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Nonlinear dynamics of a mathematical model on action potential duration and calcium transient in paced cardiac cells
1. | Department of Mathematics, MOE-LSC, Shanghai Jiao Tong University, Shanghai, 200240, China |
2. | Department of Mathematics, Shanghai Jiao Tong University, Shanghai 200240 |
References:
[1] |
R. Aguilar-Lpez, R. Martnez-Guerra, H. Puebla and R. Hernndez-Surez, High order sliding-mode dynamic control for chaotic intracellular calcium oscillations, Nonlinear Analysis : Real World Appl., 11 (2010), 217-231.
doi: 10.1016/j.nonrwa.2008.10.054. |
[2] |
J. W. M. Bassani, W. Yuan and D. M. Bers, Fractional SR Ca release is regulated by trigger Ca and SR Ca content in cardiac myocytes, Am. J. Physiol., 268 (1995), C1313-C1319. |
[3] |
D. M. Bers, Cardiac excitation-contraction coupling, Nature, 415 (2002), 198-205.
doi: 10.1038/415198a. |
[4] |
H. Bien, L. Yin and E. Entcheva, Calcium instabilities in mammalian cardiomyocyte networks, Biophysical Journal, 90 (2006), 2628-2640.
doi: 10.1529/biophysj.105.063321. |
[5] |
E. Chudin, J. Goldhaber, A. Garfinkel, J. Weiss and B. Kogan, Intracellular Ca(2+) dynamics and the stability of ventricular tachycardia, Biophysics Journal, 77 (1999), 2930-2941.
doi: 10.1016/S0006-3495(99)77126-2. |
[6] |
D. E. Euler, Cardiac alternans: mechanisms and pathophysiological significance, Cardiovascular Research, 42 (1999), 583-590.
doi: 10.1016/S0008-6363(99)00011-5. |
[7] |
J. I. Goldhaber, L. H. Xie, T. Duong, C. Motter, K. Khuu and J. N. Weiss, Action potential duration restitution and alternans in rabbit ventricular myocytes: the key role of intracellular calcium cycling, Circulation Research, 96 (2005), 459-466.
doi: 10.1161/01.RES.0000156891.66893.83. |
[8] |
M. R. Guevara, L. Glass and A. Shrier, Phase locking, period-doubling bifurcations, and irregular dynamics in periodically stimulated cardiac cells, Science, 214 (1981), 1350-1353.
doi: 10.1126/science.7313693. |
[9] |
G. M. Hall, S. Bahar and D. J. Gauthier, Prevalence of rate-dependent behaviors in cardiac muscle, Phys. Rev. Lett., 82 (1999), 2995-2998.
doi: 10.1103/PhysRevLett.82.2995. |
[10] |
A. Karma, Electrical alternans and spiral wave breakup in cardiac tissue, Chaos, 4 (1994), 461-472.
doi: 10.1063/1.166024. |
[11] |
Y. A. Kuznetsov, "Elements of Applied Bifurcation Theory," Applied Mathematical Sciences, 3rd edition, Springer-Verlag, New York, LLC 2004. |
[12] |
C. H. Luo and Y. Rudy, A dynamic model of the cardiac ventricular action potential. I. Simulations of ionic currents and concentration changes, Circulation Research, 74 (1994), 1071-1096.
doi: 10.1161/01.RES.74.6.1071. |
[13] |
R. Mehra, Global public health problem of sudden cardiac death, Journal of Electrocardiology, 40 (2007), S118-S122.
doi: 10.1016/j.jelectrocard.2007.06.023. |
[14] |
J. B. Nolasco and R. W. Dahlen, A graphic method for the study of alternation in cardiac action potentials, J. Appl. Physiol., 25 (1968), 191-196. |
[15] |
N. F. Otani and R. F. Gilmour, Memory models for the electrical properties of local cardiac systems, Journal of Theoretical Biology, 187 (1997), 409-436.
doi: 10.1006/jtbi.1997.0447. |
[16] |
Z. Qu, Y. Shiferaw and J. N. Weiss, Nonlinear dynamics of cardiac excitation-contraction coupling: an iterated map study, Phys. Rev. E, 75 (2007), 011927.
doi: 10.1103/PhysRevE.75.011927. |
[17] |
T. R. Shannon, K. S. Ginsburg and D. M. Bers, Potentiation of fractional sarcoplasmic reticulum calcium release by total and free intra-sarcoplasmic reticulum calcium concentration, Biophysical Journal, 78 (2000), 334-343.
