Time-recursive solution to the inverse problem of electrocardiography: a model-based approach

Abstract

This paper presents a new approach to the estimation of epicardial potentials from measured body surface potentials. This problem is ill-posed, and regularization techniques, through incorporation of a priori information on the solution, provide an efficient way of improving the quality of the estimates. During a cardiac cycle, the time-evolution of the epicardial potentials presents a very structured character which is the consequence of underlying propagation phenomena. In order to account for this a priori information, we introduce a linear prediction model that explicitly relates the epicardial potentials at two consecutive time instants. The linear prediction model, along with the usual relationship between epicardial and body surface potentials, makes up a state-space representation of the system. Epicardial potentials can then be estimated using efficient time-recursive techniques such as Kalman filtering. Simulation results obtained with real epicardial data indicate the validity of the linear prediction model; comparison of the reconstructed epicardial potentials with those produced by existing methods confirm the interest of the ap-