The Role of Nonlinear Dynamics in Cardiac Arrhythmia Control

Heart Disease

Volumn 1, Issue 4, 1999, Pages 190-200

  Christini, David J ^a   Stein, Kenneth M ^a   Markowitz, Steven M ^a   Mittal, Suneet ^a   Slotwiner, David J ^a   Lerman, Bruce R ^a  

^a WEILL CORNELL MEDICAL COLLEGE   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

ANIMAL; ARTICLE; HEART ARRHYTHMIA; HUMAN; NONLINEAR SYSTEM;

ANIMAL; ARRHYTHMIA; HUMAN; NONLINEAR DYNAMICS; SUPPORT, U.S. GOV'T, P.H.S.;

EID: 0033188439     PISSN: 1521737X     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (106)

1. Glass L, Hunter P, McCulloch A (eds.). Theory of Heart: Biomechanics, Biophysics, and Nonlinear Dynamics of Cardiac Function. New York: Springer-Verlag, 1991.
2. Panfilov AV, Holden AV (eds.) Computational Biology of the Heart. Chichester, UK: Wiley, 1997.
3. Winfree AT. Evolving perspectives during 12 years of electrical turbulence. Chaos 1998;8:1-19.
4. Garfinkel A, Spano ML, Ditto WL, Weiss JN. Controlling cardiac chaos. Science 1992;257:1230-1235.
5. Christini DJ, Collins JJ. Using chaos control and tracking to suppress a pathological nonchaotic rhythm in a cardiac model. Phys Rev E 1996;53:R49-R52.
6. Brandt ME, Chen G. Feedback control of a quadratic map model of cardiac chaos. Int J Bifurcation Chaos 1996;6:715-723.
7. Brandt ME, Shih HT, Chen G. Linear time-delay feedback control of a pathological rhythm in a cardiac conduction model. Phys Rev E 1997;56:R1334-R1337.
8. Watanabe M, Robert F, Gilmour J. Strategy for control of complex low dimensional dynamics in cardiac tissue. J Mathematical Biol 1996:35:73-87.
9. Hall K, Christini DJ, Tremblay M, Collins JJ, Glass L, Billette J. Dynamic control of cardiac alternans. Phys Rev Lett 1997;78:4518-4521.
10. Biktashev VN, Holden AV. Resonant drift of an autowave vortex in a bounded medium. Physics Lett A 1993;181:216-224.
11. Biktashev VN, Holden AV. Design principles of a low voltage cardiac defibril lator based on the effect of feedback resonant drift. J Theoretical Biol 1994 169:101-112.
12. Biktashev VN, Holden AV. Control of re-entrant activity in a model of mammalian atrial tissue. Proc R Soc Lond Series B 1995;260:211-217.
13. Biktashev VN, Holden AV. Resonant drift of autowave vortices in two dimensions and the effects of boundaries and inhomogeneities. Chaos Solitons Fractals 1995;5:575-622.
14. Biktashev VN, Holden AV. Re-entrant activity and its control in a model of mammalian ventricular tissue. Proc R Soc Lond Series B 1996;263:1373-1382.
15. Biktashev VN, Holden AV. Reentrant waves and their elimination in a model of mammalian ventricular tissue. Chaos 1998;8:48-56.
16. Strogatz SH. Nonlinear Dynamics and Chaos. Reading, MA: Addison-Wesley. 1994.
17. May RM. Simple mathematical models with very complicated dynamics. Nature 1976;261:459-467.
18. Mackey MC, Glass L. Oscillation and chaos in physiological control systems Science 1977;197:287-289.
19. Glass L, Mackey MC. Pathological conditions resulting from instabilities if physiological control systems. Ann N Y Acad Sci 1979;316:214-235.
20. Mackey MC, Milton JG. Dynamical diseases. Ann N Y Acad Sci 1987;504 16-32.
21. Guevara MR, Glass L, Shrier A. Phase locking, period-doubling bifurcations and irregular dynamics in periodically stimulated cardiac cells. Science 1981; 214:1350-1353.
22. Bélair J, Glass L, an der Heiden U, Milton J. Dynamical disease: identification temporal aspects and treatment strategies of human illness. Chaos 1995;5;1-5.
23. Weiss JN, Garfinkel A, Spano ML, Ditto WL. Chaos and chaos control to biology. J Clin Invest 1994;93:1355-1360.
24. Glass L. Dynamics of cardiac arrhythmias. Physics Today 1996;49:40-45.
25. Nise NS. Control Systems Engineering. Redwood City, CA: Benjamin/Cummings, 1992.
26. Lindner JF, Ditto WL. Removal, suppression, and control of chaos by nonlinear design. Appl Mech Rev 1995;48:795-808.
27. Ott E, Grebogi C, Yorke JA. Controlling chaos. Phys Rev Lett 1990;64:1196-1199.
