Section: New Results

Inverse problems: parameter estimation, data assimilation and ECGi

• Data assimilation: In A. Gérard PhD thesis, it is showed that accounting for the anisotropy in the atria is crucial to reconstruct correctly activation maps compatible with a mono-domain model from sparse punctuals activation times. To this purpose, we have developed a new data assimilation method for the mono-domain model, using a Luenberger filter and a Kalman-type filter (ROUKF), based on the dissimilarity measure introduced in A. Collin PhD thesis.

• Parameter estimation: We have been working on the following theoretical question: What are the condition under which the parameters, in the mathematical codomain and bidomain models, are identifiables. Then we proposed an algorithm capable of estimating different ion-channels conductance parameters. mettre ref?

• ECGI: Several approaches have been investigated to improve the resolution of ECGi.

  • development of a new algorithm to choose the regularization coefficient for the resolution of ECGi with the Method of Fondamental Solutions (MFS).

  • a study using a parametrized model of action potentials, showing that accounting for the endocardium can improve the resolution of ECGi.

  • in joint work with Laura Bear (IHU Liryc), development of a new method for improving the resolution of ECGI by combining several solutions obtained with various numerical methods (FEM and MFS). The method is based on the selection of the smallest residuals on the torso surface.

  • Development of new methods for the ECGI problem, based on machine learning methods. The idea is to learn activation maps from body surface signals.

  • collaborative work on the set up of an experimental platform for the experimental non-invasive validation of the reconstruction of cardiac signals