Identifying wave sources using flow velocity method in excitable media

Excitable media, particularly cardiac tissue, exhibit diverse spatiotemporal wave patterns, among which abnormal waves (e.g., focal activity, rotational activity) can induce life-threatening cardiac arrhythmias. Locating and classifying the sources of these abnormal waves is crucial for guiding clinical treatment. Nevertheless, existing methods mostly only identify phase singularities (PSs) of spiral waves and fail to cover other important sources of target waves and waves rotating around obstacles. To overcome this, we propose a method that can identify spiral waves, target waves, and waves rotating around obstacles, as well as accurately locate their sources. The method involves two steps: (1) the computation of the transmembrane potential velocity field using optical flow techniques, with the zero-velocity fixed points identified as potential wave sources, and (2) the classification of the types of these fixed points via the Jacobian matrix analysis. Validation using simulated datasets generated by the Luo-Rudy model demonstrates the method's effectiveness: it robustly and accurately identifies wave types and locates their sources even in complex scenarios involving obstacles or background noise.