Detection of Blood CO2 Influences on Cerebral Hemodynamics Using Transfer Entropy

Cerebral hemodynamics describes an important physiological system affected by components such as blood pressure, CO2 levels, and endothelial factors. Recently, novel techniques have emerged to analyse cerebral hemodynamics based on the calculation of entropies, which quantifies or describes changes in the complexity of this system when it is affected by a pathological or physiological influence. One recently described measure is transfer entropy, which allows for the determination of causality between the various components of a system in terms of their flow of information, and has shown positive results in the multivariate analysis of physiological signals. This study aims to determine whether conditional transfer entropy reflects the causality in terms of entropy generated by hypocapnia on cerebral hemodynamics. To achieve this, non-invasive signals from 28 healthy individuals who undertook a hyperventilation maneuver were analyzed using conditional transfer entropy to assess the variation in the relevance of CO2 levels on cerebral blood velocity. By employing a specific method to discretize the signals, it was possible to differentiate the influence of CO2 levels during the hyperventilation phase (22.0% and 20.3% increase for the left and right hemispheres, respectively) compared to normal breathing, which remained higher during the recovery phase (15.3% and 15.2% increase, respectively).

Statistical Approaches to Identify Pairwise and High-Order Brain Functional Connectivity Signatures on a Single-Subject Basis

Keeping up with the shift towards personalized neuroscience essentially requires the derivation of meaningful insights from individual brain signal recordings by analyzing the descriptive indexes of physio-pathological states through statistical methods that prioritize subject-specific differences under varying experimental conditions. Within this framework, the current study presents a methodology for assessing the value of the single-subject fingerprints of brain functional connectivity, assessed both by standard pairwise and novel high-order measures. Functional connectivity networks, which investigate the inter-relationships between pairs of brain regions, have long been a valuable tool for modeling the brain as a complex system. However, their usefulness is limited by their inability to detect high-order dependencies beyond pairwise correlations. In this study, by leveraging multivariate information theory, we confirm recent evidence suggesting that the brain contains a plethora of high-order, synergistic subsystems that would go unnoticed using a pairwise graph structure. The significance and variations across different conditions of functional pairwise and high-order interactions (HOIs) between groups of brain signals are statistically verified on an individual level through the utilization of surrogate and bootstrap data analyses. The approach is illustrated on the single-subject recordings of resting-state functional magnetic resonance imaging (rest-fMRI) signals acquired using a pediatric patient with hepatic encephalopathy associated with a portosystemic shunt and undergoing liver vascular shunt correction. Our results show that (i) the proposed single-subject analysis may have remarkable clinical relevance for subject-specific investigations and treatment planning, and (ii) the possibility of investigating brain connectivity and its post-treatment functional developments at a high-order level may be essential to fully capture the complexity and modalities of the recovery.

On the Validity of Single Regression Strategy for Granger Causality Assessment in Cardiovascular and Cardiorespiratory Control Studies

Granger causality (GC) analysis is based on the comparison between prediction error variances computed over the full and restricted models after identifying the coefficients of appropriate vector regressions. GC markers can be computed via a double regression (DR) approach identifying two separate, independent models and a single regression (SR) strategy optimizing the description of the dynamics of the target over the full model and, then, reusing some parts of it in the restricted model. The present study compares the SR and DR strategies over heart period (HP), systolic arterial pressure (SAP) and respiration (R) beat-to-beat series collected during a graded orthostatic challenge induced by head-up tilt in 17 healthy individuals (age: 21-36 yrs; median: 29 yrs; 9 females and 8 males). We found that the DR approach was more powerful than the SR one in detecting the expected stronger involvement of the baroreflex during the challenge, while the expected weaker cardiorespiratory coupling was identified by both SR and DR strategies. The less powerful ability of the SR approach was the result of the greater variance of GC markers compared to the DR strategy. We conclude that, contrary to the suggestions present in literature, the SR approach is not necessarily associated with a smaller dispersion of GC markers. Moreover, we suggest that additional factors, such as the strategy utilized to build embedding spaces and metric utilized to compare prediction error variances, might play an important role in differentiating SR and DR approaches.

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.

Information decomposition in the frequency domain: a new framework to study cardiovascular and cardiorespiratory oscillations

While cross-spectral and information-theoretic approaches are widely used for the multivariate analysis of physiological time series, their combined utilization is far less developed in the literature. This study introduces a framework for the spectral decomposition of multivariate information measures, which provides frequency-specific quantifications of the information shared between a target and two source time series and of its expansion into amounts related to how the sources contribute to the target dynamics with unique, redundant and synergistic information. The framework is illustrated in simulations of linearly interacting stochastic processes, showing how it allows us to retrieve amounts of information shared by the processes within specific frequency bands which are otherwise not detectable by time-domain information measures, as well as coupling features which are not detectable by spectral measures. Then, it is applied to the time series of heart period, systolic and diastolic arterial pressure and respiration variability measured in healthy subjects monitored in the resting supine position and during head-up tilt. We show that the spectral measures of unique, redundant and synergistic information shared by these variability series, integrated within specific frequency bands of physiological interest and reflect the mechanisms of short-term regulation of cardiovascular and cardiorespiratory oscillations and their alterations induced by the postural stress. This article is part of the theme issue 'Advanced computation in cardiovascular physiology: new challenges and opportunities'.

