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An Averaged Nonlinear Model of Hemodynamics on the Vessel Graph

An Averaged Nonlinear Model of Hemodynamics on the Vessel Graph Di erential Equations, Vol. 37, No. 7, 2001, pp. 949{956. Translated from Di erentsial'nye Uravneniya, Vol. 37, No. 7, 2001, pp. 905{912. Original Russian Text Copyright c 2001 by Bunicheva, Mukhin, Sosnin, Favorskii. NUMERICAL METHODS An Averaged Nonlinear Model of Hemodynamics on the Vessel Graph A. Ya.Bunicheva, S. I. Mukhin, N.V.Sosnin, and A.P.Favorskii Moscow State University, Moscow, Russia Received March 1, 2001 INTRODUCTION In the present paper, we consider the possibility of constructing a simpli ed nonlinear model of hemodynamics [1] on a graph of elastic vessels and using it as a basic unit in the construction of a nite-di erence approximation [2] to the equations of hemodynamics. We pay great attention to the veri cation of the numerical solution. In particular, we com- pare the numerical solution with the exact solution of the linearized problem [3, 4] and carry out a comparative analysis of the numerical and exact solutions in the case of a steady ow. 1. THE EQUATIONS OF HEMODYNAMICS We use the natural assumption that the length of a vessel is much larger than its thickness, which permits one to use the quasi-one-dimensional approximation. The blood ow in a vessel in the quasi-one-dimensional approximation is described http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Differential Equations Springer Journals

An Averaged Nonlinear Model of Hemodynamics on the Vessel Graph

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Publisher
Springer Journals
Copyright
Copyright © 2001 by MAIK “Nauka/Interperiodica”
Subject
Mathematics; Difference and Functional Equations; Ordinary Differential Equations; Partial Differential Equations
ISSN
0012-2661
eISSN
1608-3083
DOI
10.1023/A:1011905604368
Publisher site
See Article on Publisher Site

Abstract

Di erential Equations, Vol. 37, No. 7, 2001, pp. 949{956. Translated from Di erentsial'nye Uravneniya, Vol. 37, No. 7, 2001, pp. 905{912. Original Russian Text Copyright c 2001 by Bunicheva, Mukhin, Sosnin, Favorskii. NUMERICAL METHODS An Averaged Nonlinear Model of Hemodynamics on the Vessel Graph A. Ya.Bunicheva, S. I. Mukhin, N.V.Sosnin, and A.P.Favorskii Moscow State University, Moscow, Russia Received March 1, 2001 INTRODUCTION In the present paper, we consider the possibility of constructing a simpli ed nonlinear model of hemodynamics [1] on a graph of elastic vessels and using it as a basic unit in the construction of a nite-di erence approximation [2] to the equations of hemodynamics. We pay great attention to the veri cation of the numerical solution. In particular, we com- pare the numerical solution with the exact solution of the linearized problem [3, 4] and carry out a comparative analysis of the numerical and exact solutions in the case of a steady ow. 1. THE EQUATIONS OF HEMODYNAMICS We use the natural assumption that the length of a vessel is much larger than its thickness, which permits one to use the quasi-one-dimensional approximation. The blood ow in a vessel in the quasi-one-dimensional approximation is described

Journal

Differential EquationsSpringer Journals

Published: Oct 12, 2004

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