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Fermi-Pasta-Ulam auto recurrence in the description of the electrical activity of the heart
M A Novopashin1, A V Shmid1, A A Berezin1
1EC-leasing Moscow, Russia.
Abstract:
The authors proposed and mathematically described model of a new type of the Fermi-Pasta-Ulam recurrence (the FPU auto recurrence) and hypothesized an adequate description of the heart's electrical dynamics within the observed phenomenon. The dynamics of the FPU auto recurrence making appropriate electrical dynamics of the normal functioning of the heart in the form of an electrocardiogram (ECG) was obtained by a computer model study. The model solutions in the form of the FPU auto recurrence - ECG Fourier spectrum were evaluated for resistance to external disturbances in the form of random effects, as well as periodic perturbation at a frequency close to the heart beating rate of about 1Hz. In addition, in order to simulate the dynamics of myocardial infarction model, studied the effect of the surface area of the myocardium on the stability and shape of the auto recurrence - ECG spectrum. It has been found that the intense external disturbing periodic impacts at a frequency of about 1Hz lead to a sharp disturbance spectrum shape FPU auto recurrence - ECG structure. In addition, the decrease in the surface of the myocardium by 50% in the model led to the destruction of structures of the auto recurrence - ECG, which corresponds to the state of atrial myocardium. Research models have revealed a hypothetical basis of coronary heart disease in the form of increasing the energy of high-frequency harmonics spectrum of the auto recurrence by reducing the energy of low-frequency harmonic spectrum of the auto recurrence, which ultimately leads to a sharp decrease in myocardial contractility. In order to test the hypothesis has been studied more than 20,000 ECGs both healthy people and patients with cardiovascular disease. As a result of these studies, it was found that the dynamics of the electrical activity of normal functioning of the heart can be interpreted by the display of the detected by authors the FPU auto recurrence, and coronary heart disease is a violation of the energy ratio between the low and high frequency harmonics of the FPU auto recurrence Fourier spectrum equal to the ECG spectrum. Thus, the hypothesis has been confirmed.
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