Alexander Schaefer1, Jennifer S Brach2, Subashan Perera3, Ervin Sejdić4. 1. Department of Electrical and Computer Engineering, Swanson School of Engineering, University of Pittsburgh, Pittsburgh, PA 15261, USA. 2. Department of Physical Therapy, University of Pittsburgh, Pittsburgh, PA 15260, USA. 3. Department of Medicine, Division of Geriatrics, University of Pittsburgh, Pittsburgh, PA 15261, USA. 4. Department of Electrical and Computer Engineering, Swanson School of Engineering, University of Pittsburgh, Pittsburgh, PA 15261, USA. Electronic address: esejdic@ieee.org.
Abstract
BACKGROUND: The time evolution and complex interactions of many nonlinear systems, such as in the human body, result in fractal types of parameter outcomes that exhibit self similarity over long time scales by a power law in the frequency spectrum S(f)=1/f(β). The scaling exponent β is thus often interpreted as a "biomarker" of relative health and decline. NEW METHOD: This paper presents a thorough comparative numerical analysis of fractal characterization techniques with specific consideration given to experimentally measured gait stride interval time series. The ideal fractal signals generated in the numerical analysis are constrained under varying lengths and biases indicative of a range of physiologically conceivable fractal signals. This analysis is to complement previous investigations of fractal characteristics in healthy and pathological gait stride interval time series, with which this study is compared. RESULTS: The results of our analysis showed that the averaged wavelet coefficient method consistently yielded the most accurate results. COMPARISON WITH EXISTING METHODS: Class dependent methods proved to be unsuitable for physiological time series. Detrended fluctuation analysis as most prevailing method in the literature exhibited large estimation variances. CONCLUSIONS: The comparative numerical analysis and experimental applications provide a thorough basis for determining an appropriate and robust method for measuring and comparing a physiologically meaningful biomarker, the spectral index β. In consideration of the constraints of application, we note the significant drawbacks of detrended fluctuation analysis and conclude that the averaged wavelet coefficient method can provide reasonable consistency and accuracy for characterizing these fractal time series.
BACKGROUND: The time evolution and complex interactions of many nonlinear systems, such as in the human body, result in fractal types of parameter outcomes that exhibit self similarity over long time scales by a power law in the frequency spectrum S(f)=1/f(β). The scaling exponent β is thus often interpreted as a "biomarker" of relative health and decline. NEW METHOD: This paper presents a thorough comparative numerical analysis of fractal characterization techniques with specific consideration given to experimentally measured gait stride interval time series. The ideal fractal signals generated in the numerical analysis are constrained under varying lengths and biases indicative of a range of physiologically conceivable fractal signals. This analysis is to complement previous investigations of fractal characteristics in healthy and pathological gait stride interval time series, with which this study is compared. RESULTS: The results of our analysis showed that the averaged wavelet coefficient method consistently yielded the most accurate results. COMPARISON WITH EXISTING METHODS: Class dependent methods proved to be unsuitable for physiological time series. Detrended fluctuation analysis as most prevailing method in the literature exhibited large estimation variances. CONCLUSIONS: The comparative numerical analysis and experimental applications provide a thorough basis for determining an appropriate and robust method for measuring and comparing a physiologically meaningful biomarker, the spectral index β. In consideration of the constraints of application, we note the significant drawbacks of detrended fluctuation analysis and conclude that the averaged wavelet coefficient method can provide reasonable consistency and accuracy for characterizing these fractal time series.
Authors: David C Caccia; Donald Percival; Michael J Cannon; Gary Raymond; James B Bassingthwaighte Journal: Physica A Date: 1997-12-01 Impact factor: 3.263
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