28. Christini DJ, Collins JJ. Using noise and chaos control to control nonchaotic systems. Phys Rev E 1995;52:5806-5809.
29. Ditto WL, Rauseo SN, Spano ML. Experimental control of chaos. Phys Rev Lett 1990;65:3211-3214.
30. Hunt ER. Stabilizing high-period orbits in a chaotic system: the diode resonator. Phys Rev Lett 1991;67:1953-1955.
31. Hayes S, Grebogi C, Ott E, Mark A. Experimental control of chaos for communication. Phys Rev Lett 1994;73:1781-1784.
32. Kittel A, Pyragas K, Richter R. Prerecorded history of a system as an experimental tool to control chaos. Phys Rev E 1994;50:262-268.
33. Gauthier DJ, Sukow DW, Concannon HM, Socolar JES. Stabilizing unstable periodic orbits in a fast diode resonator using continuous time-delay autosynchronization. Phys Rev E 1994;50:2343-2346.
34. Roy R, Murphy TW Jr, Maier TD, Gills Z, Hunt ER. Dynamical control of a chaotic laser: experimental stabilization of a globally coupled system. Phys Rev Lett 1992;68:1259-1262.
35. Bielawski S, Derozier D, Glorieux P. Experimental characterization of unstable periodic orbits by controlling chaos. Phys Rev A 1993;47:R2492-R2495.
36. Colet P, Roy R, Wiesenfeld K. Controlling hyperchaos in a multimode laser model. Phys Rev E 1994;50:3453-3457.
37. Peng B, Petrov V, Showalter K. Controlling chemical chaos. J Phys Chem 1991;95:4957-4959.
38. Petrov V, Gáspár V, Masere J, Showalter K. Controlling chaos in the Belousov-Zhabotinsky reaction. Nature 1993;361:240-243.
39. Hübinger B, Doerner R, Martienssen W, Herdering W, Pitka R, Dressler U. Controlling chaos experimentally in systems exhibiting large effective Lyapunov exponents. Phys Rev E 1994;50:932-948.
40. Jan de Korte R, Schouten JC, van den Bleck CM. Experimental control of a chaotic pendulum with unknown dynamics using delay coordinates. Phys Rev E 1995;52:3358-3365.
41. Starrett J, Tagg R. Control of a chaotic parametrically driven pendulum. Phys Rev Lett 1995;74:1974-1977.
42. Christini DJ, Collins JJ, Linsay PS. Experimental control of high-dimensional chaos: the driven double pendulum. Phys Rev E 1996;54:4824-4827.
43. Simson MB, Spear JF, Moore EN. Stability of an experimental atrioventricular reentrant tachycardia in dogs. Am J Physiol 1981;240:H947-H953.
44. Ross DL, Dassen WRM, Vanagt EJ, Brugada P, Bär FWHM, Wellens HJJ. Cycle length alternation in circus movement tachycardia using an atrioventricular accessory pathway. Circulation 1982;65:862-868.
45. Sun J, Amellal F, Glass L, Billette J. Alternans and period-doubling bifurcations in atrioventricular nodal conduction. J Theoretical Biol 1995;173:79-91.
46. Frame LH, Simson MB. Oscillations of conduction, action potential duration, and refractoriness. Circulation 1988;78:1277-1287.
47. Glass L, Josephson ME. Resetting and annihilation of reentrant abnormally rapid heartbeat. Phys Rev Lett 1995;75:2059-2062.
48. Nomura T, Glass L. Entrainment and termination of reentrant wave propagation in a periodically stimulated ring of excitable media. Phys Rev E 1996;53: 6353-6360.
49. Xie F, Qu Z, Garfinkel A. Dynamics of reentry around a circular obstacle in cardiac tissue. Phys Rev E 1998;58:6355-6358.
50. Moe GK. On the multiple wavelet hypothesis of atrial fibrillation. Arch Int Pharmacodynamics 1962;140:183-188.
51. Jalife J, Gray RA, Morley GE, Davidenko JM. Self-organization and the dynamical nature of ventricular fibrillation. Chaos 1998;8:79-93.
52. Fenton F, Karma A. Vortex dynamics in three-dimensional continuous myocardium with fiber rotation: filament instability and fibrillation. Chaos 1998;8: 20-47.
53. Assenheimer M, Steinberg V. Transition between spiral and target states in Rayleigh-Benard convection. Nature 1994;367:345-347.
54. Winfree AT. Spiral waves of chemical activity. Science 1972;175:634-636.
55. Allessie MA, Bonke FIM, Schopman FJG. Circus movement in rabbit atrial muscle as a mechanism of tachycardia. Circ Res 1973;33:54-62.
