Multivariate Granger causality analysis of fMRI data

Abstract

This article describes the combination of multivariate Granger causality analysis, temporal down-sampling of fMRI time series, and graph theoretic concepts for investigating causal brain networks and their dynamics. As a demonstration, this approach was applied to analyze epoch-to-epoch changes in a hand-gripping, muscle fatigue experiment. Causal influences between the activated regions were analyzed by applying the directed transfer function (DTF) analysis of multivariate Granger causality with the integrated epoch response as the input, allowing us to account for the effects of several relevant regions simultaneously. Integrated responses were used in lieu of originally sampled time points to remove the effect of the spatially varying hemodynamic response as a confounding factor; using integrated responses did not affect our ability to capture its slowly varying affects of fatigue. We separately modeled the early, middle, and late periods in the fatigue. We adopted graph theoretic concepts of clustering and eccentricity to facilitate the interpretation of the resultant complex networks. Our results reveal the temporal evolution of the network and demonstrate that motor fatigue leads to a disconnection in the related neural network.

Figure 1

A time series from M1 overlaid on the activation paradigm. Red: 3.5 s contraction. Blue: 6.5 s intertrial interval. [Color figure can be viewed in the online issue, which is available at www.interscience.wiley.com.]

Figure 2

A sample activation map obtained from the fatigue motor task showing the regions of interest. ▪ SMA, ▴M1, * S1, ♥ P, ◂ PM.

Figure 3

Left: Original fMRI time series. Right: Summary time series (yellow patch shows the first time window). [Color figure can be viewed in the online issue, which is available at www.interscience.wiley.com.]

Figure 4

The temporal variation of significance value α (α = 1−P) for all possible connections between the ROIs. The direction of influence, as indicated by the black arrow, is from the columns to the rows. The red bars indicate the connections that passed the significance threshold of α = 0.95 and the green ones that did not. [Color figure can be viewed in the online issue, which is available at www.interscience.wiley.com.]

Figure 5

A network representation of Figure 4. The significant links are represented as solid arrows and the P‐value of the connections are indicated by the width of the arrows. The major node in each window is also indicated as dark ovals.

Figure 6

Thresholded difference networks. Left: window 1–window 2. Right: window 2–window 3. Red indicates positive difference whereas blue indicates negative difference.

Figure 7

Networks obtained from raw time series for the three windows. The significant links (P <0.05) are represented as solid arrows and the P‐value of the connections are indicated by the width of the arrows.