Detection of regular rotational activity during cardiac arrhythmia using the Helmholtz decomposition for directed graphs

We introduce DGM-CURL, a novel method to detect reentry in cardiac activation based on the Helmholtz Decomposition for directed graphs. DGM-CURL is an extension to our open-source diagnostic framework Directed Graph Mapping (DGM). We compare DGM-CURL to two existing methods, Phase Mapping (PM), and Directed Cycle Search (DGM-CYCLE). Four datasets are explored: (1) simulated two-dimensional functional reentry, (2) simulated three-dimensional anatomical reentry, (3) clinical electroanatomical atrial tachycardia (AT) mapping data, and (4) experimental rat ventricular fibrillation (VF) optical mapping data. Results indicate general agreement between all three methods. Applying DGM-CURL on networks created by looking at differences in local activation times between nodes, we find that high curl values identify graph nodes that balance the inflow and outflow of these differences, indicating areas of reentry. We stress the importance of using multiple algorithms to detect rotational activity as each method is prone to errors. Using a combined approach decreases the susceptibility to errors and offers a more complete picture of the dynamics of rotational drivers in cardiac arrhythmias.