Numerical Modeling of Fluid-Structure Interaction of Blood in a Vein by Simulating Conservation of Mass and Linear Momentum with the Finite Element Method in FEniCS

In medicine a fundamental understanding for blood flow in human arteries is significantly important. In socalled hemodynamics engineers all over the world simulate blood flows in healthy and diseased vessels. Scientific findings in this area help to improve cardiovascular assisting devices and to plan surgical operations. The difficulty with such simulations is the interaction of the blood flow with the elastic vessel wall, which deforms due to changing flow conditions. We will present a two-dimensional model for blood flowing through an arterial vessel and investigate the balance of mass and the balance of linear momentum. We will adjust these balance equations appropriately and define time dependent boundary conditions. The necessary partial differential equations for the fluid-structure interaction will be solved by using the finite element method in FEniCS 1]. (© 2013 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)