Model using in the state space for inverse problem
solution to heart rhythm dynamics
O.L. Anosov 
, A.V. Kirykhin , Yu.K. Kononovitch ,
O.Ya. Butkovskii 
, Yu.A. Kravtsov 
Vladimir Regional Cardio Center;
Vladimir State Tech. Univ.;
Space Res. Inst., Russ. Acad. Sci.
Procedure for reconstruction of nonlinear nonstationary dynamic system from observed time series is proposed, based upon models identification in the state space. The having been carried out investigations on the discrete models (logistic map) and on the continuous models (Rössler attractor) showed that the procedure allows to reconstruct the system dynamic model form from the observed time series, to distinguish its functioning conditions and to determine the model parameter values in the presence of additive noise, as well as to reveal the minor (less 0.5%) control parameters change in time.
The developed procedure was utilized for analyses of cardiac cycle duration series (RR-intervals), registered during clinical experiment aimed at studying of cardiac regulation system behavior during stress level increasing. The stress level was initiated by the calibrated exertion on veloergometer of Metabolic Measurement System SensorMedics 2900 during the loading test. Simultaneously, we carried out the exhale gas analysis, arterial pressure and RR-interval duration were measured. The investigations were performed in the mode of step-by-step load increasing, at steps of 0%, 20%, 40% and 60% from the maximum load. The data, registered at each step till the patient reached the stationary response to the load, were subjected to further analysis.
The experiment has shown, making use of the proposed procedure, that one can
manage to separate the model small-dimensional core in the virtue of
nonlinear differential equation system of the third power. The separated
model small-dimensional core comprises nonlinearities of type
, typical for microscopic processes, occurring in
biological systems, in particular, in the cellular membranes [1] and
in the model offered for the description of cardiac arrhythmia [2].
The form of the reconstructed model core doesn't change due to the stress level increasing, however, its parameter values change monotonously. Certain parameter dependencies from the stress level obtain clearly pronounced extremums. The extremums position in these dependencies practically coincide with the point of aerobic-anaerobic metabolism change-over (anaerobic threshold), calculated by Metabolic Measurement System SensorMedics 2900 by the patient's exhale gas analysis.