Detection of Regular Rotational Activity During Cardiac Arrhythmia Using the Helmholtz Decomposition for Directed Graphs

This paper introduces a novel method to detect re-entry called DGM-CURL based on the Helmholtz Decomposition for directed graphs, fully integrated into our opensource software OpenDGM.We apply this method alongside two existing methods Phase Mapping (PM) and Directed Cycle Search (DGM-CYCLE) to assess their degree of agreement.Four datasets are explored: (1) simulated two-dimensional functional re-entry, (2) simulated three-dimensional anatomical re-entry, (3) clinical electroanatomical atrial tachycardia (AT) mapping data (4) experimental rat ventricular fibrillation (VF) data.Results indicate general agreement between all three methods.Applying the Helmholtz decomposition to edge weights equal to the differences in local activation time, we observe that large values indicate graph nodes conserving the in-and output of these differences in the original graph, highlighting areas of re-entry.We stress the importance of using multiple algorithms to detect rotational activity as each method is prone to errors.Using a combined approach decreases this susceptibility to errors and offers a more complete picture of the dynamics of rotational drivers in cardiac arrhythmia.