Learning partially directed functional networks from meta-analysis imaging data

Abstract

We propose a new exploratory method for the discovery of partially directed functional networks from fMRI meta-analysis data. The method performs structure learning of Bayesian networks in search of directed probabilistic dependencies between brain regions. Learning is based on the co-activation of brain regions observed across several independent imaging experiments. In a series of simulations, we first demonstrate the reliability of the method. We then present the application of our approach in an extensive meta-analysis including several thousand activation coordinates from more than 500 imaging studies. Results show that our method is able to automatically infer Bayesian networks that capture both directed and undirected probabilistic dependencies between a number of brain regions, including regions that are frequently observed in motor-related and cognitive control tasks.

Figure 1

A simple Bayesian network representing four variables.

Figure 2

Two Markov-equivalent networks describing interdependencies between three variables.

Figure 3

Equivalence classes (CPDAGs) of three randomly generated small Bayesian networks.

Figure 4

(a) Size of training data sets required for learning a graph structure with up to 5 nodes. (b) Number of times each network connection was detected out of 100 trials of structure learning from randomly generated networks with 3 to 5 nodes. Connections belonging to the correct CPDAG are plotted in red.

Figure 5

Number of times each network connection was detected out of 100 trials of structure learning from randomly generated networks with up to 16 nodes. Connections belonging to the correct CPDAG are plotted in red.

Figure 6

Top: Two Bayesian networks encoding non-contradictory statistical dependencies between 4 nodes. Bottom: ’Mixture’ of the two networks.

Figure 7

Top: Two Bayesian networks encoding partially contradictory statistical dependencies between 4 nodes. Bottom: ’Mixing’ the two networks results in a graph that does not meet the requirements of a DAG.

Figure 8

Axial and sagittal views exemplifying the result from ALE as first meta-analysis processing step.

Figure 9

Axial and sagittal views of the 13 most often co-occurring regions determined by the replicator process, plus right anterior insula. Slices correspond to those presented in Figure 8.

Figure 10

Most reliably detected connections in the CPDAG of cortical areas determined from data set 1.

Figure 11

Most reliably detected connections in the CPDAG of cortical areas determined from data set 2.

Figure 12

Most reliably detected connections in the CPDAG of cortical areas determined from data set 3. Connections that were detected in 50%, 35%, and 25% of all trials are plotted in bold, medium, and thin lines, respectively.