Estimating Dynamic Functional Brain Connectivity with a Sparse Hidden Markov Model

Estimating dynamic functional network connectivity (dFNC) of the brain from functional magnetic resonance imaging (fMRI) data can reveal both spatial and temporal organization and can be applied to track the developmental trajectory of brain maturity as well as to study mental illness. Resting state fMRI (rs-fMRI) is regarded as a promising task since it reflects the spontaneous brain activity without an external stimulus. The sliding window method has been successfully used to extract dFNC but typically assumes a fixed window size. The hidden Markov model (HMM) based method is an alternative approach for estimating time-varying connectivity. In this paper, we propose a sparse HMM based on Gaussian HMM and Gaussian graphical model (GGM). In this model, the time-varying neural processes are represented as discrete brain states which are described with functional connectivity networks. By enforcing the sparsity on the precision matrix, we can get interpretable connectivity between different functional regions. The optimization of our model can be realized with the expectation maximization (EM) and graphical least absolute shrinkage and selection operator (glasso) algorithms. The proposed model is validated on both simulated blood oxygenation-level dependent (BOLD) time series and rs-fMRI data. Results indicate that the proposed model can capture both stationary and abrupt brain activity fluctuations. We also compare dFNC patterns between children and young adults from the Philadelphia Neurodevelopmental Cohort (PNC) study. Both spatial and temporal behavior of the dFNC are analyzed and compared. The results provide insight into the developmental trajectory across childhood and motivate further research on brain connectivity.