M. Ćosić1* and N. Miljković2,3
1 Laboratory of Physics, Vinča Institute of Nuclear Sciences – National Institute of the Republic of Serbia, University of Belgrade, P.O. Box 522, Belgrade, Serbia
2 University of Belgrade – School of Electrical Engineering, Belgrade, Serbia
3 Faculty of Electrical Engineering, University of Ljubljana, Ljubljana, Slovenia
mcosic [at] vinca.rs
Abstract
We have developed a new method for analyzing the long scalar experimental data. By the time delay embedding, the oscillatory nature of the data was transformed into a sequence of loops of the system phase space trajectory. The proposed method reduces the classification of all possible loop types and rules of their succession.
The proposed method will be presented by analyzing the experimental data obtained from the Holter electrocardiogram of an arbitrarily chosen 79-year-old male patient and a 24-year-old healthy female individual. In the case of the patient, the system’s trajectory consists of only 8 of the most simple loop types. Out of 64 possible loop transitions, only 49 play a significant role in the observed system dynamics. Further, we constructed a stochastic finite state machine capable of reproducing observed system trajectory statistically. We have observed many metamorphoses of the phase space distribution from clustered to branched.
The Holter electrocardiogram of a 24-year-old healthy individual showed no changes in the phase distribution shape, and the corresponding finite state machine has the same number of states but with radically different distributions of the transition probabilities.
Our method shows more sensitivity in detecting pathological states than standard heart rate variability assessments. Its topological nature makes it very robust to the disturbing effect of noise. Although, additional research on a larger experimental sample is required before the usefulness of the proposed morphological approach can be rightfully assessed. Results presented for just the two subjects clearly show the great potential of the dynamist approach aided with constructing the finite state machine.
Keywords: Poincaré plot, morphological method, heart rate variability, RR tachogram
Acknowledgement: The research was funded by the Ministry of Science, Technological Development, and Innovation of the Republic of Serbia (grant Nos. 451-03-47/2023-01/ 200017 and 451-03-66/2024-03/ 200017)..