Efficient Estimation of Time-Dependent Brain Functional Connectivity Using Anatomical Connectivity Constraints

There is ongoing interest in the dynamics of resting state brain networks (RSNs) as potential predictors of cognitive and behavioural states. Multivariate Autoregressors (MAR) are used to model regional brain activity as a linear combination of past activity in other regions. The coefficients of the MAR are taken as estimates of effective brain connectivity. However, assumption of stationarity, and the large number of coefficients renders the MAR impractical for estimating brain networks from standard neuroimaging time-series of limited durations. We propose HsMM-MAR-AC, a novel sparse hybrid discrete-continuous model for the efficient estimation of time-dependent effective brain networks from non-stationary brain activity time-series. Discrete quasi-stationary Brain States, and the fast switching between them, are modelled by a Hidden semi-Markov Model whose continuous emissions are drawn from a sparse MAR. The coefficients of the MAR are restricted by Anatomical Brain Connectivity information in two ways: 1) Effective direct connectivity between two brain regions is only considered if the corresponding anatomical connection exists; and 2) the autoregressors lag associated with each connection is based on the fiber length between the two regions, such that only one lag per connection is estimated. We test the accuracy of HsMM-MAR-AC in recovering simulated resting state networks of various durations, and at different thresholds of anatomical restrictions. We demonstrate that HsMM-MAR-AC recovers the RSNs more accurately than the benchmark method of the sliding window, with as little as 4 minutes of data. We also show that when the anatomical restrictions are relaxed, longer time-series are needed to estimate the networks, and became computationally unfeasible without anatomical restrictions. HsMM-MAR-AC offers an efficient model for estimating time-dependent Effective Connectivity from neuroimaging data that exploits the advantages of Hidden Markov and MAR models without identifiability problems, excessive demand on data collection, or unnecessary computational effort.