The objective of this work is to address the formulation of an adequate model of the external tissue environment when studying a portion of the arterial tree with fluid-structure interaction. Whereas much work has already been accomplished concerning flow and pressure boundary conditions associated with truncations in the fluid domain, very few studies take into account the tissues surrounding the region of interest to derive adequate boundary conditions for the solid domain. In this paper, we propose to model the effect of external tissues by introducing viscoelastic support conditions along the artery wall, with two-possibly distributed-parameters that can be adjusted to mimic the response of various physiological tissues. In order to illustrate the versatility and effectiveness of our approach, we apply this strategy to perform patient-specific modeling of thoracic aortae based on clinical data, in two different cases and using a distinct fluid-structure interaction methodology for each, namely an Arbitrary Lagrangian-Eulerian (ALE) approach with prescribed inlet motion in the first case and the coupled momentum method in the second case. In both cases, the resulting simulations are quantitatively assessed by detailed comparisons with dynamic image sequences, and the model results are shown to be in very good adequacy with the data.

We present a partitioned procedure for fluid-structure interaction problems in which contacts among different deformable bodies can occur. A typical situation is the movement of a thin valve (e.g. the aortic valve) immersed in an incompressible viscous fluid (e.g. the blood). In the proposed strategy the fluid and structure solvers are considered as independent "black-boxes" that exchange forces and displacements; the structure solvers are moreover not supposed to manage contact by themselves. The hypothesis of non-penetration among solid objects defines a non-convex optimization problem. To solve the latter, we use an internal approximation algorithm that is able to directly handle the cases of thin structures and self-contacts. A numerical simulation on an idealized aortic valve is finally realized with the aim of illustrating the proposed scheme. Résumé : Nous présentons un algorithme de couplage partitionné pour des problèmes d'interaction fluide-structure dans lesquels des contacts peuvent se produire entre plusieurs solidesélastiques immergés. La méthode s'applique par exemple aux valves aortiques (qui sont constituées de trois valvules baignées dans un fluide visqueux incompressible). La stratégie proposée considère les solveurs fluide et structure comme des "boites noires" indépendantes. De plus, le solveurs structure n'est pas supposé savoir gérer le contact. La contrainte de non pénétration entre les solides n'est pas convexe. Le problème est résolu de manière itérative en considérant une suite de problèmes avec contrainte convexe. L'algorithme, qui est capable de traiter l'autocontact et les structures minces, est illustré sur une configuration idéalisée de valves aortiques.Mots-clés : interaction fluide-structure, contact, valves cardiaques FSI and multi-body contact. Appliaticon to aortic valves 3

In this report, we propose a semi-implicit coupling scheme for the numerical simulation of fluid-structure interaction systems involving a viscous incompressible fluid. The scheme is stable irrespectively of the so-called addedmass effect and allows for conservative time-stepping within the structure. The efficiency of the scheme is based on the explicit splitting of the viscous effects and geometrical/convective non-linearities, through the use of the ChorinTemam projection scheme within the fluid. Stability comes from the implicit pressure-solid coupling and a specific Robin treatment of the explicit viscoussolid coupling, derived from Nitsche's method.Key-words: Fluid-structure interaction, Chorin-Temam projection scheme, Robin interface conditions, Nitsche's method, fluid incompressibility, addedmass effect, time discretization, semi-implicit coupling, partitioned scheme.Preprint submitted for publication to SIAM Journal on Scientific Computing * INRIA, REO project-team † Correspondence to: miguel.fernandez@inria.fr Résumé : Dans ce rapport, nous proposons un schéma de couplage semiimplicite pour la simulation numérique de problèmes d'interaction fluide-structure où intervient un fluide visqueux incompressible. Le schéma est stable indépendamment de l'effet de masse-ajoutée et permet d'utiliser une discrétisa-tion conservative pour la structure. L'efficacité du schéma repose sur le décou-plage explicite des effets visqueux et non-linéaires (convection et géometrie), grâce au schéma de Chorin-Temam. La stabilité provient du couplage implicite solide-pression et d'un traitement spécifique du couplage explicite par des conditions de type Robin, dérivéesà partir de la méthode de Nitsche.

A procedure for modeling the heart valves is presented. Instead of modeling complete leaflet motion, leaflets are modeled in open and closed configurations. The geometry of each configuration can be defined, for example, from in vivo image data. This method enables significant computational savings compared with complete fluid-structure interaction and contact modeling, while maintaining realistic three-dimensional velocity and pressure distributions near the valve, which is not possible from lumped parameter modeling. Leaflets are modeled as immersed, fixed surfaces over which a resistance to flow is assigned. On the basis of local flow conditions, the resistance values assigned for each configuration are changed to switch the valve between open and closed states. This formulation allows for the pressure to be discontinuous across the valve. To illustrate the versatility of the model, realistic and patient-specific simulations are presented, as well as comparison with complete fluid-structure interaction simulation.