Detection of crossover points in detrended fluctuation analysis: an application to EEG signals of patients with epilepsy

Abstract

Motivation The quantification of long-range correlation of electroencephalogram (EEG) signals is an important research direction for its relevance in helping understanding the brain activity. Epileptic seizures have been studied in the past years where different non-linear statistical approaches have been employed to understand the relationship between the EEG signal and the epilepitc discharge. One of the most widely used method for to analyse long memory processes is the detrended fuctuation analysis (DFA). However, no objective and pragmatic methods have been developed to detect crossover points and reference channels in DFA. Results In this paper, we propose: (i) two automatic approaches that successfully detect crossover points in DFA related methods on the log-log plot; and (ii) a criteria to choose the reference channel for the log-amplitude function. Moreover, the DFA is applied to EEG signals of 10 epileptic patients collected from the CHB-MIT database, being the log-amplitude function used to compare the different brain hemispheres by making use of the methodology proposed in the paper. The existence of long-range power-law correlations is demonstrated and indicates that the EEG signals of epileptic patients present three well defined regions with the first region showing a 1/f 1/f noise (pink noise) for seven subjects and a random walk behaviour for three subjects. The second and third regions show anti-persistence behaviour. Moreover, the results of the log-amplitude function were divided in two groups: (i) the first, including seven subjects, where the increase in the scales results in an increase in the fluctuation in the the frontal channels; and (ii) the second, included three subjects, where the fluctuation for large scales are greater for the parietal channels. Availability The functions used in this paper are available in the R package DFA (Mesquita et al., 2020). Supplementary information Supplementary information are available at Bioinformatics online.

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“…which can be computationally obtained by [30]. Repeat the operation for a broad range of n-size box, eg, [31] recommend taking a sample on the grid between 4 ≤ n ≤ T /4. The figure 2 display the steps of DFA for two n-size boxes, the first with 60 minutes (figure 2c) and the second with 30 minutes (figure 2d).…”