Quantifying the causal strength of multivariate cardiovascular couplings with momentary information transfer

Directional coupling detection through cross-distance vectors

Inferring the coupling direction from measured time series of complex systems is challenging. We propose a state-space-based causality measure obtained from cross-distance vectors for quantifying interaction strength. It is a model-free noise-robust approach that requires only a few parameters. The approach is applicable to bivariate time series and is resilient to artefacts and missing values. The result is two coupling indices that quantify coupling strength in each direction more accurately than the already established state-space measures. We test the proposed method on different dynamical systems and analyze numerical stability. As a result, a procedure for optimal parameter selection is proposed, circumventing the challenge of determining the optimal embedding parameters. We show it is robust to noise and reliable in shorter time series. Moreover, we show that it can detect cardiorespiratory interaction in measured data. A numerically efficient implementation is available at https://repo.ijs.si/e2pub/cd-vec.

Information flow in the rat thalamo-cortical system: spontaneous vs. stimulus-evoked activities

The interaction between the thalamus and sensory cortex plays critical roles in sensory processing. Previous studies have revealed pathway-specific synaptic properties of thalamo-cortical connections. However, few studies to date have investigated how each pathway routes moment-to-moment information. Here, we simultaneously recorded neural activity in the auditory thalamus (or ventral division of the medial geniculate body; MGv) and primary auditory cortex (A1) with a laminar resolution in anesthetized rats. Transfer entropy (TE) was used as an information theoretic measure to operationalize “information flow”. Our analyses confirmed that communication between the thalamus and cortex was strengthened during presentation of auditory stimuli. In the resting state, thalamo-cortical communications almost disappeared, whereas intracortical communications were strengthened. The predominant source of information was the MGv at the onset of stimulus presentation and layer 5 during spontaneous activity. In turn, MGv was the major recipient of information from layer 6. TE suggested that a small but significant population of MGv-to-A1 pairs was “information-bearing,” whereas A1-to-MGv pairs typically exhibiting small effects played modulatory roles. These results highlight the capability of TE analyses to unlock novel avenues for bridging the gap between well-established anatomical knowledge of canonical microcircuits and physiological correlates via the concept of dynamic information flow.

Physical fitness contributes to cardio-respiratory synchronization

Cardio-respiratory synchronization is a phenomenon of particular interest- especially at a 1:1 ratio- and may give greater insight into the underlying mechanisms of cardio-respiratory communication. Synchronization of this ratio is hypothesised to occur when breathing rate exceeds heart rate, which is the premise of this research. A novel experimental design focused on guiding elevated respiration to induce the entrainment of heart rate, and produce an equivalent rise in value. Application of instantaneous phase for identification and analysis of synchronization allowed for a reliable method of measuring the interaction between these stochastic processes. We have identified 1:1 phase synchronization in all volunteers measured. Longer synchronization episodes were observed reliably in athletic individuals, corroborating previous research for spontaneous breathing. This observation suggests that cardio-respiratory synchronization at all respiration rates is associated with a common underlying communication mechanism. Furthermore, it presents cardio-respiratory synchronization as a potential future measurement of fitness and autonomic health.

Detecting and quantifying causal associations in large nonlinear time series datasets

Identifying causal relationships and quantifying their strength from observational time series data are key problems in disciplines dealing with complex dynamical systems such as the Earth system or the human body. Data-driven causal inference in such systems is challenging since datasets are often high dimensional and nonlinear with limited sample sizes. Here, we introduce a novel method that flexibly combines linear or nonlinear conditional independence tests with a causal discovery algorithm to estimate causal networks from large-scale time series datasets. We validate the method on time series of well-understood physical mechanisms in the climate system and the human heart and using large-scale synthetic datasets mimicking the typical properties of real-world data. The experiments demonstrate that our method outperforms state-of-the-art techniques in detection power, which opens up entirely new possibilities to discover and quantify causal networks from time series across a range of research fields.

Control of heart rate through guided high-rate breathing

Understanding the complex dynamics of cardio-respiratory coupling sheds light on the underlying mechanisms governing the communication between these two physiological systems. Previous research has predominantly considered the coupling at respiratory rates slower than the heart rate and shown that respiratory oscillations lead to modulation and/or synchronization of the heart rate. Whereas the mechanisms of cardio-respiratory communication are still under discussion, peripheral nervous regulation is considered to be the predominant factor. This work offers a novel experimental design and applies the concept of instantaneous phase to detect cardio-respiratory entrainment at elevated respiration rates, close to the resting heart rate. If such 1:1 entrainment exists, it would suggest direct neuronal communication between the respiration and heart centres in the brain. We have observed 1:1 entrainment in all volunteers, with consistently longer synchronization episodes seen in physically fitter people, and demonstrated that cardio-respiratory synchronization at both low and high respiration rates is associated with a common underlying communication mechanism.

