Alireza Ghodrati

Lead selection and wavefront-based models for the inverse problem of electrocardiography

Date: Tuesday Oct 18th

Abstract:

Inverse electrocardiography, or cardiac electric imaging, has potential for clinical application to non-invasively diagnose and characterize cardiac disease. In this thesis we address two aspects of the problem. First we investigate the "lead selection problem", the solution of which would make practical implementation of an inverse electrocardiography system more feasible. Second, we introduce a novel approach of wavefront-based source modeling, which enable us to include dynamic wavefront-based constraints into the inverse algorithm to attempt to better estimate the inverse solution (the cardiac electrical image).

In the lead selection problem, the goal is to use measurements from reduced-lead sets of electrode locations, chosen from a large number of possible such locations. We address two related problems. In the first, we describe and compare several methods to estimate the solution from such reduced-lead measurements sets, both with and without knowledge of prior statistics of the measurements. We present simulation results which indicate that deleting rows of the forward matrix corresponding to the unmeasured leads works best when no prior statistics are available, and that Bayesian (or least-squares) estimation works best in the presence of prior statistics. The second related problem we address is that of selecting the locations of smaller lead sets from a large set of possible locations while optimizing the resulting inverse solution. We propose three criteria whose optimization each leads to a corresponding optimum lead set, and introduce approximate suboptimal algorithms based on those criteria. We indicate via simulations that inverse solutions corresponding to these sub-optimum lead sets are improved compared to inverse solutions corresponding to a uniformly spaced lead set with the same number of leads.

In the second part of our work, we introduce two wavefront-based methods for the inverse problem of electrocardiography. which we term wavefront-based curve reconstruction and wavefront-based potential reconstruction. In the curve reconstruction approach, the epicardial activation wavefront is modeled as a curve evolving on the heart surface, where the evolution is governed by factors derived phenomenologically from prior measured data. The body-surface potential / wavefront relationship is modeled via an intermediate mapping of wavefront to epicardial potentials, again derived phenomenologically. The continuous curve is taken as the state in a state-space formulation and the inverse problem is solved via an appropriate version of the Extended Kalman smoother. In the potential reconstruction approach, we iteratively construct an estimate of epicardial potentials by first estimating the wavefront curve and then using a simplified model to generate an estimate of the potentials from that curve. We then use that estimate as an initial solution in a Tikhonov regularization scheme. The approach is applied inside a time-recursive iterative scheme.

Simulation results using measured canine epicardial data show considerable improvement in both reconstructing activation wavefronts using wavefront-based curve reconstruction and in reconstructing epicardial potentials using wavefront-based potential reconstruction, with respect to standard Tikhonov solutions. In particular the curve reconstruction method accurately finds the anisotropic propagation early after epicardial pacing, and the potential reconstruction method finds the wavefront (regions of sharp gradient of the potential) accurately and with minimal smoothing.

Committee:
Prof. Dana Brooks, NU (Advisor)
Prof. Rob MacLeod, University of Utah
Prof. Eric Miller, NU
Prof. Gilead Tadmor, NU