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Ural Math. J., 2019, Volume 5, Issue 1, Pages 109–126 (Mi umj79)  

A mathematical model of an arterial bifurcation

German L. Zavorokhin

St. Petersburg Department of the Steklov Mathematical Institute, Russian Academy of Sciences, 27, Fontanka, St.Petersburg, 191023, Russia

Abstract: An asymptotic model of an arterial bifurcation is presented. We propose a simple approximate method of calculation of the pressure drop matrix. The entries of this matrix are included in the modified transmission conditions, which were introduced earlier by Kozlov and Nazarov, and which give better approximation of 3D flow by 1D flow near a bifurcation of an artery as compared to the classical Kirchhoff conditions. The present modeling takes into account the heuristic Murrey cubic law.

Keywords: Stokes’ flow, bifurcation of a blood vessel, modified Kirchhoff conditions, pressure drop matrix, Murrey’s law.

Funding Agency Grant Number
Linköping University
Russian Foundation for Basic Research 16-31-60112


DOI: https://doi.org/10.15826/umj.2019.1.011

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Citation: German L. Zavorokhin, “A mathematical model of an arterial bifurcation”, Ural Math. J., 5:1 (2019), 109–126

Citation in format AMSBIB
\Bibitem{Zav19}
\by German~L.~Zavorokhin
\paper A mathematical model of an arterial bifurcation
\jour Ural Math. J.
\yr 2019
\vol 5
\issue 1
\pages 109--126
\mathnet{http://mi.mathnet.ru/umj79}
\crossref{https://doi.org/10.15826/umj.2019.1.011}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=MR3995660}
\elib{https://elibrary.ru/item.asp?id=38948067}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85071448655}


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