Chaotic dynamics applied to signal complexity in phase space and in time domain

Abstract In the past few years fractal analysis techniques have gained increasing attention in signal and image processing in Medicine. We concentrate on using fractal techniques for analysis of encephalographic data (EEG). Better understanding of general principles that govern discrete dynamics of these signals can help to reveal `the signatures' of different physiological and pathological states. Fractal complexity of the signal in time domain, calculated using Higuchi's algorithm, seems to be the simplest method and may also be used in other biomedical applications.

[1]  R. Kerner The Principle of Self-Similarity and Its Applications to the Description of Noncrystalline Matter , 1998 .

[2]  W Klonowski,et al.  Representing and defining patterns by graphs: applications to sol-gel patterns and to cytoskeleton. , 1988, Bio Systems.

[3]  Wlodzimierz Klonowski Probabilistic-topological theory of systems with discrete interactions: II. Calculation of the hypergraph probabilistic representation; the difference a posteriori algorithm , 1988 .

[4]  J. Wackermann,et al.  Beyond mapping: estimating complexity of multichannel EEG recordings. , 1996, Acta neurobiologiae experimentalis.

[5]  W. Klonowski,et al.  Non-linearity and statistics - implications of hormesis on dose-response analysis , 1999 .

[6]  Wlodzimierz Klonowski Probabilistic-topological theory of systems with discrete interactions: I. System representation by a hypergraph , 1988 .

[7]  W. Klonowski,et al.  Application of standard chaotic quantifiers for chemotherapy assessing by EEG-signal analysis , 2000 .

[8]  FRACTAL ANALYSIS OF MULTI-CHANNEL EEG-DATA IN PATIENTS WITH SEASONAL AFFECTIVE DISORDER , 2000 .

[9]  W. Klonowski Signal and image analysis using chaos theory and fractal geometry , 2000 .

[10]  Benoit B. Mandelbrot,et al.  Fractal Geometry of Nature , 1984 .

[11]  T. Mattfeldt,et al.  Spatial Pattern Analysis using Chaos Theory: A Nonlinear Deterministic Approach to the Histological Texture of Tumours , 1998 .

[12]  W. B. Marks,et al.  Fractal methods and results in cellular morphology — dimensions, lacunarity and multifractals , 1996, Journal of Neuroscience Methods.

[13]  Werner Lutzenberger,et al.  Fractal dimensions of short EEG time series in humans , 1997, Neuroscience Letters.

[14]  T. Vicsek Fractal Growth Phenomena , 1989 .

[15]  Alex Pentland,et al.  Fractal-Based Description of Natural Scenes , 1984, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[16]  Wlodzimierz Klonowski,et al.  Application of Chaos Theory for EEG-signal Analysis in Patients with Seasonal Affective Disorder , 2000 .

[17]  E. Weibel,et al.  Fractals in Biology and Medicine , 1994 .

[18]  E T Bullmore,et al.  Fractal analysis of electroencephalographic signals intracerebrally recorded during 35 epileptic seizures: evaluation of a new method for synoptic visualisation of ictal events. , 1994, Electroencephalography and clinical neurophysiology.

[19]  F. Takens Detecting strange attractors in turbulence , 1981 .

[20]  P. Agostino Accardo,et al.  Use of the fractal dimension for the analysis of electroencephalographic time series , 1997, Biological Cybernetics.

[21]  T. Higuchi Approach to an irregular time series on the basis of the fractal theory , 1988 .

[22]  Ya. B. Zel'Dovich,et al.  FRACTALS AND DIMENSIONS , 1990 .

[23]  H. Holzhütter,et al.  Interrelations between glycolysis and the hexose monophosphate shunt in erythrocytes as studied on the basis of a mathematical model. , 1988, Bio Systems.

[24]  W Klonowski,et al.  Quantitative measure of complexity of EEG signal dynamics. , 1999, Acta neurobiologiae experimentalis.

[25]  Hai-Shan Wu,et al.  Fractal Characterization of Nuclear Texture in Breast Cytology:Frequency and Spatial Domain Approaches , 1998 .