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DAD characterization in electromechanical cardiac models
1. | Department of Mathematics, Politecnico di Milano, Piazza Leonardo da Vinci 32, 20133 Milan, Italy, Italy |
References:
[1] |
C. Antzelevitch and S. Sicouri, Clinical relevance of cardiac arrhythmias generated by afterdepolarizations: Role of M cells in the generation of U waves, triggered activity and torsade de pointes, J. Am. Coll. Cardiol., 23 (1994), 259-277. |
[2] |
J. Mészáros, D. Khananshvili and G. Hart, Mechanisms underlying delayed afterdepolarizations in hypertrophied left ventricular myocytes of rats, Am. J. Physiol.-Heart. C., 281 (2001), H903-H914. |
[3] |
D. D. Friel, $[Ca^{2+}]_i$ oscillations in symphathetic neurons: An experimental test of a theoretical model, Biophys. J., 68 (1995), 1752-1766. |
[4] |
R. FitzHugh, Impulses and physiological states in theoretical models of nerve membrane, Biophys. J., 1 (1961), 445-466. |
[5] |
J. Nagumo, S. Arimoto and S. Yoshizawa, An active pulse transmission line simulating nerve axon, Proc. IRE, 50 (1962), 2061-2070. |
[6] |
J. Keener and J. Sneyd, "Mathematical Physiology," Ed. Springer Verlag, Berlin, 1998. |
[7] |
P. Biscari and C. Lelli, Spike transitions in the FitzHugh-Nagumo model, Eur. Phys. J. Plus, 126 (2011), 1-9. |
[8] |
A. Tonnelier, The McKean's caricature of the Fitzhugh-Nagumo model I. The space-clamped system, SIAM J. Appl. Math., 63 (2002), 459-484.
doi: 10.1137/S0036139901393500. |
[9] |
K. Schlotthauer and D. M. Bers, Sarcoplasmic reticulum $Ca^{2+}$ release causes myocyte depolarization: Underlying mechanism and threshold for triggered action potentials, Circ. Res., 87 (2000), 774-780. |
[10] |
Y. Xie, D. Sato, A. Garfinkel, Z. Qu and J. Weiss, So little source, so much sink: Requirements for afterdepolarizations to propagate in tissue, Biophys. J., 99 (2010), 1408-1415. |
[11] |
C. H. Luo and Y. Rudy, A dynamic model of the cardiac ventricular action potential II. Afterdepolarization, triggered activity, and potentiation, Circ. Res., 74 (1994), 1097-1113. |
[12] |
N. A. Wedge, M. S. Branicky and M. C. Cavusoglu, Proc. $26^{th}$ Int. Conf. IEEE engineering in medicine and biology society, Ed. IEEE, New York, (2004), 3027-3030. |
[13] |
M. P. Nash and A. V. Panfilov, Electromechanical model of excitable tissue to study reentrant cardiac arrhythmias, Prog. Biophys. Mol. Bio., 85 (2004), 501-522. |
[14] |
C. Lelli, "Attraction Basin of the Equilibrium Configuration in the FitzHugh-Nagumo Model," Acta Appl. Math., 2012.
doi: 10.1007/s10440-012-9744-9. |
[15] |
M. W. Green and B. D. Sleeman, On FitzHugh's nerve axon equations, J. Math. Biol., 1 (1974), 153-163. |
[16] |
C. Lelli, "Characterization of Delayed After-Depolarization in Extended FitzHugh-Nagumo Models," Ph.D. Thesis, Politecnico di Milano, 2012. |
[17] |
S. P. Hastings, Single and multiple pulse waves for the FitzHugh-Nagumo equations, SIAM J. Appl. Math., 42 (1982), 247-260.
doi: 10.1137/0142018. |
[18] |
Y. M. Usachev and S. A. Thayer, All-or-None $Ca^{2+}$ release from intracellular stores triggered by $Ca^{2+}$ influx through voltage-gated $Ca^{2+}$ channels in rat sensory neurons, J. Neuosci., 17 (1997), 7404-7414. |
[19] |
C. Cherubini, S. Filippi, P. Nardinocchi and L. Teresi, An electromechanical model of cardiac tissue: Constitutive issues and electrophysiological effects, Progr. Biophys. Molec. Biol., 97 (2008), 562-573. |
[20] |
D. Ambrosi, G. Arioli, F. Nobile and A. Quarteroni, Electromechanical coupling in cardiac dynamics: The active strain approach, SIAM J. Appl. Math., 71 (2011), 605-621.
doi: 10.1137/100788379. |
[21] |
J. M. Rogers and A. D. McCulloch, A Collocation-Galerkin finite element model of cardiac action potential propagation, IEEE Trans. Biomed. Eng., 41 (1994), 743-757. |
[22] |
R. R. Aliev and A. V. Panfilov, A simple two-variable model of cardiac excitation, Chaos Sol. Fract., 7 (1996), 293-301. |
[23] |
J. Rinzel and J. B. Keller, Traveling wave solutions of a nerve conduction equation, Biophys. J., 13 (1973), 1313-1337. |
[24] |
M. E. Gurtin, E. Fried and L. Anand, "The Mechanics and Thermodynamics of Continua," Ed. Cambridge University Press, 2010. |
[25] |
S. M. Pogwizd, K. Schlotthauer, L. Li, W. Yuan and D. M. Bers, Arrhythmogenesis and contractile dysfunction in heart failure: Roles of sodium-calcium exchange, inward rectifier potassium current, and residual $\beta$-adrenergic responsiveness, Circ. Res., 88 (2001), 1159-1167. |
[26] |
N. P. Smith, D. P. Nickerson, E. J. Crampin and P. J. Hunter, Multiscale computational modelling of the heart, Acta Numer., 13 (2004), 371-431.
