Effects of experimental and modeling errors on electrocardiographic inverse formulations

Abstract

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.

Forward Problem of Electrocardiography

“…6 This raises the question: how much detail is required to produce a sufficiently accurate forward model? Previous studies have shown that it is necessary to include realistic heart and torso geometries, [7][8][9][10] but the extent to which the inhomogeneous electric properties of internal structures needs to be accounted for is less clear. There is a reasonable consensus that body surface potential distributions are not significantly affected by the liver, stomach, 11 blood vessels, 11,12 intestines, spleen, kidney, spine, sternum, and other bones.…”

Inverse Solution Mapping of Epicardial Potentials

“…[31][32][33] We attempted to minimize these inaccuracies by constructing customized torso and cardiac geometries for each patient from CT scans obtained the day before the procedure and with the use of the L-curve method for identification of a regularization parameter, which has been thought to be more robust in the presence of geometric errors. 34 It is possible that differences in body position, intravascular volume, or other factors may have changed the geometry between the imaging and mapping studies. Similarly, we were unable to control error introduced by respiration (which may change both thoracic conductance and relative cardiothoracic position) or other changes in patient position during the procedure, nor was it possible to control for error introduced by cardiac motion during ventricular activation, particularly during VT.…”

“…17,34,[36][37][38] Mapping of myocardial scar was performed using only contact electroanatomic mapping in this study. Proximity of pacing sites to myocardial scar was assessed from epicardial maps only, not endocardial maps.…”

Rapid construction of a patient-specific torso model from 3D ultrasound for non-invasive imaging of cardiac electrophysiology

“…The accuracy of the geometric model is known to be the single greatest determinant of the final accuracy of a computed inverse solution (CHENG et al, 2003b). From this extensive simulation study, it was found that torso size and shape and the size and position of the heart within the torso had the largest influences on the accuracy of the inverse solution.…”