Biomedical Engineering Reference
In-Depth Information
Fig. 12.8.
Left panel: difference (in cm/s) between the fluid velocity computed in the rigid domain
simulation and the one computed in the 4DIB simulation (left); velocity (in cm/s) computed with
the 4DIB approach (right); both at peak systole. Right panel: difference (in dyne/cm
2
) between the
WSS computed in the rigid domain simulation and the one computed in the 4DIB simulation (left);
WSS (in dyne/cm
2
) computed with the 4DIB approach (right); both at peak systole
Quantification of the errors of the registration process is reported in [69]. A more
detailed analysis of the error as a function of the number of nodes
n
S
and triangles
n
T
used in each couple of frames is however still missing.
Numerical tests have been run with
LifeV
to evaluate the difference between
the velocity and wall shear stress (WSS) fields computed with the 4DIB approach
and those computed on a rigid domain blood flow simulation. The choice of aorta is
motivated by the fact that here the vessel deformation is relevant (mostly as a con-
sequence of the motion of the heart) and is supposed to affect significantly the blood
motion. To discretize the ALE Navier-Stokes system, we have chosen a first-order
time advancing scheme and a finite element approximation for the space dependence
(
1
bubble for the fluid velocity).
Both the velocity and the WSS fields exhibits a considerable difference with re-
spect to the rigid domain case, as shown in Fig. 12.8. In particular, the relative
L
2
norm of the difference between the 4DIB fields and the rigid domain fields has an
average over the cardiac cycle of 84.52 % for the velocity and 83.18 % for the WSS.
We also performed an
in-silico
consistency test of the 4DIB approach with respect
to a FSI simulation, assumed to be the reference benchmark solution. In particular
we have first run a FSI simulation, obtaining the fluid velocity and pressure fields
and the displacement of the vessel wall. Then, we have used this displacement as if it
was retrieved from images to feed a 4DIB simulation, with the same inflow/outflow
boundary conditions and fluid properties as in the FSI case. The comparison of the
results obtained with the two approaches has shown a good agreement, being below
1 % of relative difference, on both velocity and WSS. Notice that the computational
time required by the 4DIB simulation is about twice the cost of a rigid simulation
(see [69]).
These tests show that (i) when a relevant motion affects the vessel like in the
aortic case, the 4DIB approach is a viable way for a more realistic description of
1
for the pressure and
P
P
