Skip to main page content
Access keys NCBI Homepage MyNCBI Homepage Main Content Main Navigation
, 1 (3), 222-241

Large-scale DCMs for Resting-State fMRI


Large-scale DCMs for Resting-State fMRI

Adeel Razi et al. Netw Neurosci.


This paper considers the identification of large directed graphs for resting-state brain networks based on biophysical models of distributed neuronal activity, that is, effective connectivity. This identification can be contrasted with functional connectivity methods based on symmetric correlations that are ubiquitous in resting-state functional MRI (fMRI). We use spectral dynamic causal modeling (DCM) to invert large graphs comprising dozens of nodes or regions. The ensuing graphs are directed and weighted, hence providing a neurobiologically plausible characterization of connectivity in terms of excitatory and inhibitory coupling. Furthermore, we show that the use of to discover the most likely sparse graph (or model) from a parent (e.g., fully connected) graph eschews the arbitrary thresholding often applied to large symmetric (functional connectivity) graphs. Using empirical fMRI data, we show that spectral DCM furnishes connectivity estimates on large graphs that correlate strongly with the estimates provided by stochastic DCM. Furthermore, we increase the efficiency of model inversion using functional connectivity modes to place prior constraints on effective connectivity. In other words, we use a small number of modes to finesse the potentially redundant parameterization of large DCMs. We show that spectral DCM-with functional connectivity priors-is ideally suited for directed graph theoretic analyses of resting-state fMRI. We envision that directed graphs will prove useful in understanding the psychopathology and pathophysiology of neurodegenerative and neurodevelopmental disorders. We will demonstrate the utility of large directed graphs in clinical populations in subsequent reports, using the procedures described in this paper.

Keywords: Bayesian inference; Dynamic causal modeling; Effective connectivity; Functional connectivity; Graph theory; Large-scale networks; Resting state; fMRI.

Conflict of interest statement

Competing Interests: The authors have declared that no competing interests exist.


<b>Figure 1.</b>
Figure 1.
This figure shows the plots of the averaged free energy over participants as we increase the number of prior eigenmodes m. The left panel shows the profile of free energy (as a proxy for log-model evidence) for stochastic DCM. One can see that free energy first increases with a peak at m = 10 and then decreases. Using 36 modes (equal to the number of nodes) means that there are effectively no prior constraints. In the right panel, we show a similar plot for spectral DCM. We now see that the free energy plateaus at around m = 10.
<b>Figure 2.</b>
Figure 2.
This figure uses regression plots to illustrate the correspondence between the averaged parameter estimates over participants from two (stochastic and spectral) inversion schemes. The left panel shows the relationship in the absence of any prior constraint. We see that the parameter estimates are highly correlated (rho = 0.67). The plot on the right shows the equivalent results when we used an optimal number of prior modes, in terms of those that maximizes the free energy, for each subject and then averaged the parameter estimates over participants. We again see that there is high correlation between the parameter estimates of the two inversion schemes (rho = 0.65). We excluded the self-connections (diagonal entries) when doing this analysis as they are scaled parameters.
<b>Figure 3.</b>
Figure 3.
This figure shows the regressions comparing the parameter estimates for each inversion scheme separately. On the left, we compare the averaged parameter estimate from spectral DCM when we used no prior constraint (full) and when we used an optimal number of modes, selected on the basis of free energy, for each subject (reduced). We see that the parameter estimates are highly correlated (rho = 0.93). The right-hand plot shows the parameter estimates for stochastic DCM, which also evidence high correlations (rho = 0.94).
<b>Figure 4.</b>
Figure 4.
This figure shows the regression of parameter estimates from spectral DCM (left panel) and the high conformance between functional and effective connectivity (spectral DCM with all modes). The plot in the left panel illustrates the validity of parameter estimates when we used m = 10 modes for every participant, relative to using an optimal number of modes for each subject. We again see a high correlation between the estimated connectivity parameters (rho = 0.94). The right panel plots functional connectivity against effective connectivity, which unsurprisingly showed a strong correlation (rho = 0.70).
<b>Figure 5.</b>
Figure 5.
This figure illustrates the sparse structure of effective connectivity after applying Bayesian model reduction to eliminate redundant connections. Top row: These three effective connectivity matrices correspond to the full or parent estimate for this particular subject (A), the equivalent matrix following Bayesian model reduction with 10 prior modes (B), and, finally (on the right) after eliminating redundant connections (shown in dark black, which are the majority of the connections here) with Bayesian model reduction (C). Lower row: These show different characterizations of symmetric and asymmetric connectivity. The left panel (D) shows the functional connectivity matrix associated with (or generated by) the (reduced) effective connectivity on the upper right. The effective connectivity has been separated into symmetric (E) and antisymmetric components (F), in the lower middle and right panels respectively. Note the sparse nature of effective connectivity, in relation to functional connectivity (when comparing the lower left and middle panels). This difference illustrates the general phenomena that functional connections can be mediated vicariously via indirect effective connections.
<b>Figure 6.</b>
Figure 6.
This figure shows the 36 ROIs (Raichle, 2011) that form seven large-scale brain modes or intrinsic networks. The graphics show a typical participants (same as in Figure 5) inverted graph after applying Bayesian model reduction to connections. The brain regions, represented as balls, are color-coded for various networks. The edges or connections are shown by directed arrows where the width of the arrows reflects the strength of the coupling. The color of the arrows represents the excitatory (green) and inhibitory (red) coupling among neuronal populations. We show the brain in sagittal (A), coronal (B), and axial (C) views.
<b>Figure 7.</b>
Figure 7.
This figure shows the averaged functional (A) and effective connectivity (B) over 19 subjects. The diagonal for the functional connectivity represents the correlation of each region with itself. The correlations within each network are quite distinctive, and the relationship between networks is visually evident. We see similar patterns in the effective connectivity matrix but there are clear asymmetries in the connectivity. We have also shown averaged effective connectivity matrix after Bayesian reduction and binarization (C) and when the weights are retained (D).
<b>Figure 8.</b>
Figure 8.
This figure is in the same format as Figure 7. The graphics show the averaged functional (A) and effective connectivity (B) over 19 subjects after down-sampling the 36 ROIs to the seven networks or modes. For the seven modes, we have also plotted averaged effective connectivity matrix after Bayesian reduction and binarization (C) and when the weights are retained (D).
<b>Figure 9.</b>
Figure 9.
This figure shows the hemispheric asymmetries as a scatter plot, using the averaged effective connectivity estimates as shown in Figure 7B. We used nodal in-strengths and out-strengths to identify these asymmetries. The in-strength summarizes the sum of all weighted connections entering the node, while the out-strength is the sum of all the weighted connections going out from a particular node. On the scatter plot, regions that lie above the diagonal line are net senders or sources, whereas regions that lie below the diagonal line are the net receivers or sinks.
<b>Figure 10.</b>
Figure 10.
This figure shows the hemispheric asymmetries as a bar plot based on the effective connectivity estimates after Bayesian model reduction as shown in Figure 7D. The nodal in-strength and out-strength are calculated as in Figure 9.

