Investigation of the blood flow in deformable vessels using stabilized finite element method

The study and simulation of blood flow in the cardiovascular system have many applications such as pathologies studies, surgical planning, and design of medical devices. Several works within this area consider the problem using a rigid wall assumption, while blood velocity and pressure in large arteries are greatly influenced by vessel wall dynamics. The Coupled Momentum Method (CMM) is based on a strong coupling of degrees-of-freedom of the fluid and the solid domains. This coupling is made by considering that the deformation of the wall, in a variational level, become a boundary condition for the fluid domain. As an advantage, description of motion (Eulerian) may be kept the same and a fixed mesh. In this study, blood is considered a Newtonian fluid and the wall a thin-walled linear elastic. This work is focused on using fluid-structure interaction in 3D geometries to evaluate the blood and vessel dynamics in contrast to the rigid wall formulation what is considered only a fluid dynamic problem. For realistic and physiological parameters, CMM has demonstrated to be a good alternative for the simulation of blood flow in large arteries by virtue of representing more realistic phenomena than a rigid wall model. The results were obtained using FEniCS and Python, and are in agreement with the theoretical and numerical solutions from the literature.