Section: Scientific Foundations

Fondation 1

The foundations of research project are as follows.

• Mathematical analysis of the reaction-diffusion systems of equations called the monodomain and bidomain models [2] , [1] and [5] .

• Numerical schemes to simulate cell models of cardiac electrophysiology and the monodomain and bidomain systems of equations [3] , [4] and [7] , [6] .

A list of detailed objectives is:

• Enhance the the fundamental understanding of the models used in cardiac electrophysiology.

• Take into account two kinds of heterogeneities from intermediate scales: coupling between 0D, 1D, 2D and 3D systems of differential equations; model the multiscale behavior of a 3D tissue through asymptotic or multiscale analysis (for example involved in infarct modeling).

• Derive intermediate models based on a simplified description of the physics, in particular to account efficiently for the various measures and stimulation electrodes used for catheterization.

• Improve the numerical techniques that discretize these equations, guarantee their accuracy and robustness, search for high-order robust schemes (space and time).

• Make use of high performance computing technical possibilities in order to explore the behavior of the models. Collaborate therefore with our colleagues from the IHU LIRYC in order to identify the mechanisms of the cardiac electrical pathologies.

• Solve some inverse problems of different nature.

  • data assimilation or parameter identification-like problems with two objectives,

    • build specific models from experimental data;

    • build personalized models from clinical data, including non-invasive electrical recordings (see next item).

  • reconstruction of cardiac electrical signals, either from experimental data (catheter, optical mapping...) or from clinical data (catheter, ECG recordings,...).