A Coupled Momentum Method to Model Blood Flow in Deformable Arteries

Blood velocity and pressure fields in large arteries are greatly influenced by the deformability of the vessel. 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 geometries. Computing blood flow in deformable domains using standard techniques like the ALE method remains an intractable problem for realistic anatomic and physiologic models. We have developed a new method to model 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, by assuming that for a thin-walled structure the internal traction due to the fluid friction is felt uniformly through the vessel wall. We consider a strong coupling of the degrees of freedom of the fluid and the solid domains, and a linear membrane model (enhanced with through-plane stiffness) for the vessel wall. We have used the generalized-alpha method to integrate the time evolution of the resulting equations for the deformable system. 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 (including pre-stressing the membrane). Implementation issues will be discussed and initial results with simple geometries will be presented.