multiscale information storage of linear long-range correlated stochastic processes

Information storage, reflecting the capability of a dynamical system to keep predictable information during its evolution over time, is a key element of intrinsic distributed computation, useful for the description of the dynamical complexity of several physical and biological processes. Here we introduce a parametric approach which allows one to compute information storage across multiple timescales in stochastic processes displaying both short-term dynamics and long-range correlations (LRC). Our analysis is performed in the popular framework of multiscale entropy, whereby a time series is first "coarse grained" at the chosen timescale through low-pass filtering and downsampling, and then its complexity is evaluated in terms of conditional entropy. Within this framework, our approach makes use of linear fractionally integrated autoregressive (ARFI) models to derive analytical expressions for the information storage computed at multiple timescales. Specifically, we exploit state space models to provide the representation of lowpass filtered and downsampled ARFI processes, from which information storage is computed at any given timescale relating the process variance to the prediction error variance. This enhances the practical usability of multiscale information storage, as it enables a computationally reliable quantification of a complexity measure which incorporates the effects of LRC together with that of short-term dynamics. The proposed measure is first assessed in simulated ARFI processes reproducing different types of autoregressive dynamics and different degrees of LRC, studying both the theoretical values and the finite sample performance. We find that LRC alter substantially the complexity of ARFI processes even at short timescales, and that reliable estimation of complexity can be achieved at longer timescales only when LRC are properly modeled. Then, we assess multiscale information storage in physiological time series measured in humans during resting state and postural stress, revealing unprecedented responses to stress of the complexity of heart period and systolic arterial pressure variability, which are related to the different role played by LRC in the two conditions.

Comparison of short-term heart rate variability indexes evaluated through electrocardiographic and continuous blood pressure monitoring

Heart rate variability (HRV) analysis represents an important tool for the characterization of complex cardiovascular control. HRV indexes are usually calculated from electrocardiographic (ECG) recordings after measuring the time duration between consecutive R peaks, and this is considered the gold standard. An alternative method consists of assessing the pulse rate variability (PRV) from signals acquired through photoplethysmography, a technique also employed for the continuous noninvasive monitoring of blood pressure. In this work, we carry out a thorough analysis and comparison of short-term variability indexes computed from HRV time series obtained from the ECG and from PRV time series obtained from continuous blood pressure (CBP) signals, in order to evaluate the reliability of using CBP-based recordings in place of standard ECG tracks. The analysis has been carried out on short time series (300 beats) of HRV and PRV in 76 subjects studied in different conditions: resting in the supine position, postural stress during 45° head-up tilt, and mental stress during computation of arithmetic test. Nine different indexes have been taken into account, computed in the time domain (mean, variance, root mean square of the successive differences), frequency domain (low-to-high frequency power ratio LF/HF, HF spectral power, and central frequency), and information domain (entropy, conditional entropy, self entropy). Thorough validation has been performed using comparison of the HRV and PRV distributions, robust linear regression, and Bland-Altman plots. Results demonstrate the feasibility of extracting HRV indexes from CBP-based data, showing an overall relatively good agreement of time-, frequency-, and information-domain measures. The agreement decreased during postural and mental arithmetic stress, especially with regard to band-power ratio, conditional, and self-entropy. This finding suggests to use caution in adopting PRV as a surrogate of HRV during stress conditions.

Entropy Measures in Analysis of Head up Tilt Test Outcome for Diagnosing Vasovagal Syncope

The paper presents possible applications of entropy measures in analysis of biosignals recorded during head up tilt testing (HUTT) in patients with suspected vasovagal syndrome. The study group comprised 80 patients who developed syncope during HUTT (57 in the passive phase of the test (HUTT(+) group) and 23 who had negative result of passive phase and developed syncope after provocation with nitroglycerine (HUTT(−) group)). The paper focuses on assessment of monitored signals’ complexity (heart rate expressed as R-R intervals (RRI), blood pressure (sBP, dBP) and stroke volume (SV)) using various types of entropy measures (Sample Entropy (SE), Fuzzy Entropy (FE), Shannon Entropy (Sh), Conditional Entropy (CE), Permutation Entropy (PE)). Assessment of the complexity of signals in supine position indicated presence of significant differences between HUTT(+) versus HUTT(−) patients only for Conditional Entropy (CE(RRI)). Values of CE(RRI) higher than 0.7 indicate likelihood of a positive result of HUTT already at the passive phase. During tilting, in the pre-syncope phase, significant differences were found for: (SE(sBP), SE(dBP), FE(RRI), FE(sBP), FE(dBP), FE(SV), Sh(sBP), Sh(SV), CE(sBP), CE(dBP)). HUTT(+) patients demonstrated significant changes in signals’ complexity more frequently than HUTT(−) patients. When comparing entropy measurements done in the supine position with those during tilting, SV assessed in HUTT(+) patients was the only parameter for which all tested measures of entropy (SE(SV), FE(SV), Sh(SV), CE(SV), PE(SV)) showed significant differences.

