numerical simulation of the fluid-structure interaction in stented aneurysms

Numerical simulation of the Fluid-Structure Interaction in

stented aneurysms

M.-A. FERNÁNDEZ, J.-F. GERBEAU, J. MURAINRIA / 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.

We will denote the contact surface (interface) between the solid and the fluid as .

Mathematical ModelingGeometry

We consider two cases: Aneurysm with and without stent-graft.

stent-graft

aneurysm wall

Mesh generated from medical images: Laboratoire de Biomécanique et Génie Biomédical, UTC.

Mathematical ModelingGeometry

Two interfaces:• Aneurysm• Stent

fluid - solid - fluidsolid - fluid

Fluid at each side of the stent.

To impose continuity in velocity and jump in pressure across the stent structure we follow [Fernández-Gerbeau-Martin M2AN ‘08], where this interface is unfolded creating two portions of fluids communicated through the stent.

Mathematical ModelingFluid and Structure: Partitioned Scheme

Structure: Lagrangian formulation

Fluid: ALE formulation

Where: solid displacement, fluid velocity and pressure, harmonic extension to fluid of the solid velocity at the interface.

Restrictions on the interface • Kinematical (Dirichlet)

• Dynamical (Neumann)

Mathematical ModelingInteraction

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 case of physiological flows.The condition must be satisfied for the fluid

But it is not necessarily true from the solid part.

Robin-Neumann coupling conditionsInteraction

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].


The Robin-Neumann coupling conditions on are

With this scheme, the Dirichlet condition is relaxed through the Robin condition.

Navier-Stokes equation + initial conditions +


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 +



MASTER FSI




MASTER FSIuntil




Numerical Example

• Test: Blocked aneurysm wall To asses the preservation of the volume in the intra-aneurysmal sac.

• 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

numerical simulation of the fluid-structure interaction in stented aneurysms

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