doi: 10.1016/S0006-3495(00)76596-9. |
[18] |
Y. Shiferaw and A. Karma, Turing instability mediated by voltage and calcium diffusion in paced cardiac cells, Proc. Natl. Acad. Sci., 103 (2006), 5670-5675.
doi: 10.1073/pnas.0511061103. |
[19] |
Y. Shiferaw, Z. Qu, A. Garfinkel, A. Karma and J. N. Weiss, Nonlinear dynamics of paced cardiac cells, Annals of the New York Academy of Sciences, 1080 (2006), 376-394.
doi: 10.1196/annals.1380.028.x. |
[20] |
Y. Shiferaw, D. Sato and A. Karma, Coupled dynamics of voltage and calcium in paced cardiac cells, Phys. Rev. E, 71 (2005), 021903.
doi: 10.1103/PhysRevE.71.021903. |
[21] |
Y. Shiferaw, M. A. Watanabe, A. Garfinkel, J. N. Weiss and A. Karma, Model of intracellular calcium cycling in ventricular myocytes, Biophysical Journal, 85 (2003), 3666-3686.
doi: 10.1016/S0006-3495(03)74784-5. |
[22] |
M. D. Stubna, R. H. Rand and R. F. Gilmour, Analysis of a non-linear partial difference equation, and its application to cardiac dynamics, Journal of Difference Equations and Applications, 8 (2002), 1147-1169.
doi: 10.1080/1023619021000054006. |
[23] |
R. Thul and S. Coombes, Understanding cardiac alternans: A piecewise linear modeling framework, Chaos, 20 (2010), 045102.
doi: 10.1063/1.3518362. |
[24] |
E. G. Tolkacheva, M. M. Romeo and D. J. Gauthier, Control of cardiac alternans in a mapping model with memory, Physica D: Nonlinear Phenomena, 194 (2004), 385-391.
doi: 10.1016/j.physd.2004.03.008. |
[25] |
M. L. Walker and D. S. Rosenbaum, Repolarization alternans: implications for the mechanism and prevention of sudden cardiac death, Cardiovascular Research, 57 (2003), 599-614.
doi: 10.1016/S0008-6363(02)00737-X. |
[26] |
G. S. B. Williams, G. D. Smith, E. A. Sobie and M. S. Jafri, Models of cardiac excitation-contraction coupling in ventricular myocytes, Mathematical Biosciences, 226 (2010), 1-15.
doi: 10.1016/j.mbs.2010.03.005. |
show all references
References:
[1] |
R. Aguilar-Lpez, R. Martnez-Guerra, H. Puebla and R. Hernndez-Surez, High order sliding-mode dynamic control for chaotic intracellular calcium oscillations, Nonlinear Analysis : Real World Appl., 11 (2010), 217-231.
doi: 10.1016/j.nonrwa.2008.10.054. |
[2] |
J. W. M. Bassani, W. Yuan and D. M. Bers, Fractional SR Ca release is regulated by trigger Ca and SR Ca content in cardiac myocytes, Am. J. Physiol., 268 (1995), C1313-C1319. |
[3] |
D. M. Bers, Cardiac excitation-contraction coupling, Nature, 415 (2002), 198-205.
doi: 10.1038/415198a. |
[4] |
H. Bien, L. Yin and E. Entcheva, Calcium instabilities in mammalian cardiomyocyte networks, Biophysical Journal, 90 (2006), 2628-2640.
doi: 10.1529/biophysj.105.063321. |
[5] |
E. Chudin, J. Goldhaber, A. Garfinkel, J. Weiss and B. Kogan, Intracellular Ca(2+) dynamics and the stability of ventricular tachycardia, Biophysics Journal, 77 (1999), 2930-2941.
doi: 10.1016/S0006-3495(99)77126-2. |
[6] |
D. E. Euler, Cardiac alternans: mechanisms and pathophysiological significance, Cardiovascular Research, 42 (1999), 583-590.
doi: 10.1016/S0008-6363(99)00011-5. |
[7] |
J. I. Goldhaber, L. H. Xie, T. Duong, C. Motter, K. Khuu and J. N. Weiss, Action potential duration restitution and alternans in rabbit ventricular myocytes: the key role of intracellular calcium cycling, Circulation Research, 96 (2005), 459-466.
doi: 10.1161/01.RES.0000156891.66893.83. |
[8] |
M. R. Guevara, L. Glass and A. Shrier, Phase locking, period-doubling bifurcations, and irregular dynamics in periodically stimulated cardiac cells, Science, 214 (1981), 1350-1353.