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.

Cardiovascular and respiratory variability during orthostatic and mental stress: A comparison of entropy estimators

The aim of this study is to characterize cardiovascular and respiratory signals during orthostatic and mental stress as reflected in indices of entropy and complexity, providing a comparison between the performance of different estimators. To this end, the heart rate variability, systolic blood pressure, diastolic blood pressure and respiration time series were extracted from the recordings of 61 healthy volunteers undergoing a protocol consisting of supine rest, head-up tilt test and mental arithmetic task. The analysis was performed in the information domain using measures of entropy and conditional entropy, estimated through model-based (linear) and model-free (binning, nearest neighbor) approaches. Our results show that different types of stress elicited different responses in the employed indices. On one hand, entropy mainly reflected known changes in the variance of physiological time series. On the other hand, the information conveyed by conditional entropy allowed to characterize the complexity of the four time series during the two stress tasks: we found that cardiac and vascular dynamics underwent a reduction in complexity as a consequence of postural stress, while vascular and respiratory complexity increased as a result of mental stress. As for the performance of different estimators, we did not find substantial differences between model-based and model-free approaches, possibly indicating that significant non-linear dynamics did not appear in the studied conditions.

Is the Cushing mechanism a dynamic blood pressure-stabilizing system? Insights from Granger causality analysis of spontaneous blood pressure and cerebral blood flow

Blood pressure (BP) regulation is widely recognized as being integral to the control of end-organ perfusion, but it remains unclear whether end-organ perfusion also plays a role in driving changes in BP. A randomized and placebo-controlled study design was followed to examine feedback relationships between very-low-frequency fluctuations in BP and cerebral blood flow (CBF) in humans under placebo treatment and α₁-adrenergic blockade. To determine the causal relations among hemodynamic variables, BP, middle cerebral artery blood velocity (MCAv), and end-tidal CO ₂ time-series were decimated, low-pass filtered (<0.07 Hz), fitted to vector autoregressive models, and tested for Granger causality in the time domain. Results showed that 1) at baseline, changes in BP and MCAv often interact in a closed-loop; and 2) α₁-adrenergic blockade results in the dominant causal direction from BP to MCAv. These results suggest that, between subjects, cerebral pressure-flow interactions at time scales < 0.07 Hz are frequently bidirectional, and that in the presence of an intact autonomic nervous system BP may be regulated by reflex pathways sensitive to changes in CBF.

Symbolic dynamics of animal interaction

Since its introduction nearly two decades ago, transfer entropy has contributed to an improved understanding of cause-and-effect relationships in coupled dynamical systems from raw time series. In the context of animal behavior, transfer entropy might help explain the determinants of leadership in social groups and elucidate escape response to predator attacks. Despite its promise, the potential of transfer entropy in animal behavior is yet to be fully tested, and a number of technical challenges in information theory and statistics remain open. Here, we examine an alternative approach to the computation of transfer entropy based on symbolic dynamics. In this context, a symbol is associated with a specific locomotory bout across two or more consecutive time instants, such as reversing the swimming direction. Symbols encapsulate salient locomotory patterns and the associated permutation transfer entropy quantifies the ability to predict the patterns of an individual given those of another individual. We demonstrate this framework on an existing dataset on fish, for which we have knowledge of the underlying cause-and-effect relationship between the focal subject and the stimulus. Symbolic dynamics offers an intuitive and robust approach to study animal behavior, which could enable the inference of causal relationship from noisy experimental observations of limited duration.

