期刊
SIAM JOURNAL ON APPLIED MATHEMATICS
卷 62, 期 3, 页码 990-1018出版社
SIAM PUBLICATIONS
DOI: 10.1137/S0036139999355199
关键词
coronary blood flow; finite difference; mathematical model
An efficient finite difference model of blood flow through the coronary vessels is developed and applied to a geometric model of the largest six generations of the coronary arterial network. By constraining the form of the velocity pro le across the vessel radius, the three-dimensional Navier-Stokes equations are reduced to one-dimensional equations governing conservation of mass and momentum. These equations are coupled to a pressure-radius relationship characterizing the elasticity of the vessel wall to describe the transient blood flow through a vessel segment. The two step Lax-Wendroff finite difference method is used to numerically solve these equations. The flow through bifurcations, where three vessel segments join, is governed by the equations of conservation of mass and momentum. The solution to these simultaneous equations is calculated using the multidimensional Newton-Raphson method. Simulations of blood flow through a geometric model of the coronary network are presented demonstrating physiologically realistic flow rates, washout curves, and pressure distributions.
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