Multiscale Lempel-Ziv complexity for EEG measures

Abstract

Objective: To demonstrate that the classical calculation of Lempel-Ziv complexity (LZC) has an important limitation when applied to EEGs with rapid rhythms, and to propose a multiscale approach that overcomes this limitation.

Methods: We have evaluated, both with simulated and real EEGs, whether LZC calculation neglects functional characteristics of rapid EEG rhythms. In addition, we have proposed a procedure to obtain multiple binarization sequences that yield a spectrum of LZC, and we have explored whether complexity would be better captured using this computation.

Results: In our simulated signals, classical LZC did not capture modulations of a rapid component when a slower component of more amplitude was included in the signal. In real EEGs from healthy participants with eyes closed and eyes open, classical LZC calculation failed to show any difference between these two conditions. However, a multiscale LZC showed that complexity was lower for eyes closed than for eyes open conditions.

Conclusions: As hypothesized, our new approximation captures the complexity of series with fast components masked by slower rhythms.

Significance: The method we introduce significantly improves LZC calculation, and it allows a better characterization of complexity of EEG signals.

Keywords: Complexity; EEG; Lempel–Ziv; Multiscale method.