Possible improvements of the method of fundamental solution to solve the ECGI problem

Despite all the success of electrocardiographic imaging (ECGi), the understanding and treatment of many cardiac diseases is not feasible yet without an improvement of the inverse problem. A meshless method based on the method of fundamental solution (MFS) was adapted to ECGi. In the MFS, the potential is expressed as summation over a discrete set of virtual point sources placed outside of the domain of interest. This formulation yields to a linear system, which involves contributions of the Dirichlet and the homogenous Neumann (HN) conditions at torso surface in an equivalent manner. HN conditions requires accurate computation of the normals at the torso surface, and due to the meshing, non-physiological conditions are applied to the top, bottom of torso and arms. Finally, the virtual sources are placed by inflating and deflating the heart and torso surfaces with respect to the heart’s geometric center. However, for some heart-torso geometries, this geometrical center is a poor reference. First, we studied the effect of weighting the MFS objective function in consideration of the Dirichlet and HN conditions respectively. Second, we proposed a new distribution of torso sources by projecting for each electrode the closest heart’s point. Finally, we compared the solution from both modifications with the standard MFS one, using both in-silico and experimental data. A small quotient between the norms of the HN part of the MFS matrix and its respective Dirichlet part (~10-3) was found, indicating the negligibility of the HN conditions in the standard MFS method. Not including HN conditions in the reconstruction had significantly higher CCs (p<0.0001), and lower REs (p<0.0001) than including them. The new sources decreased the ill-posedness in a ~12%, reducing the effect of the regularization parameter in time and space. The MFS modifications proposed reduce the ill-posedness and provide results in better agreement with the reference data.

Judit Chamorro-Servent, Laura Bear, Josselin Duchateau, Mark Potse, Rémi Dubois, et al.. Possible improvements of the method of fundamental solution to solve the ECGI problem. Workshop Liryc, Oct 2016, Pessac, France. ⟨hal-01410756⟩ (lien externe)