Abstract

The aim of this paper is to simulate the bloodstream through a network of blood vessels with a Finite Element Method in one dimension. A one dimensional system of partial differential equations is used. This system can be written in hyperbolic conservation form with the state variables cross-sectional area, the flow, the velocity and the pressure. To solve the system of partial differential equations, numerically correct boundary conditions have to be considered. For the input, a pressure function is used. To simulate the load downstream and the compliance of the arterial segments, a Windkessel model consisting of three elements is used.  By simulating bifurcations the considered abstract vascular network can be build up. For that a nonlinear system of equations is set up and solved. The partial differential equation system cannot be solved analytically. Hence, to solve it a numerical Finite Element Method is used. In this context, a Taylor Galerkin method of second order with basic functions of first order is used. The model is implemented by using the mathematical software MATLAB. To verify the model, several simulations are done, using an abstract arterial tree built up by thirteen central arterial segments. In all simulations, the parameters of the Windkessel model and the parameters of the arterial segments are based on experiments and on physiological values. In all tests, physiologically realistic results are obtained.