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Zapiski Nauchnykh Seminarov POMI, 2015, Volume 438, Pages 138–177 (Mi znsl6190)  
This article is cited in 4 scientific papers (total in 4 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
Full-text PDF (350 kB) Citations (4)
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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 0.38.237.2014
Received: 15.10.2015
English version:
Journal of Mathematical Sciences (New York), 2017, Volume 224, Issue 1, Pages 94–118
DOI: https://doi.org/10.1007/s10958-017-3398-0
Bibliographic databases:
Document Type: Article
UDC: 517.958:539.3(5)+531.3-324
Language: Russian
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
\Bibitem{KozNaz15}
\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
\mathnet{http://mi.mathnet.ru/znsl6190}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=3501073}
\transl
\jour J. Math. Sci. (N. Y.)
\yr 2017
\vol 224
\issue 1
\pages 94--118
\crossref{https://doi.org/10.1007/s10958-017-3398-0}
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    • This publication is cited in the following 4 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
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