Abstract

EEG rhythms are rarely stationary; they emerge as brief, burst-like events whose timing and shape carry information about brain state. We developed models to segment transient  patterns—especially α-spindles(8–12 Hz)—as trajectories of a two-dimensional Ornstein–Uhlenbeck (OU) process with a stable focus. The approach yields three interpretable parameters (decay, intrinsic frequency, noise) that can be estimated in real time via two complementary routes: (i) global estimators from the signal’s amplitude distribution, autocorrelation, and Hilbert-phase dynamics; and (ii) a segmentation-driven fit that matches empirical spindle duration/amplitude distributions to OU simulations.  We will show applications to anesthesia monitoring, where α–δ dynamics and spindle fragmentation capture transitions in depth of anesthesia beyond conventional band-power metrics, and discuss how this representation can interface with interpretable forecasting (e.g., early warnings of  suppressions).