GCM Help Pages
Main Before you start Computing GCMs Viewing GCMs Interpreting GCMs Advanced More Help	Main Introduction Granger causality mapping is a technique which explores directed influences (effective connectivity) between distinct regions in fMRI data. See Roebroeck, Formisano, Goebel (Neuroimage 25(1):230-42, 2005) for a detailed description of the technique. In short, a Granger Causality Map (GCM) is computed with respect to a single selected reference region, and maps both sources of influence to the reference region and targets of influence from the reference region over the brain. Justifying its name, GCM makes use of the concept of Granger causality to define what 'influence' or 'causality' means in the context of fMRI time-series. A (discrete) time-series X[t] is said to Granger cause a (discrete) time-series Y[t], if the past of X improves the prediction of the current value of Y, given that all other relevant sources of influence (at the very least Y's own past) have been taken into account. Analogously, and independently, Granger causality from Y to X can be defined. Finally, instantaneous influence (correlation) between X and Y is said to exist when values X[t] improve predictions of contemporaneous values Y[t] (or vice versa, instantaneous correlation is symmetric), taking into account all other relevant sources of influence (at the very least the past of both X and Y). Temporal information in the data is used to define the existence and direction of influences without a directed graph model of assumed regional connections. These definitions can be applied to fMRI time-series with the use of Vector Auto-Regressive (VAR) models. The GCMPlugin maps influence (effective connectivity) over the brain for a given reference region by repeatedly (for every voxel in a volume) pairing the time-course of the reference region with the time-course of a voxel and computing the three influence terms: Influence (Granger causality) from the reference region to the voxel (Ref2Vox) Influence (Granger causality) from the voxel to the reference region (Vox2Ref) Instantaneous correlation between reference region and voxel without a direction (Inst) The GCMPlugin allows each of the three resulting maps (GCMs) to be viewed. However, in Roebroeck et al. (2005) it is argued that the most unbiased view on directed interactions is given by the the difference Ref2Vox-Vox2Ref (the dGCM), which has a positive value at voxels where influence from the reference region dominates (i.e. that are targets of influence from the reference region) and a negative value at voxels where influence to the reference region dominates (i.e. that are sources of influence to the reference region).

GCM Help Pages

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Before you start
Computing GCMs
Viewing GCMs
Interpreting GCMs
Advanced
More Help

Main

Introduction

Granger causality mapping is a technique which explores directed influences (effective connectivity) between distinct regions in fMRI data. See Roebroeck, Formisano, Goebel (Neuroimage 25(1):230-42, 2005) for a detailed description of the technique. In short, a Granger Causality Map (GCM) is computed with respect to a single selected reference region, and maps both sources of influence to the reference region and targets of influence from the reference region over the brain. Justifying its name, GCM makes use of the concept of Granger causality to define what 'influence' or 'causality' means in the context of fMRI time-series. A (discrete) time-series X[t] is said to Granger cause a (discrete) time-series Y[t], if the past of X improves the prediction of the current value of Y, given that all other relevant sources of influence (at the very least Y's own past) have been taken into account. Analogously, and independently, Granger causality from Y to X can be defined. Finally, instantaneous influence (correlation) between X and Y is said to exist when values X[t] improve predictions of contemporaneous values Y[t] (or vice versa, instantaneous correlation is symmetric), taking into account all other relevant sources of influence (at the very least the past of both X and Y). Temporal information in the data is used to define the existence and direction of influences without a directed graph model of assumed regional connections. These definitions can be applied to fMRI time-series with the use of Vector Auto-Regressive (VAR) models.

The GCMPlugin maps influence (effective connectivity) over the brain for a given reference region by repeatedly (for every voxel in a volume) pairing the time-course of the reference region with the time-course of a voxel and computing the three influence terms:

Influence (Granger causality) from the reference region to the voxel (Ref2Vox)
Influence (Granger causality) from the voxel to the reference region (Vox2Ref)
Instantaneous correlation between reference region and voxel without a direction (Inst)

The GCMPlugin allows each of the three resulting maps (GCMs) to be viewed. However, in Roebroeck et al. (2005) it is argued that the most unbiased view on directed interactions is given by the the difference Ref2Vox-Vox2Ref (the dGCM), which has a positive value at voxels where influence from the reference region dominates (i.e. that are targets of influence from the reference region) and a negative value at voxels where influence to the reference region dominates (i.e. that are sources of influence to the reference region).