Brain Waves and White Matter: New Perspectives on 50 Years of Toy Models

Electric potentials (EEG) were first recorded on the human scalp in 1924 and have since become a key window into brain activity. However, no consensus has emerged regarding their origins. Over the past 50 years, EEG has been modeled using two distinct mathematical approaches: local network models, which focus on cell membrane properties such as synaptic rise and decay times [E4,E5], and global models, which emphasize axon propagation delays in white matter [E6,Z9].Global models predict longitudinal waves of synaptic activity, akin to sound waves in an opera house. These large-scale brain waves are recorded as electric potentials or electric fields on the scalp or cortex, though they should not be confused with the (transverse) electromagnetic fields governed by Maxwell’s equations.The foundational global model is classified into “Toy Model Levels” (1–11) based on its physiological accuracy and ability to replicate EEG dynamics. These models predict the dynamics of EEG frequency bands—delta, theta, alpha, beta, and gamma—which occur in certain brain states, selectively modulated by neocortical excitability. Key topics include EEG dynamics, dispersion relations, white matter properties, resonance phenomena, wave packets, and complex systems theory