Rational modeling of multi-lead QRS complexes in ECG signals

Abstract. The main topic of this paper is the relation between the QRS complexes recorded from different pairs of electrodes of the same ECG signal. The electrode combinations I, II, III, aVR, aVL, aVF will be considered. Our aim is to provide a simple mathematical model for explaining and demonstrating the relation between the records. The model we construct is based on elementary rational functions having a single pole of second order. The records are then represented in a proper three dimensional function space determined by the pole. We show that the same pole turns to be optimal for each of the electrode combinations. For finding the optimal pole we have developed a hyperbolic version of the Nelder–Mead algorithm. We also show that if we extend the function space by adding the elementary rational functions with the same pole of order one, three, and four etc. then a good approximation of QRS complexes can be given for all of the records. We used the Physionet database [3] for testing our model.