Abstract: We propose a state-space approach for studying the dynamic relationship between multiple brain regions. Our approach decomposes the observed multiple time series into measurement error and the BOLD (blood oxygenation level dependent) 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 via a routine application of the Kalman filter and smoother. In this paper, we apply our model to a functional magnetic resonance imaging data set to investigate the attentional control network in the brain.
Key words and phrases: Effective connectivity, functional magnetic resonance imaging, Kalman filter, state-space model.