Multiphasic Mixture Modeling and Simulation of Coronary Circulation

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In this research, based on the multiphasic mixture theory, a hierarchical coronary theoretical model is proposed for the coronary system, in which the vessels have tree structure gradually bifurcating from artery and vein to capillary bed, by treating the myocardial matrix as solid phase and blood in each hierarchy of the vessel tree as specific fluid phase. Furthermore, the incompressible condition of the solid and fluid phases was imposed by applying Lagrange multiplier method. The residual weighted method was introduced for finite element formulation and followed by the descritization. The tangential stiffness matrix was derived for iterative computation of the nonlinear problems. Since the fluid variables have large degrees of freedom at a node due to the hierarchy structure, for the computational efficiency, the finite element equations were reformulated by adopting pressure as nodal variable instead of the relative velocity of fluid phase. The formulation was implemented into a home-made program and built in a multi-scale and multi-physics heart simulator. The numerical examples show that the characteristic predominate wave form of arteries (or veins) blood flow in diastolic (or systolic) can be represented by applying the proposed model and thus suggest the usability in the clinical application. It is expected that the effect of the myocardial contraction on the intramyocardial pressure and furthermore on the blood perfusion in coronary system can be elucidated by applying the proposed approach and to make contribution to etiology elucidation of the ischemic heart disease and diagnostic treatment.