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

• Published in: SIAM journal on applied mathematics Vol. 62; no. 3; pp. 990 - 1018
• Main Authors: Smith, N P, Pullan, A J, Hunter, P J
• Format: Journal Article
• Language: English
• Published: Philadelphia Society for Industrial and Applied Mathematics 2002
• Subjects: Applied mathematics; Bifurcation (mathematics); Bifurcations; Blood flow; Blood vessels; Computer simulation; Conservation; Dimensional analysis; Elasticity; Geometry; Heart; Mathematical analysis; Mathematical models; Navier Stokes equations; Networks; Physiology; Segments; Three dimensional; Velocity; Viscosity
• ISSN: 0036-1399; 1095-712X
• DOI: 10.1137/S0036139999355199

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 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 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.