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.Keywords-electrocardiographic imaging (ECGI), Krylov inversion, Monte Carlo sampling, uncertainty quantification
IntroductionCardiac ablation is an interventional procedure in which a clinician internally locates and destroys regions of cardiac tissue responsible for spontaneous pathological heart beats or reentrant wave activity. However, this invasive therapy can last many hours, and abnormal heart rhythms, or arrhythmias, frequently re-occur following the procedure [1,2]. One noninvasive approach to reducing proceFrance, and Johnson are with the Scientific Computing and Imaging Institute, University of Utah. Email: {jfrance, crj}@sci.utah.edu. This project was supported by grants from the NIH National Institute of General Medical Sciences (P41 GM103545-18) from the National Institutes of Health. dure times and the risk of recurrence is known as electrocardiographic imaging (ECGI). ECGI uses a patient's CT and MRI images to approximate a computational geometry, and combines this with ECG recordings into a mathematical model that predicts the origin of an arrhythmia.This inverse problem of electrocardiography may one day become a standard in ablation procedures, allowing clinicians to more quickly and accurately locate pathological heart tissue, since the ECGI prediction for the source of an arrhythmia essentially tells a clinician ahead of time where to ablate [3]. ECGI involves solving Laplace's equation [4,5] to obtain the systemwhere A ∈ R m×n , h ∈ R n , and y ∈ R m . The transfer matrix A relates the heart surface voltages h to the true body surface voltages y * . However, the observed body surface ECG re...