Non-invasive reconstruction of dynamic myocardial transmembrane potential with graph-based total variation constraints

Non-invasive reconstruction of electrophysiological activity in the heart is of great significance for clinical disease prevention and surgical treatment. The distribution of transmembrane potential (TMP) in three-dimensional myocardium can help us diagnose heart diseases such as myocardial ischemia and ectopic pacing. However, the problem of solving TMP is ill-posed, and appropriate constraints need to be added. The existing state-of-art method total variation minimisation only takes advantage of the local similarity in space, which has the problem of over-smoothing, and fails to take into account the relationship among frames in the dynamic TMP sequence. In this work, the authors introduce a novel regularisation method called graph-based total variation to make up for the above shortcomings. The graph structure takes the TMP value of a time sequence on each heart node as the criterion to establish the similarity relationship among the heart. Two sets of phantom experiments were set to verify the superiority of the proposed method over the traditional constraints: infarct scar reconstruction and activation wavefront reconstruction. In addition, experiments with ten real premature ventricular contractions patient data were used to demonstrate the accuracy of the authors’ method in clinical applications.