Linear Dynamical System Response Modeling of Trial-to-Trial Amplitude Variability in Event-Related MEG/EEG

We propose a linear dynamical system response (LDSR) model to describe amplitude variability across trials in event-related magnetoencephalographic/electroencephalographic (MEG/EEG) data. Variability across trials may reflect habituation, fatigue, or changes in cognitive states of the brain. A wide range of trial-to-trial variability can be represented using the LDSR model, including the constant response (CR) model as a limiting case. The spatiotemporal signal waveform is assumed constant but unknown, and is represented using a linear combination of spatial and temporal basis functions. The background noise is assumed to be spatially correlated with unknown covariance matrix. We obtain the maximum-likelihood estimates of the amplitude variability and signal waveform via a generalized Expectation-Maximization algorithm. The expectation step involves a Kalman fixed-interval smoother which tracks the trial-to-trial amplitude variability while the maximization step estimates the signal waveform, spatial noise covariance, and LDSR model parameters. We demonstrate the effectiveness of the proposed model using both real and simulated evoked response data. The performance of the algorithm is analyzed in terms of the mean squared error of the amplitude estimates.