Formulation of the Theoretical Model of Coronary Circulation Based on Mixture Theory

Abstract

The disorder of the coronary circulation system, which supplies blood for the working heart, may cause ischemic heart disease such as myocardial infarction, angina pectoris. On the other hand, the interaction between intramyocardial pressure and coronary blood flow is recognized to be an important factor that influences the hemodynamics of coronary circulation. In this work, a multiphasic model for coronary circulation system is proposed based on mixture theory by treating the myocardial matrix and the blood in hierarchical coronary system as solid phase and multi-fluid phase respectively. The governing equations and constitutive relations have been derived by applying conservation laws and entropy inequality in the framework of mixture theory. The microscopic properties, such as the viscosity of blood or the compliance of the micro vessel are represented by their macroscopic counterparts. The abilities of representing the characteristic behavior of coronary system have been confirmed by numerical examples.