ARUP; ISBN: 978-0-9562121-5-3 - CMBBE 2012 - Cardiff University

3.2 Hemodynamic simulation
In order to evaluate the cerebral blood flow within both aneurysms, the governing
Navier-Stokes equations for continuity and momentum are solved using the commercial
software package ANSYS Fluent® 13.0 (Ansys Inc., Canonsburg, PA, USA). Blood as
a suspension of plasma and cellular components is treated as an isothermal,
incompressible (ρ = 1055 kg/m³) and Newtonian fluid with a constant dynamic viscosity
η = 4.265 · 10 -3 Pa·s [9]. Although the viscosity of blood can show a strong shear
dependency, a comparison with the typically used Carreau-Yasuda model showed no
significant difference in the velocity profiles for the present range of diameters [10].
The time-dependent inflow boundary condition is presented in Figure 2(a) for one
cardiac cycle (T = 0.99 s). This flow rate is approximated using a complex Fourier
series, which consists of multiple Fourier coefficients [5]. The vessel walls are assumed
to be rigid and no-slip boundary conditions are implemented. To assure an independent
outflow through all vessels, a traction-free condition is assumed.
3.3 Analysis
In the scope of this study most widely used indicators like the maximum magnitude of
the velocity vectors or highest wall shear stresses are evaluated. Additionally, regions of
elevated pressure values are detected. In order to decrease numerical errors and achieve
periodicity, only the third cardiac cycle is analyzed, discarding the first two cycles [11].
To investigate unsteady effects appearing within one heart beat, the parameters defined
in Equations (1) and (2) are discussed. The time-averaged wall shear stresses (AWSS) as
well as the oscillatory shear index (OSI) provide information regarding stressed regions
on the arterial surface and may supply hints with respect to the rupture probability [12].
1
AWSS =
T
T
∫WSS ⋅
T ⎛
⎞
⎜
1
⎟
⎜ ∫WSS
⋅ dt
1 T ⎟
0
OSI = ⎜1−
T ⎟
(2)
2 ⎜ 1
⋅ ⎟
⎜ ∫ WSS dt
⎟
⎝
T 0 ⎠
Figure 2(b-c) illustrates the ROI where the ruptures occurred and the analyses are
particularly focused on these areas. Post-processing is accomplished with EnSight® 9.2
(CEI Inc., Apex, NC, USA) and ParaView 3.10 (Kitware Inc., Clifton Park, NY, USA).
Fig. 2: Inflow boundary condition (a), regions where the ruptures occurred (b-c)
0
dt
(1)