Cardiovascular Dynamics – Multiple Time Scales, Oscillations and Noise

Modelling the cardiovascular system (CVS) presents a challenging and important problem. The CVS is a complex dynamical system that is vital to the function of the human organism, and it reflects numerous different states of health and disease. Its complexity lies in a combination of oscillatory modes spanning a wide frequency scale that can synchronize for short episodes of time, coupled with a strong stochastic contribution. Motivated by these properties, we discuss the problem of characterising dynamics when there is a combination of oscillatory components in the presence of strong noise and, in particular, where the characteristic frequencies and corresponding amplitudes vary in time. We show that, where there are several noisy oscillatory modes, the slower modes are difficult to characterise because the length of the recorded time series is inevitably limited in real measurements. We argue that, in the case of strong noise combined with a limited observation time, such oscillatory dynamics with several modes may appear to manifest as a 1 f -like behaviour. We also show that methods of time-frequency analysis can provide a basis for characterising noisy oscillations, but that a straightforward characterisation of multi-scale oscillatory dynamics in the presence of strong noise still remains an unsolved problem.