Numerical simulation of the
Fluid-Structure Interaction in
stented aneurysms
M.-A. FERNÁNDEZ, J.-F. GERBEAU, J. MURA
INRIA / REO Team
Paris-Rocquencourt France.
EndoCom
Outline
• Motivation
• Mathematical modeling
• Robin-Neumann coupling conditions
• Numerical Examples
• Conclusions
Motivation
Abdominal Aortic Aneurysms (AAA) is
a bulbous enlargement of the aorta
that eventually may burst.
A common treatment is the
implantation of an Stent-Graft. To
improve the follow-up of AAA, a
device
allowing
the
remote
monitoring of the intra-aneurismal
pressure is currently in development
at ENDOCOM project.
Mathematical Modeling
Geometry
We consider two cases:
Aneurysm with and without
stent-graft.
We will denote the
contact surface
(interface) between
the solid and the
fluid as .
stent-graft
Mesh generated from medical
images: Laboratoire de Biomécanique
et Génie Biomédical, UTC.
aneurysm
wall
Mathematical Modeling
Geometry
Two interfaces:
• Aneurysm
• Stent
fluid - solid - fluid
Fluid at each side of the stent.
To impose continuity in velocity and
solid - fluid
jump in pressure across the stent
structure we follow [FernándezGerbeau-Martin M2AN ‘08], where
this interface is unfolded creating two
portions of fluids communicated
through the stent.
Mathematical Modeling
Fluid and Structure: Partitioned Scheme
Fluid: ALE formulation
Structure: Lagrangian formulation
Where:
solid displacement,
fluid velocity and pressure,
harmonic extension to fluid of the solid velocity at the interface.
Mathematical Modeling
Interaction
Restrictions on the interface
• Kinematical (Dirichlet)
• Dynamical (Neumann)
A special issue is the problem of enclosed fluid between the
stent and aneurysm wall.
Moreover, we have to face large added-mass effects, as in the
The condition
must be satisfied for the fluid
case
of physiological flows.
But it is not necessarily true from the solid part.
Robin-Neumann coupling conditions
Interaction
We use of Robin condition for the fluid on
:
The parameter plays the role of compliance, relaxing the
kinematic condition during the Fluid-Structure iterations.
It has been shown that this scheme can successfully tackle
problems with a large added-mass effect and it shows good
convergence properties [Badia-Nobile-Vergara. J. Comput. Phys.’08 /
Fernández-Maday-Mullaert. Preprint].
Robin-Neumann coupling conditions
Interaction
The Robin-Neumann coupling conditions on
are
With this scheme, the Dirichlet condition is relaxed through
the Robin condition.
Robin-Neumann coupling conditions
Interaction
More precisely, the coupling algorithm consist in iterations between
the solid and the fluid solvers by exchange force and velocity.
MASTER FSI
Elasticity equation + initial
conditions +
Navier-Stokes equation + initial
conditions +
Robin-Neumann coupling conditions
Interaction
More precisely, the coupling algorithm consist in iterations between
the solid and the fluid solvers by exchange force and velocity.
MASTER FSI
Elasticity equation + initial
conditions +
Navier-Stokes equation + initial
conditions +
Robin-Neumann coupling conditions
Interaction
More precisely, the coupling algorithm consist in iterations between
the solid and the fluid solvers by exchange force and velocity.
MASTER FSI
Elasticity equation + initial
conditions +
Navier-Stokes equation + initial
conditions +
Robin-Neumann coupling conditions
Interaction
More precisely, the coupling algorithm consist in iterations between
the solid and the fluid solvers by exchange force and velocity.
MASTER FSI
until
Elasticity equation + initial
conditions +
Navier-Stokes equation + initial
conditions +
Numerical Example
• Test: Blocked aneurysm wall  To asses the preservation of the volume in
the intra-aneurysmal sac.
Numerical Example
• Test: Aneurysm wall pressure for different sizes
Numerical Example
Numerical Example
Conclusions
• The Robin-Neumann coupling algorithm can be successfully applied to
the simulation of a stented AAA, involving an enclosed fluid.
• Convergence rate of the method sensitive to the choice of the Robin
parameter .
• Simulations confirm that in presence of the stent the intrasac pressure is
reduced.
• Maximal intrasac pressure decreases as the aneurysm radius increases,
which is in agreement with experimental results.
• The intrasac pressure is almost constant in space (not in time) with
respect to the lumen pressure.
Thank you