Oscillatory flow in a tube with time-dependent wall deformation and its application to Myocardial Bridges

Abstract

In this paper we numerically investigate a one-dimensional model of blood flow in the human coronary arteries. The nonlinear hyperbolic system is expressed in terms of the cross-sectional area, flow velocity and pressure (A, u, p). The more widely studied linearised system is also discussed where conservation of static pressure, instead of total pressure, is enforced. The method of outgoing characteristics is used to satisfy the interface conditions, while a three-element windkessel model is adopted as outflow condition at the terminals of the network. Inside the segmental domain the leap-frog method is used for numerical integration. Within the context of this model we pay particular attention to the case when abrupt or smooth, space and time dependent variation of cross-sectional area of an artery is caused by externally prescribed motion of the vessel walls (e.g. myocardial bridge, flow watch). The derivation of the model and the numerical implementation are detailed. They are applied to model numerical experiments of the arterial system. Additionally to a system studied in [10, 15, 22, 28] the coronary arteries are parameterised. The main features of the flow through myocardial bridges are discussed.