A Modified Heart Dipole Model for the Generation of Pathological ECG Signals

In this paper, we introduce a new dynamic model of simulation of electrocardiograms ($ECG$s) affected by pathologies starting from the well-known McSharry dynamic model for the $ECG$s without cardiac disorders. In particular, the McSharry model has been generalized (by a linear transformation and a rotation) for simulating $ECG$s affected by heart diseases verifying, from one hand, the existence and uniqueness of the solution and, on the other hand, if it admits instabilities. The results, obtained numerically by a procedure based on a Four Stage Lobatto IIIa formula, show the good performances of the proposed model in producing $ECG$s with or without heart diseases very similar to those achieved directly on the patients. Moreover, verified that the $ECG$s signals are affected by uncertainty and/or imprecision through the computation of the linear index and the fuzzy entropy index (whose values obtained are close to unity), these similarities among $ECG$s signals (with or without heart diseases) have been quantified by a well-established fuzzy approach based on fuzzy similarity computations highlighting that the proposed model to simulate $ECG$s affected by pathologies can be considered as a solid starting point for the development of synthetic pathological $ECG$s signals.