Reducing the Errors in the Forward Model for ElectroCardiographic Imaging
Electrocardiographic Imaging (ECGI) is a technology which has attracted a lot of recent attention that non-invasively images the electrical activity of the heart to identify normal and abnormal behavior and has great promise to help pre-procedure planning and screening and diagnosis. It does so by solving the inverse problem to take electrocardiographic measurements on the body surface (ECG) and a model of the torso volume conductor and characterize the unknown electrical activty of the heart, here described by the distribution of electrical potentials on the heart surface.
However, ECGI has some limitations that impede its application to routine clinical practice. One of them is the ill-posedness of this inverse problem that causes inverse solutions to be unreliable even with small levels of noise in the inputs and the model. Specifically, in order to solve this inverse problem, one needs to first characterize the propagation of current from the heart to the body surface. This relationship is generally obtained by solving Laplace's equation numerically in the geometry of the volume conductor to generate a forward solution, typically in the form of a "forward matrix". Model mismatch in this forward solution, along with measurement noise, are significant factors in inverse solution error. To overcome this limitation, we propose to characterize these sources of noise both in the measurements and in the forward matrix.
With that objective we have developed a method to parameterize the variations in the forward matrix generated by heart movements due to respiration. Direct modeling of this parameterization is not tractable, so rather we learn it with sufficient sampling of the manifold of possible forward matrices and a smooth interpolant. This method provides a mapping from the parameters describing the translation and rotation of the heart to forward matrices. This mapping allows us to optimize over these geometry transformation parameters to find the position of the heart that best explains the measured ECG across consecutive heart bearts. We will present this geometry reconstruction method as well as some of its encouraging preliminary results.