Research PaperDynamic Cross-Entropy

- Dynamic Cross-Entropy (DCE) quantifies the degree of regularity of EEG signals in selected frequency bands.
- DCE analysis can be used to analyze the transition from order to chaotic behavior in complex nonlinear systems.
- The presence of bifurcations is consistent with transitions into less ordered states and chaos.
- The transition to irregular dynamics appears to follow a similar path in case of logistic equation and in the brain.

BackgroundComplexity measures for time series have been used in many applications to quantify the regularity of one dimensional time series, however many dynamical systems are spatially distributed multidimensional systems.New MethodWe introduced Dynamic Cross-Entropy (DCE) a novel multidimensional complexity measure that quantifies the degree of regularity of EEG signals in selected frequency bands. Time series generated by discrete logistic equations with varying control parameter r are used to test DCE measures.ResultsSliding window DCE analyses are able to reveal specific period doubling bifurcations that lead to chaos. A similar behavior can be observed in seizures triggered by electroconvulsive therapy (ECT). Sample entropy data show the level of signal complexity in different phases of the ictal ECT. The transition to irregular activity is preceded by the occurrence of cyclic regular behavior. A significant increase of DCE values in successive order from high frequencies in gamma to low frequencies in delta band reveals several phase transitions into less ordered states, possible chaos in the human brain.Comparison with Existing MethodTo our knowledge there are no reliable techniques able to reveal the transition to chaos in case of multidimensional times series. In addition, DCE based on sample entropy appears to be robust to EEG artifacts compared to DCE based on Shannon entropy.ConclusionsThe applied technique may offer new approaches to better understand nonlinear brain activity.