Influence of Blood Rheology and Outflow Boundary Conditions in Numerical Simulations of Cerebral Aneurysms - Mathematical Methods and Models in Biomedicine - page 156

3D-0D Coupling

The coupling of the 0D model ( 26 ) with the 3D fluid equations corresponds to
imposing the linear counterpart of the absorbing boundary condition for the 1D
model, W 2 =

0, directly on the 3D artificial section. The coupling is achieved by
forcing the pressure given by the resistance of the 0D model at the 3D interface
section Γ art , similarly to the 3D-1D coupling. An explicit coupling is applied,

meaning that the mean pressure at the current time step, P n + 1 , is computed by means
of expression ( 26 ) using the flow rate on the artificial section at the previous time
step, Q n , and it is prescribed at the artificial section at the current time step. Thus,
as in [ 13 ], the defective averaged data condition

ρβ
√ 2 A 5 / 4
0

P ( n + 1 ) = Q ( n ) ,

on Γ art , (27)

is prescribed by means of a Neumann boundary condition ( 24 ) on the 3D artificial
section.

4 Numerical Simulation Setup

In this work, the hemodynamics inside an intracranial saccular aneurysm is analyzed
in an anatomically realistic geometry, as well as in idealized geometries. The
idealized geometries serve as test cases with reduced complexity of the flow field,
allowing for a better understanding of the effects of changing the fluid models, the
boundary conditions, and in evaluating steady and unsteady simulations. Moreover,
the numerical simulations in the idealized geometries have lower computational
costs than in the realistic ones, allowing to conduct a comprehensive series of
tests. While clinical decisions should be based on numerical simulations using
anatomically realistic patient-specific geometries, idealized models provide insight
into the hemodynamics with respect to choices in modeling and numerical setup.
In both steady and unsteady cases, the fluid is initially at rest and then the inflow
flow rate is linearly increased with a parabolic profile to a final steady-state flux
Q 67 cm 3 s − 1 , such that = 2 .

tQ
t ramp ,

Q ramp
in

( t )= for t < t ramp , (28)

Q in = Q , for t > t ramp , (29)

where t ramp is the time length of the linear ramp, and it is set to t ramp = 1s in

67 cm 3 s − 1 ,is
obtained through the relationship between flow rate and vessel areas, derived from
measurements in internal carotid and vertebral arteries [ 5 ].

all test cases. The reference value for the inflow condition, Q = 2 .