On the nature of heart rate variability in a breathing normal subject: A stochastic process analysis

Abstract

Human heart rate is moderated by the autonomous nervous system acting predominantly through the sinus node (the main cardiac physiological pacemaker). One of the dominant factors that determine the heart rate in physiological conditions is its coupling with the respiratory rhythm. Using the language of stochastic processes, we analyzed both rhythms simultaneously taking the data from polysomnographic recordings of two healthy individuals. Each rhythm was treated as a sum of a deterministic drift term and a diffusion term (Kramers-Moyal expansion). We found that normal heart rate variability may be considered as the result of a bidirectional coupling of two nonlinear oscillators: the heart itself and the respiratory system. On average, the diffusion (noise) component measured is comparable in magnitude to the oscillatory (deterministic) term for both signals investigated. The application of the Kramers-Moyal expansion may be useful for medical diagnostics providing information on the relation between respiration and heart rate variability. This interaction is mediated by the autonomous nervous system, including the baroreflex, and results in a commonly observed phenomenon--respiratory sinus arrhythmia which is typical for normal subjects and often impaired by pathology.

Introduction to Controversial Topics in Nonlinear Science: Is the Normal Heart Rate Chaotic?

“…43 Wessel et al 46 used regression methods to investigate this coupling and concluded that most of the variability of the heart rhythm is directly caused by fluctuations of the respiratory rhythm. Buchner et al 8 investigated the bidirectional coupling between respiration and heart rate control using stochastic methods. Finally, studies of the scaling properties suggest that the multiple feedback loops operating over different time scales would lead to the observed scaling properties.…”

Cardiorespiratory coupling in health and disease

“…One of them is based on the calculation of Kramers-Moyal coefficients such that the functional shape of them provides information about interactions between respiratory and heart beat oscillators (Buchner et al, 2009). This analysis is based on the assumption that HR can be considered as a stochastic process with Gaussian noise.…”

“…This analysis is based on the assumption that HR can be considered as a stochastic process with Gaussian noise. Thus, HRV can be described by the Langevin equation X′(t)=D1(X,t)+sqrt(2D2(X,t))Γ(t), where X(t) is time-series data, Γ(t) is Gaussian noise with zero mean value, D1(X,t) and D2(X,t) are first and second order coefficients of Kramers-Moyal expansion (Buchner et al, 2009; Petelczyc et al, 2009). By extracting from the data first D1(X,t) and second D2(X,t) terms, and neglecting the higher order term due to its small value, the HRV can be reconstructed through the Langevin equation (Tabar et al, 2006).…”

“…By using a similar approach, Buchner et al in 2009 analyzed polysomnographic recordings and calculated Kramers-Moyal expansion terms from nighttime data series of respiration and heart beat oscillators. The authors predicted that coupling of two independent autonomous systems such as respiratory and heart oscillators may underlie the nature of the HRV (Petelczyc et al, 2009).…”

Characterization of local complex structures in a recurrence plot to improve nonlinear dynamic discriminant analysis

“…A study even demonstrated that the Brownian system, reflecting a random motion of small particles suspended in a fluid or gas, resulted in certain characteristic patchy patterns due to irregular disruption properties [4]. RP has also been applied in analysis of human heart rate variability (HRV), which are not only nonlinear [15,16], but also nonstationary [17,18] and noisy [19,20]. For example, studies demonstrated that certain square patch-type patterns were associated with the onset of ventricular tachycardia (VT) [21], and certain nonlinear patterns in RP were associated with the development of aging [22].…”