Source Localization Probability Maps for Uncertainty Quantification in Electrocardiographic Imaging

This study aimed to develop a new probabilistic visualization analysis to study source localization uncertainty in electrocardiographic imaging (ECGI). Using Monte Carlo error propagation, we developed probability maps that illustrate uncertainty in source localization compared to the ground truth source location. We used these probability maps to quantify the impact of noise amplitude and iterative Krylov regularization on source localization. Artificial Gaussian white noise was added to the body surface potentials between (0.5% and 9% of their amplitudes) to simulate noisy observations. We solved the inverse problem to recover heart surface potentials using the conjugate gradient least squares (CGLS) and preconditioned CGLS (PCGLS) algorithms with the Laplacian over the heart surface as a right preconditioner. We forward propagated these inverse solutions, and performed 200 CGLS and PCGLS Monte Carlo inversions per noise level. For each sample, we recorded the top 1% of lowest potential locations, and normalized across all samples to form empirical probability maps for source localization. Increasing the noise amplitude increased both the uncertainty and inaccuracy for source localization, with PCGLS outperforming CGLS across all noise amplitudes. We conclude that the concept of a source localization probability map may be useful clinically in identifying origins of arrhythmia in cardiac tissue.