doi: 10.1126/science.7313693. |
[9] |
G. M. Hall, S. Bahar and D. J. Gauthier, Prevalence of rate-dependent behaviors in cardiac muscle, Phys. Rev. Lett., 82 (1999), 2995-2998.
doi: 10.1103/PhysRevLett.82.2995. |
[10] |
A. Karma, Electrical alternans and spiral wave breakup in cardiac tissue, Chaos, 4 (1994), 461-472.
doi: 10.1063/1.166024. |
[11] |
Y. A. Kuznetsov, "Elements of Applied Bifurcation Theory," Applied Mathematical Sciences, 3rd edition, Springer-Verlag, New York, LLC 2004. |
[12] |
C. H. Luo and Y. Rudy, A dynamic model of the cardiac ventricular action potential. I. Simulations of ionic currents and concentration changes, Circulation Research, 74 (1994), 1071-1096.
doi: 10.1161/01.RES.74.6.1071. |
[13] |
R. Mehra, Global public health problem of sudden cardiac death, Journal of Electrocardiology, 40 (2007), S118-S122.
doi: 10.1016/j.jelectrocard.2007.06.023. |
[14] |
J. B. Nolasco and R. W. Dahlen, A graphic method for the study of alternation in cardiac action potentials, J. Appl. Physiol., 25 (1968), 191-196. |
[15] |
N. F. Otani and R. F. Gilmour, Memory models for the electrical properties of local cardiac systems, Journal of Theoretical Biology, 187 (1997), 409-436.
doi: 10.1006/jtbi.1997.0447. |
[16] |
Z. Qu, Y. Shiferaw and J. N. Weiss, Nonlinear dynamics of cardiac excitation-contraction coupling: an iterated map study, Phys. Rev. E, 75 (2007), 011927.
doi: 10.1103/PhysRevE.75.011927. |
[17] |
T. R. Shannon, K. S. Ginsburg and D. M. Bers, Potentiation of fractional sarcoplasmic reticulum calcium release by total and free intra-sarcoplasmic reticulum calcium concentration, Biophysical Journal, 78 (2000), 334-343.
doi: 10.1016/S0006-3495(00)76596-9. |
[18] |
Y. Shiferaw and A. Karma, Turing instability mediated by voltage and calcium diffusion in paced cardiac cells, Proc. Natl. Acad. Sci., 103 (2006), 5670-5675.
doi: 10.1073/pnas.0511061103. |
[19] |
Y. Shiferaw, Z. Qu, A. Garfinkel, A. Karma and J. N. Weiss, Nonlinear dynamics of paced cardiac cells, Annals of the New York Academy of Sciences, 1080 (2006), 376-394.
doi: 10.1196/annals.1380.028.x. |
[20] |
Y. Shiferaw, D. Sato and A. Karma, Coupled dynamics of voltage and calcium in paced cardiac cells, Phys. Rev. E, 71 (2005), 021903.
doi: 10.1103/PhysRevE.71.021903. |
[21] |
Y. Shiferaw, M. A. Watanabe, A. Garfinkel, J. N. Weiss and A. Karma, Model of intracellular calcium cycling in ventricular myocytes, Biophysical Journal, 85 (2003), 3666-3686.
doi: 10.1016/S0006-3495(03)74784-5. |
[22] |
M. D. Stubna, R. H. Rand and R. F. Gilmour, Analysis of a non-linear partial difference equation, and its application to cardiac dynamics, Journal of Difference Equations and Applications, 8 (2002), 1147-1169.
doi: 10.1080/1023619021000054006. |
[23] |
R. Thul and S. Coombes, Understanding cardiac alternans: A piecewise linear modeling framework, Chaos, 20 (2010), 045102.
doi: 10.1063/1.3518362. |
[24] |
E. G. Tolkacheva, M. M. Romeo and D. J. Gauthier, Control of cardiac alternans in a mapping model with memory, Physica D: Nonlinear Phenomena, 194 (2004), 385-391.
doi: 10.1016/j.physd.2004.03.008. |
[25] |
M. L. Walker and D. S. Rosenbaum, Repolarization alternans: implications for the mechanism and prevention of sudden cardiac death, Cardiovascular Research, 57 (2003), 599-614.
doi: 10.1016/S0008-6363(02)00737-X. |
[26] |
G. S. B. Williams, G. D. Smith, E. A. Sobie and M. S. Jafri, Models of cardiac excitation-contraction coupling in ventricular myocytes, Mathematical Biosciences, 226 (2010), 1-15.
doi: 10.1016/j.mbs.2010.03.005. |
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