Effective connectivity analysis: testing commonalities and differences across multisubjects´ network by state-space model

In fMRI experiments, data from multiple subjects are usually collected. Combining the information from multiple subjects allows us to look for congruence or divergence of such patterns in the fMRI data across individuals. Inter-subject commonalities and differences in the connectivity pattern are seldom investigated in effective connectivity studies. In this paper, we propose a state-space modeling framework to study the dynamic relationship between multiple brain regions and also account for the individual variability in effective connectivity analysis. Our approach decomposes the observed multiple time series into measurement error and the BOLD signals. The proposed model consists of the activation and connectivity equations. In the activation equation, we model the observed signals at each brain region as a function of the BOLD signal. One special feature of our model for capturing the complexities of the dynamic processes in the brain is that the region-specific time-varying coefficients in the activation equation are subsequently modelled, in the connectivity equation, as a function of the BOLD signals at other brain regions. Because our model has a state-space representation, the parameters are readily estimated by maximum likelihood method.