Spatial regularization of the electrocardiographic inverse problem and its application to endocardial mapping

Numeric regularization methods for solving the inverse problem of electrocardiography in realistic volume conductor models have been mostly limited to uniform regularization in the spatial domain. A method of spatial regularization (SR) was 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 time instant through the heartbeat. The inverse problem was solved in the left ventricle by reconstructing endocardial surface electrograms based on cavitary electrograms measured with the use of a noncontact, multielectrode probe. The results were validated based on electrograms measured in situ at the same endocardial locations using an integrated, multielectrode basket-catheter. A probe-endocardium three-dimensional model was determined from multiplane fluoroscopic images. The boundary element method was applied to solve the boundary value problem and derive the relationship between endocardial 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 ms] were superior to electrograms reconstructed using ZOT regularization (RE = 0.59, CC = 0.79, activation error = 4.9 ms). Therefore, regularization based on spatial spectral components of the model improves the solution of the inverse problem of electrocardiography compared to uniform regularization.