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

Mathematical Model of the Korotkoff Sounds

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

DOI: 10.31058/

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

Download PDF | Views 402 | Download 241


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.


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


© 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.


[1] Pedley T.J. The Fluid Mechanics of Large Blood Vessels. Cambridge Univ. Press, Cambridge, 1980.
[2] Volobuev A.N. Flow of Liquid in vessels with elastic walls. Usp. Fiz. Nauk, 1995, 165(2), 177-186, (Russian).
[3] Tsaturyan A. The Korotkov sounds or what the doctor is listening to when measuring arterial blood pressure?
Available online: (accessed on 27 November 2017).
[4] Grigoryan S.S.; Saakyan Yu.Z.; Tsaturyan A.K. On the generation mechanism of Korotkov sound. Dokl. Acad. Nauk USSR. 1980, 251, 570-579.
[5] Grigoryan S.S.; Saakyan Yu.Z.; Tsaturyan A.K. On the origin of the “infinite” Korotkov tone. Dokl. Acad. Nauk USSR. 1981, 259, 793-801.
[6] Tsaturyan A. Korotkoff sounds and measurement of arterial blood pressure. Report on the School of Engineering Sciences, Southampton, England, 2006, 10, 18.
[7] Pihler-Puzović D. Flows in collapsible channels. Thesis Ph.D., University of Cambridge, 2011.
[8] Pedley T.J.; Pihler-Puzovic D. Flow and oscillations in collapsible tubes: physiological applications and low-dimensional models. IUTAM Symposium on transition and turbulence in flow through deformable tubes and channels, Sadhana, Springer India, 2015, 40(3), 891-909.
[9] Gonzalez F. The origin of Korotkoff sounds and their role in sphygmomanometry. PhD Thesis, Univ. of Florida, Gainesville, 1974.
[10] Ablowitz M.J.; Segur H. Solitons and the Inverse Scattering Transform. SIAM, Philadelphia, 1981.
[11] Zayko Y.N. Shock wave instability in viscid flow with respect to transverse perturbations. Techn. Phys. Lett. 1991, 17(14), 20-21.
[12] Zayko Y.N., Explicit solutions of the nonlinear acoustic equations. Techn. Phys. Lett. 1994, 20(10), 79-81.
[13] Zayko Y.N. Wave Propagation in a Liquid Flowing in a Channel with Elastic Walls. Technical Physics Letters, 2001, 27(8), 677-678.
[14] Zayko Y.N. A Model of Liquid Flow in a Channel with Elastic Walls. Techn. Phys. Lett. 2002, 28(12), 1024-1026.
[15] Zayko Y.N. Flows of Liquids in Tubes with Elastic Walls. TEPE, 2013, 2(4), 114-116.
[16] Zayko Y.N. Application of Two-Fluid Model for Flow Treating in Pipe of Circle Profile. Proc. of the Saratov State Univ., Ser. Physics. 2013, 13 (1), 73-76.
[17] Karpman V.I. Nonlinear Waves in Dispersive Media, Pergamon, Oxford, 1994.
[18] Naugol’nykh К.А.; Ostrovskiy L.A. Nonlinear Wave Processes in Acoustic. Moscow: Nauka, 1990.
[19] Lamb G.L.; JR. Elements of soliton theory, A Willey-Interscience Publications, NY, 1980.
[20] Vol’mir A.S. Nonlinear dynamics of plates and shells Nauka, Moscow, 1972 (Russian).
[21] Landau L.D.; Lifshitz E.M. Course of Theoretical Physics, Fluid Mechanics; Pergamon, New York, 1987, 6.
[22] Arfken G. Mathematical Methods for Physicists, Academic Press, NY and London, 1966.
[23] Janke E.; Emde F.; Lösch F.; Tafeln Höherer Funktionen, B.G. Teubner Verlagsgeselschaft, Stuttgart, 1960.
[24] Ramakrishnan D. Using Korotkoff Sounds to Detect the Degree of Vascular Compliance in Different Age Groups. J Clin Diagn Res. 2016, 10(2), CC04–CC07.
[25] Wang X.; Fullana J.M.; Lagree P.Y. Verification and comparison of four numerical schemes for a 1D viscoelastic blood flow model, arXiv:1302.5505v4 [] 16 Sep 2014.
[26] Acosta S.; Puelzb C.; Riviereb B.; Pennya D. J.; Rusina C.G. Numerical Method of Characteristics for One–Dimensional Blood Flow, arXiv:1411.5574v3 [physics.comp-ph] 27 Mar 2015.
[27] Sultanov R.A.; Guster D.; Engelbrekt B. Blankenbecler R.; 3D Computer Simulations of Pulsatile Human Blood Flows in Vessels and in the Aortic Arch: Investigation of Non-Newtonian Characteristics of Human Blood, arXiv:0802.2362v1 [physics.comp-ph] 17 Feb 2008.
[28] Sultanov R.A.; Guster D. Computer Simulations of Pulsatile Human Blood Flow Through 3D-Models of the Human Aortic Arch, Vessels of Simple Geometry and a Bifurcated Artery: Investigation of Blood Viscosity and Turbulent Effects, arXiv:0811.1363v1 [physics.flu-dyn] 9 Nov 2008.

Related Articles