There are a growing number of neuroimaging methods that model spatio-temporal patterns of brain activity to allow more meaningful characterizations of brain networks. This paper proposes dynamic graphical models (DGMs) for dynamic, directed functional connectivity. DGMs are a multivariate graphical model with time-varying coefficients that describe instantaneous directed relationships between nodes. A further benefit of DGMs is that networks may contain loops and that large networks can be estimated. We use network simulations and human resting-state fMRI (N = 500) to investigate the validity and reliability of the estimated networks. We simulate systematic lags of the hemodynamic response at different brain regions to investigate how these lags potentially bias directionality estimates. In the presence of such lag confounds (0.4-0.8 s offset between connected nodes), our method has a sensitivity of 72%-77% to detect the true direction. Stronger lag confounds have reduced sensitivity, but do not increase false positives (i.e., directionality estimates of the opposite direction). In human resting-state fMRI, the default mode network has consistent influence on the cerebellar, the limbic and the auditory/temporal networks. We also show a consistent reciprocal relationship between the visual medial and visual lateral network. Finally, we apply the method in a small mouse fMRI sample and discover a highly plausible relationship between areas in the hippocampus feeding into the cingulate cortex. We provide a computationally efficient implementation of DGM as a free software package for R.

Original publication




Journal article



Publication Date





340 - 353


Big Data Institute, Li Ka Shing Centre for Health Information and Discovery, Nuffield Department of Population Health, University of Oxford, United Kingdom; Department of Statistics, University of Warwick, United Kingdom; Institute of Digital Healthcare, WMG, University of Warwick, United Kingdom. Electronic address: