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Zapiski Nauchnykh Seminarov POMI, 2012, Volume 409, Pages 80–106 (Mi znsl5513)  
This article is cited in 9 scientific papers (total in 9 papers)

Asymptotic models of the blood flow in arterias and veins

V. A. Kozlova, S. A. Nazarovbc

a Department of Mathematics, Linkopings Universitet, Linkoping, Sweden
b Institute of Problems of Mechanical Engineering, Russian Academy of Sciences, St. Petersburg, Russia
c St. Petersburg State University, St. Petersburg, Russia
Full-text PDF (342 kB) Citations (9)
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Abstract: Asymptotic analysis is applied for obtaining one-dimensional models of the blood flow in narrow, thin-walled, elastic vessels. The models for arteries and veins essentially distinguish from each other, and the reason for this is the structure of their walls as well as the operationing conditions. Although the obtained asymptotic models are simple, they explain various effects known in medical practice, in particular, describe the mechanism of vein-muscle pumping of blood.
Key words and phrases: modeling of thin-walled blood vessels, laminate elastic walls, Reinolds equation.
Received: 26.11.2012
English version:
Journal of Mathematical Sciences (New York), 2013, Volume 194, Issue 1, Pages 44–57
DOI: https://doi.org/10.1007/s10958-013-1505-4
Bibliographic databases:
Document Type: Article
UDC: 517.958+539.3(5)+531.3-324
Language: Russian
Citation: V. A. Kozlov, S. A. Nazarov, “Asymptotic models of the blood flow in arterias and veins”, Mathematical problems in the theory of wave propagation. Part 42, Zap. Nauchn. Sem. POMI, 409, POMI, St. Petersburg, 2012, 80–106; J. Math. Sci. (N. Y.), 194:1 (2013), 44–57
Citation in format AMSBIB
\Bibitem{KozNaz12}
\by V.~A.~Kozlov, S.~A.~Nazarov
\paper Asymptotic models of the blood flow in arterias and veins
\inbook Mathematical problems in the theory of wave propagation. Part~42
\serial Zap. Nauchn. Sem. POMI
\yr 2012
\vol 409
\pages 80--106
\publ POMI
\publaddr St.~Petersburg
\mathnet{http://mi.mathnet.ru/znsl5513}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=3032230}
\transl
\jour J. Math. Sci. (N. Y.)
\yr 2013
\vol 194
\issue 1
\pages 44--57
\crossref{https://doi.org/10.1007/s10958-013-1505-4}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84898984656}
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  • https://www.mathnet.ru/eng/znsl/v409/p80
    • This publication is cited in the following 9 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
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