Nonlinear analysis of the pharmacological conversion of sustained atrial fibrillation in conscious goats by the class Ic drug cibenzoline

Chaos

Volumn 7, Issue 3, 1997, Pages 430-446

  Hoekstra, Bart P T ^a   Diks, Cees G H ^b   Allessie, Maurits A ^c   Degoede, Jacob ^a  

^a LEIDEN UNIVERSITY   (Netherlands)

^b UNIVERSITY OF KENT   (United Kingdom)

^c MAASTRICHT UNIVERSITY   (Netherlands)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 3042958887     PISSN: 10541500     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.166216     Document Type: Article

References (57)

1. S. H. Hohnloser and Y.-G. Li, "Drug treatment of atrial fibrillation: What have we learned?" Current Opinion Cardiol. 12, 24-32 (1997).
2. A. E. Epstein, A. P. Hallstrom, W. I. Rogers, P. R. Liebson, A. A. Seals, J. L. Anderson, J. D. Cohen, R. J. Capone, and D. G. Wyse for the Cardiac Arrhythmia Suppression Trial Investigators, "Mortality following ventricular arrhythmia suppression by encainide, flecainide, and moricizine after myocardial infarction," J. Am. Med. Assoc. 270, 2451-2455 (1993).
3. T. R. Chay, "Bifurcations in heart rhythms," Int. J. Bifurcation Chaos 5, 1439-1486 (1995).
4. C. F. Starmer, A. A. Lastra, V. V. Nesterenko, and A. O. Grant, "Proarrhythmic response to sodium channel blockade. Theoretical model and numerical experiments," Circulation 84, 1364-1377 (1991).
5. C. F. Starmer, D. N. Romashko, R. S. Reddy, Y. I. Zilberter, J. Starobin, A. O. Grant, and V. I. Krinsky, "Proarrhythmic response to potassium channel blockade. Numerical studies of polymorphic tachyarrhythmias," Circulation 92, 595-605 (1995).
6. M. O. Arnsdorf and G. J. Sawicki, "Flecainide and the electrophysiologic matrix: The effects of flecainide acetate on the determinants of cardiac excitability in sheep purkinje fibers," J. Cardiovasc. Electrophysiol. 7, 1172-1182 (1996).
7. Y. Cha, A. Wales, P. Wolf, S. Shahrokni, N. Sawhney, and G. K. Feld, "Electrophysiological effects of the new class III antiarrhythmic drug dofetilide compared to the class IA antiarrhythmic drug quinidine in experimental canine atrial flutter: Role of dispersion of refractoriness in antiarrhythmic efficacy," J. Cardiovasc. Electrophysiol. 7, 809-827 (1996).
8. E. M. Vaughan Williams, "Classification of anti-arrhythmic drugs," in Cardiac Arrhythmias, edited by E. Sandoe, E. Flensted-Jense, and K. H. Olesen (Astra, Sodertalie Sweden, 1970), pp. 449-472.
9. E. Ott, Chaos in Dynamical Systems (Cambridge University Press, Cambridge, 1993).
10. E. Ott, T. Sauer, and J. A. Yorke, Coping with Chaos; Analysis of Chaotic Data and the Exploitation of Chaotic Systems (Wiley, New York, 1994).
11. H. D. I. Abarbanel, R. Brown, J. L. Sidorowich, and L. Sh. Tsimring, "The analysis of observed chaotic data in physical systems," Rev. Mod. Phys. 65, 1331-1392 (1993).
12. P. Grassberger, T. Schreiber, and C. Schaffrath, "Nonlinear time sequence analysis," Int. J. Bifurcation Chaos 1, 521-547 (1991).
13. F. Ravelli and R. Antolini, "Complex dynamics underlying the human electrocardiogram," Biol. Cybern. 67, 57-65 (1992).
14. D. T. Kaplan and R. J. Cohen, "Is fibrillation chaos?," Circ. Res. 67, 886-892 (1990).
15. F. X. Witkovvski, K. M. Kavanagh, P. A. Penkoske, R. Plonsey, M. L. Spano, W. L. Ditto, and D. T. Kaplan, "Evidence for determinism in ventricular fibrillation," Phys. Rev. Lett. 75, 1230-1233 (1995).
