For citation:
Pavlov A. N., Janson N. B., Anishchenko V. S., Gridnev V. I., Dovgalevsky P. Y. Diagnostics of cardio-vascular diseases with help of largest lyapunov exponent of RR-sequences. Izvestiya VUZ. Applied Nonlinear Dynamics, 1998, vol. 6, iss. 2, pp. 3-14. DOI: 10.18500/0869-6632-1998-6-2-3-14
Diagnostics of cardio-vascular diseases with help of largest lyapunov exponent of RR-sequences
A method for presenting a discrete sequence of cardiointervals as a smooth time dependence, which allows one to apply to the given data sets the algorithm for largest Lyapunov exponent computation ш suggested. Processing the data banks of RR-intervals of patients suffering from coronary artery disease and also those who survived after myocardial infarction has shown that the largest Lyapunov exponent may serve as а diagnostic tool being able to distinguish between different groups of patients with more confidence than the standard methods for time series processing accepted in cardiology.
- Goldberger AL, West BJ. Fractals in physiology and medicine. Yale J. Biol. Med. 1987;60(5):421-435.
- Babloyantz А, Destexhe А. Is а normal heart а periodic oscillator? Biol. Cybern. 1988;58(3):203-211. DOI: 10.1007/BF00364139.
- Goldberger AL, Rigney DR, West BJ. Chaos аnd fractals in human physiology. Sci. Аm. 1990;262(2):42-49. DOI: 10.1038/scientificamerican0290-42.
- Glass L, Mackey MC. From Clocks to Chaos: The Rhythms of Life. Princeton: Princeton University Press; 1988. 248 p.
- Glass L. Theory оf heart: Biomechanics, Biophysics, and Nonlinear Dynamics of Cardiac Function. N. Y.: Springer; 1991. 611 p.
- Glass L. Cardiac arrhythmias and circle maps — A classical problem. Chaos. 1991;1(1):13-19. DOI: 10.1063/1.165810.
- Peng CK, Mietus J, Hausdorff JM, Havlin S, Stanley HE, Goldberger AL. Long-range anticorrelations and non-Gaussian behavior of the heartbeat. Phys. Rev. Lett. 1993;70(9):1343-1346. DOI: 10.1103/PhysRevLett.70.1343.
- Peng CK, Havlin S, Stanley HE, Goldberger AL. Quantification оf scaling exponents and crossover phenomena in nonstationary heartbeat time series. Chaos. 1995;5(1):82-87. DOI: 10.1063/1.166141.
- Peng СК, Havlin S, Stanley HE, Goldberger AL. Fractal scaling properties in nonstationary heartbeat time series. AIP Conf. Proc. 1996;375:615-627. DOI: 10.1063/1.51000.
- Frison TW, Peng CK, Goldberger А, Katz RA. Chaotic data analysis of heart R-R Interval EKG data. AIP Conf. Proc. 1996;375:658-668. DOI: 10.1063/1.51003.
- Ulbikas J, Cenys А, Zemaityte D, Varoneckas G. Correlations in heart beat data аs quantitative characterization оf heart pathology. AIP Conf. Proc. 1996;375:669-675. DOI: 10.1063/1.51004.
- Zebrowski JJ, Poplawska W, Baranowski R. Pattern entropy а tool for non-linear dynamical analysis оf а biological nonstationary system: the human heart. Acta Physica Polonika В. 1995;26(6):1055-1064.
- Baranowski R, Zebrowski JJ, Poplawska W, Mananas MA, Jane R, Caminal P, Chojnowska L, Rydlewska-Sadowska W, Vinolas X, Guindo J, Bayes de Luna A. 3-dimensional Poincare plots оf the QT intervals — аn approach to nonlinear QT analysis. In: Computers in Cardiology. 1995, Vienna, Austria. P. 789-792. DOI: 10.1109/CIC.1995.482783.
- Bigger JT, Fleiss JL, Steinman RC, Rolnitzky LM, Kieiger RE, Rottman JN. Correlations among time and frequency domain measures of heart period variability two weeks after acute myocardial infarction. Am. J. Cardiol. 1992;69(9):891-898. DOI: 10.1016/0002-9149(92)90788-z.
- Rosenblum M, Kurths J. A model оfor neural control of the heart rate. Physica А: Stat. Mech. Appl. 1995;215(4):439-450. DOI: 10.1016/0378-4371(95)00041-5.
- Seidel H, Herzel H. Modelling Heart Rate Variability Due to Respiration and Baroreflex. In: Mosekilde E, Mouritsen OG, editors. Modelling the Dynamics of Biological Systems. Springer Series in Synergetics. Vol. 65. Berlin: Springer; 1995. P. 205-229. DOI: 10.1007/978-3-642-79290-8_11.
- Bezerianos А, Bountis T, Papaioannou G, Polydoropoulos P. Nonlinear time series analysis of electrocardiograms. Chaos. 1995;5(1):95-101. DOI: 10.1063/1.166104.
- Garfinkel A, Spano ML, Ditto WL, Weiss JN. Controlling cardiac chaos. Science. 1992;257(5074):1230-1235. DOI: 10.1126/science.1519060.
- Anishchenko VS, Saparin PI. Normalized entropy as a diagnostic criterion of human cardio-vascular system reaction on the external influence. Izvestiya VUZ. Applied Nonlinear Dynamics. 1993;1(3-4):54-64. (in Russian).
- Anishchenko VS, Saparin PI, Kurths J, Witt А, Foss А. Analysis of human heart rate dynamics based on the criterion of renormalized entropy. Izvestiya VUZ. Applied Nonlinear Dynamics. 1994;2(3-4):55-64. (in Russian).
