Power-law scaling of brain wave activity associated with mental fatigue

This paper investigates the cause and detection of power-law scaling of brain wave activity due to the heterogeneity of the brain cortex, considered as a complex system, and the initial condition such as the alert or fatigue state of the brain. Our starting point is the construction of a mathematical model of global brain wave activity based on EEG measurements on the cortical surface. The model takes the form of a stochastic delay-differential equation (SDDE). Its fractional diffusion operator and delay operator capture the responses due to the heterogeneous medium and the initial condition. The analytical solution of the model is obtained in the form of a Karhunen-Loève expansion. A method to estimate the key parameters of the model and the corresponding numerical schemes are given. Real EEG data on driver fatigue at 32 channels measured on 50 participants are used to estimate these parameters. Interpretation of the results is given by comparing and contrasting the alert and fatigue states of the brain. The EEG time series at each electrode on the scalp display power-law scaling, as indicated by their spectral slopes in the low-frequency range. The diffusion of the EEG random field is non-Gaussian, reflecting the heterogeneity of the brain cortex. This non-Gaussianity is more pronounced for the alert state than the fatigue state. The response of the system to the initial condition is also more significant for the alert state than the fatigue state. These results demonstrate the usefulness of global SDDE modelling complementing the time series approach for EEG analysis.