.. .. Problématique,

.. .. Choix-du-modèle-direct,

. .. Exemples-de-graphes-d'activations, 150 6.2.2 Comparaison avec la méthode RoUKF : conductivité constante 155 6.2.3 Conductivité distribuée dans l'espace

. .. J-u, 186 6.4.2 Preuve de l'existence d'un minimum pour

.. .. Conclusion,

, et [t a (x i+1

M. Équipe and . Bordeaux,

, Pour l'estimation séquentielle nous avons utilisé une méthode liée état-paramètres basée sur une mesure de dissimilarité D(z, u) issue de la communauté du traitement d'image

, Cette fonctionnelle s'adapte assez bien à l'utilisation des données d'activations, mais il pourrait être intéres-sant de voir si d'autres mesures de dissimilarité ne pourraient pas convenir, d'autant plus que nous pourrions avoir accès à d, Cette fonctionnelle nécessite dans notre cas la construction de l'objet z(x, t) permettant de déterminer la position du front de dépolarisation à l'instant t

, Une deuxième amélioration que nous voyons dans l'utilisation de la méthode séquentielle est l'amélioration de notre code de calcul CEPS ainsi que le couplage réalisé avec la bibliothèque d'assimilation de données Verdandi, Nous avons énoncé dans ce manuscrit

, Les difficultés apparaissent en général -lorsque nous regardons les cas continus en temps -dans l'étude des variations des différentes fonctionnelles. En effet, nous avons introduit des fonctionnelles dépendant implicitement de la variable temporelle soit au travers d'une contrainte u(x, t a (x)) = u a soit en intégrant sur l'ensemble d'activation S a . Cette dépendance implicite en temps rend difficile l'étape de discrétisation des différents problèmes adjoints. Nous pensons qu'en introduisant une fonctionnelle dont la dépendance en temps serait explicite faciliterait alors la résolution du problème adjoint. Comme pour le cas séquentiel, l'utilisation d'autres données que les temps d'activations, Nous avons vu dans ce manuscrit que l'assimilation de données variationnelle donnait lieu à la résolution de problèmes adjoint complexes

, Les élèments finis de Lagrange P1/P2 pour la résolution des EDP 2. Les principaux modèles de propagation du potentiel d'action : le modèle monodomaine et bidomaine

, la prise en compte de maillages multi-dimensionnels (1D/2D/3D)

, Une multitude de modèle ioniques

, Des schémas d'intégrations en temps multi-pas Rush-Larsen, SBDF 6. Plusieurs formats d'entrées-sorties disponibles comme VTK

, Il utilise le parallèlisme en mémoire distribuée grâce à son couplage avec les bibliothèques MPI et PETSc. Nous pouvons d'ailleurs voir sur la figure A.1 une vue d'ensemble de l'organisation du logiciel. Nous avons donc profité des éléments déjà en place au sein de CEPS pour y ajouter la possibilité d'utiliser le modèle bicouche dont nous avons parlé dans le chapitre 2. Nous avons également réaliser un couplage de CEPS avec la bibliothèque d'assimilation de données Verdandi, CEPS est est écrit en C++11 avec un grand nombre de templates et jouit du polymorphisme dynamique. Il compte actuellement environ 23596 lignes de codes dans la branche principale (sans compter les fichiers tests)

, A.2 Cardiac Electrophysiology Simulator : CEPS

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