Electrocardiographic Imaging Using a Spatio-Temporal Basis of Body Surface Potentials—Application to Atrial Ectopic Activity

Abstract

Electrocardiographic imaging (ECGI) strongly relies on a priori assumptions and additional information to overcome ill-posedness. The major challenge of obtaining good reconstructions consists in finding ways to add information that effectively restricts the solution space without violating properties of the sought solution. In this work, we attempt to address this problem by constructing a spatio-temporal basis of body surface potentials (BSP) from simulations of many focal excitations. Measured BSPs are projected onto this basis and reconstructions are expressed as linear combinations of corresponding transmembrane voltage (TMV) basis vectors. The novel method was applied to simulations of 100 atrial ectopic foci with three different conduction velocities. Three signal-to-noise ratios (SNR) and bases of six different temporal lengths were considered. Reconstruction quality was evaluated using the spatial correlation coefficient of TMVs as well as estimated local activation times (LAT). The focus localization error was assessed by computing the geodesic distance between true and reconstructed foci. Compared with an optimally parameterized Tikhonov-Greensite method, the BSP basis reconstruction increased the mean TMV correlation by up to 22, 24, and 32% for an SNR of 40, 20, and 0 dB, respectively. Mean LAT correlation could be improved by up to 5, 7, and 19% for the three SNRs. For 0 dB, the average localization error could be halved from 15.8 to 7.9 mm. For the largest basis length, the localization error was always below 34 mm. In conclusion, the new method improved reconstructions of atrial ectopic activity especially for low SNRs. Localization of ectopic foci turned out to be more robust and more accurate. Preliminary experiments indicate that the basis generalizes to some extent from the training data and may even be applied for reconstruction of non-ectopic activity.

Considering New Regularization Parameter-Choice Techniques for the Tikhonov Method to Improve the Accuracy of Electrocardiographic Imaging

“…We focused on the introduction and validation of new automatic regularization parameter-choice methods, combining information not only about the residual norm but also about the solution norm. This choice is based on the idea of later introducing the physiologically-based prior information on the regularization term in order to improve the ECGI inverse problem, as shown in recent manuscripts (Figuera et al, 2016; Cluitmans et al, 2017; Duchateau et al, 2018; Schuler et al, 2018). To introduce the physiologically-based prior information, regularization techniques need to adjust its solution norm constraint on this information.…”

“…This study assumed that no a priori physiologically information about the epicardial potentials were available, while studying regularization parameter-choice methods that can be adjusted to problems introducing different l2-norm constraints. Due to the increasing number of work that proposes the incorporation electrophysiological knowledge (Figuera et al, 2016; Cluitmans et al, 2017; Duchateau et al, 2018; Schuler et al, 2018), it would be interesting to see how the U-curve and ADPC adapted methods perform when including electrophysiological prior knowledge into a l2-norm constraint.…”

Space–time shape uncertainties in the forward and inverse problem of electrocardiography

“…, where u 0 is the discrete zero order Tikhonov solution. The discrete regularisation term in (10) then reads…”

“…4 More recently, physiology-based and spatio-temporal regularisation approaches have also been considered. 9,10 The potential-based forward problem is particularly attractive when the torso is assumed as a homogeneous electric conductor. Then, the forward problem can be conveniently recast into an integral formulation involving only the boundaries of the torso, that is, the epicardium and the chest, with no need of solving the problem in the full threedimensional (3D) domain.…”

“…Approximated or smoothed versions of TV are therefore popular 4 . More recently, physiology‐based and spatio‐temporal regularisation approaches have also been considered 9,10 …”