In vivo cardiac phase response curve elucidates human respiratory heart rate variability

Kralemann, Björn; Frühwirth, Matthias; Pikovsky, Arkady; Rosenblum, Michael G.; Kenner, Thomas; Schäefer, Jochen; Moser, M.

doi:10.1038/ncomms3418

Cited by 132 publications

(190 citation statements)

References 58 publications

(81 reference statements)

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“…Rather, this higher predictive information could be due to the progressive entrainment of the typical LF and HF oscillations of HPV resulting from the decrease of the breathing frequency, which is reflected by an increased information storage using the classical entropy decomposition based on SE and TE, and by an increased cross information using the alternative decomposition based on CE and cSE. Such an entrainment, which is supposed to enhance the oscillatory characteristics of HPV, might also contribute to strengthen the coupling of the cardiac and respiratory oscillators which has been clearly documented using phase dynamic models of cardiorespiratory interactions [7,8,51] and was confirmed also with continuously slowing the frequency of paced breathing [7,52]. According to these interpretations the same physiological phenomenon, i.e., the increased respiratory sinus arrhythmia observed during paced breathing at slow breathing rates, may be seen in terms of an increased coupling function from the respiratory to the cardiac oscillator using phase dynamics, and in terms of an enhanced information storage in the cardiac system induced by alterations of the respiratory driver using information dynamics.…”

Section: Resultsmentioning

confidence: 99%

Information Decomposition in Bivariate Systems: Theory and Application to Cardiorespiratory Dynamics

Faes

Porta

Nollo

2015

Entropy

115

155

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Abstract:In the framework of information dynamics, the temporal evolution of coupled systems can be studied by decomposing the predictive information about an assigned target system into amounts quantifying the information stored inside the system and the information transferred to it. While information storage and transfer are computed through the known self-entropy (SE) and transfer entropy (TE), an alternative decomposition evidences the so-called cross entropy (CE) and conditional SE (cSE), quantifying the cross information and internal information of the target system, respectively. This study presents a thorough evaluation of SE, TE, CE and cSE as quantities related to the causal statistical structure of coupled dynamic processes. First, we investigate the theoretical properties of these measures, providing the conditions for their existence and assessing the meaning of the information theoretic quantity that each of them reflects. Then, we present an approach for the exact computation of information dynamics based on the linear Gaussian approximation, and exploit this approach to characterize the behavior of SE, TE, CE and cSE in benchmark systems with known dynamics. Finally, we exploit these measures to study cardiorespiratory dynamics measured from healthy subjects during head-up tilt and paced breathing protocols. Our main result is that the combined evaluation of the measures of information dynamics allows to infer the causal effects associated with the observed OPEN ACCESSEntropy 2015, 17 278 dynamics and to interpret the alteration of these effects with changing experimental conditions.

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Section: Resultsmentioning

confidence: 99%

Information Decomposition in Bivariate Systems: Theory and Application to Cardiorespiratory Dynamics

Faes

Porta

Nollo

2015

Entropy

115

155

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“…There are a number of other methods for dynamical inference and coupling functions assessment, including those based on least squares and kernel smoothing fits [13,47], dynamical Bayesian inference [17], maximum likelihood (multiple-shooting) methods [15], stochastic modeling [48] and the phase resetting curve [49]. Below, the dynamical Bayesian inference [17] will be presented and applied.…”

Section: A Dynamical Bayesian Inferencementioning

confidence: 99%

“…Decomposition of a coupling function can also facilitate a description of the functional contributions from each separate subsystem within the coupling relationship. Different methods for coupling function detection have been applied widely in chemistry [10,11,[14][15][16], in cardiorespiratory physiology [12,13,17], in neuroscience [18][19][20], in mechanical interactions [21], in social sciences [22] and in secure communications [23]. The study of coupling function is a very active and expanding field of research [24].…”

Section: Introductionmentioning

confidence: 99%

“…For example, the reconstructed coupling function of BelousovZhabotinsky chemical interactions revealed how there could be higher-harmonics and bi-stability of the synchronization state [10], the knowledge of the coupling function of one pairwise interaction was used to predict the synchronization and clustering of a network of electrochemical oscillators [11], and the form of the cardiorespiratory coupling function was linked to respiratory sinus arrythmia (RSA), a known mechanism in physiology [12,13]. The coupling function as a whole can be described in terms of its strength and form.…”

