Analyzing asymmetry in brain hierarchies with a linear state-space model of resting-state fMRI data
The study of functional brain connectivity in resting-state functional magnetic resonance imaging (rsfMRI) data has traditionally focused on zero-lag statistics. However, recent research has emphasized the need to account for dynamic aspects due to the complex patterns of time-varying co-activations among brain regions. In this regard, the importance of non-zero-lag statistics in studying complex brain interactions has been emphasized, both in terms of modeling and data analysis. Here, we show how a time-lag description is incorporated within the framework of dynamic causal modeling (DCM) resulting in an asymmetric state interaction matrix known as effective connectivity (EC). Asymmetry in EC is conventionally associated with the directionality of interactions between brain regions and is frequently employed to distinguish between incoming and outgoing node connections. We will revisit this interpretation by employing a decomposition of the EC matrix. This decomposition enables us to isolate the steady-state differential crosscovariance matrix, which is responsible for modeling the information flow and introducing time irreversibility. In other words, by modeling the off-diagonal part of the differential covariance, the system landscape may exhibit a curl steady-state flow component that breaks detailed balance and diverges the dynamics from equilibrium. Our empirical results reveal that only the outgoing strengths of the EC matrix relate with the flow described by the differential cross-covariance, while the so-called incoming strengths are primarily driven by the zero-lag covariance, specifically the precision matrix, thus reflecting conditional independence rather than directionality.