Context
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 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.
The ECGI procedure
In order to solve the ECGI inverse problem many steps have to be taken into acount: image segmentation, mesh generation, mathematical approaches, numerical algorithms and scientific visualization.
Image Segmentation and Mesh Generation
Mathematical 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 .
Numerical Algorithms
They have to be very acccurate but also sufficiently fast in order to be used in clinical applications
Visualization
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.