NUMERICAL ANALYSIS OF MYOCARDIAL BLOOD SUPPLY ON A GRAPH OF ELASTIC VESSELS

We analyze a mathematical model of blood supply to the arterial part of the myocardium. The model is defined on a graph of elastic vessels that includes the vessel radii and geometry. A nu-merical analysis of myocardial blood supply is carried out allowing for the elasticity of the blood vessels and for some pathologies of blood supply to the myocardium. In the mathematical model of blood supply to the myocardium constructed in [1, 2], blood was treated as a homogeneous viscous incompressible fluid, the arteries as rigid impermeable cylindrical pipes, and the blood flow was assumed constant and laminar. In reality, however, the heart vessels form an elastic system capable of controlled contraction and expansion. In the present article, we develop a mathematical model based on the model of [1, 2] that allows for the elasticity of the blood vessels. The dependence between the circulation rate and the pressure difference ∆p p p = −1 2 driving the circula-tion is generally derived from the Poiseuille law Q p p L r