Coronary flow mechanics: an anatomically based mathematical model of coronary blood flow coupled to cardiac contraction

Abstract

Coronary blood flow through the ventricular contraction cycle has been investigated in this thesis using an anatomically accurate computational model. Using Strahler ordered morphological data and an avoidance algorithm a three dimensional finite element model has been constructed of the largest six generations of the coronary arterial network within an anatomically accurate finite element model of the left and right ventricles. Segment radii, lengths and connectivity are consistent with the literature, local network branch angles are consistent with the principle of minimum shear stress at bifurcations, and an even spatial distribution of vessel segments throughout the myocardium has been achieved. A finite difference collocation grid has been generated on the coronary finite element mesh. The Navier Stokes equations governing blood flow through elastic vessels have been reduced to one dimension and are solved on this finite difference grid using the two step Lax Wendroff method. Blood flows at bifurcations are calculated using an iterative method ensuring conservation of mass and momentum. The microcirculation networks are modelled using a lumped parameter model incorporating the nonlinear variation of resistance and compliance with pressure by fitting results from published anatomical data. The venous network is assumed to parallel the generated arterial model. The calculated blood flow through the network model demonstrates physiological pressure drops, flow rates and a regional distribution within the ventricular geometry consistent with experimental data. The intramyocardial pressure (IMP) exerted on the coronary vasculature during contraction is calculated from quasi-static solutions of the equations of finite deformation applied to the ventricular model with a nonlinear anisotropic constitutive law. IMP is found to vary approximately linearly between ventricular pressure at the endocardium and atmospheric pressure at the epicardium. IMP and vessel stretch are included in the transmural pressure radius relationship to model the effect of myocardial deformation on coronary flow. The calculated coronary blood flow through the contraction cycle shows that arterial flow is predominantly diastolic while venous flow is significantly increased during systole. Calculated time varying velocity profiles in the large epicardial vessels compare well with published experimental results. Regionally averaged velocities in small vessels show that arterial inflow is most significantly impeded at the left ventricular endocardium. Furthermore, the large time constant associated with the capillary and venule networks limits the filling of these vessels during diastole particularly at the endocardium. An increase in heart rate, modelled by reducing the time for diastole causes an increase in small vessel epicardial blood flow and a decrease in blood flow through small vessels within the myocardium. The decrease in flow is most pronounced at the left ventricular endocardium.