1D hyperbolic models for blood flow in arteries

The study of blood flow dynamics through mathematical models and numerical simulations is an important, non invasive tool to help the prediction of pathologies, as well as the consequences of surgery. In particular, the application of mathematical simplified models has proved to give useful information at fair computational costs, allowing also for the simulation of large arterial networks. In this work a reduced one-dimensional (1D) model is studied for blood flow in arteries, describing the evolution in time and one dimensional space coordinate of the mean pressure, flow rate and area, illustrating the wave propagation behaviour of blood flow in arteries. The hyperbolic system of equations is discretized in space using a second order Taylor-Galerkin method, and in time with the Lax-Wendroff scheme. The model was tested using a variety of non-physiological and physiological conditions occurring in the human arterial network. Properties and strengths of the model, regarding the numerical simulations in view of clinical applications are analyzed, and their limitations and drawbacks commented.