Fractal and multifractal properties of electrographic recordings of human brain activity.

The brain is a system operating on multiple time scales, and characterisation of dynamics across time scales remains a challenge. One framework to study such dynamics is that of fractal geometry. However, currently there exists no established method for the study of brain dynamics using fractal geometry, due to the many challenges in the conceptual and technical understanding of the methods. We aim to highlight some of the practical challenges of applying fractal geometry to brain dynamics and propose solutions to enable its wider use in neuroscience. Using intracranially recorded EEG and simulated data, we compared monofractal and multifractal methods with regards to their sensitivity to signal variance. We found that both correlate closely with signal variance, thus not offering new information about the signal. However, after applying an epoch-wise standardisation procedure to the signal, we found that multifractal measures could offer non-redundant information compared to signal variance, power and other established EEG signal measures. We also compared different multifractal estimation methods and found that the Chhabra-Jensen algorithm performed best. Finally, we investigated the impact of sampling frequency and epoch length on multifractal properties. Using epileptic seizures as an example event in the EEG, we show that there may be an optimal time scale for detecting temporal changes in multifractal properties around seizures. The practical issues we highlighted and our suggested solutions should help in developing a robust method for the application of fractal geometry in EEG signals. Our analyses and observations also aid the theoretical understanding of the multifractal properties of the brain and might provide grounds for new discoveries in the study of brain signals. These could be crucial for understanding of neurological function and for the developments of new treatments.