Development of a model for the potential distribution on a spherical intracardiac catheter within a three compartment ellipsoidal ventricle

The purpose of this work was to develop a model that will describe the potential distribution on the surface of a spherical intracardiac catheter within an approximated three compartment ellipsoidal ventricle. Currently, no model exists that describes this potentials distribution. The model was derived based on a solution of Laplace's equation in spherical coordinates. Numerical simulations were performed using the derive model. This allowed for more realize approximations of ventricular shape and catheter position than the analytical model alone. We found that the analytical model is dependent upon an infinite sun of Legendre functions and system parameters (tissue resistivities, injected current, catheter and ventricular geometry.