Section: Introductionmentioning

confidence: 99%

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Time-varying coupling functions: Dynamical inference and cause of synchronization transitions

Stankovski

2017

Phys. Rev. E

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Interactions in nature can be described by their coupling strength, direction of coupling and coupling function. The coupling strength and directionality are relatively well understood and studied, at least for two interacting systems, however there can be a complexity in the interactions uniquely dependent on the coupling functions. Such a special case is studied here -synchronization transition occurs only due to the time-variability of the coupling functions, while the net coupling strength is constant throughout the observation time. To motivate the investigation, an example is used to present an analysis of cross-frequency coupling functions between delta and alpha brainwaves extracted from the electroencephalography (EEG) recording of a healthy human subject in a freerunning resting state. The results indicate that time-varying coupling functions are a reality for biological interactions. A model of phase oscillators is used to demonstrate and detect the synchronization transition caused by the varying coupling functions, during an invariant coupling strength. The ability to detect this phenomenon is discussed with the method of dynamical Bayesian inference, which was able to infer the time-varying coupling functions. The form of the coupling function acts as an additional dimension for the interactions and it should be taken into account when detecting biological or other interactions from data.

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“…Examples include arrays of lasers [15,90], electronic Josephson junctions [91,92], the Circadian rhythm [93,94], and the beating of the heart [95][96][97], amongst others.…”

Section: Introductionmentioning

confidence: 99%

Improving Reduced Variable Models for Complex Systems via Experiment

Blaha

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Populations of simple interacting oscillators can give rise to complex dynamics.Real-world examples of such systems abound in biology, chemistry, and physics.Reduced-variable models can describe these systems. The phase model is a particularly successful reduced-variable model which, in its simplest form, each element is represented by one variable, the phase of oscillation. The phase model can be constructed from observable variables, without specific knowledge of underlying phenomenological behavior. Such reduced variable models are easier to construct and more generalizable than models derived from underlying physics or chemistry.In this dissertation, we study the dynamics of a population of coupled electrochemical oscillators in order to modify the phase model to expand its applicability.Specifically, we develop a two-phase model, a phase and radius model, and models with network coupling.We analyze data from two coupled oscillators with a standard one-dimensional phase model and a newer two-dimensional phase model. The same quantity of data is needed for either model. The two-dimensional analysis reveals behaviors and coupling parameters in theoretical and experimental examples that the onedimensional analysis does not show. The two-dimensional model could be useful in systems that exhibit learning due to its ability to distinguish stimulation and reaction. We extend the Stuart-Landau model to describe clustering dynamics for higher harmonic oscillators. We present examples of asymmetrical clusters arising from networks of higher harmonic oscillators. We show that the amplitude of oscillation is functionally influenced by coupling; we believe this "amplitude coupling function" has not been previously described. This function can be constructed from the original time series with no additional measurements.Recently, combined phase and amplitude models have gained attention; we explore the conditions where a phase and amplitude model is useful. We show experimentally a change in cluster state due only to changes in coupling strength. Such a transition is not possible with a phase-only model. Simulations with the extended Stuart-Landau model match experimental results. We demonstrate a method for predicting the amplitude coupling function from the coupling. Prior to this study, the relationship between stimulation and response was not known for the amplitude. We suggest that the phase and amplitude model will be most useful (1) in modeling high-harmonic oscillations, and (2) where coupling exceeds the "weak coupling" approximation of the phase-only model. iv

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In vivo cardiac phase response curve elucidates human respiratory heart rate variability

Cited by 132 publications

References 58 publications

Information Decomposition in Bivariate Systems: Theory and Application to Cardiorespiratory Dynamics

Information Decomposition in Bivariate Systems: Theory and Application to Cardiorespiratory Dynamics

Time-varying coupling functions: Dynamical inference and cause of synchronization transitions

Improving Reduced Variable Models for Complex Systems via Experiment

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