Nonlinear dynamics of paced cardiac cells

Annals of the New York Academy of Sciences

Volumn 1080, Issue , 2006, Pages 376-394

  Shiferaw, Yohannes ^a   Qu, Zhilin ^a   Garfinkel, Alan ^a   Karma, Alain ^b   Weiss, James N ^a  

^a UNIVERSITY OF CALIFORNIA   (United States)

^b NORTHEASTERN UNIVERSITY   (United States)

Author keywords

Alternans; Calcium cycling; Cardiac arrhythmias; Nonlinear dynamics

Indexed keywords

CALCIUM;

ACTION POTENTIAL; CELL MEMBRANE POTENTIAL; CONFERENCE PAPER; ELECTRIC POTENTIAL; HEART MUSCLE CELL; MATHEMATICAL PARAMETERS; NONLINEAR SYSTEM;

EID: 33845623272     PISSN: 00778923     EISSN: 17496632     Source Type: Book Series    
DOI: 10.1196/annals.1380.028.x     Document Type: Conference Paper

References (57)

1. KARMA, A. 1994. Electrical alternans and spiral wave breakup in cardiac tissue. Chaos 4: 461-472.
2. GARFINKEL, A., Y.H. KIM, O. VOROSHILOVSKY, et al. 2000. Preventing ventricular fibrillation by flattening cardiac restitution. Proc. Natl. Acad. Sci. USA 97: 6061-6066.
3. QU, Z. & A. GARFINKEL. 1999. An advanced algorithm for solving partial differential equation in cardiac conduction. IEEE Trans. Biomed. Eng. 46: 1166-1168.
4. QU, Z., J.N. WEISS & A. GARFINKEL. 2000. From local to global spatiotemporal chaos in a cardiac tissue model. Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics 61: 727-732.
5. EULER, D.E. 1999. Cardiac alternans: mechanisms and pathophysiological significance. Cardiovasc. Res. 42: 583-590.
6. WALKER, M.L. & D.S. ROSENBAUM. 2003. Repolarization alternans: implications for the mechanism and prevention of sudden cardiac death. Cardiovasc. Res. 57: 599-614.
7. PASTORE, J.M., S.D. GIROUARD, K.R. LAURITA, et al. 1999. Mechanism linking T-wave alternans to the genesis of cardiac fibrillation. Circulation 99: 1385-1394.
8. PRUVOT, E.J. & D.S. ROSENBAUM. 2003. T-wave alternans for risk stratification and prevention of sudden cardiac death. Curr. Cardiol. Rep. 5: 350-357.
9. ROSENBAUM, D.S., L.E. JACKSON, J.M. SMITH, et al. 1994. Electrical alternans and vulnerability to ventricular arrhythmias. N. Engl. J. Med. 330: 235-241.
10. ARMOUNDAS, A.A., M. OSAKA, T. MELA, et al. 1998. T-wave alternans and dispersion of the QT interval as risk stratification markers in patients susceptible to sustained ventricular arrhythmias. Am. J. Cardiol. 82: 1127-1129, A9.
11. DIAZ, M.E., D.A. EISNER & S.C. O'NEILL. 2002. Depressed ryanodine receptor activity increases variability and duration of the systolic Ca2+ transient in rat ventricular myocytes. Circ. Res. 91: 585-593.
12. HUSER, J., Y.G. WANG, K.A. SHEEHAN, et al. 2000. Functional coupling between glycolysis and excitation-contraction coupling underlies alternans in cat heart cells. J. Physiol. 524: 795-806.
13. EISNER, D.A., H.S. CHOI, M.E. DIAZ, et al. 2000. Integrative analysis of calcium cycling in cardiac muscle. Circ. Res. 87: 1087-1094.
14. CHUDIN, E., J. GOLDHABER, A. GARFINKEL, et al. 1999. Intracellular Ca(2+) dynamics and the stability of ventricular tachycardia. Biophys. J. 77: 2930-2941.
15. DIAZ, M.E., S.C. O'NEILL & D.A. EISNER. 2004. Sarcoplasmic reticulum calcium content fluctuation is the key to cardiac alternans. Circ. Res. 94: 650-656.
16. NOLASCO, J.B. & R.W. DAHLEN. 1968. A graphic method for the study of alternation in cardiac action potentials. J. Appl. Physiol. 25: 191-196.
