One-dimensional blood flow modelling in the human arterial system with Finite Volume Methods

In this thesis, it is investigated how the blood flow changes in different physiological situations, using a one-dimensional model, that describes the blood flow in compliant vessels. The one-dimensional model, that describes the blood flow, is derived based on the physical laws of conservation of momentum and conservation of mass. A high resolution flux differencing scheme is applied to a stented artery, a tapered artery, an arterial bifurcation and a network of the 55 main arteries in the human arterial tree. It is found that inserting a stent led to an increase in the peak pressure and a dip below the equilibrium pressure, just before the stent. The nonlinearities in the model are shown using a long tapered artery, in the form of the steepening of the pulse. The current treatment of the bifurcations has led to reasonable physical reflections, in the bifurcation test cases. The network of 55 arteries showed that bifurcations play an important role in the blood flow patterns and, as such, they should not be ignored when considering a single blood vessel. Further research should focus on the implementation of a vascular prosthesis and more advanced treatments of the bifurcations.