Geodesic
A mathematical model of an arterial bifurcation
Ural mathematical journal, Tome 5 (2019) no. 1, pp. 109-126

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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. 
@article{UMJ_2019_5_1_a10,
     author = {German L. Zavorokhin},
     title = {A mathematical model of an arterial bifurcation},
     journal = {Ural mathematical journal},
     pages = {109--126},
     publisher = {mathdoc},
     volume = {5},
     number = {1},
     year = {2019},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/UMJ_2019_5_1_a10/}
}
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German L. Zavorokhin. A mathematical model of an arterial bifurcation. Ural mathematical journal, Tome 5 (2019) no. 1, pp. 109-126. http://geodesic.mathdoc.fr/item/UMJ_2019_5_1_a10/