Use of Activation Time Based Kalman Filtering in Inverse Problem of Electrocardiography

The goal of this study is to solve inverse problem of electrocardiography (ECG) in terms of epicardial potentials using body surface (torso) potential measurements. The problem is ill-posed and regularization must be applied. Kalman filter is one of the regularization approaches, which includes both spatial and temporal correlations of epicardial potentials. However, in order to use the Kalman filter, one needs the state transition matrix (STM) that models the time evolution of the epicardial potentials. In inverse ECG literature, STM is either chosen as identity matrix or calculated from true epicardial potentials. The latter approach gives better results, however 1) It yields a matrix equation with a large size. 2) Not realistic. In this study we address the 1(st) shortcoming. Usually epicardial potential in one lead only depends on a limited number of leads; STM entries are close to zero for the remaining leads. In this study, we used simulated torso potentials, and constructed STM from true epicardial potentials. We used three different approaches to reduce the dimension of the problem: epicardial potential at one lead is assumed to be related to 1) Only the leads in its neighborhood, 2) The leads that are activated at around the same time (close activation times), (3) Both the leads with close activation times and its first order neighbors. The STM estimation problem is redefined to calculate only the limited number of related entries; the remaining STM entries are set to zero, hence reducing the problem size. The calculated STM is then used in the Kalman filter to estimate the epicardial potential distribution and later in the Kalman smoother to further reduce errors