Multivariate Autoregressive Model with Instantaneous Effects to Improve Brain Connectivity Estimation

Evaluation of brain connectivity in the frequency domain is based on prior multivariate autoregressive (MVAR) model identification from multichannel neurological time series. The MVAR model commonly used in neuroscience applications accounts only for lagged effects among the time series and forsakes instantaneous effects. However, zero-lag interactions are likely to occur among simultaneously recorded neural signals, and the impact of their exclusion on connectivity measures has not been investigated yet. In this study we propose the use of an extended MVAR model including instantaneous effects, and compare its performance to that of the traditional MVAR approach using the Partial Directed Coherence (PDC). We show by simulations that, in presence of zero-lag correlations, the PDC derived from traditional MVAR modeling may produce misleading frequency domain connectivity evaluation, and that in such situations the correct connectivity pattern is recovered using the extended MVAR model. Then we provide examples of multichannel EEG recordings in which instantaneous effects are found to be far from negligible, and thus extended MVAR modeling seems more suitable to elucidate direction and strength of the interactions among EEG rhythms.