A Modified Heart Dipole Model for the Generation of Pathological <i>ECG</i> Signals

• Main Authors: Mario Versaci, Giovanni Angiulli, Fabio La Foresta
• Format: Article
• Language: English
• Published: MDPI AG 2020-11-01
• Series: Computation
• Subjects: electrocardiogram (ECG) signals; McSharry models; Heart Dipole Model; existence and uniqueness of the solution; equilibrium point stability
• Online Access: https://www.mdpi.com/2079-3197/8/4/92

In this paper, we introduce a new dynamic model of simulation of electrocardiograms (<inline-formula><math display="inline"><semantics><mrow><mi>E</mi><mi>C</mi><mi>G</mi></mrow></semantics></math></inline-formula>s) affected by pathologies starting from the well-known McSharry dynamic model for the <inline-formula><math display="inline"><semantics><mrow><mi>E</mi><mi>C</mi><mi>G</mi></mrow></semantics></math></inline-formula>s without cardiac disorders. In particular, the McSharry model has been generalized (by a linear transformation and a rotation) for simulating <inline-formula><math display="inline"><semantics><mrow><mi>E</mi><mi>C</mi><mi>G</mi></mrow></semantics></math></inline-formula>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 <inline-formula><math display="inline"><semantics><mrow><mi>E</mi><mi>C</mi><mi>G</mi></mrow></semantics></math></inline-formula>s with or without heart diseases very similar to those achieved directly on the patients. Moreover, verified that the <inline-formula><math display="inline"><semantics><mrow><mi>E</mi><mi>C</mi><mi>G</mi></mrow></semantics></math></inline-formula>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 <inline-formula><math display="inline"><semantics><mrow><mi>E</mi><mi>C</mi><mi>G</mi></mrow></semantics></math></inline-formula>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 <inline-formula><math display="inline"><semantics><mrow><mi>E</mi><mi>C</mi><mi>G</mi></mrow></semantics></math></inline-formula>s affected by pathologies can be considered as a solid starting point for the development of synthetic pathological <inline-formula><math display="inline"><semantics><mrow><mi>E</mi><mi>C</mi><mi>G</mi></mrow></semantics></math></inline-formula>s signals.