Improving the electrocardiographic inverse solution by Kalman filtering
Berrier, Keith Lee
Sorensen, Danny C.
Doctor of Philosophy
To advance methods for managing heart rhythm abnormalities, improved methods are needed to map the electrical activity of the heart. The solution of the discrete, ill-posed endocardial inverse problem of electrocardiography was examined. Existing solutions to the inverse problem of electrocardiography contain inaccuracies due to limitations in the techniques used. The regularization methods used to solve the ill-conditioned numeric model of this inverse problem are, generally, spatial and ignore the temporal nature of the problem. In this study, the Duncan and Horn formulation of the Kalman filter was used to incorporate temporal information in the solution. The method simultaneously maps multiple electrical events inside the heart and creates realistic, three-dimensional representations (by indirect means) on a beat-by-beat basis. The results were validated using in situ, noncontact cavitary and contact endocardial potentials (electrograms). The potentials were measured using an integrated, multielectrode probe-basket catheter placed in the canine left ventricle. The three-dimensional, probe-endocardium model was determined from multiplane fluoroscopic images. The boundary element method was then applied to solve the boundary value problem and determine a linear relationship between endocardial and probe potentials. The Paige and Saunders solution of the Duncan and Horn formulation was compared to the commonly used Tikhonov, Twomey, and several other regularization methods. Endocardial potentials (electrograms) were reconstructed during both sinus and paced rhythms. The Paige and Saunders technique reconstructed endocardial potentials at an average total relative error of 13% (potential amplitude) which was superior to solutions obtained with zero-order Tikhonov (31%), first-order Tikhonov (19%), and Twomey (44%) regularizations. Likewise, activation error from the Paige and Saunders solution (2.9 ms) was smaller than that of zero-order Tikhonov (4.8 ms), first-order Tikhonov (5.4 ms), and Twomey (5.8 ms) regularizations. Therefore, including temporal information by means of the Duncan and Horn formulation of the Kalman filter improved the solution of the inverse problem of electrocardiography.
Mathematics; Biomedical engineering