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

Meshing the heart and measurement surfaces can be time consuming, especially when dealing with complicated geometries or cardiac motion. To overcome this, a meshless method based on the method of fundamental solutions (MFS) has been adapted to non-invasive electrocardiographic imaging (ECGI). In the MFS, potentials are expressed as a summation over a discrete set of virtual point sources placed outside of the domain of interest (named ‘pseudo-boundary’). It is well-known that optimal placement of the pseudo-boundary can improve the efficacy of the MFS. Despite this, there have been no attempts to optimize their placement in the ECGI problem as far as we are aware. In the standard MFS, the sources are placed in two pseudo-boundaries constructed by inflating and deflating the heart and torso surfaces with respect to the geometric center of the heart. However, for some heart-torso geometries, this geometric center is a poor reference. We here show that adaptive placement of the pseudo-boundaries (depending on the distance between the torso electrodes and the nearest heart locations) improves the conditioning of the inverse problem, making it less sensitive to the regularization process.