Assessing Synergy/Redundancy of Baroreflex and Non-Baroreflex Components of the Cardiac Control during Sleep

Cardiovascular regulation and autonomic function change across sleep stages and compared to wake. Little information is present in literature about cardiac control during sleep especially in relation to new information-theoretic quantities such as synergy and redundancy. In the present work we compute synergy and redundancy of baroreflex and non-baroreflex components of the cardiac control according to two information-theoretic approaches, namely predictive information decomposition (PID) and minimal mutual information (MMI) methods. We applied a bivariate approach to heart period (HP) and systolic arterial pressure (SAP) beat-to-beat variability series during sleep in a healthy subject. PID approach computes the net balance between synergy and redundancy, while MMI calculates the two quantities as separate entities. Results suggested that: i) redundancy was dominant over synergy during NREM phases; ii) redundancy increased during NREM phase; iii) synergy did not change across the sleep stages. We interpret this result as a consequence of the vagal enhancement, slowing and deepening of respiration during NREM phases. These preliminary findings support the potential of assessing redundancy/synergy of baroreflex-related and unrelated regulations during sleep to improve our knowledge about physiological mechanisms.

Multiscale Information Decomposition Dissects Control Mechanisms of Heart Rate Variability at Rest and During Physiological Stress

Heart rate variability (HRV; variability of the RR interval of the electrocardiogram) results from the activity of several coexisting control mechanisms, which involve the influence of respiration (RESP) and systolic blood pressure (SBP) oscillations operating across multiple temporal scales and changing in different physiological states. In this study, multiscale information decomposition is used to dissect the physiological mechanisms related to the genesis of HRV in 78 young volunteers monitored at rest and during postural and mental stress evoked by head-up tilt (HUT) and mental arithmetics (MA). After representing RR, RESP and SBP at different time scales through a recently proposed method based on multivariate state space models, the joint information transfer TRESP,SBP→RR is decomposed into unique, redundant and synergistic components, describing the strength of baroreflex modulation independent of respiration (USBP→RR), nonbaroreflex (URESP→RR) and baroreflex-mediated (RRESP,SBP→RR) respiratory influences, and simultaneous presence of baroreflex and nonbaroreflex respiratory influences (SRESP,SBP→RR), respectively. We find that fast (short time scale) HRV oscillations—respiratory sinus arrhythmia—originate from the coexistence of baroreflex and nonbaroreflex (central) mechanisms at rest, with a stronger baroreflex involvement during HUT. Focusing on slower HRV oscillations, the baroreflex origin is dominant and MA leads to its higher involvement. Respiration influences independent on baroreflex are present at long time scales, and are enhanced during HUT.

Paced Breathing Increases the Redundancy of Cardiorespiratory Control in Healthy Individuals and Chronic Heart Failure Patients

Synergy and redundancy are concepts that suggest, respectively, adaptability and fault tolerance of systems with complex behavior. This study computes redundancy/synergy in bivariate systems formed by a target X and a driver Y according to the predictive information decomposition approach and partial information decomposition framework based on the minimal mutual information principle. The two approaches assess the redundancy/synergy of past of X and Y in reducing the uncertainty of the current state of X. The methods were applied to evaluate the interactions between heart and respiration in healthy young subjects (n = 19) during controlled breathing at 10, 15 and 20 breaths/minute and in two groups of chronic heart failure patients during paced respiration at 6 (n = 9) and 15 (n = 20) breaths/minutes from spontaneous beat-to-beat fluctuations of heart period and respiratory signal. Both methods suggested that slowing respiratory rate below the spontaneous frequency increases redundancy of cardiorespiratory control in both healthy and pathological groups, thus possibly improving fault tolerance of the cardiorespiratory control. The two methods provide markers complementary to respiratory sinus arrhythmia and the strength of the linear coupling between heart period variability and respiration in describing the physiology of the cardiorespiratory reflex suitable to be exploited in various pathophysiological settings.

The complexity-entropy causality plane based on multiscale power spectrum entropy of financial time series

The complexity of financial time series is an important issue for nonlinear dynamic systems. We propose multiscale power spectral entropy. Based on this method, this paper uses the complex entropy causal plane ( C p s e ) to evaluate the complexity of the stock market. Multiscale power spectral entropy takes full advantage of the interrelationships between data in state space and estimates system complexity from different temporal resolutions. Then, we use a complex causal entropy plane to track changes in stock signals. The simulation data are used to test the performance of this method. Finally, we compare the C p s e method with the traditional power spectral entropy method. The results show that the C p s e method is more sensitive to changes in the stock market and can fully extract the intrinsic dynamics of the stock sequence.

Towards understanding the complexity of cardiovascular oscillations: Insights from information theory

Cardiovascular complexity is a feature of healthy physiological regulation, which stems from the simultaneous activity of several cardiovascular reflexes and other non-reflex physiological mechanisms. It is manifested in the rich dynamics characterizing the spontaneous heart rate and blood pressure variability (HRV and BPV). The present study faces the challenge of disclosing the origin of short-term HRV and BPV from the statistical perspective offered by information theory. To dissect the physiological mechanisms giving rise to cardiovascular complexity in different conditions, measures of predictive information, information storage, information transfer and information modification were applied to the beat-to-beat variability of heart period (HP), systolic arterial pressure (SAP) and respiratory volume signal recorded non-invasively in 61 healthy young subjects at supine rest and during head-up tilt (HUT) and mental arithmetics (MA). Information decomposition enabled to assess simultaneously several expected and newly inferred physiological phenomena, including: (i) the decreased complexity of HP during HUT and the increased complexity of SAP during MA; (ii) the suppressed cardiorespiratory information transfer, related to weakened respiratory sinus arrhythmia, under both challenges; (iii) the altered balance of the information transferred along the two arms of the cardiovascular loop during HUT, with larger baroreflex involvement and smaller feedforward mechanical effects; and (iv) an increased importance of direct respiratory effects on SAP during HUT, and on both HP and SAP during MA. We demonstrate that a decomposition of the information contained in cardiovascular oscillations can reveal subtle changes in system dynamics and improve our understanding of the complexity changes during physiological challenges.