  Time Varying Functional Connectivity (TVFC) investigates how the interactions
among brain regions vary over the course of an fMRI experiment. The transitions
between different individual connectivity states can be modulated by changes in
underlying physiological mechanisms that drive functional network dynamics,
e.g., changes in attention or cognitive effort as measured by pupil dilation.
In this paper, we develop a multi-subject Bayesian framework for estimating
dynamic functional networks as a function of time-varying exogenous
physiological covariates that are simultaneously recorded in each subject
during the fMRI experiment. More specifically, we consider a dynamic Gaussian
graphical model approach, where a non-homogeneous hidden Markov model is
employed to classify the fMRI time series into latent neurological states,
borrowing strength over the entire time course of the experiment. The
state-transition probabilities are assumed to vary over time and across
subjects, as a function of the underlying covariates, allowing for the
estimation of recurrent connectivity patterns and the sharing of networks among
the subjects. Our modeling approach further assumes sparsity in the network
structures, via shrinkage priors. We achieve edge selection in the estimated
graph structures, by introducing a multi-comparison procedure for
shrinkage-based inferences with Bayesian false discovery rate control. We apply
our modeling framework on a resting-state experiment where fMRI data have been
collected concurrently with pupillometry measurements, leading us to assess the
heterogeneity of the effects of changes in pupil dilation, previously linked to
changes in norepinephrine-containing locus coeruleus, on the subjects'
propensity to change connectivity states.
