FPU Recurrence in the Coupled Blood Pressure Dynamics in Magisterial and Small Arteries Networks and the Character of its Interaction with the Heart Electrical Activity

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FPU Recurrence in the Coupled Blood Pressure Dynamics in Magisterial and Small Arteries Networks and the Character of its Interaction with the Heart Electrical Activity

Cardiovascular Pharmacology: Open Access. 2017. Vol. 6(6). No. 230. P. 1–6.

Shmid A., Novopashin M. A., Berezin A. A.

Computer model simulating the coupled blood pressure dynamics in magisterial and small arteries with the heart electrical dynamics has been suggested. The Fermi-Pasta-Ulam auto recurrence in the description of the electrical activity of the heart has demonstrated the universal role of the FPU recurrence in the study of dynamical systems. The heart electrical dynamics was described by the coupled Van der Pol differential equations with time lags, linked with two additively coupled nonlinear differential equations circumscribing the blood pressure dynamics in the networks of magisterial and small arteries. The arterial blood pressure dynamics was interpreted as coupled FPU recurrences showing a rich variety of resulting FPU spectra, which were referred to different states of Cardio Vascular System. Synchronous registering of the real ECG and Pulse Wave Fourier dynamic images allowed to unify the characteristic Fourier pictures of the heart electrical activity with the hydrodynamic blood parameters developing in the networks of two types of arteries. The computer study of the suggested model and comparison of its results with the real data proved that the ECG Fourier parameters coupled with the Pulse Wave Fourier parameters form the FPU spectra that increase stability of Cardio Vascular System and can be used for diagnostics as well as for evaluation of the therapeutic arrangements results.

Priority areas: IT and mathematics mathematics

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Shmid A., Novopashin M. A., Berezin A. A., [б.и.], 2017.

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 ...

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