- Kurths J, Voss А, Saparin Р, Witt А, Kleiner HJ, Wessel N. Quantitative analysis оf heart rate variability. Chaos. 1995;5(1):88-94. DOI: 10.1063/1.166090.
- Voss А, Kurths J, Kleiner HJ, Witt А, Saparin Р, Dietz R, Fiehring Н, Wessel N. Neue methoden fur die erkennung von hochrisikopatienten in der kardiologie. Biomedizinische Technik. 1994;39(6):134-143. DOI: 10.1515/bmte.1994.39.6.134.
- Anishchenko VS, Safonova MA, Saparin РI. The instrument computer-system for complicated autooscillation regimes analysis. Soviet Journal of Communications Technology and Electronics. 1992;37(3):467-478. (in Russian).
- Saparin РI, Zaks MA, Kurths J, Voss А, Anishchenko VS. Reconstruction and structure of electrocardiogram phase portraits. Phys. Rev. E. 1996;54(1):737-742. DOI: 10.1103/PhysRevE.54.737.
- Dmitrieva NV. Symmetric approach to electrocardiogram analysis. Biology Bulletin. 1989;3:450-457. (in Russian).
- Dmitrieva NV. Symmetric approach to the analysis of electrical and contractile activity of cardiocytes. Biology Bulletin. 1992;2:270. (in Russian).
- Anishchenko VS, Yanson NB, Pavlov AN. Work of the Human Heart: A Regular Process? Journal of Communications Technology and Electronics. 1997;42(8):936-940.
- Pavlov AN, Yanson NB. Application of the mathematical model reconstruction technique to the electrocardiogram. Izvestiya VUZ. Applied Nonlinear Dynamics. 1997;5(1):93-108. (in Russian).
- Anishchenko VS, Yanson NB, Pavlov AN. Saddle focus in the model of electrical activity of the human heart. Tech. Phys. Lett. 1996;22(4):78-83. (in Russian).
- Yanson NB, Pavlov AN, Balanov AG, Anishchenko VS. The problem of reconstruction of the mathematical model in relation to the electrocardiogram. Tech. Phys. Lett. 1996;22(16):57-62. (in Russian).
- Janson NB, Pavlov AN, Anishchenko VS. One method for restoring inhomogeneous attractors. Int. J. Bifurc. Chaos. 1998;8(4-5):825-833. DOI: 10.1142/S0218127498000620.
- Heart rate variability: standards of measurement, physiological interpretation and clinical use. Task Force of the European Society of Cardiology and the North American Society of Pacing and Electrophysiology. Circulation. 1996;93(5):1043-1065.
- DeBoer RW, Karemaker JM, Strackee J. Comparing spectra оf а series оf point events particularly for heart rate variability data. IEEE Trans. Biomed. Eng. 1984;31(4):384-387. DOI: 10.1109/TBME.1984.325351.
- Klimontovich YuL. Turbulent Movement and Chaos Structure. M.: Nauka; 1990. 316 p. (in Russian).
- Klimontovich YuL. Relative ordering criteria in open systems. Phys. Usp. 1996;39(11):1169-1179. DOI: 10.1070/pu1996v039n11abeh000181.
- Wolf А, Swift JB, Swinney HL, Vastano JA. Determining Lyapunov exponents from а time series. Physica D. 1985;16(3):285-317. DOI: 10.1016/0167-2789(85)90011-9.
- Pikovsky AS, Rosenblum MG, Osipov GV, Kurths J. Phase synchronization of chaotic oscillators by external driving. Physica D. 1997;104(3-4):219-238. DOI: 10.1016/S0167-2789(96)00301-6.
- Paladin G, Serva M, Vulpiani A. Complexity in dynamical systems with noise. Phys. Rev. Lett. 1995;74(1):66-69. DOI: 10.1103/PhysRevLett.74.66.
- Loreto V, Paladin G, Vuipiani А. Concept оf complexity in random dynamical systems. Phys. Rev. E. 1996;53(3):2087-2097. DOI: 10.1103/physreve.53.2087.
- Janson NB, Paviov AN, Neiman AB, Anishchenko VS. Reconstruction оf dynamical and geometrical properties оf chaotic attractors from threshold—crossing inter— spike intervals. Phys. Rev. Е. 1998;58(1):4-7. DOI: 10.1103/PhysRevE.58.R4.
- Anishchenko VS, Astakhov VV. Experimental study of the mechanism of the appearance and the structure of a strange attractor in an oscillator with inertial nonlinearity. Soviet Journal of Communications Technology and Electronics. 1983;28(6):1109-1115. (in Russian).
- Anishchenko VS. Complex oscillations in simple systems. М.: Nauka; 1990. 312 p. (in Russian).
- Rossler ОЕ. An equation for continuous chaos. Phys. Lett. А. 1976;57(5):397-398. DOI: 10.1016/0375-9601(76)90101-8.
- Packard NH, Crutchfield JP, Farmer JD, Shaw RS. Geometry from а time series. Phys. Rev. Lett. 1980;45(9):712-716. DOI: 10.1103/physrevlett.45.712.
- Takens F. Detecting strange attractors in turbulence. In: Rand D, Young LS, editors. Dynamical Systems and Turbulence, Warwick 1980. Lecture Notes in Mathematics. Vol 898. Berlin: Springer; 1980. P. 366-381. DOI: 10.1007/BFb0091924.
- Breeden JL, Packard NH. A learning algorithm for optimal representation оf experimental data. Int. J. Bifurc. Chaos. 1994;4(2):311-326. DOI: 10.1142/S0218127494000228.
- 289 reads