Inter-individual Relationships between Sympathetic Arterial Baroreflex Function and Cerebral Perfusion Control in Healthy Males

Maintenance of adequate cerebral perfusion during normal physiological challenges requires integration between cerebral blood flow (CBF) and systemic blood pressure control mechanisms. Previous studies have shown that cardiac baroreflex sensitivity (BRS) is inversely related to some measures of cerebral autoregulation. However, interactions between the sympathetic arterial baroreflex and cerebral perfusion control mechanisms have not been explored. To determine the nature and magnitude of these interactions we measured R–R interval, blood pressure, CBF velocity, and muscle sympathetic nerve activity (MSNA) in 11 healthy young males. Sympathetic BRS was estimated using modified Oxford method as the relationship between beat-to-beat diastolic blood pressure (DBP) and MSNA. Integrated control of CBF was quantified using transfer function analysis (TFA) metrics derived during rest and Tieck's autoregulatory index following bilateral thigh cuff deflation. Sympathetic BRS during modified Oxford trials was significantly related to autoregulatory index (r = 0.64, p = 0.03). Sympathetic BRS during spontaneous baseline was significantly related to transfer function gain (r = −0.74, p = 0.01). A more negative value for sympathetic BRS indicates more effective arterial baroreflex regulation, and a lower transfer function gain reflects greater cerebral autoregulation. Therefore, these findings indicate that males with attenuated CBF regulation have greater sympathetic BRS (and vice versa), consistent with compensatory interactions between blood pressure and cerebral perfusion control mechanisms.

Assessing the strength of cardiac and sympathetic baroreflex controls via transfer entropy during orthostatic challenge

The study assesses the strength of the causal relation along baroreflex (BR) in humans during an incremental postural challenge soliciting the BR. Both cardiac BR (cBR) and sympathetic BR (sBR) were characterized via BR sequence approaches from spontaneous fluctuations of heart period (HP), systolic arterial pressure (SAP), diastolic arterial pressure (DAP) and muscle sympathetic nerve activity (MSNA). A model-based transfer entropy method was applied to quantify the strength of the coupling from SAP to HP and from DAP to MSNA. The confounding influences of respiration were accounted for. Twelve young healthy subjects (20-36 years, nine females) were sequentially tilted at 0°, 20°, 30° and 40°. We found that (i) the strength of the causal relation along the cBR increases with tilt table inclination, while that along the sBR is unrelated to it; (ii) the strength of the causal coupling is unrelated to the gain of the relation; (iii) transfer entropy indexes are significantly and positively associated with simplified causality indexes derived from BR sequence analysis. The study proves that causality indexes are complementary to traditional characterization of the BR and suggests that simple markers derived from BR sequence analysis might be fruitfully exploited to estimate causality along the BR.This article is part of the themed issue 'Mathematical methods in medicine: neuroscience, cardiology and pathology'.

Entropy measures, entropy estimators, and their performance in quantifying complex dynamics: Effects of artifacts, nonstationarity, and long-range correlations

Entropy measures are widely applied to quantify the complexity of dynamical systems in diverse fields. However, the practical application of entropy methods is challenging, due to the variety of entropy measures and estimators and the complexity of real-world time series, including nonstationarities and long-range correlations (LRC). We conduct a systematic study on the performance, bias, and limitations of three basic measures (entropy, conditional entropy, information storage) and three traditionally used estimators (linear, kernel, nearest neighbor). We investigate the dependence of entropy measures on estimator- and process-specific parameters, and we show the effects of three types of nonstationarities due to artifacts (trends, spikes, local variance change) in simulations of stochastic autoregressive processes. We also analyze the impact of LRC on the theoretical and estimated values of entropy measures. Finally, we apply entropy methods on heart rate variability data from subjects in different physiological states and clinical conditions. We find that entropy measures can only differentiate changes of specific types in cardiac dynamics and that appropriate preprocessing is vital for correct estimation and interpretation. Demonstrating the limitations of entropy methods and shedding light on how to mitigate bias and provide correct interpretations of results, this work can serve as a comprehensive reference for the application of entropy methods and the evaluation of existing studies.

Assessing the evolution of redundancy/synergy of spontaneous variability regulation with age

OBJECTIVE

We exploited a model-based Wiener-Granger causality method in the information domain for the evaluation of the transfer entropy (TE) and interaction TE (ITE), the latter taken as a measure of the net balance between redundancy and synergy, to describe the interactions between the spontaneous variability of heart period (HP) and systolic arterial pressure (SAP) and the effect of respiration (R) on both variables.

APPROACH

Cardiac control was typified via the genuine TE from SAP to HP, that from R to HP, and the ITE from SAP and R to HP, while vascular control was characterized via the genuine TE from HP to SAP, that from R to SAP, and the ITE from HP and R to SAP. The approach was applied to study age-related modifications of cardiac and vascular controls in a cohort of 100 healthy humans (age from 21 to 70 years, 54 males) recorded at supine rest (REST) and during active standing (STAND). A surrogate approach was exploited to test the significance of the computed quantities.

