Biological Sciences, Vol. 1, Issue 1, Dec  2017, Pages 31-38; DOI: 10.31058/j.bs.2017.11003 10.31058/j.bs.2017.11003

Mathematical Model of the Korotkoff Sounds

Biological Sciences, Vol. 1, Issue 1, Dec  2017, Pages 31-38.

DOI: 10.31058/j.bs.2017.11003

Yuriy N. Zayko 1*

1 Department of Applied Informatics, Faculty of Public Administration, Russian Presidential Academy of National Economy and Public Administration, Stolypin Volga Region Management Institute, Saratov, Russia

Received: 27 November 2017; Accepted: 30 December 2017; Published: 9 January 2018

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Abstract

In this article briefly describes the main areas of research of the Korotkoff sounds accompanying the blood pressure measurement process. It is noted that the existing approaches, unlike the approach of the author do not sufficiently involve the achievements of modern hydrodynamics. This applies in particularly to the study of flows in tubes with elastic walls. A brief overview of the authors works in this area is presented. Based on these results, a model describing the Korotkoff sounds is presented. This model is based on the equation derived from the Navier-Stokes equations by the method of multiscale decompositions. Its solution in the form of a shock wave with a perturbed front is explored. We find the equation for the frequency of the shock wave front vibrations. The stability of a one-dimensional shock wave with respect to small perturbations is also investigated. It is concluded that the blood flow acquires a more complex transverse structure with an increase in the heart rate. This phenomenon will help to understand the turbulence development in the blood flow, for example, with atrial flutter.

Keywords

Blood Flow, Blood Pressure, Navier-Stokes Equations, Tubes with Elastic Walls, Korotkoff Sounds, Shock Wave

Copyright

© 2017 by the authors. Licensee International Technology and Science Press Limited. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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