Estimation of Cortical Interactions from EEG/MEG
Identification of the nature of interactions between different cortical regions is an important step towards better understanding of healthy and diseased brain function. Electroencephalography (EEG) and magnetoencephalography (MEG) offer a window on the electrical behavior of cortical neuronal populations through non-invasive measurement of the electric and magnetic fields, respectively, they generate at the scalp. EEG and MEG have nearly unlimited temporal resolution, but the transformation from the activity in the cortex to that measured at the scalp involves an ill-conditioned spatial mixing operator. Typically EEG/MEG has low signal to noise ratio also. We employ a linear model for dynamic interactions between cortical regions - the multivariable autoregressive (MVAR) model - and describe the dynamics of the observed data using a state-space formulation. A state equation represents the MVAR model of cortical interactions and an observation equation accounts for the mixing operator and noise. An expectation-maximization algorithm is used to estimate the MVAR model parameters. Comparison of anatomic and effective connectivity in normal and spina bifida subjects illustrates the approach. The problem of verifying the correctness of a model and estimation method is addressed by introducing a cross-validation metric of model effectiveness. Intracranial data from an epilepsy patient is employed to demonstrate the proposed cross-validation strategy.