A dedicated nonlinear oscillator model able to reproduce the pulse shape, refractory time, and phase sensitivity of the action potential of a natural pacemaker of the heart is developed. The phase space of the oscillator contains a stable node, a hyperbolic saddle, and an unstable focus. The model reproduces several phenomena well known in cardiology, such as certain properties of the sinus rhythm and heart block. In particular, the model reproduces the decrease of heart rate variability with an increase in sympathetic activity. A sinus pause occurs in the model due to a single, well-timed, external pulse just as it occurs in the heart, for example due to a single supraventricular ectopy. Several ways by which the oscillations cease in the system are obtained (models of the asystole). The model simulates properly the way vagal activity modulates the heart rate and reproduces the vagal paradox. Two such oscillators, coupled unidirectionally and asymmetrically, allow us to reproduce the properties of heart rate variability obtained from patients with different kinds of heart block including sino-atrial blocks of different degree and a complete AV block (third degree). Finally, we demonstrate the possibility of introducing into the model a spatial dimension that creates exciting possibilities of simulating in the future the SA the AV nodes and the atrium including their true anatomical structure.

The logistic map with a delayed feedback is studied as a generic model. The stability of the model and its bifurcation scheme is analyzed as a function of the feedback amplitude and of the delay. Stability analysis is performed semianalytically. A relation between the delay and the periodicity of the orbit, which explains why some terms used in chaos control are ineffective, was found. The consequences for chaos control are discussed. The structure of bifurcations is found to depend strongly on the parity and on the length of the delay. Boundary crisis, the tangent, the Neimark, as well as the period-doubling bifurcations occur in this system. The effective dimension of the model is also discussed.

Objective : To quantify the presence of cardiorespiratory interaction in a group of 41 healthy subjects performing a subset of the Ewing test battery. Approach : We measure the empirical distribution of the cardiorespiratory coupling time (RI), defined as the time from inspiration onset to R peaks in the ECG. The study protocol is a subset of the Ewing test battery. The respiratory function was measured with a thoracic belt and heart rate was obtained from a two channel ECG measurement. Both series of fiducial points were determined using custom software. Additionally, we determine the presence of cardiorespiratory coupling (CRC) and cardiorespiratory interaction (CRI) using Shannon entropy, synchrograms and coordigrams. Main results : We observe that the RI distribution is asymmetric and nonuniform. These features are a manifestation of the causal relation between heart action and respiration. The preceding R peak strongly affects a position of inspiration onset. From the asymmetry of the RI distribution we conclude that this relation is stronger than the relation between inspiration onset and the following R peak. We use a suitable choice of surrogate data to prove that the result cannot be falsified. We observe a dual structure of the RI histograms, which may be related to the respiratory rhythmogenesis. We compare the sensitivity of RI histograms with other measures of CRI and CRC. In 46% of subjects, CRC appears in at least one stage of the examination, most often in resting states. In states of increased stress—orthostasis or physical (exercise)—the strength of coupling is visibly diminished. The nonuniform structure of the RI histogram is more sensitive to the presence of CRI than synchrograms or coordigrams are, as is well visible in the group averages. We also refer to the question of the most proper mathematical description of cardiorespiratory dynamics (phase domain or time domain). Finally, we formulate the hypothesis that the arterial blood pressure is a common driver of cardiac and respiratory rhythms. Significance : Analysis of the asymmetry of RI histograms is an interesting and sensitive method to study cardiorespiratory interaction and autonomic balance, in order to assess physical and mental health. The dual structure of the RI histograms which we have observed suggests the possible presence of a twofold mechanism for respiratory rhythmogenesis, as proposed by Galletly and Larsen.

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: Rehabilitation positively affects the modulation of the autonomic nervous system (ANS). There are no papers evaluating the influence of Nordic walking training (NW) on ANS activity among chronic heart failure (CHF) patients. The aim of study was to assess the influence of NW on...