Free access article

ESAIM: Proc., September 2005, Vol. 14, pp. 48-62
DOI: 10.1051/proc:2005005

An embedded surface method for valve simulation. Application to stenotic aortic valve estimation

Paola Causin¹, Nuno Diniz dos Santos², Jean-Frédéric Gerbeau³, Carine Guivier⁴ and Paul Métier<sup>5

1</sup>  CMCS/IACS, Ecole Polytechnique Fédérale de Lausanne, CH-1015 Lausanne, Switzerland; paola.causin@epfl.ch
²  INRIA - Projet REO - B.P.105 F-78153 Le Chesnay Cedex, France; Nuno-Miguel.Diniz-Dos-Santos@inria.fr
³  INRIA - Projet REO - B.P.105 F-78153 Le Chesnay Cedex, France; Jean-Frederic.Gerbeau@inria.fr
⁴  IRPHE UMR 6594, Equipe de Biomécanique Cardiovasculaire, Institut Méditerranéen de Technologie, F-13451 Marseille cedex 20, France; guivier.carine@esm2.imt-mrs.fr
⁵  Commissariat à l'Énergie Atomique (CEA), DEN/DM2S/SFME/LTMF Saclay, F-91191 Gif sur Yvette Cedex, France; pmetier@cea.fr

Abstract
This work deals with the modelling and the simulation of a moving rigid valve in a blood flow. We consider a fluid-structure coupling between an unsteady incompressible Navier-Stokes system for the fluid, and an ODE for the structure with a rotation angle as only degree of freedom. The kinematic constraint on the fluid-structure interface is enforced via a Lagrange multiplier. A fictitious domain approach allows us to use a fixed grid for the fluid domain, and also to easily consider large valve displacements. We present numerical results and we discuss clinical indexes used to characterize aortic valve stenosis.

Résumé
Nous présentons un travail de modélisation et simulation d'une valve rigide dans un écoulement sanguin. Nous considérons un couplage fluide-structure où l'écoulement sanguin est régi par le système de Navier-Stokes instationnaire incompressible, tandis que la dynamique de la valve est ramenée à une EDO correspondant à une rotation. La contrainte cinématique à l'interface fluide-structure est imposée par un multiplicateur de Lagrange. Une approche de type domaine fictif nous permet d'adopter un maillage fixe pour le domaine fluide et de traiter aisément les grands déplacements de la valve. Nous présentons des simulations numériques et nous discutons d'indices cliniques utilisés pour caractériser des sténoses aortiques.

Key words: fluid-structure interaction, Navier-Stokes, fictitious domain, Lagrange multiplier, valve, stenosis, aorta


© EDP Sciences, ESAIM 2005

The OpenURL standard is a protocol for transmission of metadata describing the resource that you wish to access. An OpenURL link contains article metadata and directs it to the OpenURL server of your choice. The OpenURL server can provide access to the resource and also offer complementary services (specific search engine, export of references...). The OpenURL link can be generated by different means.

• If your librarian has set up your subscription with an OpenURL resolver, OpenURL links appear automatically on the abstract pages.
• You can define your own OpenURL resolver with your EDPS Account. In this case your choice will be given priority over that of your library.
• You can use an add-on for your browser (Firefox or I.E.) to display OpenURL links on a page (see http://www.openly.com/openurlref/). You should disable this module if you wish to use the OpenURL server that you or your library have defined.