A mathematical approach to demonstrate R to T wave concordance of the human ECG

R-to-T-wave concordance within the same lead of the human electrocardiogram (ECG) has been under discussion for decades, as the QRS complex with its R-wave represent depolarization and the T-wave repolarization. Extracellular recorded monophasic action potential (MAP) of the human heart muscle fibre resembles the first derivation of the intracellular MAP over time, showing R-to-T-wave discordance. While a single fibre monophasic electrophysiology lacks many aspects of the ECG, bipolar registration for the different layers of the ventricular wall (transmural gradient) gives more detailed information about the local MAP, as endo-, meso- and epicardium show a MAP time difference (voltage gradient) dependent positioning of the T-wave, within a simultaneously recorded epicardial ECG. Without an integrated consideration of the heterogenous (endo-, meso- and epimyocardial) MAP, T-wave concordance cannot be explained, as it would provide a homogenous model like the single heart muscle fibre MAP. A closed form representation of the potential difference to explain concordance was found. We developed a 3-dimensional, time dependent setup simulating the transmural gradient. The time-dependent spatial integrals, which account for the extracellular loading-density (which is inversely related to MAP) along all layers show concordance. These functions allow to calculate the electric potential at any point in space at any given time within the QT-Interval. The closed form solution of the electric potential enables to identify the corresponding T-wave morphologies. Inversely, pathological patterns in the action potential can then be identified from the ECG. Our approach is an attempt to overcome the inverse problem and to reduce empiricism, as change of T-wave morphology can be assigned.