Abstract
A foundation of medical research is time series analysis—the behavior of variables of interest with respect to time. Time series data are often analyzed using the mean, with statistical tests applied to mean differences, and has the assumption that data are stationary. Although widely practiced, this method has limitations. Here we present an alternative statistical approach with sample analysis that provides a summary statistic accounting for the non-stationary nature of time series data. This work discusses the use of entropy as a measurement of the complexity of time series, in the context of Neuroscience, due to the non-stationary characteristic of the data. To elucidate our argument, we conducted entropy analysis on a sample of electroencephalographic (EEG) data from an interventional study using non-invasive electrical brain stimulation. We demonstrated that entropy analysis could identify intervention-related change in EEG data, supporting that entropy can be a useful “summary” statistic in non-linear dynamical systems.
Highlights
Following Prigogine [1], entropy is a measurement of complexity, among time series (TS) or signal data, which associates the amount of information to a probability distribution
Data was acquired via Electroencephalogram technique, and its time series process was summarized using entropy indices
The dynamic across the brain network connectivity is a complex phenomenon of substantial relevance which could help neurologists to understand better some diseases and help on the development of new treatments
Summary
Following Prigogine [1], entropy is a measurement of complexity, among time series (TS) or signal data, which associates the amount of information to a probability distribution. The first is perfectly regular, alternating between 0 and 1, such as 0,1,0,1,0,1,0,1,0,1,..., whereas the second is constructed by randomly drawing 0 and 1 with probability 1/2 each, for example 0,1,0,0,1,1,0,1,1,1,0,1,0,1,1,0,. Moments of this example, such as mean and standard deviation, will not distinguish them because both series have mean and deviation equals to 1/2, respectively. Transcranial direct current stimulation (tDCS) is a non-invasive neuromodulation technique that delivers a weak electrical current to the brain using electrodes attached to the scalp. Depending on the electrical current polarity (among other factors), the direct effects of tDCS include the change in neuronal excitability [13]. Using functional magnetic resonance imaging, Lang et al [17] showed that the tDCS application over the right primary motor cortex (M1)
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