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July  2013, 33(7): 2651-2665. doi: 10.3934/dcds.2013.33.2651

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, Italy, Italy

Received  April 2012 Revised  November 2012 Published  January 2013

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, 92C2.
Citation: Paolo Biscari, Chiara Lelli. DAD characterization in electromechanical cardiac models. Discrete & Continuous Dynamical Systems, 2013, 33 (7) : 2651-2665. doi: 10.3934/dcds.2013.33.2651
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show all references

References:
[1]

J. Am. Coll. Cardiol., 23 (1994), 259-277. Google Scholar

[2]

Am. J. Physiol.-Heart. C., 281 (2001), H903-H914. Google Scholar

[3]

Biophys. J., 68 (1995), 1752-1766. Google Scholar

[4]

Biophys. J., 1 (1961), 445-466. Google Scholar

[5]

Proc. IRE, 50 (1962), 2061-2070. Google Scholar

[6]

Ed. Springer Verlag, Berlin, 1998.  Google Scholar

[7]

Eur. Phys. J. Plus, 126 (2011), 1-9. Google Scholar

[8]

SIAM J. Appl. Math., 63 (2002), 459-484. doi: 10.1137/S0036139901393500.  Google Scholar

[9]

Circ. Res., 87 (2000), 774-780. Google Scholar

[10]

Biophys. J., 99 (2010), 1408-1415. Google Scholar

[11]

Circ. Res., 74 (1994), 1097-1113. Google Scholar

[12]

Ed. IEEE, New York, (2004), 3027-3030. Google Scholar

[13]

Prog. Biophys. Mol. Bio., 85 (2004), 501-522. Google Scholar

[14]

Acta Appl. Math., 2012. doi: 10.1007/s10440-012-9744-9.  Google Scholar

[15]

J. Math. Biol., 1 (1974), 153-163.  Google Scholar

[16]

Ph.D. Thesis, Politecnico di Milano, 2012. Google Scholar

[17]

SIAM J. Appl. Math., 42 (1982), 247-260. doi: 10.1137/0142018.  Google Scholar

[18]

J. Neuosci., 17 (1997), 7404-7414. Google Scholar

[19]

Progr. Biophys. Molec. Biol., 97 (2008), 562-573. Google Scholar

[20]

SIAM J. Appl. Math., 71 (2011), 605-621. doi: 10.1137/100788379.  Google Scholar

[21]

IEEE Trans. Biomed. Eng., 41 (1994), 743-757. Google Scholar

[22]

Chaos Sol. Fract., 7 (1996), 293-301. Google Scholar

[23]

Biophys. J., 13 (1973), 1313-1337.  Google Scholar

[24]

Ed. Cambridge University Press, 2010.  Google Scholar

[25]

Circ. Res., 88 (2001), 1159-1167. Google Scholar

[26]

Acta Numer., 13 (2004), 371-431. doi: 10.1017/S0962492904000200.  Google Scholar

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