Selecting parameters for phase space reconstruction of the electrocorticogram (ECoG)

Area of Science:

• Neuroscience
• Complexity Science
• Signal Processing

Background:

• Estimating correlation dimension (D2) from empirical data, like electroencephalograms (EEG), faces criticism due to arbitrary parameter choices in phase space reconstruction.
• Key parameters, time-delay (T) and embedding dimension (M), significantly influence the reliability of D2 estimates, especially for noisy and non-stationary biological signals.
• Previous methods lacked a robust framework for analyzing the scaling behavior of D2 with respect to T and M across varying data lengths.

Purpose of the Study:

• To establish an analytic and statistical framework for examining the scaling behavior of D2 concerning time-delay (T) and embedding dimension (M).
• To determine the stability and parameter dependencies of D2 estimates for cat EEG signals across different data lengths.
• To investigate the phase-dependence of EEG signals by comparing D2 estimates with phase-randomized surrogates.

Main Methods:

• Employed an analytic and statistical framework to analyze the scaling behavior of D2 with respect to T and M.
• Utilized five different data lengths (N = 4096 to 20480) and an 8x8 grid of cat EEG data.
• Performed multiple analysis of variance (MANOVA) to test for significant interactions between T and M, and compared EEG data with phase-randomized surrogates.

Main Results:

• The correlation dimension (D2) remained invariant across all data lengths only within a narrow time-delay (T) range of 10-16 for an embedding dimension (M) of 4.
• A statistically significant interaction between T and M was identified, indicating D2 is highly correlated with T as a function of M.
• EEG signals showed statistically significant differences from phase-randomized surrogates across all data lengths for T = 10-16, confirming phase-dependence of D2.

Conclusions:

• The study validates that D2 for EEG is phase-dependent when it is invariant with respect to data length, specifically within the identified T and M ranges.
• Findings provide critical insights into the appropriate selection of parameters for phase space reconstruction in analyzing complex biological signals like EEG.
• Results have implications for refining current models of electrocorticography (ECoG) generation and understanding neural signal integration in the brain.