Section: New Results

Modeling in electrocardiology

Participants : Bedr'Eddine Ainseba, Jacques Henry, Yves Coudière, Simon Labarthe, Alejandro Lopez Rincon.

Modeling the electrical activity of the atria

The first year of the PhD thesis of Simon Labarthe has been dedicated to three main activities :

• a review of medical and mathematical literature about anatomy and physiology of atria and atrial fibrillation, numerical simulation of cardiac activity, mathematical analysis of cardiac models.

• the numerical implementation of simulation tools has been developed : the software is able to take into account a real 3D or 2D manifold geometry with realistic fibre orientation to simulate the bidomain or monodomain problem. Geometrical tools facilitating the fibre orientation construction have been added.

• numerical and theoretical studies of the modeling and the influence of fibre orientation in the atria and the pulmonary veins have been initiated.

Inverse problem in electrocardiology

The PhD thesis of Alejandro Lopez is devoted to improving the resolution of the inverse problem to recover the potential map on the heart from the measured potentials on the torso.

To have a best solution of the inverse problem many steps were taken. First, a software to solve the finite element method in 3d for the Poisson equation was created, and compared to an analytical solution. Also a software for the heat equation was created to prepare the the monodomain equation. The improvement of the forward solution helps to improve the inverse solution. An article explaining the software was included in the book "VEHÍCULOS AEROESPACIALES" (aerospace vehicles) published by the Sociedad Mexicana de Ciencia y Tecnología Aeroespacial (Mexican Society of Aerospace Science, and Technology) [19] .

The second step was to develop a static solution of the inverse problem constructing a transfer matrix (heart to thorax), and solving with conjugate gradient. An article describing this software was accepted in the 22nd International Conference on Electronics, Communications and Computers.

As a third step the boundary element method was implemented to see the advantages and disadvantages in comparison with the finite element method.

The next step was to implement the monodomain model of the heart, to try to solve the problem of identification of parameters (in progress).