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Статья

Coupled blood pressure dynamics in magisterial and small arteries networks and its stabilizing effect on heart functioning within the framework of computer model

Annals of Circulation. 2018. No. 3. P. 4-7.
Shmid A., Berezin A., Novopashin M.

Computer model coupled blood pressure dynamics in magisterial and small arteries networks and
its stabilizing effect on heart functioning 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 distributed dynamical systems. The heart electrical dynamics was described by
the coupled Van der Pol differential equations with a time lag, linked with two additively coupled nonlinear
differential equations circumscribing the blood pressure dynamics in the networks of magisterial and
small arteries. The mathematical model developed by Yuen and Lake for description of the deep wave
dynamics within the nonlinear Shrodinger (NSE) equation was used for description of the magisterial
arterial blood pressure whereas for small arteries blood pressure dynamics was used the approach
elaborated by Zabusky and Kruskal within the framework of the Korteveg de Vries (KdV) equation. 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.