16. P. van Leeuwen, H. Bettermann, U. an der Heiden, and H. C. Kümmell, "Circadian aspects of apparent correlation dimension in human heart rate dynamics," Am. J. Physiol. 269, H130-H134 (1995).
17. P. I. Saparin, M. A. Zaks, J. Kurths, A. Voss, and V. S. Anishchenko, "Reconstruction and structure of electrocardiogram phase portraits," Phys. Rev. E 54, 737-742 (1996).
18. T. Schreiber and D. T. Kaplan, "Nonlinear noise reduction for electrocardiograms," Chaos 6, 87 (1996).
19. A. Casaleggio, A. Corana, R. Ranjan, and N. V. Thakor, "Dimensional analysis of the electrical activity in fibrillating isolated hearts," Int. J. Bifurcation Chaos 6, 1547-1561 (1996).
20. B. P. T. Hoekstra, C. G. H. Diks, M. A. Allessie, and J. DeGoede, "Non-linear analysis of epicardial atrial electrograms of electrically induced atrial fibrillation in man," J. Cardiovasc. Electrophysiol. 6, 419-440 (1995).
21. J. Brugada, S. Gürsoy, P. Brugada, J. Atié, G. Guiraudon, and E. Andries, "Cibenzoline transforms random re-entry into ordered re-entry in the atria," Eur. Heart. J. 14, 267-272 (1993).
22. M. C. E. F. Wijffels, C. J. H. J. Kirchhof, R. Dorland, and M. A. Allessie, "Atrial fibrillation begets atrial fibrillation. A study in awake chronically instrumented goats," Circulation 92, 1954-1968 (1995).
23. F. Takens, "Detecting strange attractors in turbulence," in Dynamical Systems and Turbulence (Warwick 1980), Lecture Notes in Mathematics, edited by D. A. Rand and L.-S. Young (Springer, Berlin, 1981), vol. 898, pp. 366-381.
24. A. M. Fraser and H. L. Swinney, "Independent coordinates for strange attractors from mutual information," Phys. Rev. A 33, 1134-1140 (1986).
25. P. Grassberger and I. Procaccia, "Measuring the strangeness of strange attractors," Physica D 9, 189-208 (1983).
26. F. Takens, "Invariants related to dimensions and entropy," Atas do 13. Coloquio Brasileiro de Matematica, 1983, pp. 353-359.
27. J. Theiler, "Spurious dimensions from correlation algorithms applied to limited time-series data," Phys. Rev. A 34, 2427-2432 (1986).
28. P. Grassberger, "An optimized box-assisted algorithm for fractal dimensions," Phys. Lett. A, 148, 63-68 (1990).
29. M. Ding, C. Grebogi, E. Ott, T. Sauer, and J. A. Yorke, "Plateau onset of correlation dimension: When does it occur?," Phys. Rev. Lett. 70, 3872-3875 (1993).
30. J. G. Caputo and P. Atten, "Metric entropy: an experimental means for characterizing and quantifying chaos," Phys. Rev. A 35. 1311-1316 (1987).
31. S. Pincus, "Approximate entropy (ApEn) as a complexity measure," Chaos 5, 110-117 (1995).
32. D. T. Kaplan, M. I. Furman, S. M. Pincus, S. M. Ryan, and L. A. Lipsitz, "Aging and the complexity of cardiovascular dynamics," Biophys. J. 59, 945-949 (1991).
33. P. Gaspard and X.-J. Wang, "Noise, chaos and (∈,τ)-entropy per unit time," Physics Reports 235, 291-343 (1993).
34. L. S. Tsimring, "Nested strange attractors in spatiotemporal chaotic systems," Phys. Rev. E 48, 3421-3426 (1993).
35. C. Diks, J. C. van Houwelingen, F. Takens, and J. DeGoede, "Reversibility as a criterion for discriminating time series," Phys. Lett. A 210, 221-228 (1995).
36. K. T. S. Konings, C. J. H. J. Kirchhof, J. R. L. M. Smeets, H. J. J. Wellens, O. C. Penn, and M. A. Allessie, "High-density mapping of electrically induced atrial fibrillation in humans," Circulation 89, 1665-1680 (1994).
37. Y. A. Kuznetsov, Elements of Applied Bifurcation Theory, Springer Series in Applied Mathematical Sciences (Springer-Verlag, Berlin, 1994).
