Simulation numérique du système cardiovasculaire

Les progrès réalisés en mathématiques appliquées permettent aujourd’hui d’envisager la simulation sur ordinateur de certains compartiments du système cardiovasculaire. Nous proposons de faire un point sur quelques modèles, en nous focalisant sur la simulation de l’écoulement du sang dans des artères déformables et sur la simulation de la contraction du myocarde sous l’effet de la propagation d’un signal électrique. Nous tentons également de présenter des applications possibles de ce type de travaux.In this article, we aim at giving a non-technical overview of some mathematical models currently used in the numerical simulation of the cardiovascular system. A hierarchy of models for blood flows in large arteries is briefly described as well as an electromechanical model for the heart. We discuss some possible applications of the numerical simulations of such models, for example the optimization of prostheses. We also address the issue of the data assimilation for the calibration of the models

Une Formulation mixte de plaques ou l'effort tranchant est approché dans son espace naturel

Projet MODULEFRésumé disponible dans le fichier PD

Etude numérique du verrouillage de quelques méthodes d'éléments finis pour les coques

Projet MODULEFLe verrouillage numérique est un phénomène susceptible d'affecter toutes les méthodes d'éléments finis de coques minces et les arguments utilisés dans la littérature pour garantir que telle ou telle méthode n'en souffre pas sont rarement convaincants. On propose ici une méthodologie simple pour détecter numériquement le verrouillage et on l'utilise pour tester quelques éléments issus des codes CESAR-LCPC et MODULEF qui s'avèrent tous sujets à ce problème, quoiqu'à des degrés divers de gravité

A Locking-Free Approximation of Curved Rods by Straight Beam Elements

Projet MODULEFWe consider an elastic model for a curved rod with arbitrary three-dimen­sional geometry, incorporating shear and membrane as well as bending and torsion effects. We define an approximation procedure based on a discretization by linear Timoshenko beam elements. Introducing an equivalent mixed problem, we establish optimal error estimates independent of the thickness, thereby proving that shear and membrane locking is avoided. The approximation scheme is tested on specific examples and the numerical results confirm the estimates obtained by theory

Filtering for distributed mechanical systems using position measurements: perspectives in medical imaging

International audienceWe propose an effective filtering methodology designed to perform estimation in a distributed mechanical system using position measurements. As in a previously introduced method, the filter is inspired from robust control feedback, but here we take full advantage of the estimation specificity to choose a feedback law that can act on displacements instead of velocities and still retain the same kind of dissipativity property which guarantees robustness. This is very valuable in many applications for which positions are more readily available than velocities, as in medical imaging. We provide an in-depth analysis of the proposed procedure, as well as detailed numerical assessments using a test problem inspired from cardiac biomechanics, as medical diagnosis assistance is an important perspective for this approach. The method is formulated first for measurements based on Lagrangian displacements, but we then derive a nonlinear extension allowing to instead consider segmented images, which of course is even more relevant in medical applications

Robust filtering for joint state parameter estimation for distributed mechanical systems

International audienceWe present an effective filtering procedure for jointly estimating state variables and parameters in a distributed mechanical system. This method is based on a robust, low-cost filter related to collocated feedback and used to estimate state variables, and an $H^\infty$ setting is then employed to formulate a joint state-parameter estimation filter. In addition to providing a tractable filtering approach for an infinite-dimensional mechanical system, the $H^\infty$ setting allows to consider measurement errors that cannot be handled by Kalman type filters, e.g. for measurements only available on the boundary. For this estimation strategy a complete error analysis is given, and a detailed numerical assessment - using a test problem inspired from cardiac biomechanics - demonstrates the effectiveness of our approach

Fundamental principles of data assimilation underlying the Verdandi library: applications to biophysical model personalization within euHeart

International audienceWe present the fundamental principles of data assimilation underlying the Verdandi library, and how they are articulated with the modular architecture of the library. This translates -- in particular -- into the definition of standardized interfaces through which the data assimilation library interoperates with the model simulation software and the so-called observation manager. We also survey various examples of data assimilation applied to the personalization of biophysical models, in particular for cardiac modeling applications within the euHeart European project. This illustrates the power of data assimilation concepts in such novel applications, with tremendous potential in clinical diagnosis assistance

Coupling schemes for the FSI forward prediction challenge: comparative study and validation

International audienceThis paper presents a numerical study in which several partitioned solution procedures for incompressible fluid-structure interaction are compared and validated against the results of an experimental FSI benchmark. The numerical methods discussed cover the three main families of coupling schemes: strongly coupled, semi-implicit and loosely coupled. Very good agreement is observed between the numerical and experimental results. The comparisons confirm that strong coupling can be efficiently avoided, via semi-implicit and loosely coupled schemes, without compromising stability and accuracy.Cet article présente une étude numérique dans laquelle plusieurs algorithmes partitionnés pour l'interaction fluide structure sont comparés et validés avec des résultats expérimentaux. Les méthodes numériques discutées couvrent les trois familles principales de schémasde couplage: fortement couplés, semi implicites et faiblement couplés. Un très bon accord est obtenu entre les résultats numériques et expérimentaux. Les comparaisons confirment que le couplage fort peut être contourné efficacement, par l'intermédiaire de schémas semi implicites et faiblement couplés, sans compromettre la stabilité et la précision