Similar articles

  • Construct Validation of a DCM for Resting State fMRI
    A Razi et al. Neuroimage 106, 1-14. PMID 25463471.
    Recently, there has been a lot of interest in characterising the connectivity of resting state brain networks. Most of the literature uses functional connectivity to exam …
  • On Nodes and Modes in Resting State fMRI
    KJ Friston et al. Neuroimage 99 (100), 533-47. PMID 24862075. - Review
    This paper examines intrinsic brain networks in light of recent developments in the characterisation of resting state fMRI timeseries--and simulations of neuronal fluctua …
  • Regression DCM for fMRI
    S Frässle et al. Neuroimage 155, 406-421. PMID 28259780.
    The development of large-scale network models that infer the effective (directed) connectivity among neuronal populations from neuroimaging data represents a key challeng …
  • Network Discovery With DCM
    KJ Friston et al. Neuroimage 56 (3), 1202-21. PMID 21182971.
    This paper is about inferring or discovering the functional architecture of distributed systems using Dynamic Causal Modelling (DCM). We describe a scheme that recovers t …
  • fMRI in Non-human Primate: A Review on Factors That Can Affect Interpretation and Dynamic Causal Modeling Application
    DB Jovellar et al. Front Neurosci 13, 973. PMID 31619951. - Review
    Dynamic causal modeling (DCM)-a framework for inferring hidden neuronal states from brain activity measurements (e. g., fMRI) and their context-dependent modulation-was d …
See all similar articles

Cited by 15 PubMed Central articles

See all "Cited by" articles


    1. Biswal B. B., Mennes M., Zuo X.-N., Gohel S., Kelly C., Smith S. M., … Milham M. P. (2010). Toward discovery science of human brain function. Proceedings of the National Academy of Sciences, 107, 4734–4739. - PMC - PubMed
    1. Breakspear M. (2004). “Dynamic” connectivity in neural systems: Theoretical and empirical considerations. Neuroinformatics, 2(2), 205–226. 10.1385/NI:2:2:205 - DOI - PubMed
    1. Bullmore E., & Sporns O. (2009). Complex brain networks: Graph theoretical analysis of structural and functional systems. Nat Rev Neurosci, 10(3), 186–198. 10.1038/nrn2575 - DOI - PubMed
    1. Carlson R. (1999). Inverse eigenvalue problems on directed graphs. Transactions of the American Mathematical Society, 351(10), 4069–4088. 10.1090/s0002-9947-99-02175-3 - DOI
    1. Chung F. (2005). Laplacians and the Cheeger inequality for directed graphs. Annals of Combinatorics, 9(1), 1–19. 10.1007/s00026-005-0237-z - DOI

LinkOut - more resources