17. GUEVARA, M.R., L. GLASS & A. SHRIER. 1981. Phase locking, period-doubling bifurcations, and irregular dynamics in periodically stimulated cardiac cells. Science 214: 1350-1353.
18. GUEVARA, M.R., G. WARD, A. SHRIER & L. GLASS. 1984. Electrical alternans and period doubling bifurcations. IEEE Comput. Cardiol. 167-170.
19. BEELER, G.W. & H. REUTER. 1977. Reconstruction of the action potential of ventricular myocardial fibres. J. Physiol. 268: 177-210.
20. LUO, C.H. & Y. RUDY. 1994. A dynamic model of the cardiac ventricular action potential. I. Simulations of ionic currents and concentration changes. Circ. Res. 74: 1071-1096.
21. Fox, J.J., J.L. MCHARG & R.F. GILMOUR, JR. 2002. Ionic mechanism of electrical alternans. Am. J. Physiol. Heart Circ. Physiol. 282: H516-H530.
22. JAFRI, M.S., J.J. RICE & R.L. WINSLOW. 1998. Cardiac Ca2+ dynamics: the roles of ryanodine receptor adaptation and sarcoplasmic reticulum load. Biophys. J. 74: 1149-1168.
23. RICE, J.J., M.S. JAFRI & R.L. WINSLOW. 1999. Modeling gain and gradedness of Ca2+ release in the functional unit of the cardiac diadic space. Biophys. J. 77: 1871-1884.
24. BONDARENKO, V.E., G.P. SZIGETI, G.C. BETT, et al. 2004. Computer model of action potential of mouse ventricular myocytes. Am. J. Physiol. Heart Circ. Physiol. 287: H1378-H1403.
25. BONDARENKO, V.E., G.C. BETT & R.L. RASMUSSON. 2004. A model of graded calcium release and L-type Ca2+ channel inactivation in cardiac muscle. Am. J. Physiol. Heart Circ. Physiol. 286: H1154-H1169.
26. QU, Z., J.N. WEISS & A. GARFINKEL. 1999. Cardiac electrical restitution properties and stability of reentrant spiral waves: a simulation study. Am. J. Physiol. 276: H269-H283.
27. LUO, C.H. & Y. RUDY. 1991. A model of the ventricular cardiac action potential. Depolarization, repolarization, and their interaction. Circ. Res. 68: 1501-1526.
28. KARMA, A. 1993. Spiral breakup in model equations of action potential propagation in cardiac tissue. Phys. Rev. Lett. 71: 1103-1106.
29. NOBLE, D. 1962. A modification of the Hodgkin-Huxley equations applicable to Purkinje fibre action and pace-maker potentials. J. Physiol. 160: 317-352.
30. FENTON, F. & A. KARMA. 1998. Vortex dynamics in three-dimensional continuous myocardium with fiber rotation: filament instability and fibrillation. Chaos 8: 20-47.
31. GETTES, L.S. & H. REUTER. 1974. Slow recovery from inactivation of inward currents in mammalian myocardial fibres. J. Physiol. 240: 703-724.
32. GOLDHABER, J.I., L.H. XIE, T. DUONG, et al. 2005. Action potential duration restitution and alternans in rabbit ventricular myocytes: the key role of intracellular calcium cycling. Circ. Res. 96: 459-466.
33. DE HEMPTINNE, A. 1971. The frequency dependence of outward current in frog auricular fibres. An experimental and theoretical study. Pflugers Arch. 329: 332-340.
34. HAUSWIRTH, O., D. NOBLE & R.W. TSIEN. 1972. Separation of the pace-maker and plateau components of delayed rectification in cardiac Purkinje fibres. J. Physiol. 225:211-235.
35. HUA, F. & R.F. GILMOUR, JR. 2004. Contribution of IKr to rate-dependent action potential dynamics in canine endocardium. Circ. Res. 94: 810-819.
36. JANVIER, N.C., S.O. MCMORN, S.M. HARRISON, et al. 1997. The role of Na(+)-Ca2+ exchange current in electrical restitution in ferret ventricular cells. J. Physiol. 504: 301-314.
