Biomedical Engineering Reference
In-Depth Information
Table 13.2. Different meshes considered for the numerical simulation: the boundary layer meshes
(BL mesh) such as in Fig. 13.11b) and the fully unstructured meshes (U mesh) such as in
Fig. 13.11c) with three different mesh sizes h : fine, middle and coarse. For the BL meshes, the
ratio h
/
h n is taken to be 10
BL Mesh
Fine
Middle
Coarse
# Nodes
212.633
57.318
23.697
U Mesh
Fine
Middle
Coarse
# Nodes
154.732
36.490
8.508
cms 2
is
μ =
0
.
035 g
/ (
)
. The densities for blood and arterial wall are respectively
cm 3 . Timings and validation for FSI solver used were
already discussed in [12], while in [11] the scalability issue was addressed. The sim-
ulations reported in this work were run on the Cray XT6 supercomputer in the UK
National Supercomputing Service HECToR 7 .
The FSI simulations are computationally expensive, so that they are run in paral-
lel. As an example, the middle meshes are run on 48 cores, using 24 MPI processes
per node; and the simulation takes about 8 hours to run for one heartbeat with the
fine mesh. Due to the computational cost and since we are interested in the compar-
ison of the WSS for the different meshes we did not run the simulation for several
heartbeats, which would be necessary to reach periodicity and to obtain physiolog-
ical results. We just ran for one heartbeat starting from a zero initial condition and
we compared systolic hemodynamic values.
Fig. 13.12 shows the results obtained with the boundary layer mesh of middle
size. The streamlines show clearly the secondary flows which are in agreement with
the WSS values. The flow impinging on the bed of the junction creates a region of
high wall shear stress. Moreover, the blood flow is accelerated in the outlet popliteal
artery since the graft is sewed on an artery of smaller diameter. This mismatch in
diameter creates also a region of high wall shear stress near the outlet. The observed
flow behavior in such an end-to-side bypass do not occur naturally in arteries and is
widely implicated in the initiation of the disease formation processes [20, 32].
Fig. 13.13 shows the WSS distribution at peak systole obtained for the six dif-
ferent meshes. WSS shows to be quantitatively better evaluated on the meshes with
boundary layer, while even the finest mesh without boundary layer shows a substan-
tial underestimation of the WSS with respect to all the the meshes with boundary
layer.
cm 3 and
ρ f =
1 g
/
ρ s =
1
.
2 g
/
13.5 Conclusions
We have presented a pipeline for generating spatially-adapted, high-quality tetrahe-
dral meshes from a given STL triangulation and have shown its effectiveness for
different cardiovascular simulations.
7
http://www.hector.ac.uk
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