However, spatial and temporal variation in scale invariant structure of the biomedical signal often appears.
Most commonly, the monofractal structure of biomedical signals are defined by a single power law exponent and assumes that the scale invariance is independent on time and space. Monofractal and multifractal structures of the biomedical signal are particular kind of scale invariant structures. Fractal analyses are therefore promising prognostic and diagnostic tools in biomedical signal processing. Several reports during the last decade suggest that changes in the scale invariant structure of biomedical signals reflect changes in the adaptability of physiological processes and successful treatment of pathological conditions might change fractal structure and improve health ( Goldberger, 1996 Goldberger et al., 2002). Scale invariant structures are also found in spatial phenomena like the branching of the nervous system and lungs (e.g., Bassingthwaighte et al., 1990 Abbound et al., 1991 Weibel, 1991 Krenz et al., 1992), bone structure ( Parkinson and Fazzalari, 1994), and are able to differentiate between healthy and cancer tissues ( Atupelage et al., 2012). The scale invariant structures of inter-spike-interval of neuron firing, inter-stride-interval of human walking, inter-breath-interval of human respiration, and inter-beat intervals of the human heart has differentiated between healthy and pathological conditions (e.g., Ivanov et al., 1999 Peng et al., 2002 Zheng et al., 2005 Hausdorff, 2007), and between different types of pathological conditions (e.g., Wang et al., 2007). Fractal analyses are frequently employed in biomedical signal processing to define the scale invariant structure in ECG, EEG, MR, and X-ray pictures (cf. Fractal analyses estimates the power law exponent, H, that defines the particular kind of scale invariant structure of the biomedical signal. Formally, the biomedical signal X( t) are scale invariant when X( ct) = c HX( t). A biomedical signal has a scale invariant structure when the structure repeats itself on subintervals of the signal. Biomedical signals from a wide range of physiological phenomena posses a scale invariant structure. The structural characteristics of biomedical signals are often visually apparent, but not captured by conventional measures like the average amplitude of the signal. The main aim of the tutorial is to give the reader a simple self-sustained guide to the implementation of MFDFA and interpretation of the resulting multifractal spectra. After introducing MFDFA, the tutorial discusses the best practice of MFDFA in biomedical signal processing.
E IN MATLAB CODE
All Matlab tools needed are available in Introduction to MFDFA folder at the website MFDFA are introduced in Matlab code boxes where the reader can employ pieces of, or the entire MFDFA to example time series. The tutorial presents MFDFA step-by-step in an interactive Matlab session. The present tutorial is an introduction to multifractal detrended fluctuation analysis (MFDFA) that estimates the multifractal spectrum of biomedical time series. The multifractal spectrum identifies the deviations in fractal structure within time periods with large and small fluctuations.
E IN MATLAB SERIES
Department of Neuroscience, Norwegian University of Science and Technology, Trondheim, Norwayįractal structures are found in biomedical time series from a wide range of physiological phenomena.