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Zapiski Nauchnykh Seminarov POMI, 2014, Volume 426, Pages 64–86 (Mi znsl6032)  
This article is cited in 5 scientific papers (total in 5 papers)

A simple one-dimensional model of a false aneurysm in the femoral artery

V. A. Kozlova, S. A. Nazarovbc

a Department of Mathematics, Linkopings Universitet, 581 83 Linkoping, Sweden
b St. Petersburg State University, St. Petersburg, Russia
c Institute of Problems of Mechanical Engineering, Russian Academy of Sciences, St. Petersburg, St. Petersburg, Russia
Full-text PDF (257 kB) Citations (5)
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Abstract: Using the dimension reduction procedure, one-dimensional model of the periodic blood flow in the artery, which flows out through a small hole in the thin elastic artery wall connected to a spindle-shaped hematoma, is constructed. This model is described by a system of two parabolic and one hyperbolic equations provided with mixed boundary and periodicity conditions. The blood exchange between the artery and the hematoma is expressed by the Kirchhoff matching conditions. Despite the simplicity, the constructed model allows us to describe a damping of pulsating blood flow by the hematoma and determine the conditions of its growth. In medicine, considered biological object is called a false aneurysm.
Key words and phrases: circulatory system, aneurysm, hematoma, blood vessel, dimension reduction, Reynolds equation.
Received: 02.10.2014
English version:
Journal of Mathematical Sciences (New York), 2016, Volume 214, Issue 3, Pages 287–301
DOI: https://doi.org/10.1007/s10958-016-2778-1
Bibliographic databases:
Document Type: Article
UDC: 517.958+539.3(5)+531.3--324
Language: Russian
Citation: V. A. Kozlov, S. A. Nazarov, “A simple one-dimensional model of a false aneurysm in the femoral artery”, Mathematical problems in the theory of wave propagation. Part 44, Zap. Nauchn. Sem. POMI, 426, POMI, St. Petersburg, 2014, 64–86; J. Math. Sci. (N. Y.), 214:3 (2016), 287–301
Citation in format AMSBIB
\Bibitem{KozNaz14}
\by V.~A.~Kozlov, S.~A.~Nazarov
\paper A simple one-dimensional model of a~false aneurysm in the femoral artery
\inbook Mathematical problems in the theory of wave propagation. Part~44
\serial Zap. Nauchn. Sem. POMI
\yr 2014
\vol 426
\pages 64--86
\publ POMI
\publaddr St.~Petersburg
\mathnet{http://mi.mathnet.ru/znsl6032}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=3485306}
\transl
\jour J. Math. Sci. (N. Y.)
\yr 2016
\vol 214
\issue 3
\pages 287--301
\crossref{https://doi.org/10.1007/s10958-016-2778-1}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84960335133}
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    • This publication is cited in the following 5 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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