State Space Oscillator Models for Neural Data Analysis

Neural oscillations reflect the coordinated activity of neuronal populations across a wide range of temporal and spatial scales, and are thought to play a significant role in mediating many aspects of brain function, including attention, cognition, sensory processing, and consciousness. Brain oscillations are typically analyzed using frequency domain methods such as nonparametric spectral analysis, or time domain methods based on linear bandpass filtering. A typical analysis might seek to estimate the power within an oscillation sitting within a particular frequency band. A common approach to this problem is to estimate the signal power within that band, in frequency domain using the power spectrum, or in time domain by estimating the power or variance in a bandpass filtered signal. A major conceptual flaw in this approach is that neural systems, like many physiological or physical systems, have inherent broad-band "1/f" dynamics, whether or not an oscillation is present. Calculating power-in-band, or power in a bandpass filtered signal, can therefore be misleading, since such calculations do not distinguish between broadband power within the band of interest, and true underlying oscillations. In this paper, we present an approach for analyzing neural oscillations using a combination of linear oscillatory models. We estimate the parameters of these models using an expectation maximization (EM) algorithm, and employ AIC to select the appropriate model and identify the oscillations present in the data. We demonstrate the application of this method to univariate electroencephalogram (EEG) data recorded at quiet rest and during propofol-induced unconsciousness.