Spatial regularization of the electrocardiographic inverse problem and itsapplication to endocardial mapping

Numeric regularization methods for solving the inverse problem of electroca rdiography in realistic volume conductor models have been mostly limited to uniform regularization in the spatial domain. A method of spatial regulari zation (SR) mas developed and tested in canine, where each spatial spectral component of the volume conductor model was considered separately and a SR operator was selected based on explicit a posteriori criterion at each tim e instant through the heartbeat. The inverse problem was solved in the left ventricle by reconstructing endocardial surface electrograms based on cavi tary electrograms measured with the use of a noncontact, multielectrode pro be. The results mere validated based on electrograms measured in situ at th e same endocardial locations using an integrated, multielectrode basket cat heter. A probe-endocardium three-dimensional model was determined from mult iplane fluoroscopic images. The boundary element method mas applied to solv e the boundary value problem and derive the relationship between endocardia l and probe potentials. Endocardial electrograms were reconstructed during both normal and paced rhythms using SR as well as standard, uniform, zeroth order Tikhonov (ZOT) regularization, Compared to endocardial electrograms measured by the basket, electrograms reconstructed using SR [relative error (RE) = 0.32, correlation coefficient (CC) = 0.97, activation error = 3.3 m s] were superior to electrograms reconstructed using ZOT regularization (RE = 0.59, CC = 0.79, activation error = 4.9 ms). Therefore, regularization b ased on spatial spectral components of the model improves the solution of t he inverse problem of electrocardiography compared to uniform regularizatio n.