A conditional Granger causality model approach for group analysis in functional magnetic resonance imaging

Abstract

Granger causality model (GCM) derived from multivariate vector autoregressive models of data has been employed to identify effective connectivity in the human brain with functional magnetic resonance imaging (fMRI) and to reveal complex temporal and spatial dynamics underlying a variety of cognitive processes. In the most recent fMRI effective connectivity measures, pair-wise GCM has commonly been applied based on single-voxel values or average values from special brain areas at the group level. Although a few novel conditional GCM methods have been proposed to quantify the connections between brain areas, our study is the first to propose a viable standardized approach for group analysis of fMRI data with GCM. To compare the effectiveness of our approach with traditional pair-wise GCM models, we applied a well-established conditional GCM to preselected time series of brain regions resulting from general linear model (GLM) and group spatial kernel independent component analysis of an fMRI data set in the temporal domain. Data sets consisting of one task-related and one resting-state fMRI were used to investigate connections among brain areas with the conditional GCM method. With the GLM-detected brain activation regions in the emotion-related cortex during the block design paradigm, the conditional GCM method was proposed to study the causality of the habituation between the left amygdala and pregenual cingulate cortex during emotion processing. For the resting-state data set, it is possible to calculate not only the effective connectivity between networks but also the heterogeneity within a single network. Our results have further shown a particular interacting pattern of default mode network that can be characterized as both afferent and efferent influences on the medial prefrontal cortex and posterior cingulate cortex. These results suggest that the conditional GCM approach based on a linear multivariate vector autoregressive model can achieve greater accuracy in detecting network connectivity than the widely used pair-wise GCM, and this group analysis methodology can be quite useful to extend the information obtainable in fMRI.

Figure 1

BOLD response at both amygdalae in both conditions. Only the left amygdala decreases over time in the emotion condition but not in the identity condition. BOLD responses are derived from left and right amygdala activation clusters for the contrasts emotion vs. control and identity vs. control.

Figure 2

“Glass brain” showing main clusters of activation with a threshold of t(11)>4.0. Left inferior prefrontal sulcus, right amygdala, and anterior cingulate cortex activations for the group illustrated on this rendered 3D brain. The Granger causal connectivity network was constructed in which the thickness of connecting arrows indicated the strengths of the causal influences in both conditions (p<0.05).

Figure 3

The directed influence with the sub-network, which is composed of ACC (sACC and pACC) and amygdala (left and right). All Granger causalities have been calculated within itself over four repeated blocks in the emotion condition. P means pACC, S means sACC, R means right amygdala and L means left amygdala. The connecting arrows indicate Granger causal directionality.

Figure 4

Habituation. The peak BOLD response habituates at the left amygdala in the emotion condition. Peak response = mean % signal change values for 9-18s time points. Responses derived from left amygdala cluster and Granger causality from pACC/sACC to left amygdala is presented for the contrast. Negative number indicates opposite Granger causality directionality.

Figure 5

RSNs detected by kernel-ICA. RSN a is visual network. RSN b is the core network. RSN c is auditory network. RSN d is central-executive network. RSN e is motor-sensory network. RSN f is DMN. RSN g is self-referential network.

Figure 6

DMN is mainly composed of medial temporal lobes, bilateral inferior parietal lobes (IPL), medial prefrontal cortex (mPFC), and posterior cingulate cortex (PCC) etc.

Figure 7

Four ROIs and causality within DMN. A. Time series in each ROIs are extracted from seed a, seed b, seed c, seed d by region growing method. B. The lines with arrows represent the coupling Granger causality.

Figure 8

A. Causality between DMN components and other RSNs. The lines with arrows represent the coupling Granger causality. RSN a is excluded for the detection of no significance; B. Causality between entire DMN and other RSNs. The lines with arrows represent the coupling Granger causality. RSN a is excluded for the detection of no significance.