On the evidence of deterministic chaos in ECG: Surrogate and predictability analysis

Chaos

Volumn 8, Issue 2, 1998, Pages 495-502

  Govindan, R B ^a   Narayanan, K ^a   Gopinathan, M S ^a  

^a INDIAN INSTITUTE OF TECHNOLOGY MADRAS   (India)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0000670820     PISSN: 10541500     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.166330     Document Type: Article

References (40)

1. L. Glass, A. L. Goldberger, M. Courtemanche, and A. Shrier, "Nonlinear dynamics, chaos and complex cardiac arrhythmias," Proc. R. Soc. London, Ser. A 413, 9-26 (1987).
2. B. J. West, A. L. Goldberger, G. Rouner, and V. Bhargava, "Nonlinear dynamics of the heart beat I. The AV junction passive conduit or active oscillator?," Physica D 17, 198-206 (1985).
3. A. Destexhe, J. A. Sepulchre, and A. Babloyantz, "A comparative study of the experimental quantification of deterministic chaos," Phys. Lett. A 132, 101-106 (1988).
4. F. Ravelli and R. Anbolin, "Complex dynamics underlying the human electrocardiogram," Biol. Cybern. 67, 57-65 (1992).
5. J. P. Zbilut, G. Mayor-Kress, and K. Gust, "Dimensional analysis of heart rate variability in heart transplant recipients," Math. Biosci. 90, 49-70 (1988).
6. N. Pradhan and D. Narayana Dutt, "A nonlinear perspective: In understanding the neurodynamics of EEG," Comput. Biol. Med. 23, 425-442 (1993).
7. J. Röschke and J. Aldenhoff, "The dimensionality of human's electroencephalogram during sleep," Biol. Cybern. 64, 307-313 (1991).
8. W. Lutzenberger, H. Preissl, and F. Pulvermiiller, "Fractal dimension of electroencephalographic time series and underlying brain processes," Biol. Cybern. 73, 477-482 (1995).
9. L. Glass and P. Hunter, "There is a theory of heart," Physica D 43, 1-16 (1990).
10. M. Palus, "Nonlinearity in normal human EEG: cycles, temporal asymmetry, non-stationarity, and randomness, not chaos," Biol. Cybern. 75, 389-396 (1996).
11. F. Mitschke and M. Dämmig, "Chaos versus noise in experimental data," Int. J. Bifurcation Chaos 3, 693-701 (1993).
12. J. P. Eckmann and D. Ruelle, "Fundamental limitations for estimating dimensions and Lyapunov exponents in dynamical systems," Physica D 56, 185-187 (1992).
13. R. Brown and P. Bryant, "Computing the Lyapunov spectrum of a dynamical system from an observed time series," Phys. Rev. A 43, 2787-2806 (1991).
14. M. Sano and Y. Sawada, "Measurement of the Lyapunov spectrum from a chaotic time series," Phys. Rev. Lett. 55, 1082-1085 (1985).
15. A. Wolf, J. B. Swift, H. L. Swinney, and J. A. Vastano, "Determining Lyapunov exponents from a time series," Physica D 16, 285-317 (1985).
16. S. Sato and Y. Sawada, "Practical methods of measuring the generalized dimension and the largest Lyapunov exponent in high dimensional chaotic system," Prog. Theor. Phys. 77, 1-5 (1987).
17. M. T. Rosentein, J. J. Collins, and C. J. DeLuca, "A practical method for calculating largest Lyapunov exponents from small data sets," Physica D 65, 117-134 (1993).
18. A. Casseleggio and A. Carana, "Correlation dimension estimation from electrocardiograms," Chaos Solitons Fractals 5, 713-726 (1995).
19. A. Babloyantz and A. Destexhe, "Is the normal heart a periodic oscillator," Biol. Cybern. 58, 203-211 (1988).
