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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. MURA INRIA / REO Team Paris- Rocquencourt France. EndoCom. Outline. Motivation Mathematical modeling Robin-Neumann coupling conditions Numerical Examples Conclusions.

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Numerical simulation of the Fluid-Structure Interaction in stented aneurysms

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  1. Numericalsimulation of the Fluid-Structure Interaction instented aneurysms M.-A. FERNÁNDEZ, J.-F. GERBEAU, J. MURA INRIA / REO Team Paris-Rocquencourt France. EndoCom

  2. Outline • Motivation • Mathematical modeling • Robin-Neumann coupling conditions • Numerical Examples • Conclusions

  3. 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.

  4. MathematicalModelingGeometry 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

  5. MathematicalModelingGeometry Two interfaces: • Aneurysm • Stent • 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. fluid - solid - fluid solid - fluid

  6. MathematicalModelingFluid 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.

  7. MathematicalModelingInteraction 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 case of physiological flows. The condition must be satisfied for the fluid But it is not necessarily true from the solid part.

  8. Robin-NeumanncouplingconditionsInteraction 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].

  9. Robin-NeumanncouplingconditionsInteraction The Robin-Neumann coupling conditions on are • With this scheme, the Dirichlet condition is relaxed through the Robin condition.

  10. Robin-NeumanncouplingconditionsInteraction More precisely, the coupling algorithm consist in iterations between the solid and the fluid solvers by exchange force and velocity. MASTER FSI Navier-Stokes equation + initial conditions + Elasticity equation + initial conditions +

  11. Robin-NeumanncouplingconditionsInteraction More precisely, the coupling algorithm consist in iterations between the solid and the fluid solvers by exchange force and velocity. MASTER FSI Navier-Stokes equation + initial conditions + Elasticity equation + initial conditions +

  12. Robin-NeumanncouplingconditionsInteraction More precisely, the coupling algorithm consist in iterations between the solid and the fluid solvers by exchange force and velocity. MASTER FSI Navier-Stokes equation + initial conditions + Elasticity equation + initial conditions +

  13. Robin-NeumanncouplingconditionsInteraction More precisely, the coupling algorithm consist in iterations between the solid and the fluid solvers by exchange force and velocity. MASTER FSI until Navier-Stokes equation + initial conditions + Elasticity equation + initial conditions +

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

  15. Numerical Example • Test: Aneurysm wall pressure for different sizes

  16. Numerical Example

  17. Numerical Example

  18. 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.

  19. Thank you

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