Accuracy of quadratic versus linear interpolation in noninvasive Electrocardiographic Imaging (ECGI)

Electrocardiographic Imaging (ECGI) is a cardiac functional imaging modality, noninvasively reconstructing epicardial potentials, electrograms and isochrones (activation maps) from multi-channel body surface potential recordings. The procedure involves solving Laplace's equation in the source-free volume conductor between torso and epicardial surfaces, using Boundary Element Method (BEM). Previously, linear interpolation (LI) on three-noded triangular surface elements was used in the BEM formulation. Here, we use quadratic interpolation (QI) for potentials over six-noded linear triangles. The performance of LI and QI in ECGI is evaluated through direct comparison with measured data from an isolated canine heart suspended in a human-torso-shaped electrolyte tank. QI enhances the accuracy and resolution of ECGI reconstructions for two different inverse methods, Tikhonov regularization and Generalized Minimal Residual (GMRes) method, with the QI-GMRes combination providing the highest accuracy and resolution. QI reduces the average relative error (RE) between reconstructed and measured epicardial potentials by 25%. It preserves the amplitude (average RE reduced by 48%) and morphology of electrograms better (average correlation coefficient for QI similar to 0.97, LI similar to 0.92). We also applied QI to ECGI reconstructions in human subjects during cardiac pacing, where QI locates ventricular pacing sites with higher accuracy (<= 10 mm) than LI (<= 18 mm).