A two-step inverse solution for a single dipole cardiac source

Abstract

Introduction: The inverse problem of electrocardiography noninvasively localizes the origin of undesired cardiac activity, such as a premature ventricular contraction (PVC), from potential recordings from multiple torso electrodes. However, the optimal number and placement of electrodes for an accurate solution of the inverse problem remain undetermined. This study presents a two-step inverse solution for a single dipole cardiac source, which investigates the significance of the torso electrodes on a patient-specific level. Furthermore, the impact of the significant electrodes on the accuracy of the inverse solution is studied. Methods: Body surface potential recordings from 128 electrodes of 13 patients with PVCs and their corresponding homogeneous and inhomogeneous torso models were used. The inverse problem using a single dipole was solved in two steps: First, using information from all electrodes, and second, using a subset of electrodes sorted in descending order according to their significance estimated by a greedy algorithm. The significance of electrodes was computed for three criteria derived from the singular values of the transfer matrix that correspond to the inversely estimated origin of the PVC computed in the first step. The localization error (LE) was computed as the Euclidean distance between the ground truth and the inversely estimated origin of the PVC. The LE obtained using the 32 and 64 most significant electrodes was compared to the LE obtained when all 128 electrodes were used for the inverse solution. Results: The average LE calculated for both torso models and using all 128 electrodes was 28.8 ± 11.9 mm. For the three tested criteria, the average LEs were 32.6 ± 19.9 mm, 29.6 ± 14.7 mm, and 28.8 ± 14.5 mm when 32 electrodes were used. When 64 electrodes were used, the average LEs were 30.1 ± 16.8 mm, 29.4 ± 12.0 mm, and 29.5 ± 12.6 mm. Conclusion: The study found inter-patient variability in the significance of torso electrodes and demonstrated that an accurate localization by the inverse solution with a single dipole could be achieved using a carefully selected reduced number of electrodes.

Keywords: body surface potential mapping; greedy algorithm; inverse problem of electrocardiography; premature ventricular contractions; transfer matrix.