An application of observability to the reconstruction of cardiac electrical events

The inverse electrocardiographic problem of determining the epicardial potential distribution from body surface potential is addressed. Taking the heart-torso system as a dynamical system governed by Laplace´s equation, the problem is formulated as an observability problem with the electrical potential distribution on the surface of the heart as input and the potential distribution on the torso as output. The problem then becomes the reconstruction of as much information as possible about the state of the system using only a finite number of measurements on the torso. In this study, an analytical solution of this problem in the form of a generalized Fourier series was obtained under the assumption of an idealized geometry: a coaxial cylinder representing the human torso and cardiac surface. An algorithm was developed to numerically find the solution of Laplace´s equation from discrete measurements on the boundary (body surface)