About the team
EPICARD in few words
EPICARD is an associate team between the Carmen project at Inria and “Laboratoire de Modélisation Mathématique et Numérique dans les Sciences de l’Ingénieur ” (LAMSIN). The goal of this association is to develop new mathematical approaches for solving different inverse problems in cardiac electrophysiology.
The team regroups also researchers from LAMSIN MohammedV university and from Université Technologique de Compiègne.
From Inria: Mostfa Bendahmane, Yves Coudière, Jacques Henry, Amel Karoui, Pauline Migerditichan and Nejib Zemzemi
From LAMSIN: Abir Amri, Ben Abda Amel, Rabeb Chamekh, Henda El Fekih, Fadhel Jday, Nabil Gmati Moez Kallel, Jamila Lassoued, Moncef Mahjoub
From MohamedV university: Rajae Aboulaich, El Mahdi El Guarmah, Najib Fikal and Keltoum Chahour.
From UTC de Compiègne (Laboratoire de mathématiques appliquées de Compiègne): Faker Ben Belgacem and Faten Jelassi.
The LIRYC institute is one of six French university hospital institutions created in 2011 as part of the ”investments for the future” program (”Investissements d’avenir”) to boost medical research and innovation.
This institute, headed by Professor Michel Haissaguerre with clinicians from the University Hospital of Bordeaux and basic scientist teams is devoted to understanding the mechanism of AF and VF and developing new approaches to treat these cardiac pathologies. Carmen is an Inria team that is involved in the LIRYC institute by offering the modeling and simulation component of the project. One of the most used interventions to prevent and/ or stop VF and AF is radio-frequency ablation. This intervention requires an accurate targeting of the substrate to be ablated. The recent non-invasive technology used in guiding medical doctors to target these substrates is based on an inverse electrical mapping technique also known as electrocardiographic imaging (ECGI). With this approach, potentials on the outer (epicardial) surface of the heart are computed from potentials measured on the body surface using information on the geometry of the heart and the 3D locations of measured potentials. This is exactly the data completion Cauchy problem for elliptic equations. An ECGI mapping system was approved for use in Europe in 2011 and is available for clinical and basic science research at the LIRYC Institute in Bordeaux.
In this context, we would like to create a the EPICARD project, and the goal is to implement and test different mathematical approaches solving the ECGI problem but also to invent and design new mathematical approaches to study the problem differently than what has been done in the literature. In particular, physiologically detailed model personalization has not been considered in the literature mainly because of the mathematical and numerical challenge that it raises.
The ECGI procedure
In order to solve the ECGI inverse problem many steps have to be taken into account: image segmentation, mesh generation, mathematical approaches, numerical algorithms and scientific visualization.
Image Segmentation and Mesh Generation
In this team project we aim to provide novel formulation of this inverse problem and compare them to the state-of-the-art procedure. We already have got promising results with the following methods:
- Iterative Kozlov- Maz’ya-Fomin (KMF) method .
- A domain decomposition approach for solving the Inverse problem in electrocardiography .
- A Steklov-Poincaré Variational Formulation of the Inverse Problem in Cardiac Electrophysiology .
- A Machine Learning Technique Regularization of the Inverse Problem in Cardiac Electrophysiology .
- Factorization of boundary problems method for solving ECGI .
Our aim is to build a library that allows comparing these methods to the methods develepped by the project team members and other approches in the littterature.
They have to be very acccurate but also sufficiently fast in order to be used in clinical applications
Numerical algorithms provide tables with numbers. The interpretation of this data is difficult without a good representation.
Visualization tools, like paraview, help in representing this data with images and movies that medical doctors could easily interpret.
Example of normal case
Example of a re-entree case
Gallery of preliminary results