Comparison of potential- and activation-based formulations for the inverse problem of electrocardiology

Abstract

Two predominant source formulations for the inverse problem of electrocardiology currently exist. They involve the reconstruction of epicardial potentials or myocardial activation times from noninvasively recorded torso surface potentials. Each of these formulations have their advantages, however, they have not been systematically compared against each other. We present results from a simulation study which compared a number of epicardial potential (Tikhonov, Truncated singular value decomposition (TSVD), Greensite-Tikhonov and Greensite-TSVD), and a myocardial activation time formulation for the inverse problem of electrocardiology. A number of different methods were also used to determine the appropriate level of regularization (optimal, L-curve, zero-crossing, and composite residual and smoothing operator) to apply to each formulation. The simulation study was conducted using an anatomically based boundary element porcine model with a variety of cardiac sources. Varying levels of geometric error were introduced to the system and solutions were computed using each of the inverse algorithms. Results show that under pure Gaussian noise potential-based methods performed best at low noise levels while the activation-based method was less effected by higher noise levels. In the presence of correlated geometric error, the activation-based method out performed the potential methods, with the Greensite-Tikhonov method being the most favored potential-based method when using the L-curve or zero-crossing method to determine the regularization parameter.

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.…”

Anatomically Realistic Three-Dimensional Meshes of the Pelvic Floor & Anal Canal for Finite Element Analysis

“…The smoothing constraint is given in Equation 2 and is added to the original objective function in Equation 1. (2) where Ω is the entire solution domain and the weighting values α and β penalize changes in volume and excessive curvature respectively. Altering these weights alters the Sobolev value.…”

“…In order to determine the 'ideal' α and β Sobolev weights for use in the fitting procedures, two 'L'-curve plots were produced; one for the two-dimensional surface meshes -represented by the bladder (see Figure 5) -and one for the levator ani, puborectalis and external anal sphincter muscle group (presented as LAPREXSPH) -representing the three-dimensional volume meshes (see Figure 6). Using the 'L'-curves an 'optimal' point or region can be identified (i.e., a point where reducing α and/or β does not provide any significant gains in reducing RMS error) [7], [2]. To produce the plots each weighting value was independently varied from 0.5 to 1 × 10 −5 and the resulting RMS value for each weighting combination was calculated and plotted on the curve following the fitting of each of the representative meshes.…”

Model generation interface for simulation of left ventricular motion

“…A simulation of ECG generation has been performed utilizing the results of such a study [13]. In most of these studies, a particular phenomenon, such as the stress distribution in the normal heart or the reproduction of the ECG, is considered.…”