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Zap. Nauchn. Sem. POMI, 2015, Volume 438, Pages 138–177 (Mi znsl6190)  

This article is cited in 3 scientific papers (total in 3 papers)

Transmission conditions in a one-dimensional model of bifurcating blood vessel with an elastic wall

V. A. Kozlova, S. A. Nazarovbcd

a Linkopings Universitet, 581 83 Linkoping, Sweden
b St. Petersburg State University, St. Petersburg, Russia
c St. Petersburg State Polytechnical University, St. Petersburg, Russia
d Institute of Problems of Mechanical Engineering, Russian Academy of Sciences, St. Petersburg, Russia

Abstract: We derive transmission conditions at a bifurcation point in a one-dimensional model of blood vessels by using a three-dimensional model. Both classical Kirchhoff conditions ensuring the continuity of pressure and zero flux flow in the node has to be modified in order to reflect properly the elastic properties of blood vessels and the nodes themselves. A simple approximate calculation scheme for the new physical parameters in the transmission conditions is proposed. We develop a simplified model of straight fragments of arteries with localized defects such as lateral micro-aneurysms and cholesterol plaques – these models also require setting transmission conditions.

Key words and phrases: artery bifurcation, branching of blood vessels, modified Kirchhoff conditions, elastic walls, thin flow, matrix of pressure jumps.

Funding Agency Grant Number
Linköping University
Saint Petersburg State University

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English version:
Journal of Mathematical Sciences (New York), 2017, 224:1, 94–118

Bibliographic databases:

Document Type: Article
UDC: 517.958:539.3(5)+531.3-324
Received: 15.10.2015

Citation: V. A. Kozlov, S. A. Nazarov, “Transmission conditions in a one-dimensional model of bifurcating blood vessel with an elastic wall”, Mathematical problems in the theory of wave propagation. Part 45, Zap. Nauchn. Sem. POMI, 438, POMI, St. Petersburg, 2015, 138–177; J. Math. Sci. (N. Y.), 224:1 (2017), 94–118

Citation in format AMSBIB
\by V.~A.~Kozlov, S.~A.~Nazarov
\paper Transmission conditions in a~one-dimensional model of bifurcating blood vessel with an elastic wall
\inbook Mathematical problems in the theory of wave propagation. Part~45
\serial Zap. Nauchn. Sem. POMI
\yr 2015
\vol 438
\pages 138--177
\publ POMI
\publaddr St.~Petersburg
\jour J. Math. Sci. (N. Y.)
\yr 2017
\vol 224
\issue 1
\pages 94--118

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    This publication is cited in the following articles:
    1. V. A. Kozlov, S. A. Nazarov, “A one-dimensional model of flow in a junction of thin channels, including arterial trees”, Sb. Math., 208:8 (2017), 1138–1186  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
    2. V. A. Kozlov, S. A. Nazarov, “Effective one-dimensional images of arterial trees in the cardiovascular system”, Dokl. Phys., 62:3 (2017), 158–163  crossref  mathscinet  isi  scopus
    3. V. A. Kozlov, S. A. Nazarov, “Model meshkovidnoi anevrizmy bifurkatsionnogo uzla arterii”, Matematicheskie voprosy teorii rasprostraneniya voln. 47, Zap. nauchn. sem. POMI, 461, POMI, SPb., 2017, 174–194  mathnet
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