Using Benford’s Law for analysis of the electroencephalogram

Abstract

We investigated the first-digit distribution of simulated and real EEG signals recorded during wakefulness and various sleep stages. Furthermore, we examined how variables such as noise or patient age influence the first-digit distribution and affect its conformity with Benford’s Law. Simulated 1/f noise episodes, which serve as proxies for EEG data, were generated with varying spectral exponents to explore how these changes influence the first-digit distribution. Additionally, we analyzed sleep EEG data from an open-source database to compare the first-digit distributions across different sleep stages, particularly focusing on N3 sleep, which shares similarities with EEG patterns observed under general anesthesia.

Our results demonstrate that the first-digit distribution is influenced by the investigated features, i.e., spectral exponent, vigilance state, and age. Deviations from wakefulness cause deviations from the Benford distribution. Moreover, age-related variations in EEG data may lead to changes in first-digit distributions, potentially offering new insights into how aging affects brain activity. These findings suggest that applying Benford’s Law to EEG analysis could complement existing methods for patient monitoring. The results from our investigation justify the next step of applying this method to anesthesia data.