Data Assimilation in Cardiovascular Fluid–Structure Interaction Problems: An Introduction - Fluid-Structure Interaction and Biomedical Applications - page 461

Fig. 6.11 Aneurysm simulation. Top-left : Mesh used for the simulation. Bottom-left : Piecewise
linear approximation of the Young's modulus E in the forward simulation. Top-right : Velocity
vectors and pressure at time t D 0:96 s. Bottom-right : Comparison between the displacement
obtained with the forward simulation, the noisy data and the computed displacement, at time t D
0:96 sandforP D 0:1

which we prescribe the piecewise linear Young's modulus shown in Fig. 6.11
(bottom-left). For the forward simulation, we take E a D 4 10 6 dyne/cm 2 ;E b D
10 7 dyne/cm 2 ;E c D 5 10 6 dyne/cm 2 . We prescribe at the inlet a parabolic profile
for the velocity, whose maximum u max lies on the axis of symmetry and it is given by
u max D u 0 max C A max sin 2t
T

I 0 ;

where u 0 max D 5 cm/s, A D 55cm/s and T D 0:6s. At the outlet we prescribe the
absorbing boundary conditions proposed in [ 57 ]. We run the simulation for two heart
beats, i.e., for 0<t 2T . We add a uniform noise P to the forward displacement
fwd and we use the result as data for the control problem. In Fig. 6.11 (bottom-
right) we report a comparison between the displacement obtained with the forward
simulation, the noisy data and the computed displacement at time t D 0:96s. The
agreement is very good.