Space Rescaling in the MFS Method Improves the ECGI Reconstruction

The method of fundamental solutions (MFS) has been extensively used for the electrocardiographic imaging (ECGI) inverse problem. One of its advantages is that it is a meshless method. We remarked that the using cm instead of mm as a space unit has a high impact on the reconstructed inverse solution. Our purpose is to refine this observation, by introducing a rescaling coefficient in space and study its effect on the MFS inverse solution. Results are provided using simulated test data prepared using a reaction-diffusion model. We then computed the ECGI inverse solution for rescaling coefficient values varying from 1 to 100, and computed the relative error (RE) and correlation coefficient (CC). This approach improved the RE and CC by at least 10% but can go up to 40% independently of the pacing site. We concluded that the optimal coefficient depends on the heterogeneity and anisotropy of the torso and does not depend on the stimulation site. This suggests that it is related to an optimal equivalent conductivity estimation in the torso domain.