One-dimensional, nonlinear determinism characterizes heart rate pattern during paced respiration.

This study focuses on the dynamic pattern of heart rate variability in the frequency range of respiration, the so-called respiratory sinus arrhythmia. Forty experimental time series of heart rate data from four healthy adult volunteers undergoing a paced respiration protocol were used as an empirical basis. For pacing-cycle lengths >8 s, the heartbeat intervals are shown to obey a rule that can be expressed by a one-dimensional circle map (next-angle map). Circle maps are introduced as a new type of model for time series analyses to characterize the nonlinear dynamic pattern underlying the respiratory sinus arrhythmia during voluntary paced respiration. Although these maps are not chaotic, the dynamic pattern shows typical imprints of nonlinearity. By starting from a piecewise linear model, which describes the different circle maps obtained from the empirical time series for various pacing frequencies, time invariant measures can be introduced that characterize the dynamic pattern of heart rate variability during voluntary slow-paced respiration.

[Methodology in the analysis of asymmetry in fluctuations of heart rate]. / Methodik der Analyse der Asymmetrie in den Fluktuationen der Herzfrequenz.

Time series of R-R intervals show fluctuations which are neither symmetric regarding the changes in length of heart beats nor regarding the number of heart beats during the phases of heart rate acceleration and deceleration. These features of heart rate variability cannot be quantified by the analysis of the beat-to-beat variability or by the spectrum analysis of heart rate. The analysis of asymmetry using the distribution function of the differences between consecutive R-R intervals creates measures for the total, central, and peripheral asymmetry. These measures quantify different aspects of the shape of the distribution function. The asymmetry measures are either based on the amount of difference between consecutive R-R intervals or the number of lengthening R-R intervals in a sequence of heart beats. The analysis of asymmetry of R-R interval time series shows differences among test subjects during rest.

[Mathematical model of "respiratory sinus arrhythmia"]. / Mathematisches Modell der "respiratorischen Sinusarrhythmie".

We developed a mathematical model of "respiratory" sinus arrhythmia. The model combines a representation continuous in time of the parasympathetic and sympathetic innervation and the membrane potential of the pace maker cell of the heart with a beat-by-beat representation of the cardiovascular variables like diastolic and systolic blood pressure, pulse pressure, total peripheral resistance and baroreceptor activity. The influence of respiration is described separately by mechanical and central neural mechanisms. Using this nonlinear model of "respiratory" heart rate variability one is able to explore in a theoretical way the different heart rate variability generating mechanisms, either as isolated or combined effects on both, heart rate variability in the frequency range of respiration and in the frequency range around 0.1 Hz. By fitting a simulated RR interval time course to a physiological RR interval time course one can estimate the relative weight of the different mechanisms generating this physiological heart rate variability.