A coupled momentum method for modeling blood flow in three-dimensional deformable arteries

• Published in: Computer methods in applied mechanics and engineering Vol. 195; no. 41; pp. 5685 - 5706
• Main Authors: Figueroa, C. Alberto, Vignon-Clementel, Irene E., Jansen, Kenneth E., Hughes, Thomas J.R., Taylor, Charles A.
• Format: Journal Article
• Language: English
• Published: Amsterdam Elsevier B.V 01-08-2006; Elsevier
• Subjects: Blood flow; Computational techniques; Exact sciences and technology; Finite element; Fluid–solid interaction; Fundamental areas of phenomenology (including applications); Mathematical methods in physics; Physics; Three-dimensional; Wave propagation; Fluid–solid interaction; Wave propagation; Three-dimensional; Finite element; Blood flow; Fluid-solid interaction; Membranes; Deformability; Euler Lagrange equation; Momentum; Arteries; Finite element method; Time domain method; Initial conditions; Three dimensional flow; Blood circulation; Variational calculus; Modelling; Blood pressure; Circulatory system; Wall effects; Incompressible fluid; Man; Shear wall; Transverse shear
• ISSN: 0045-7825; 1879-2138
• DOI: 10.1016/j.cma.2005.11.011

Blood velocity and pressure fields in large arteries are greatly influenced by the deformability of the vessel. Moreover, wave propagation phenomena in the cardiovascular system can only be described considering wall deformability since blood is usually described as an incompressible fluid. However, computational methods for simulating blood flow in three-dimensional models of arteries have either considered a rigid wall assumption for the vessel or significantly simplified or reduced geometries. Computing blood flow in deformable domains using standard techniques like the ALE method remains a formidable problem for large, realistic anatomic and physiologic models of the cardiovascular system.
We have developed a new method to simulate blood flow in three-dimensional deformable models of arteries. The method couples the equations of the deformation of the vessel wall at the variational level as a boundary condition for the fluid domain. We consider a strong coupling of the degrees-of-freedom of the fluid and the solid domains, and a linear membrane model (enhanced with transverse shear) for the vessel wall. The effect of the vessel wall boundary is therefore added in a monolithic way to the fluid equations, resulting in a remarkably robust scheme. We present here the mathematical formulation of the method and discuss issues related to the fluid–solid coupling, membrane formulation, time integration method, and boundary and initial conditions. Implementation is discussed and results with simple geometries as well as large subject-specific models are presented.