56. Allessie MA, Bonke FIM, Schopman FJG. Circus movement in rabbit atrial muscle as a mechanism of tachycardia. II. The role of nonuniform recovery of excitability in the occurrence of unidirectional block, as studied with multiple microelectrodes. Circ Res 1976;39:168-177.
57. Allessie M, Bonke FIM, Schopman FJG. Circus movement in rabbit atrial muscle as a mechanism of tachycardia. III. The "leading circle" concept: a new model of circus movement in cardiac tissue without the involvement of an anatomical obstacle. Circ Res 1977;41:9-18.
58. Seigneurie RG, Chasse JL, Auger PM, Bardou AL. Role of the dispersion of refractoriness on cardiac reentries. Mathematical Biosci 1999;157:253-267.
59. Pertsov AM, Davidenko JM, Salomonsz R, Baxter WT, Jalife J. Spiral waves of excitation underlie reentrant activity in isolated cardiac muscle. Circ Res 1993; 72:631-650.
60. Fast VG, Kleber AG. Role of wavefront curvature in propagation of cardiac impulse. Cardiovas Res 1997;33:258-271.
61. Chen PS, Garfinkel A, Weiss JN, Karagueuzian HS. Spirals, chaos, and new mechanisms of wave propagation. Pacing Clin Electrophysiol 1997;20:414-421.
62. Athill CA, Ikeda T, Kim YH, Wu TJ, Fishbein MC, Karagueuzian HS, Chen PS. Transmembrane potential properties at the core of functional reentrant wave fronts in isolated canine right atria. Circulation 1998;98:1556-1567.
63. Tyson JJ, Keener JP. Spiral waves in a model of myocardium. Physica D 1987; 29:215-222.
64. Courtemanche M, Skaggs W, Winfree AT. Stable three-dimensional action potential circulation in the Fitzhugh-Nagumo model. Physica D 1990;41:173-182.
65. Courtemanche M, Winfree AT. Re-entrant rotating waves in a Beeler-Reuter based model of two-dimensional cardiac activity. Int J Bifurcation Chaos 1991; 1:431-444.
66. Keener JP. An eikonal-curvature equation for action potential propagation in myocardium. J Mathematical Biol 1991;29:629-651.
67. Krinsky V, Efimov IR, Jalife J. Vortices with linear cores in excitable media. Proc R Soc Lond Series A 1992;437:645-655.
68. Efimov IR, Krinsky VI, Jalife J. Dynamics of rotating vortices in the Beeler-Reuter model of cardiac tissue. Chaos Solitons Fractals 1995;5:513-526.
69. Fenton F, Karma A. Fiber-rotation-induced vortex turbulence in thick myocardium. Phys Rev Lett 1998;81:481-484.
70. Xu A, Guevara MR. Two forms of spiral-wave reentry in an ionic model of ischemic ventricular myocardium. Chaos 1998;8:157-174.
71. Winfree AT. Electrical instability in cardiac muscle: phase singularity and rotors. J Theoretical Biol 1989;138:353-405.
72. Panfilov AV. Spiral breakup as a model of ventricular fibrillation. Chaos 1998; 8:57-64.
73. Davidenko JM, Kent P, Jalife J. Spiral waves in normal isolated ventricular muscle. Physica D 1991;49:182-197.
74. Jalife J, Davidenko JM, Michaels DC. A new perspective on the mechanisms of arrhythmias and sudden cardiac death: Spiral waves of exciation in heart muscle. J Cardiovasc Electrophysiol 1991;2:S133-S152.
75. Davidenko JM, Pertsov AV, Salomonsz R, Baxter W, Jalife J. Stationary and drifting spiral waves of excitation in isolated cardiac muscle. Nature 1992;355: 349-351.
76. Gray RA, Jalife J, Panfilov AV, Baxter W, Cabo C, Davidenko JM, Pertsov AM. Mechanisms of cardiac fibrillation. Science 1995;270:1222-1223.
77. Gray RA, Jalife J, Panfilov A, Baxter WT, Cabo C, Davidenko JM, Pertsov AM. Nonstationary vortexlike reentrant activity as a mechanism of polymorphic ventricular tachycardia in the isolated rabbit heart. Circulation 1995;91:2454-2469.
78. Lee JJ, Kamjoo K, Hough D, Hwang C, Fan W, Fishbein MC, et al. Reentrant wave fronts in Wiggers' stage II ventricular fibrillation: characteristics and mechanisms of termination and spontaneous regeneration. Circ Res 1996;78: 660-675.
79. Cabo C, Pertsov AM, Davidenko JM, Jalife J. Electrical turbulence as a result of the critical curvature for propagation in cardiac tissue. Chaos 1998;8:116-126.
80. Kim DT, Kwan Y, Lee JJ, Ikeda T, Uchida T, Kamjoo K, et al. Patterns of spiral tip motion in cardiac tissues. Chaos 1998;8:137-148.
