Higuchi fractal dimension: An efficient approach to detection of brain entrainment to theta binaural beats

Abstract Binaural beats (BBs) are two pure tones with a small frequency difference (i.e., beat) separately presented to each ear. They cause the beat perception in the brain. BBs are used in both clinical and basic science applications. Studies in BB literature have mainly focused on linear analysis of the brain signals. Even though these approaches have produced promising findings, there may still be some facets left to be considered, which cannot be studied by linear measures. BBs entrain the brain and generate synchronous responses. Previous studies have proved that increasing brain synchronicity reduced its complexity measured by fractal dimension (FD). In this study, Higuchi fractal dimension (HFD) was used to test whether: 1) BB stimulation decreases the electroencephalogram (EEG) complexity, and 2) HFD is a reliable alternative to its common linear counterpart (i.e., relative power of the band in which the beat frequency lies) in terms of the brain entrainment detection. Results revealed that 3-min BB stimulation significantly decreased the HFD in temporal and parietal lobes, which was about half the time required to probe any changes in EEG power. Moreover, there was significant negative correlation between the relative power and HFD in these regions. In comparison to the relative power, HFD produced mostly higher classification accuracies and areas under empirical receiver operating characteristic (ROC) curve in these lobes. Our findings suggest that HFD can be a reliable replacement for relative power in terms of entrainment detection and response classification.