Mahalanobis distance.

<div><p>To improve clinical diagnoses, assessments of potential cardiac disease risk, and predictions of lethal arrhythmias, the analysis of electrocardiograms (ECGs) requires a more accurate method of weighting waveforms to efficiently detect abnormalities that appear as minute strains in the waveforms. In addition, the inverse problem of estimating the myocardial action potential from the ECG has been a longstanding challenge. To analyze the variance of the ECG waveforms and to estimate collective myocardial action potentials (APs) from the ECG, we designed a model equation incorporating the probability densities of Gaussian functions of time-series point processes in the cardiac cycle and dipoles of the collective APs in the myocardium. The equation, which involves taking the difference between the cumulative distribution functions (CDFs) that represent positive endocardial and negative epicardial potentials, fits both R and T waves. The mean, standard deviation, weights, and level of each cumulative distribution function (CDF) are metrics for the variance of the transition state of the collective myocardial AP. Clinical ECGs of myocardial ischemia during coronary intervention show abnormalities in the aforementioned specific elements of the tensor associated with repolarization transition variance earlier than in conventional indicators of ischemia. The tensor can be used to evaluate the beat-to-beat dynamic repolarization changes between the ventricular epi and endocardium in terms of the Mahalanobis distance (MD). This tensor-based cardiography that uses the differences between CDFs to show changes in collective myocardial APs has the potential to be a new analysis tool for ECGs.</p></div>