Noninvasive estimation of global activation sequence using the extended Kalman filter

Abstract

A new algorithm for 3-D imaging of the activation sequence from noninvasive body surface potentials is proposed. After formulating the nonlinear relationship between the 3-D activation sequence and the body surface recordings during activation, the extended Kalman filter (EKF) is utilized to estimate the activation sequence in a recursive way. The state vector containing the activation sequence is optimized during iteration by updating the error variance/covariance matrix. A new regularization scheme is incorporated into the "predict" procedure of EKF to tackle the ill-posedness of the inverse problem. The EKF-based algorithm shows good performance in simulation under single-site pacing. Between the estimated activation sequences and true values, the average correlation coefficient (CC) is 0.95, and the relative error (RE) is 0.13. The average localization error (LE) when localizing the pacing site is 3.0 mm. Good results are also obtained under dual-site pacing (CC = 0.93, RE = 0.16, and LE = 4.3 mm). Furthermore, the algorithm shows robustness to noise. The present promising results demonstrate that the proposed EKF-based inverse approach can noninvasively estimate the 3-D activation sequence with good accuracy and the new algorithm shows good features due to the application of EKF.

Fig. 1

The nonlinear modeling from the 3D activation sequence to the body surface potentials.

Fig. 2

The locations of the pacing sites shown in three views. (a) the 24 single pacing sites; (b) the 6 pairs of dual pacing sites.

Fig. 3

The convergence of the correlation coefficient and the relative error between the estimated and the true activation sequence during iteration. The heart is paced in the basal-left-wall region.

Fig. 4

The inverse results in simulation when (a) single-site pacing at middle-left-wall; (b) dual-site pacing at basal-left-wall and anterior-apex. In each panel, the first row is the true 3D activation sequence shown by 6 horizontal sections, arranged from base to apex; the precise pacing site(s) is indicated with green star(s). The second row is the estimated 3D activation sequence picked up from the reconstructed current densities; the current densities are inversely calculated with the weighted minimal norm (WMN) method; the estimated origin(s) of activation is indicated by green star(s). The third row is the estimated 3D activation sequence with the extended Kalman filter (EKF) when BSPMs from one beat are employed; the estimated origin(s) of activation is indicated by green star(s). The fourth row is the estimated 3D activation sequence with the extended Kalman filter (EKF) when BSPMs from multiple beats are employed; the estimated origin(s) of activation is indicated by green star(s).