Abstract
Recent years of research have shown that the complex temporal structure of ongoing oscillations is scale-free and characterized by long-range temporal correlations. Detrended fluctuation analysis (DFA) has proven particularly useful, revealing that genetic variation, normal development, or disease can lead to differences in the scale-free amplitude modulation of oscillations. Furthermore, amplitude dynamics is remarkably independent of the time-averaged oscillation power, indicating that the DFA provides unique insights into the functional organization of neuronal systems. To facilitate understanding and encourage wider use of scaling analysis of neuronal oscillations, we provide a pedagogical explanation of the DFA algorithm and its underlying theory. Practical advice on applying DFA to oscillations is supported by MATLAB scripts from the Neurophysiological Biomarker Toolbox (NBT) and links to the NBT tutorial website http://www.nbtwiki.net/. Finally, we provide a brief overview of insights derived from the application of DFA to ongoing oscillations in health and disease, and discuss the putative relevance of criticality for understanding the mechanism underlying scale-free modulation of oscillations.
Highlights
When investigating nature we often discard the observed variation and describe its properties in terms of an average, such as the mean or median (Gilden, 2001)
To facilitate understanding and encourage wider use of scaling analysis of neuronal oscillations, we provide a pedagogical explanation of the Detrended fluctuation analysis (DFA) algorithm and its underlying theory
[DFAobject,DFA_exp]=nbt_doDFA (AmplitudeEnvelope,AmplitudeEnvelopeInfo, [2 25], [0.8 30], 0.5, 1, 1, []); INSIGHTS FROM THE APPLICATION OF DFA TO NEURONAL OSCILLATIONS The discovery of long-range temporal correlations (LRTC) in the amplitude envelope of ongoing oscillations, was based on 10 subjects recorded with EEG and MEG for 20 min during eyes-closed and eyes-open rest (Linkenkaer-Hansen et al, 2001)
Summary
When investigating nature we often discard the observed variation and describe its properties in terms of an average, such as the mean or median (Gilden, 2001). For some objects or processes, the average value is a poor description, because they do not have a typical or “characteristic” scale. Such systems are broadly referred to as “scale-free” (Bassingthwaighte et al, 1994). We provide a beginner’s introduction to the Section “Fundamental Concepts Required to Understand DFA.” This is followed by the presentation of “The DFA” and the special requirements regarding “DFA applied to neuronal oscillations.”. SELF-AFFINITY Self-affinity is a property of fractal time series (Mandelbrot, 1967; Turcotte, 1997) It is a special case of self-similarity, according to which a small part of a fractal structure is similar to the whole structure. Nature hosts some intriguing examples of self-similar structures, such as the Roman cauliflower (Romanesco broccoli), in www.frontiersin.org
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