38. G. K. Moe, "On the multiple wavelet hypothesis of atrial fibrillation," Arch. Int. Pharmacodyn. Ther. 140, 183-188 (1962).
39. M. A. Allessie, W. J. E. P. Lammers, F. I. M. Bonke, and J. Hollen, "Experimental evaluation of Moe's multiple wavelet hypothesis of atrial fibrillation," in Cardiac Electrophysiology and Arrhythmias, edited by D. P. Zipes and J. Jalife (Grune and Stratton, New York, 1985), pp. 265-275.
40. J. L. Cox, T. E. Canavan, R. B. Schüssler, M. E. Cain, B. D. Lindsay, C. Stone, P. K. Smith, P. B. Corr, and J. P. Boineau, "The surgical treatment of atrial fibrillation. II. Intraoperative electrophysiologic mapping and description of the electrophysiological basis of atrial flutter and atrial fibrillation," J. Thorac. Cardiovasc. Surg. 101, 406-426 (1991).
41. B. F. Hoffman and M. R. Rosen, "Cellular mechanisms for cardiac arrhythmias," Circ. Res. 49, 1-15 (1981).
42. Z. Wang, P. Pagé, and S. Nattel, "Mechanism of flecainide's antiarrhythmic action in experimental atrial fibrillation," Circ. Res. 71, 271-287 (1992).
43. J. Wang, G. W. Bourne, Z. Wang, C. Villemaire, M. Talajie, and S. Nattel, "Comparative mechanisms of antiarrhythmic drug action in experimental atrial fibrillation. Importance of use-dependent effects on refractoriness," Circulation 88, 1030-1044 (1993).
44. C. Kirchhof, M. Wijffels, J. Brugada, J. Planellas, and M. Allessie, "Mode of action of a new class Ic drug (ORG 7797) against atrial fibrillation in conscious dogs," J. Cardiovasc. Pharmacol. 17, 116-124 (1991).
45. M. S. Spach and M. E. Josephson, "Initiating reentry: The role of non-uniform anisotropy in small circuits," J. Cardiovasc. Electrophysiol. 5, 182-209 (1994).
46. A. S. Mikhailov and V. S. Zykov, "Kinematical theory of spiral waves in excitable media: Comparison with numerical simulations," Physica D 52, 379-397 (1991).
47. A. S. Mikhailov, Foundations of Synergetics 1. Distributed Active Systems, Springer Series in Synergetics (Springer-Verlag, Berlin, 1990).
48. V. S. Zykov, Simulation of Wave Processes in Excitable Media (Manchester University Press, New York, 1987).
49. R. A. Gray and J. Jalife, "Spiral waves and the heart," Int. J. Bifurcation Chaos 6, 415-435 (1996).
50. A. T. Winfree, "Varieties of spiral wave behavior: An experimentalist's approach to the theory of excitable media," Chaos 1, 303-334 (1991).
51. H. Tong, Nonlinear Time Series Analysis: A Dynamical System Approach (Oxford University Press, Oxford, 1990).
52. D. A. Egolf and H. S. Greenside, "Relation between fractal dimension and spatial correlation length for extensive chaos," Nature 369, 129-131 (1994).
53. C. D. Cutler and D. T. Kaplan, in Nonlinear Dynamics and Time Series, Building a Bridge Between the Natural and Statistical Sciences, Fields Institute Communications (American Mathematical Society, Providence, RI, 1997).
54. P. Grassberger and I. Procaccia, "Estimation of the Kolmogorov entropy from a chaotic signal," Phys. Rev. A 28, 2591-2593 (1983).
55. J. Theiler, "Statistical precision of dimension estimators," Phys. Rev. A 41, 3038-3051 (1990).
56. J.-P. Eckmann and D. Ruelle, "Fundamental limitations for estimating dimensions and Lyapunov exponents in dynamical systems," Physica D 56, 185-187 (1992).
57. C. Diks, W. R. van Zwei, F. Takens, and J. DeGoede, "Detecting differences between delay vector distributions," Phys. Rev. E 53, 2169-2176 (1996).