Section: New Results

Adaptive placement of the pseudo-boundaries improves the conditioning of the inverse problem

In order to complete the investigaton concerning the MFS technique from [54], J. Chamorro-Servent, Y. Coudière and R. Dubois also studied the effect of the location of the virtual sources of the MFS method on the solutions of the inverse problem. Specifically, the regularization term spoils the biophysical content of the solution, and the regularization parameter must be chosen as small as possible. But the problem must be regularized enough to overcome its sensitivity to: i) noise on the measured potentials, ii) uncertainty in the location of measurement sites with respect to the surface on which the sources are distributed, iii) errors of segmentation of the geometries, iv) influence of cardiac motion, etc.

The regularization parameter can be studied in view of the singular values of the matrix, or for given measurments, the discrete Picart condition as defined by Hansen [47].

In the MFS problem, explained in section 7.3, 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. Furthermore, it has been proved in other fields that the placement of the virtual sources influences the ill-posedness of the MFS problem. However, this has not been tested for the ECGI problem.

J. Chamorro-Servent, R. Dubois and Y. Coudière proposed a new method of placement of these virtual sources based on the minimal distance of each point considered on the heart surface to the torso electrodes. The singular value analysis and the discrete Picard condition were used to optimize the location of these sources. The new distribution of sources was compared with the standard one for a set of experimental data. These data consist of simultaneous acquisition of the cardiac (on a Langendorff perfusion of the heart) and body surface potentials, in a controlled experimental environment.

The results presented by J. Chamorro-Servent et al. at CinC2016 [24] showed that the new distribution of sources made the inverse problem less ill-posed and therefore, less sensitive to the regularization parameter chosen. This improved the reconstructed potentials on the heart surface, especially when artefact (as for example the baseline) or noise were present.

Further results from the combination of the works described here and in section 7.3 were presented in a poster in the Liryc workshop of October 2016 [33] by J. Chamorro-Servent et al. A journal manuscript is currently under preparation (to submit in 2017).