A note on fractal dimensions of biomedical waveforms.

Department of Electrical Communication Engineering, Indian Institute of Science, Bangalore 560 012, India.
Computers in biology and medicine (Impact Factor: 1.27). 09/2009; 39(11):1006-12. DOI: 10.1016/j.compbiomed.2009.08.001
Source: PubMed

ABSTRACT In this paper, we study performance of Katz method of computing fractal dimension of waveforms, and its estimation accuracy is compared with Higuchi's method. The study is performed on four synthetic parametric fractal waveforms for which true fractal dimensions can be calculated, and real sleep electroencephalogram. The dependence of Katz's fractal dimension on amplitude, frequency and sampling frequency of waveforms is noted. Even though the Higuchi's method has given more accurate estimation of fractal dimensions, the study suggests that the results of Katz's based fractal dimension analysis of biomedical waveforms have to be carefully interpreted.

  • [Show abstract] [Hide abstract]
    ABSTRACT: In this study, an adaptive electroencephalogram (EEG) analysis system is proposed for a two-session, single-trial classification of motor imagery (MI) data. Applying event-related brain potential (ERP) data acquired from the sensorimotor cortices, the adaptive linear discriminant analysis (LDA) is used for classification of left- and right-hand MI data and for simultaneous and continuous update of its parameters. In addition to the original use of continuous wavelet transform (CWT) and Student's two-sample t-statistics, the 2D anisotropic Gaussian filter is proposed to further refine the selection of active segments. The multiresolution fractal features are then extracted from wavelet data by means of modified fractal dimension. The classification in session 2 is performed by adaptive LDA, which is trial-by-trial updated using the Kalman filter after the trial is classified. Compared with original active segment selection and non-adaptive LDA on six subjects from two data sets, the results indicate that the proposed method is helpful to realize adaptive BCI systems.
    Computers in biology and medicine 06/2011; 41(8):633-9. · 1.27 Impact Factor
  • Source
    [Show abstract] [Hide abstract]
    ABSTRACT: Analysis of patterns of variation of time-series, termed variability analysis, represents a rapidly evolving discipline with increasing applications in different fields of science. In medicine and in particular critical care, efforts have focussed on evaluating the clinical utility of variability. However, the growth and complexity of techniques applicable to this field have made interpretation and understanding of variability more challenging. Our objective is to provide an updated review of variability analysis techniques suitable for clinical applications. We review more than 70 variability techniques, providing for each technique a brief description of the underlying theory and assumptions, together with a summary of clinical applications. We propose a revised classification for the domains of variability techniques, which include statistical, geometric, energetic, informational, and invariant. We discuss the process of calculation, often necessitating a mathematical transform of the time-series. Our aims are to summarize a broad literature, promote a shared vocabulary that would improve the exchange of ideas, and the analyses of the results between different studies. We conclude with challenges for the evolving science of variability analysis.
    BioMedical Engineering OnLine 01/2011; 10:90. · 1.61 Impact Factor
  • Source
    [Show abstract] [Hide abstract]
    ABSTRACT: Standard methods for computing the fractal dimensions of time series are usually tested with continuous nowhere differentiable functions, but not benchmarked with actual signals. Therefore they can produce opposite results in extreme signals. These methods also use different scaling methods, that is, different amplitude multipliers, which makes it difficult to compare fractal dimensions obtained from different methods. The purpose of this research was to develop an optimisation method that computes the fractal dimension of a normalised (dimensionless) and modified time series signal with a robust algorithm and a running average method, and that maximises the difference between two fractal dimensions, for example, a minimum and a maximum one. The signal is modified by transforming its amplitude by a multiplier, which has a non-linear effect on the signal's time derivative. The optimisation method identifies the optimal multiplier of the normalised amplitude for targeted decision making based on fractal dimensions. The optimisation method provides an additional filter effect and makes the fractal dimensions less noisy. The method is exemplified by, and explained with, different signals, such as human movement, EEG, and acoustic signals.
    Computational and Mathematical Methods in Medicine 01/2013; 2013:178476. · 0.79 Impact Factor