Joint estimation of neural sources and their functional connections from MEG data

Current techniques to estimate directed functional connectivity from magnetoencephalography (MEG) signals involve two sequential steps; 1) Estimation of the sources and their amplitude time series from the MEG data by solving the inverse problem, and 2) fitting a multivariate autoregressive (MVAR) model to these time series for the estimation of AR coefficients, which reflect the directed interactions between the sources. However, such a sequential approach is not optimal since i) source estimation algorithms typically assume that the sources are independent, ii) the information provided by the connectivity structure is not used to inform the estimation of source amplitudes, and iii) the limited spatial resolution of source estimates often leads to spurious connectivity due to spatial leakage. Here, we present an algorithm to jointly estimate the source and connectivity parameters using Bayesian filtering, which does not require anatomical constraints in form of structural connectivity or a-priori specified regions-of-interest. By formulating a state-space model for the locations and amplitudes of a given number of sources, we show that estimation of functional connectivity can be reduced to a system identification problem. We derive a solution to this problem using a variant of the expectation-maximization (EM) algorithm known as stochastic approximation EM (SAEM). Compared to the traditional two-step approach, the joint approach using the SAEM algorithm provides a more accurate reconstruction of connectivity parameters, which we show with a connectivity benchmark simulation as well as with an electrocorticography-based simulation of MEG data. Using real MEG responses to visually presented faces in 16 subjects, we also demonstrate that our method gives source and connectivity estimates that are both physiologically plausible and largely consistent across subjects. In conclusion, the proposed joint-estimation approach based on the SAEM algorithm outperforms the traditional two-step approach in determining functional connectivity structure in MEG data.