The Development of SIM to Characterize Blood Volumetric Flow Rate and Hemodynamics in Human Coronary Arteries

Abstract

The genesis and progression of heart diseases are primarily originated from hemodynamic disorders. Among the important hemodynamic parameters to estimate is the blood volume flow rate (Q) in coronary arteries. Knowing how the volumetric flow rate is related to geometric and physiologic parameters is challenging. The end product of this paper is a Seven Input Model (SIM) developed to characterize blood volume flow rate in human coronary arteries which can be translated into clinical applications. Several mathematical relations were established relating all primary hemodynamic (pressure and velocity), geometric, and boundary parameters to the volume flow rate. An equation for predicting blood volumetric flow rate was first developed for arterial segments of uniform cross section by solving the set of continuity and momentum equations in cylindrical coordinates. The governing equations were coupled with a total pressure formulation at the inlet and a dynamic pressure-flow lumped model at the outlet to capture in-vivo coronary hemodynamics. The model was then generalized for an artery of variable cross section area and for arteries with low to medium stenosis severities. Two different algorithms were also developed to solve the set of developed equations; (1) a numerical algorithm following Gauss-Seidel method with successive iterative forward and backward substitution; and (2) an alternative analytical approach where an equation of blood volume flow rate was obtained and related to all model parameters, including geometry, inlet and outlet boundary parameters, blood density and viscosity, and normal shear stress at inlet. In the analytical approach, the blood flow rate is directly computed from a single developed model (SIM); local pressure and velocity distributions are then directly obtained. The performance of the developed models and algorithms were tested on (i) an artery with uniform cross section; (ii) an artery of variable cross section; and (iii) an artery with low severity symmetrical stenosis. Predictions were then compared with a full CFD 3D model for validation purposes. An excellent agreement was achieved.