Biomedical Engineering Reference
In-Depth Information
Fig. 9.11. Placement of the cerebral aneurism in the closed-loop model of the CVS and results at
coupling interfaces
In this example, the finite-element mesh of the 3D model consists of 20K nodes
and 120K tetrahedra, and the time step used was 1
10 3 s. Three cardiac cycles,
.
25
·
of period T
0 s, were run from at-rest conditions. To perform the coupling be-
tween the 3D and the 1D-0D closed-loop model we used an iterative method based
on a Broyden algorithm such that the equilibrium between the models at coupling
interfaces is achieved at each time step. In this case, the explicit approach to couple
the heterogeneous models results in an unstable coupling scheme even for time steps
30 times smaller than the one used here. In contrast to the previous example, in this
case the geometrical features of the 1D cerebral artery, replaced by a 3D model, are
significantly different. This motivated the use of strong coupling schemes. The inter-
ested reader is referred to [10, 36] for a detailed account of such coupling strategies.
The results at the coupling interfaces are presented in Fig. 9.11. In this case the
pressure pulse is almost the same at proximal and distal locations, while the flow
rate exhibits a decrease in the peak, which is the result of the presence of the en-
larged capacitance of the arterial segment due to the aneurism (same effect that in
the previous example).
Concerning the local blood flow, Fig. 9.12 presents a set of streamlines computed
at different time instants. A stagnation zone can be observed in the deepest part of
=
1
.
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