Influence of Blood Rheology and Outflow Boundary Conditions in Numerical Simulations of Cerebral Aneurysms

It is believed that the formation, growth and rupture of cerebral aneurysms is
associated with local hemodynamics. For that reason, 3D detailed simulations
of blood flow in patient-specific geometries are very important in understand-
ing this disease. However, patient-specific numerical simulations are subject
to uncertainties due to the image reconstruction, the mathematical modeling
choices, and the numerical approximations.

In this work the sensitivity of the numerical fluid solution and correspond-
ing hemodynamics indicators is studied regarding several modeling choices.
Namely, two fluid models are compared: the Newtonian and the Carreau shear-
thinning non-Newtonian models. Both are applied in an anatomically realistic
geometry and in idealized configurations. Also, both steady and unsteady in-
flow regimes are analised. On the idealized configurations four types of outflow
conditions on the side-branch of the idealized geometries are compared: the
standard traction-free condition, the no-slip condition (meaning that the side-
branch is neglected), and coupling with reduced 1D and 0D models. The two
later boundary conditions, including the models and their coupling with the
3D fluid equations, are presented and described in detail, within the scope of
the so-called Geometrical Multiscale Approach.

Results indicate large impact in changing the outflow condition in the
numerical solution. The reduced models provide good descriptions for the
side-branch in the case here studied. Results also show differences between the
steady and unsteady solutions at specific time instants of the cardiac cycle.
Differences between Newtonian and non-Newtonian simulations are important
but less significant than the sensitivity to varying the boundary conditions.