Introduction to Focus Issue: Causation inference and information flow in dynamical systems: Theory and applications

Questions of causation are foundational across science and often relate further to problems of control, policy decisions, and forecasts. In nonlinear dynamics and complex systems science, causation inference and information flow are closely related concepts, whereby "information" or knowledge of certain states can be thought of as coupling influence onto the future states of other processes in a complex system. While causation inference and information flow are by now classical topics, incorporating methods from statistics and time series analysis, information theory, dynamical systems, and statistical mechanics, to name a few, there remain important advancements in continuing to strengthen the theory, and pushing the context of applications, especially with the ever-increasing abundance of data collected across many fields and systems. This Focus Issue considers different aspects of these questions, both in terms of founding theory and several topical applications.

Basic cardiovascular variability signals: mutual directed interactions explored in the information domain

The study of short-term cardiovascular interactions is classically performed through the bivariate analysis of the interactions between the beat-to-beat variability of heart period (RR interval from the ECG) and systolic blood pressure (SBP). Recent progress in the development of multivariate time series analysis methods is making it possible to explore how directed interactions between two signals change in the context of networks including other coupled signals. Exploiting these advances, the present study aims at assessing directional cardiovascular interactions among the basic variability signals of RR, SBP and diastolic blood pressure (DBP), using an approach which allows direct comparison between bivariate and multivariate coupling measures. To this end, we compute information-theoretic measures of the strength and delay of causal interactions between RR, SBP and DBP using both bivariate and trivariate (conditioned) formulations in a group of healthy subjects in a resting state and during stress conditions induced by head-up tilt (HUT) and mental arithmetics (MA). We find that bivariate measures better quantify the overall (direct  +  indirect) information transferred between variables, while trivariate measures better reflect the existence and delay of directed interactions. The main physiological results are: (i) the detection during supine rest of strong interactions along the pathway RR  →  DBP  →  SBP, reflecting marked Windkessel and/or Frank-Starling effects; (ii) the finding of relatively weak baroreflex effects SBP  →  RR at rest; (iii) the invariance of cardiovascular interactions during MA, and the emergence of stronger and faster SBP  →  RR interactions, as well as of weaker RR  →  DBP interactions, during HUT. These findings support the importance of investigating cardiovascular interactions from a network perspective, and suggest the usefulness of directed information measures to assess physiological mechanisms and track their changes across different physiological states.

Modulations of Heart Rate, ECG, and Cardio-Respiratory Coupling Observed in Polysomnography

The cardiac component of cardio-respiratory polysomnography is covered by ECG and heart rate recordings. However, their evaluation is often underrepresented in summarizing reports. As complements to EEG, EOG, and EMG, these signals provide diagnostic information for autonomic nervous activity during sleep. This review presents major methodological developments in sleep research regarding heart rate, ECG, and cardio-respiratory couplings in a chronological (historical) sequence. It presents physiological and pathophysiological insights related to sleep medicine obtained by new technical developments. Recorded nocturnal ECG facilitates conventional heart rate variability (HRV) analysis, studies of cyclical variations of heart rate, and analysis of ECG waveform. In healthy adults, the autonomous nervous system is regulated in totally different ways during wakefulness, slow-wave sleep, and REM sleep. Analysis of beat-to-beat heart-rate variations with statistical methods enables us to estimate sleep stages based on the differences in autonomic nervous system regulation. Furthermore, up to some degree, it is possible to track transitions from wakefulness to sleep by analysis of heart-rate variations. ECG and heart rate analysis allow assessment of selected sleep disorders as well. Sleep disordered breathing can be detected reliably by studying cyclical variation of heart rate combined with respiration-modulated changes in ECG morphology (amplitude of R wave and T wave).

Quantifying information transfer and mediation along causal pathways in complex systems

Measures of information transfer have become a popular approach to analyze interactions in complex systems such as the Earth or the human brain from measured time series. Recent work has focused on causal definitions of information transfer aimed at decompositions of predictive information about a target variable, while excluding effects of common drivers and indirect influences. While common drivers clearly constitute a spurious causality, the aim of the present article is to develop measures quantifying different notions of the strength of information transfer along indirect causal paths, based on first reconstructing the multivariate causal network. Another class of novel measures quantifies to what extent different intermediate processes on causal paths contribute to an interaction mechanism to determine pathways of causal information transfer. The proposed framework complements predictive decomposition schemes by focusing more on the interaction mechanism between multiple processes. A rigorous mathematical framework allows for a clear information-theoretic interpretation that can also be related to the underlying dynamics as proven for certain classes of processes. Generally, however, estimates of information transfer remain hard to interpret for nonlinearly intertwined complex systems. But if experiments or mathematical models are not available, then measuring pathways of information transfer within the causal dependency structure allows at least for an abstraction of the dynamics. The measures are illustrated on a climatological example to disentangle pathways of atmospheric flow over Europe.