37. SAITOH, H., J.C. BAILEY & B. SURAWICZ. 1989. Action potential duration alternans in dog Purkinje and ventricular muscle fibers. Further evidence in support of two different mechanisms. Circulation 80: 1421-1431.
38. RICCIO, M.L., M.L. KOLLER & R.F. GILMOUR, JR. 1999. Electrical restitution and spatiotemporal organization during ventricular fibrillation. Circ. Res. 84: 955-963.
39. HALL, G.M., S. BAHAR & D.J. GAUTHIER. 1999. Prevalence of rate-dependent behaviors in cardiac muscle. Phys. Rev. Lett. 82: 2995.
40. DILLY, S.G. & M.J. LAB. 1988. Electrophysiological alternans and restitution during acute regional ischaemia in myocardium of anaesthetized pig. J. Physiol. 402: 315-333.
41. PRUVOT, E.J., R.P. KATRA, D.S. ROSENBAUM & K.R. LAURITA. 2004. Role of calcium cycling versus restitution in the mechanism of repolarization alternans. Circ. Res. 94: 1083-1090.
42. WATANABE, M.A. & M.L. KOLLER. 2002. Mathematical analysis of dynamics of cardiac memory and accommodation: theory and experiment. Am. J. Physiol. Heart Circ. Physiol. 282: H1534-H1547.
43. GILMOUR, R.F., JR., N.F. OTANI & M.A. WATANABE. 1997. Memory and complex dynamics in cardiac Purkinje fibers. Am. J. Physiol. 272: H1826-H1832.
44. OTANI, N.F. & R.F. GILMOUR, JR. 1997. Memory models for the electrical properties of local cardiac systems. J. Theor. Biol. 187: 409-436.
45. ELHARRAR, V. & B. SURAWICZ. 1983. Cycle length effect on restitution of action potential duration in dog cardiac fibers. Am. J. Physiol. 244: H782-H792.
46. TOLKACHEVA, E.G., D.G. SCHAEFFER, D.J. GAUTHIER & W. KRASSOWSKA. 2003. Condition for alternans and stability of the 1:1 response pattern in a "memory" model of paced cardiac dynamics. Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 67: 031904-031913.
47. KALB, S.S., E.G. TOLKACHEVA, D.G. SCHAEFFER, et al. 2005. Restitution in mapping models with an arbitrary amount of memory. Chaos 15: 23701.
48. BERS, D.M. 2002. Cardiac excitation-contraction coupling. Nature 415: 198-205.
49. BERS, D.M. 2001. Excitation-Contraction Coupling and Cardiac Contractile Force. Kluwer. Boston.
50. SHANNON, T.R., F. WANG, J. PUGLISI, et al. 2004. A mathematical treatment of integrated Ca dynamics within the ventricular myocyte. Biophys. J. 87: 3351-331.
51. WINSLOW, R.L., J. RICE & S. JAFRI. 1998. Modeling the cellular basis of altered excitation-contraction coupling in heart failure. Prog. Biophys. Mol. Biol. 69: 497-514.
52. SHIFERAW, Y., M.A. WATANABE, A. GARFINKEL, et al. 2003. Model of intracellular calcium cycling in ventricular myocytes. Biophys. J. 85: 3666-3686.
53. STERN, M.D. 1992. Theory of excitation-contraction coupling in cardiac muscle. Biophys. J. 63: 497-517.
54. CHIALVO, D.R., R.F. GILMOUR, JR. & J. JALIFE. 1990. Low dimensional chaos in cardiac tissue. Nature 343: 653-657.
55. SHIFERAW, Y., D. SATO & A. KARMA. 2005. Coupled dynamics of voltage and calcium in paced cardiac cells. Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 71: 021903-021907.
56. WIER, W.G., T.M. EGAN, JR. LOPEZ-LOPEZ & C.W. BALKE. 1994. Local control of excitation-contraction coupling in rat heart cells. J. Physiol. 474: 463-471.
57. BIEN, H., L. YIN & E. ENTCHEVA. 2006. Calcium instabilities in mammalian cardiomyocyte networks. Biophys. J. 90: 2628-2640.