Abstract
We have recently proposed an algorithmic scheme [22] for the non-subjective computation of correlation dimension from time series data. Here it is extended for the computation of generalized dimensions and the multifractal spectrum and applied to a number of EEG and ECG data sets from normal as well as certain pathological states of the brain and the cardiac system. Comparisons are drawn using a standard low dimensional chaotic system. Our method has the advantage that the analysis is done under identical prescriptions built into the algorithm and hence the comparison of resulting indices becomes non-subjective. This also enables a quantitative characterization of the relative complexity between practical time series such as, those corresponding to the changes in the physiological states of the same system, from the view point of underlying dynamics.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Spotlight issue on chaos in the cardiovascular system, Cardiovasc. Res., 31 (1996).
Special issue on the application of nonlinear dynamics to physiology, CHAOS, 8 (1998).
Focal issue on mapping and control of complex cardiac arrhythmias, CHAOS, 12 (2002).
N. Pradhan and D. Narayana Dutt, A nonlinear perspective in understanding the neurodynamics of EEG, Comput. Biol. Med., 23, 425 (1993).
W. Latzenberger, H. Preissl and F. Pulvermiller, Fractal dimension of electroencephalographic time series and underlying brain processes, Biol. Cybernet., 73, 477 (1995).
M.A.F. Harrison, I. Osorio, M.G. Frei, S. Asuri and Y.-C. Lai, Correlation dimension and integral do not predict epileptic seizures, CHAOS, 15, 033106 (2005).
L. Glass, A.L. Goldberger, M. Courtemanche and A. Shrier, Nonlinear dynamics, chaos and complex cardiac arrhythmias, Proc. R. Soc. Lond. Ser. A, 413, 9 (1987).
F.X. Witkowski, K.M. Karnagh, 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 (1995).
C.S. Poon and C.K. Merril, Decrease of cardiac chaos in congestive heart failure, Nature, 389, 492 (1997).
F. Ravelli and R. Antolini, Complex dynamics underlying the human electrocardiogram, Biol. Cybernet., 67, 57 (1992).
R.B. Govindan, K. Narayanan and M.S. Gopinathan, On the evidence of deterministic chaos in ECG: Surrogate and predictability analysis, CHAOS, 8, 495 (1998).
L. Glass and P. Hunter, There is a theory of heart, Physica D, 43, 1 (1990).
A.L. Goldberger, Is the normal heart beat chaotic or homeostatic?, News. Physiol. Sci., 6, 87 (1991).
F. Mitschke and M. Dimming, Chaos versus noise in experimental data, Int. J. Bif. Chaos, 3, 693 (1993).
N. Marwan, N. Wessel, U. Meyerfeldt, A. Schirdewan and J. Kurths, Recurrence plot based measures of complexity and their application to heart rate variability data, Phys. Rev. E, 66, 026702 (2002).
N. Wessel, C. Ziehmann, J. Kurths, U. Meyerfeldt, A. Schirdewan and A. Voss, Short term forecasting of life-threatening cardiac arrhythmias based on symbolic dynamics and finite time growth rates, Phys. Rev. E, 61, 733 (2000).
R. Brown and P. Bryant, Computing Lyapunov spectrum of a dynamical system from an observed time series, Phys. Rev. A, 43, 2787 (1991).
M. Costa, A.L. Goldberger and C.K. Peng, Multiscale entropy analysis of complex physiological time series, Phys. Rev. Lett., 89, 068102 (2002).
R.A. Thuraisingham and G.A. Gottwald, On multiscale entropy analysis for physiological data, Physica A, 366, 323 (2006).
M.B. Kennel and S. Isabelle, Method to distinguish possible chaos from colored noise and to determine embedding parameters, Phys. Rev. A, 46, 3111 (1992).
M. Small and K. Judd, Detecting nonlinearity in experimental data, Int. J. Bif. Chaos, 8, 1231 (1998).
K.P. Harikrishnan, R. Misra, G. Ambika and A.K. Kembhavi, A nonsubjective approach to the GP algorithm for analysing noisy time series, Physica D, 215, 137 (2006).
P. Grassberger and I. Procaccia, Characterisation of strange attractors, Phys. Rev. Lett., 50, 346 (1983).
P. Grassberger and I. Procaccia, Measuring the strangeness of strange attractors, Physica D, 9, 189 (1983).
T. Schreiber and A. Schmitz, Improved surrogate data for nonlinearity tests, Phys. Rev. Lett., 77, 635 (1996).
R. Hegger, H. Kantz and T. Schreiber, Practical implementation of Nonlinear time series methods: The TISEAN package, CHAOS, 9, 413 (1999).
T.C. Halsey, M.H. Jensen, L.P. Kadanof, I. Proccacia and B.I. Shraiman, Fractal measures and their singularities: The characterization of strange sets, Phys. Rev. A, 33, 1141 (1986).
H. Atmanspacher, H. Scheingraber and N. Voges, Global scaling properties of a chaotic attractor reconstructed from experimental data, Phys. Rev. A, 37, 1314 (1988).
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2009 Springer Science+Business Media B.V.
About this paper
Cite this paper
Ambika, G., Harikrishnan, K., Misra, R. (2009). Multifractal Analysis of Physiological Data: A Non-Subjective Approach. In: Dana, S.K., Roy, P.K., Kurths, J. (eds) Complex Dynamics in Physiological Systems: From Heart to Brain. Understanding Complex Systems. Springer, Dordrecht. https://doi.org/10.1007/978-1-4020-9143-8_2
Download citation
DOI: https://doi.org/10.1007/978-1-4020-9143-8_2
Publisher Name: Springer, Dordrecht
Print ISBN: 978-1-4020-9142-1
Online ISBN: 978-1-4020-9143-8
eBook Packages: Physics and AstronomyPhysics and Astronomy (R0)