### 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, Russian Federation)

#### 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.

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