Biomedical Engineering Reference
In-Depth Information
These pressure drops, together with the values of the flow rate at the side-branch
outflow, indicate that the reduced models provide appropriate outflow boundary
conditions, accounting for the side-branch. Prescribing a traction-free condition
on the hole section, or neglecting its existence by a u
0 condition, results in
significant discrepancies by considering the branched geometry. Thus, these outflow
conditions seem to be worse assumptions than coupling with the reduced models.
The differences are more pronounced in the WSS map than in the velocity cross-
section, but the minimum difference values are still found when coupling with
the reduced models. It is important to notice that despite these larger values, they
are confined to the aneurysm at the location of the side-branch, and the average
differences are extremely low.
The sensitivity of the computed solution to the boundary condition imposed at the
side-branch outflow section is depicted in Figs. 10 and 11 , where different outflow
conditions are imposed in the clipped geometry. The values of the differences are
high, both in the velocity magnitude and in the WSS, except when using the 1D and
0D boundary conditions. From these results it is possible to infer that in this case
the calculated resistance of the 0D model is consistent with the 1D model.
As before, the WSS differences are mainly localized close to the side-branch
base. In this region the values are very high, yet when considering the average in the
whole geometry, the values of the differences decrease abruptly. Thus, as expected,
the influence of the side-branch and its outflow boundary condition is particularly
important when the side-branch is located very close or within the aneurysm.
Figure 12 displays the differences that exist between the steady-state solution and
the time average of the unsteady solution, both for the velocity cross-section and the
WSS distribution, in the case of the hole geometry coupled with the 1D model. It is
possible to observe that the differences are very small, especially when considering
the average. At first sight this could indicate a great resemblance between the steady
and unsteady solutions. However, comparing the unsteady solutions of the clipped
geometry coupled with the 1D model and the branched geometry with traction-
free boundary condition, the differences are magnified at several instants of the
cardiac cycle (see Fig. 13 ). The comparison of these two cases reveals minimal
differences for the steady-state inflow conditions, as shown in Fig. 9 . Nevertheless,
these differences are again significantly higher at different instants of the cardiac
cycle, as plotted in Fig. 13 . Exhaustive conclusions cannot be drawn from steady-
state solutions, since even the average difference of the unsteady solutions of the
clipped geometry with the 1D boundary condition and the branched geometry with
the traction-free boundary condition is greater than the one for the steady-state.
This demonstrates, once again, the relevance of considering unsteady simulations,
especially when studying the influence of boundary conditions on the numerical
solutions.
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