Determinism and noise in cardiovascular dynamics

Aneta Stefanovska

Group of Nonlinear Dynamics and Synergetics,
Faculty of Electrical Engineering, University of Ljubljana, Slovenia, and
Department of Physics, Lancaster University, Lancaster, United Kingdom

Signals derived from the human cardiovascular system are well known to exhibit highly complex, nearly periodic, oscillatory behaviour whose nature is something of an enigma and still the subject of vigorous debate. The variation of cardiac frequency with time, known as heart rate variability (HRV), has been intensively investigated using both deterministic and stochastic methods. It has, for example, been variously described as chaotic, fractal, stochastic, and subject to 1/f fluctuations and it was proposed that the state of the system can be classified by the slope of its power spectrum on a log-log plot.

We illustrate some problems in characterising slow modes in real measurements and show that oscillatory dynamics under the influence of strong noise, coupled with a limited time of observation, can lead to a $1/f$-like behaviour. We review and describe some recent experiments that illuminate the problem and discuss a combination of almost periodic and stochastic frequency modulation as a signature of the system dynamics.

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Interactions in the cardiovascular system

Aneta Stefanovska

Group of Nonlinear Dynamics and Synergetics,
Faculty of Electrical Engineering, University of Ljubljana, Slovenia, and
Department of Physics, Lancaster University, Lancaster, United Kingdom

In a healthy subject in repose a volume of blood equivalent to the total amount in the body returns to the heart every minute. Several oscillatory processes characterise cardiovascular dynamics within this circulation time. Cardiac and respiratory activities act on higher frequency scales, with characteristic frequencies of 1 Hz and 0.2 Hz, respectively. The lowest frequency component, at around 0.01 Hz, has been associated with the activity of the layer of endothelial cells forming the inner surfaces of all blood vessels.

The characteristic frequencies of all the cardiovascular oscillations are found to vary in time, apparently because the oscillatory processes mutually interact. Hales and Ludwig independently described the modulation of cardiac frequency by respiration, in 1773 and 1847 respectively, a process that today is known as respiratory sinus arrhythmia. The occurrence of episodes of synchronization between the cardiac and respiratory rhythms has also been demonstrated.

Recent developments of methods based on dynamical and information theory are facilitating studies of synchronization and of the directionality of couplings between the cardiovascular oscillations. We review and discuss their characteristics in health and disease. The characteristics of the cardiac and respiratory interaction during paced respiration are used to illustrate the role of directionality of coupling in the interplay between synchronization and modulation.

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