Evaluating frequency-wise directed connectivity of BOLD signals applying relative power contribution with the linear multivariate time-series models

In this article, we propose a statistical method to evaluate directed interactions of functional magnetic-resonance imaging (fMRI) data. The multivariate autoregressive (MAR) model was combined with the relative power contribution (RPC) in this analysis. The MAR model was fitted to the data to specify the direction of connections, and the RPC quantifies the strength of connections. As the RPC is computed in the frequency domain, we can evaluate the connectivity for each frequency component. From this, we can establish whether the specified connections represent low- or high-frequency connectivity, which cannot be examined solely using the estimated MAR coefficients. We applied this analysis method to fMRI data obtained during visual motion tasks, confirming previous reports of bottom-up connectivity around the frequency corresponding to the block experimental design. Furthermore, we used the MAR model with exogenous variables (MARX) to extend our understanding of these data, and to show how the input to V1 transfers to higher cortical areas.