Tensor cardiography: a novel ECG analysis of deviations in collective myocardial Action Potential transitions based on point processes and cumulative distribution functions
Authors: Tsukada Shingo , Iwasaki Yu-ki , Tsukada Yayoi Tetsuo 
Published: May 2023

SummaryA method to estimate myocardial action potentials (APs) from electrocardiograms (ECGs) would be an advance in ECG-based diagnosis, utilised for clinical diagnosis, assessment of potential cardiac disease risk and prediction of lethal arrhythmias. However, the ECG inverse problem, which estimates the spatial distribution of AP signals from the ECG, has been considered difficult electromagnetically. For clinical ECG analysis, timescales of collective APs, synchrony and the duration of depolarisation and repolarisation is informative. Thus, we attempted to obtain the time distribution of collective AP transitions from the ECG rather than the spatial distribution.To analyse the variance of the collective myocardial APs from the ECG, we designed a model equation using the probability densities of the Gaussian function of time-series point processes in the cardiac cycle and dipoles of collective APs in the myocardium. The equation to calculate the difference between the two cumulative distribution functions (CDFs) as the positive- and negative-epicardium potential fits well with the R and T waves. The mean, standard deviation, weights, and level of each CDFs are metrics for the variance of the AP transition state of the collective myocardial AP transition states. Clinical ECGs of myocardial ischaemia during coronary intervention showed abnormalities in the aforementioned specific elements of the tensor associated with repolarisation transition variance earlier than in conventional indicators of ischaemia. The tensor could evaluate the beat-to-beat dynamic repolarisation changes between the ventricular epi and endocardium using the Mahalanobis distance (MD). Tensor Cardiography, a method that uses CDF differences CDF as the transition of a collective myocardial AP transition, has the potential to be a new analysis tool for ECGs.Author’s SummaryMyocardial action potentials (APs) which indicate electric excitation of the cells can provide important information to suggest the mechanisms of cardiac disease such as myocardial ischemia and arrhythmias. However, it has been challenging to estimate APs from electrocardiograms (ECGs). Unlike other imaging techniques like CT or MRI, the electrocardiographic inverse problem requires estimating the geometric distribution of APs from the ECG, has been considered difficult.Our approach, known as Tensor Cardiography, uses a model equation based on cumulative distribution functions (CDFs) to analyze the time series variance of collective myocardial APs from the ECG. By fitting this equation to the R and T waves, we have obtained a set of metrics that represent beat-to-beat dynamic variance of polarization and repolarization of the epi and endocardium. Our study of ECGs from myocardial ischemia during coronary intervention has demonstrated abnormalities in the tensor elements associated with repolarization, which appeared earlier and more prominently than conventional ST changes.Tensor Cardiography provides a revolutionary analysis tool for ECGs that holds enormous potential for clinical diagnosis, risk assessment, and prediction of lethal arrhythmias. Our approach shows promise as a new frontier in cardiac disease management and has significant implications for patient care.