Suchergebnisse

Comunicació presentada a: The 9th International Conference Proceedings, FIMH 2017, celebrat de l'11 al 13 de juny de 2017 a Toronto, Canadà ; The electrocardiographic imaging (ECGI) inverse problem is highly ill-posed and regularization is needed to stabilize the problem and to provide a unique solution. When Tikhonov regularization is used, choosing the regularization parameter is a challenging problem. Mathematically, a suitable value for this parameter needs to fulfill the Discrete Picard Condition (DPC). In this study, we propose two new methods to choose the regularization parameter for ECGI with the Tikhonov method: i) a new automatic technique based on the DPC, which we named ADPC, and ii) the U-curve method, introduced in other fields for cases where the well-known L-curve method fails or provides an over-regularized solution, and not tested yet in ECGI. We calculated the Tikhonov solution with the ADPC and U-curve parameters for in-silico data, and we compared them with the solution obtained with other automatic regularization choice methods widely used for the ECGI problem (CRESO and L-curve). ADPC provided a better correlation coefficient of the potentials in time and of the activation time (AT) maps, while less error was present in most of the cases compared to the other methods. Furthermore, we found that for in-silico spiral wave data, the L-curve method over-regularized the solution and the AT maps could not be solved for some of these cases. U-curve and ADPC provided the best solutions in these last cases. ; This study received financial support from the French Government under the "Investments of the Future" program managed by the National Research 12 Agency (ANR), Grant reference ANR-10-IAHU-04 and from the Conseil Régional Aquitaine as part of the project "Assimilation de données en cancérologie et cardiologie". This work was granted access to the HPC resources of TGCC under the allocation x2016037379 made by GENCI.

Robust calculations of the inverse electrocardiographic problem may require accurate specification of boundary conditions at the torso and cardiac surfaces. In particular, the numerical specification of the no-flux condition on the torso is difficult because surface normals must be computed, and because the torso may alternatively be considered infinitely far away from the heart. Using the method of fundamental solutions (MFS) proposed in [1], this boundary conditions can be taken into account in different manners. Specifically, the no-flux condition on the torso can be ignored, or weighted with respect to the Dirichlet boundary condition associated to the torso data, or can be strongly enforced through a saddle-point problem. In this article, we compare these approaches. In this work we provide a preliminary comparison of these different strategies. ; This study received financial support from the French Government as part of the "Investissements d'avenir" program managed by the National Research Agency (ANR), Grant reference ANR-10-IAHU-04 and from the Conseil R´egional Aquitaine as part of the project "Assimilation de donn´ees en canc´erologie et cardiologie".