20. J. H. Lefebvre, D. A. Goodings, M. V. Kamath, and E. Z. Fallen. "Predictability of normal heart rhythms and deterministic chaos," Chaos 3, 267-276 (1993).
21. J. Theiler, A. Longlin, B. Galdrikian, and D. D. Farmer, "Testing for nonlinearity in time series: the method of surrogate data," Physica D 58, 77-94 (1992).
22. G. Sugihara and R. M. May, "Nonlinear forecasting as a way of distinguishing chaos from measurement error in time series," Nature (London) 344, 734-741 (1990).
23. J. Blinowska and M. Malinouski, "Nonlinear and linear forecasting of the EEG time series," Biol. Cybern. 66, 159-165 (1991).
24. The MIT-BIH Arrhythmia DataBase CD-ROM, 2nd ed. (Harvard-MIT Division of Health Sciences and Technology, August 1992).
25. F. Takens, "Detecting strange attractors in turbulence," in Dynamical Systems and Turbulence, edited by D. A. Rand and L. S. Young, Lecture Notes in Mathematics 989 (Springer Heidelberg, 1981), pp. 366-381.
26. A. M. Albano, J. Muenck, C. Schwartz, A. I. Mees, and P. E. Rapp, "Singular-value decomposition and the Grassberger-Procaccia algorithm," Phys. Rev. A 38, 3017-3026 (1988).
27. P. Grassberger and I. Procaccia, "Measuring the strangeness of strange attractors," Physica D 9, 189-208 (1983).
28. J. Theiler, "On the evidence for low-dimensional chaos in an epileptic electroencephalogram," Phys. Lett. A 196, 335-341 (1995).
29. J. Fell, J. Roschke, and C. Schäffner, "Surrogate data analysis of sleep electroencephalograms reveals for nonlinearity," Biol. Cybern. 75, 85-92 (1996).
30. S. A. R. B. Rombouts, R. W. M. Keuneu, and C. J. Stam, "Investigation of nonlinear structure in multichannel EEG," Phys. Lett. A 202, 352-358 (1995).
31. B. P. T. Hoekstra, C. G. H. Diks, M. A. Allessie, and J. DeGoedge, "Nonlinear analysis of epicardial atrial electrograms of electrically induced atrial fibrillation in man," J. Cardiovascular Electrophysiology 6, 419-440 (1995).
32. P. E. Rapp, A. M. Albano, I. D. Zimmerman, and M. A. Jimenez-Monntano, "Phase-randomized surrogate can produce spurious identifications of non-random structure," Phys. Lett. A 192, 27-33 (1994).
33. T. Ikeguchi and K. Aihara, "Estimating correlation dimension of biological time series with a reliable method," J. Intelligent Fuzzy Systems 5, 33-52 (1997).
34. N. Pradhan and P. K. Sadasivan, "Relevance of surrogate-data testing in electroencephalogram analysis," Phys. Rev. E 53, 2684-2692 (1996).
35. P. E. Rapp, A. M. Albano, T. I. Schmah, and L. A. Farwell, "Filtered noise can mimic low-dimensional chaotic attractors," Phys. Rev. E 47, 2289-2297 (1993).
36. J. D. Farmer and J. J. Sidorowich, "Predicting chaotic time series," Phys. Rev. Lett. 59, 845-848 (1987).
37. M. Casdagli, "Nonlinear prediction of chaotic time series," Physica D 35, 335-356 (1989).
38. D. Lathrop and E. J. Kostelich, "Characterization of an experimental strange attractor by periodic orbits," Phys. Rev. A 40, 4028-4031 (1989).
39. K. Narayanan, R. B. Govindan, M. Ramasubba Reddy, and M. S. Gopinathan, "Dynamics of cardiac system through unstable periodic orbits," 19th Annual International Conference of the IEEE Engineering in Medicine and Biology Society, Chicago, IL, 30th Oct. to 2nd Nov. 1997, pp. 2019-2021.
40. K. Narayanan, R. B. Govindan, and M. S. Gopinathan, "Unstable periodic orbits in human cardiac rhythms" Phys. Rev. E 57, 4594-4603 (1998).