An Anatomically Based Model of Transient Coronary Blood Flow in the Heart

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Abstract
An efficient finite difference model of blood flowthrough the coronary vessels is de- veloped and applied to a geometric model of the largest six generations of the coronary arterial net- work. By constraining the form of the velocity profile 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 conserva- tion 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.