doi: 10.1017/S0962492904000200. |
show all references
References:
[1] |
C. Antzelevitch and S. Sicouri, Clinical relevance of cardiac arrhythmias generated by afterdepolarizations: Role of M cells in the generation of U waves, triggered activity and torsade de pointes, J. Am. Coll. Cardiol., 23 (1994), 259-277. |
[2] |
J. Mészáros, D. Khananshvili and G. Hart, Mechanisms underlying delayed afterdepolarizations in hypertrophied left ventricular myocytes of rats, Am. J. Physiol.-Heart. C., 281 (2001), H903-H914. |
[3] |
D. D. Friel, $[Ca^{2+}]_i$ oscillations in symphathetic neurons: An experimental test of a theoretical model, Biophys. J., 68 (1995), 1752-1766. |
[4] |
R. FitzHugh, Impulses and physiological states in theoretical models of nerve membrane, Biophys. J., 1 (1961), 445-466. |
[5] |
J. Nagumo, S. Arimoto and S. Yoshizawa, An active pulse transmission line simulating nerve axon, Proc. IRE, 50 (1962), 2061-2070. |
[6] |
J. Keener and J. Sneyd, "Mathematical Physiology," Ed. Springer Verlag, Berlin, 1998. |
[7] |
P. Biscari and C. Lelli, Spike transitions in the FitzHugh-Nagumo model, Eur. Phys. J. Plus, 126 (2011), 1-9. |
[8] |
A. Tonnelier, The McKean's caricature of the Fitzhugh-Nagumo model I. The space-clamped system, SIAM J. Appl. Math., 63 (2002), 459-484.
doi: 10.1137/S0036139901393500. |
[9] |
K. Schlotthauer and D. M. Bers, Sarcoplasmic reticulum $Ca^{2+}$ release causes myocyte depolarization: Underlying mechanism and threshold for triggered action potentials, Circ. Res., 87 (2000), 774-780. |
[10] |
Y. Xie, D. Sato, A. Garfinkel, Z. Qu and J. Weiss, So little source, so much sink: Requirements for afterdepolarizations to propagate in tissue, Biophys. J., 99 (2010), 1408-1415. |
[11] |
C. H. Luo and Y. Rudy, A dynamic model of the cardiac ventricular action potential II. Afterdepolarization, triggered activity, and potentiation, Circ. Res., 74 (1994), 1097-1113. |
[12] |
N. A. Wedge, M. S. Branicky and M. C. Cavusoglu, Proc. $26^{th}$ Int. Conf. IEEE engineering in medicine and biology society, Ed. IEEE, New York, (2004), 3027-3030. |
[13] |
M. P. Nash and A. V. Panfilov, Electromechanical model of excitable tissue to study reentrant cardiac arrhythmias, Prog. Biophys. Mol. Bio., 85 (2004), 501-522. |
[14] |
C. Lelli, "Attraction Basin of the Equilibrium Configuration in the FitzHugh-Nagumo Model," Acta Appl. Math., 2012.
doi: 10.1007/s10440-012-9744-9. |
[15] |
M. W. Green and B. D. Sleeman, On FitzHugh's nerve axon equations, J. Math. Biol., 1 (1974), 153-163. |
[16] |
C. Lelli, "Characterization of Delayed After-Depolarization in Extended FitzHugh-Nagumo Models," Ph.D. Thesis, Politecnico di Milano, 2012. |
[17] |
S. P. Hastings, Single and multiple pulse waves for the FitzHugh-Nagumo equations, SIAM J. Appl. Math., 42 (1982), 247-260.
doi: 10.1137/0142018. |
[18] |
Y. M. Usachev and S. A. Thayer, All-or-None $Ca^{2+}$ release from intracellular stores triggered by $Ca^{2+}$ influx through voltage-gated $Ca^{2+}$ channels in rat sensory neurons, J. Neuosci., 17 (1997), 7404-7414. |
[19] |
C. Cherubini, S. Filippi, P. Nardinocchi and L. Teresi, An electromechanical model of cardiac tissue: Constitutive issues and electrophysiological effects, Progr. Biophys. Molec. Biol., 97 (2008), 562-573. |
[20] |
D. Ambrosi, G. Arioli, F. Nobile and A. Quarteroni, Electromechanical coupling in cardiac dynamics: The active strain approach, SIAM J. Appl. Math., 71 (2011), 605-621.
doi: 10.1137/100788379. |
[21] |
J. M. Rogers and A. D. McCulloch, A Collocation-Galerkin finite element model of cardiac action potential propagation, IEEE Trans. Biomed. Eng., 41 (1994), 743-757. |
[22] |
R. R. Aliev and A. V. Panfilov, A simple two-variable model of cardiac excitation, Chaos Sol. Fract., 7 (1996), 293-301. |
[23] |
J. Rinzel and J. B. Keller, Traveling wave solutions of a nerve conduction equation, Biophys. J., 13 (1973), 1313-1337. |
[24] |
M. E. Gurtin, E. Fried and L. Anand, "The Mechanics and Thermodynamics of Continua," Ed. Cambridge University Press, 2010. |
[25] |
S. M. Pogwizd, K. Schlotthauer, L. Li, W. Yuan and D. M. Bers, Arrhythmogenesis and contractile dysfunction in heart failure: Roles of sodium-calcium exchange, inward rectifier potassium current, and residual $\beta$-adrenergic responsiveness, Circ. Res., 88 (2001), 1159-1167. |
[26] |
N. P. Smith, D. P. Nickerson, E. J. Crampin and P. J. Hunter, Multiscale computational modelling of the heart, Acta Numer., 13 (2004), 371-431.
doi: 10.1017/S0962492904000200. |
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