81. Chen PS, Garfinkel A, Weiss JN, Karagueuzian HS. Computerized mapping of fibrillation in normal ventricular myocardium. Chaos 1998;8:127-136.
82. Gray RA, Pertsov AM, Jalife J. Spatial and temporal organization during cardiac fibrillation. Nature 1998;392:75-78.
83. Witkowski FX, Leon LJ, Penkoske PA, Giles WR, Spano ML, Ditto WL, Winfree AT. Spatiotemporal evolution of ventricular fibrillation. Nature 1998; 392:78-82.
84. Witkowski FX, Leon LJ, Penkoske PA, Clark RB, Spano ML, Ditto WL, Giles WR. A method for visualization of ventricular fibrillation: design of a cooled fiberoptically coupled image intensified CCD data acquisition system incorporating wavelet shrinkage based adaptive filtering. Chaos 1998;8:94-102.
85. Garfinkel A, Qu Z. Nonlinear dynamics of excitation and propagation in cardiac muscle. In, Zipes D, Jalife J (eds.): Cardiac Electrophysiology: From Cell to Bedside. Third edition. Philadelphia: WB Saunders, 1999.
86. Karma A. Spiral breakup in model equations of action potential propagation in cardiac tissue. Phys Rev Lett 1993;71:1103-1106.
87. Karma A. Electrical alternans and spiral wave breakup in cardiac tissue. Chaos 1994;4:461-472.
88. Courtemanche M. Complex spiral wave dynamics in a spatially distributed ionic model of cardiac electrical activity. Chaos 1996;6:579-600.
89. Garfinkel A, Chen PS, Walter DO, Karagueuzian HS, Kogan B, Evans SJ, et al. Quasiperiodity and chaos in cardiac fibrillation. J Clin Invest 1997;99:305-314.
90. Osipov GV, Shulgin BV, Collins JJ. Controlled movement and suppression of spiral waves in excitable media. Phys Rev E 1998;58:6955-6958.
91. Davydov V, Zykov V, Mikhajlov A, Brazhnik P. Drift and resonance of spiral waves in active media. Izvestiya Vysshikh Uchebnykh Zavedenii Radiofizika 1988;31:547-582.
92. Mantel RM, Barkley D. Periodic forcing of spiral waves in excitable media. Phys Rev E 1996;54:4791-4801.
93. Hu G, Xiao J, Chua LO, Pivka L. Controlling spiral waves in a model of two-dimensional arrays of Chua's circuits. Phys Rev Lett 1998;80:1884-1887.
94. Grill S, Zykov VS, Müller SC. Feedback-controlled dynamics of meandering spiral waves. Phys Rev Lett 1995;75:3368-3371.
95. Zykov VS, Mikhailov AS, Müller SC. Controlling spiral waves in confined geometries by global feedback. Phys Rev Lett 1998;78:3398-3401.
96. Osipov GV, Collins JJ. Using weak impulses to suppress traveling waves in excitable media. Phys Rev E 1999;60:54-57.
97. Rappel WJ, Fenton F, Karma A. Spatiotemporal control of wave instabilities in cardiac tissue. Phys Rev Lett 1999;83:456-459.
98. Qu Z, Weiss JN, Garfinkel A. Cardiac electrical restitution properties and stability of reentrant spiral waves: a simulation study. Am J Physiol 1999;276: H269-H283.
99. Cao JM, Qu Z, Kim YH, Wu TJ, Garfinkel A, Weiss JN, et al. Spatiotemporal heterogeneity in the induction of ventricular fibrillation by rapid pacing: importance of cardiac restitution properties. Circ Res 1999;84:1318-1331.
100. Weiss JN, Garfinkel A, Karagueuzian HS, Qu Z, Chen PS. Chaos and the transition to ventricular fibrillation: a new approach to antiarrhythmic drug evaluation. Circulation 1999;99:2819-2826.
101. Riccio ML, Koller ML, Robert F, Gilmour J. Electrical restitution and spatiotem poral organization during ventricular fibrillation. Circ Res 1999;84:955-963.
102. Frazier DW, Wolf PD, Wharton JM, Tang ASL, Smith WM, Ideker RE. Stimulus-induced critical-point: mechanism for electrical initiation of reentry in normal canine myocardium. J Clin Invest 1989;83:1039-1052.
103. Vinson M, Pertsov A, Jalife J. Anchoring of vortex filaments in 3D excitable media. Physica D 1994;72:119-134.
104. Biktashev VN, Holden AV, Zhang H. Tension of organizing filaments of scroll waves. Philosoph Trans R Soc Lond Series A 1994;347:611-630.
105. Jalife J, Gray R. Drifting vortices of electrical waves underlie ventricular fibrillation in the rabbit heart. Acta Physiol Scand 1996;157:123-131.
106. Rosenqvist M. Pacing techniques to terminate ventricular tachycardia. Pacing Clin Electrophysiol 1995;18:592-598.