Effects of experimental and modeling errors on electrocardiographic inverse formulations

The inverse problem of electrocardiology aims to reconstruct the electrical activity occurring within the heart using information obtained noninvasively on the body surface. Potentials obtained on the torso surface can be used as input for the inverse problem and an electrical image of the heart obtained. There are a number of different inverse algorithms currently used to produce electrical images of the heart. The relative performances of these inverse algorithms at this stage is largely unknown. Although there have been many simulation studies investigating the accuracy of each of these algorithms, to date, there has been no comprehensive study which compares a wide variety of inverse methods. By performing a detailed simulation study, we compare the performances of epicardial potential [Tikhonov, Truncated singular value decomposition (TSVD), and Greensite] and myocardial activation-based (critical point) inverse simulations along with different methods of choosing, the appropriate level of regularization (optimal, L-curve, composite residual and smoothing operator, zero-crossing) to apply to each of these inverse methods. We also examine the effects of a variety of signal error, material property error, geometric error and a combination of these errors on each of the electrocardiographic inverse algorithms. Results from the simulation study show that the activation-based method is able to produce solutions which are more accurate and stable than potential-based methods especially in the presence of correlated errors such as geometric uncertainty. In general, the Greensite-Tikhonov method produced the most realistic potential-based solutions while the zero-crossing and L-curve were the preferred method for determining the regularization parameter. The presence of signal or material property error has little effect on the inverse solutions when compared with the large errors which resulted from the presence of any geometric error. In the presence of combined Gaussian and correlated errors representing conditions which may be encountered in an experimental or clinical environment, there was less variability between potential-based solutions produced by each of the inverse algorithms.