Task 7. Model of Nonlinear Dynamics of Cardiovascular System as a System of Five Coupled Oscillators
Co-ordinator: A. Stefanovska
The objectives of the task are:
(T7.1) To investigate the dynamics of the proposed model of coupled oscillators in presence of fluctuations.
(T7.2) To try to explain the experimentally observed interplay between the frequency modulation and phase synchronisation of any pair of oscillators of this multistable system.
(T7.3) To study the properties of the cardiovascular system and the model that are relevant to the existence of time-variable characteristic frequencies.
(T7.4) To establish the extent to which the oscillatory processes of the blood distribution system, and the couplings between them, are affected by cardiovascular diseases and congestive heart failure in particular, by investigating time series of simultaneously measured blood flow, blood pressure, respiration and ECG.
(T7.5) To try to explain the influence and mechanisms of diseases using
the model of coupled oscillators.
The starting point is the experimental evidence, obtained in
a number of healthy subject and subjects with various cardiovascular
diseases, that the dynamics of blood distribution is governed by five
almost periodic and mutually coupled processes [9.3
- 9.10]. The dynamical characteristics of the cardiovascular system
strongly depend on the time scale of observation. The main feature of
the system is however the existence of oscillatory processes with characteristic
frequencies shown to be invariants of the system [9.4,
9.5, 9.8]. It was also illustrated that the cardiac and respiratory
systems - two of the subsystems - are capable of mutual synchronisation
[14,
9.9, 9.10].
These pieces of experimental evidence led to the proposal of a model
of the cardiovascular system, as five coupled, autonomous, nonlinear,
oscillators [9.3].
The basic unit is an oscillator that possesses the structural stability
and robustness, consistent with physiological understanding and the
analysis of measured time series. Because the characteristic frequencies
of the cardiovascular system vary in time, the oscillator equations
include an interactive part represented by coupling terms, as well as
the autonomous part.
It is expected that, based on analyses of measured signals and
analytical, analogue and numerical investigations of the model properties,
the frequency and amplitude wandering that characterise each oscillatory
process will be reproduced and the influence of particular diseases
on the couplings will be revealed.
In more detail, the work which is to be done includes:
For tasks 7.1, 7.2 and 7.3 the effect of noise on coupled oscillators
will be investigated by analogue and digital simulations in order to
find the coupling terms that best reproduce the interplay between synchronisation
and modulation observed in measured time series. The stability of the
system without and in the presence of fluctuations will be investigated
(CR9, CO). The most probable scenarios for synchronisation-breaking
in the system of noise-perturbed coupled active oscillators will be
studied analytically (CO, CR1, CR5, CR7, CR9).
For tasks 7.3, 7.4 and 7.5 new experiments will be set up to collect data from patients with congestive heart failure, diabetes mellitus and myocardial infarction. These are very common cardiovascular diseases that lead to complex changes of the cardiovascular system. Following selection, recruitment and echocardiography, time series of blood flow, blood pressure, respiration and ECG will be simultaneously recorded under resting conditions, using the procedures described in [9.4 ,9.5] (CO and CR9). These data, together with the data recorded from more than 500 healthy subjects and patients that are in the database of CR9 will be analysed and compared using appropriate methods of time series analysis to extract the influence of diseases on the oscillations and couplings. The characteristics and nature of the coupling terms under different conditions will be established (CO, CR9) through analogue and digital simulations.