MAIN RESULTS

Trends of the genuine information transfer with age, already present in literature, were here confirmed. We originally found that: (i) at REST redundancy was predominant over synergy in both vascular and cardiac controls; (ii) the predominance of redundancy of the cardiac control was not affected by postural challenge, while STAND reduced redundancy of vascular control; (iii) the net redundancy of the cardiac control at REST gradually decreased with age, while that of vascular control remained stable; (iv) during STAND net redundancy of both cardiac and vascular controls was stable with age.

SIGNIFICANCE

The study confirms the relevance of computing genuine information transfer in cardiovascular control analysis and stresses the importance of evaluating the ITE to quantify the degree of redundancy of physiological mechanisms operating to maintain cardiovascular homeostasis.

Are Nonlinear Model-Free Conditional Entropy Approaches for the Assessment of Cardiac Control Complexity Superior to the Linear Model-Based One?

OBJECTIVE

We test the hypothesis that the linear model-based (MB) approach for the estimation of conditional entropy (CE) can be utilized to assess the complexity of the cardiac control in healthy individuals.

METHODS

An MB estimate of CE was tested in an experimental protocol (i.e., the graded head-up tilt) known to produce a gradual decrease of cardiac control complexity as a result of the progressive vagal withdrawal and concomitant sympathetic activation. The MB approach was compared with traditionally exploited nonlinear model-free (MF) techniques such as corrected approximate entropy, sample entropy, corrected CE, two k -nearest-neighbor CE procedures and permutation CE. Electrocardiogram was recorded in 17 healthy subjects at rest in supine position and during head-up tilt with table angles of 15°, 30°, 45°, 60°, and 75°. Heart period (HP) was derived as the temporal distance between two consecutive R-wave peaks and analysis was carried out over stationary sequences of 256 successive HPs.

RESULTS

The performance of the MB method in following the progressive decrease of HP complexity with tilt table angles was in line with those of MF approaches and the MB index was remarkably correlated with the MF ones.

CONCLUSION

The MB approach can be utilized to monitor the changes of the complexity of the cardiac control, thus speeding up dramatically the CE calculation.

SIGNIFICANCE

The remarkable performance of the MB approach challenges the notion, generally assumed in cardiac control complexity analysis based on CE, about the need of MF techniques and could allow real-time applications.

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.

Predictability decomposition detects the impairment of brain-heart dynamical networks during sleep disorders and their recovery with treatment

This work introduces a framework to study the network formed by the autonomic component of heart rate variability (cardiac processη) and the amplitude of the different electroencephalographic waves (brain processes δ, θ, α, σ, β) during sleep. The framework exploits multivariate linear models to decompose the predictability of any given target process into measures of self-, causal and interaction predictability reflecting respectively the information retained in the process and related to its physiological complexity, the information transferred from the other source processes, and the information modified during the transfer according to redundant or synergistic interaction between the sources. The framework is here applied to theη,δ,θ,α,σ,βtime series measured from the sleep recordings of eight severe sleep apnoea-hypopnoea syndrome (SAHS) patients studied before and after long-term treatment with continuous positive airway pressure (CPAP) therapy, and 14 healthy controls. Results show that the full and self-predictability of η, δ and θ decreased significantly in SAHS compared with controls, and were restored with CPAP forδandθbut not forη The causal predictability of η and δ occurred through significantly redundant source interaction during healthy sleep, which was lost in SAHS and recovered after CPAP. These results indicate that predictability analysis is a viable tool to assess the modifications of complexity and causality of the cerebral and cardiac processes induced by sleep disorders, and to monitor the restoration of the neuroautonomic control of these processes during long-term treatment.

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.

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.

Local active information storage as a tool to understand distributed neural information processing

Every act of information processing can in principle be decomposed into the component operations of information storage, transfer, and modification. Yet, while this is easily done for today's digital computers, the application of these concepts to neural information processing was hampered by the lack of proper mathematical definitions of these operations on information. Recently, definitions were given for the dynamics of these information processing operations on a local scale in space and time in a distributed system, and the specific concept of local active information storage was successfully applied to the analysis and optimization of artificial neural systems. However, no attempt to measure the space-time dynamics of local active information storage in neural data has been made to date. Here we measure local active information storage on a local scale in time and space in voltage sensitive dye imaging data from area 18 of the cat. We show that storage reflects neural properties such as stimulus preferences and surprise upon unexpected stimulus change, and in area 18 reflects the abstract concept of an ongoing stimulus despite the locally random nature of this stimulus. We suggest that LAIS will be a useful quantity to test theories of cortical function, such as predictive coding.