Estimation of cortical connectivity from E/MEG using nonlinear state-space models

We present the problem of estimating cortical connectivity between different regions of the cortex from scalp electroencephalographic (EEG) or magnetoencephalographic (MEG) data as system identification of a nonlinear state-space model. The state equation is based on a nonlinear multivariate autoregressive (MVAR) model with radial basis function (RBF) kernels. The RBF kernels capture the nonlinear dynamics of the cortical signals and provide a framework for measuring interactions between cortical regions of interest (ROIs) based on the definition of Granger causality. The observation equation relates the cortical signals associated with each ROI to the observed E/MEG data using a set of parsimonious spatial bases to represent spatially extended cortical sources. An expectation-maximization (EM) algorithm is derived to obtain maximum likelihood (ML) estimates of the nonlinear state-space model parameters directly from the observed data. We show that this integrated approach for measuring cortical connectivity performs significantly better than the conventional decoupled approach in which cortical signals are first estimated by solving the inverse problem followed by fitting a MVAR model.