DAD characterization in electromechanical cardiac models

Paolo Biscari; Chiara Lelli

doi:10.3934/dcds.2013.33.2651

Article Contents

2013, Volume 33, Issue 7: 2651-2665. Doi: 10.3934/dcds.2013.33.2651

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DAD characterization in electromechanical cardiac models

Paolo Biscari^1, and
Chiara Lelli^1,

1.
Department of Mathematics, Politecnico di Milano, Piazza Leonardo da Vinci 32, 20133 Milan

Received: March 31, 2012

Revised: October 31, 2012

Published: June 2013

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Abstract

We investigate the possibility of modeling the delayed afterdepolarization (DAD) occurrence in the framework of the classical FitzHugh-Nagumo (FN) dynamical system, as well as in more recent electromechanically-coupled cardiac models. Within the FN model, we identify the domain in the constitutive parameters' space for which orbits exist which exhibit a sufficiently strong secondary impulse. We then address the question whether a locally-induced secondary pulse succeeds or not in originating a self-propagating traveling impulse. Our results evidence that, in the range where secondary impulses exceed the physiological threshold for DAD onset, a local impulse almost certainly causes a traveling impulse (mechanism known as all-or-none). We then consider a recently proposed electromechanically-coupled generalization of the FN model, and show that the mechanical coupling stabilizes the system, in the sense that the more strong the coupling, the less likely is DAD to occur.

Keywords:

Electromechanical cardiac models,
spike sequence.

Mathematics Subject Classification: Primary: 37N25; Secondary: 92C10, 92C20.

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