Table 1.
List of subject numbers and data utilized.
Figure 1.
Comparison of MF-DFA spectrum from waking EEG to numerical models of mono- and multifractal processes.
Data points represent individual D(h) and h values from MF-DFA from a single time series of each type. waking: waking EEG (8 m, n = 120,000) from a single subject; shuffled: waking EEG with values shuffled prior to MF-DFA analysis; BMS: binomial multifractal series model with a = 0.6 (n = 120,000; Kantelhardt et al, 2002 [33]); LNS1: log normal sigma 0.1 multifractal model data (n = 32,768; Arneodo et al 1998 [50]; http://www.physionet.org/physiotools/multifractal/); fbm2, 5, 7; fractional Brownian motion monofractal models with Hb values of 0.2, 0.5, 0.7 as indicated (n = 120,000 each; dvfBm 1.0 R package).
Figure 2.
Variance comparison between MF-DFA and WTMM techniques.
A. For 14 subjects with 8 m of waking EEG each, divided into 30 s segments (16 segments of n = 7500 data points each per subject), multifractal spectra were calculated (total of 224 segments). Mean Hölder exponent value (mean_h), width of the Hölder exponents (width_h), mean fractal dimension (mean_D(h)) value, and height of the multifractal singularity spectrum (height_D(h)) were calculated for each segment. B. The 14 subjects’ 8 m of waking EEG were analyzed whole, and multifractal specta were calculated. Note the trend to reduced variance with increasing length of EEG tracing.
Table 2.
Individual subject data for 8 min waking EEG MF-DFA spectra.
Figure 3.
Comparison of waking EEG between MF-DFA and WTMM.
For 14 subjects with 8 m of EEG from waking data per subject, MF-DFA and WTMM spectra were calculated for each 8 m EEG series. Average multifractal spectra for each technique shown here were calculated by averaging individual spectra across subjects: mean_h±s.d. is 0.12±0.03 for MF-DFA, and 0.17±0.04 for WTMM.
Figure 4.
Comparison between MF-DFA spectra of from waking and sleep stage 2.
For 14 subjects with 8 m of EEG from both waking and sleep stage 2 per subject, EEG was divided into 16 segments of 30 s each, and MF-DFA spectra were calculated for each segment (224 segments for each state of consciousness). Average MF-DFA spectra for each consciousness state shown here were calculated by averaging across individual spectrum values for each subject. **: p<0.001 for effect of state of consciousness by general linear modeling based on mean_h.
Figure 5.
Comparison among stages of sleep for 1 minute of EEG data.
For each stage from each subject, 1 min of EEG data was used to calculate MF-DFA spectra. Average MF-DFA spectra for each consciousness state shown here were calculated by averaging across individual spectrum values for each subject. Mean h values were then calculated for the h range, and differences between sleep stages compared by paired t testing. *p<0.05; **p<0.01. Significant differences were found for the waking-REM, Sleep 1-Sleep 2, and Sleep 2-Sleep 3 comparisons.