GCM Help Pages

Before you start
Computing GCMs
Viewing GCMs
Interpreting GCMs
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Interpreting GCMs

Generally, looking at a dGCM (or one of its variants), a close to undeniable statement one can make about a positive voxel in the map is that past BOLD measurements (1 or maybe more TRs into the past) of the reference VOI helps predicting later measurements of that voxel (when linear autoregressive models are used for those predictions). Similarly, a close to undeniable statement one can make about negative voxels in the maps is that measured volumes of those voxels help predicting later measurements of the reference VOI. What that means exactly in the context of your measurements during your experiment is up to you. It could mean negative voxel B contains a blood-supplying artery that serves the reference VOI A. It could also mean that slice scan time correction was performed unaccurately with wrong parameters, such that simultaneous activity in A and B was wrongly shifted backward in time only for A. Or it could mean that A and B generally covary in their activity and microvascular differences generally cause a larger hemodynamic response delay in B, delaying its fluctuations in the BOLD signal with respect to A. Generally, however, given all preprocessing was correctly performed (see Before you start) its not unreasonable to assume that neuronal populations in A influence, affect, or modulate neuronal populations in region B. This final interpretation can be of great value in cognitive neuroscience investigations, since it allows us to speak of the interactions between neural systems and how networks of areas might collaborate in subserving cognitive functions. Nevertheless, some reservations and cautions are in order when choosing this final interpretation.

Sensitivity of GCMs depends on volume TR

GCM is based on dynamic models (VAR models) of temporal signal structure and interrelations. The estimation of such models is critically dependent on the temporal resolution in your data, that is, on your (volume) TR. Generally, The lower your TR is, the faster the interactions that can still be detected. The slower the interactions between cortical areas for a given task, the longer the TR can be to still detect them. Although simulations have suggested (Roebroeck et al., NeuroImage 2005) that interactions that have a temporal delay that is smaller than the sampling interval (TR) can still be detected, they also showed that the detection capacity rapidly decreases as the sampling interval gets further away from the influence delay.

GCMs can only be interpreted with respect to the reference VOI

Since a GCM is computed using the time-course of a reference VOI, interpretations of the maps pertaining to pairs of regions other than the reference VOI should be made with caution. Generally, all negative regions in a dGCM influence the reference VOI, which, in turn, influences all positive regions. The only other statement that a dGCM supports is that all negative regions indirectly influence all positive regions via the reference VOI.

Influences can be indirect or caused by a third region

A dGCM can give no assurance that a given influence, say from reference A to positive region B, is a direct influence. The predictive value of measurements at A for later measurements at B might occur because region A influences region C, which, in turn, modulates B. Or, it might be that a region D influences both A and B, at different time-lags. Since neither C nor D were taken into account when computing the dGCM (only the reference and voxel are entered in a bivariate model), all of these cases will show up as (spurious) influence from A to B. A partial solution when you suspect that a region C or D might be an intervening region or a common source of input, is to compute a DGCM with C or D as a reference. Investigating this map can tell you whether, e.g. A is negative and B is positive in C's map, thus confirming an intervening role for C.

GCMs give the dominant direction of influence

Because dGCMs are a difference of Ref2Vox-Vox2Ref (for statistical reasons, see Roebroeck et al., NeuroImage 2005) they will not have a high value for an equivalent birectional influence between two regions. That is, if your reference VOI A both influences another region B, and is influenced by that same region, the two will 'cancel out' and B might not show up in A's dGCM. If one of the two influence directions is stronger, then that dominant direction will be the one that shows up in the map. For instance, when reference VOI A influences region B more strongly than region B influences A (say, in a modulatory feedback situation), B will appear in the positive part of A's dGCM. On the up side of things, if your reference region A both influences a region B and is influenced by a region C very near to B, As dGCM can in principle separate B and C as fundamentally different regions were they might have otherwise been pooled into one region. If you want to have a look at the separate Ref2Vox and Vox2Ref maps, despite being statistically over-liberal (again, see Roebroeck et al., NeuroImage 2005), you can do so (see Advanced).

GCM intensity gives mixed information on strength and delay of influence

Lets say that in the dGCM for reference VOI A, two regions B and C are both in the positive part of the map. However, the positive values at B (the intensity) is higher than at C. One might conclude that that there is 'more' influence from A to B than there is from A to C. This not completely incorrect, as long you realize what 'more' might mean. Simulations (reported in Roebroeck et al., NeuroImage 2005, yes again) have shown that both stronger influences (i.e. greater efficacy), and influences at a greater time-delay (in the 10-100ms range) will yield higher computed fMRI Granger Causality values, when sampled at (realistic) TRs greater than the influence delay. Thus, 'more' influence might mean 'stronger' or 'more delayed' or both. As a related issue, GCM maps computed one data with different TRs (even if all else is equal) are generally incompatible, their values can not be quantitatively compared, because Granger causality values are dependent on sample rates.

Influences modulated by experimental conditions are most reliable

Granger Causality from one region A to another B found in a dGCM, in principle still leaves open one important alternative interpretation: that differences in hemodynamics are the underlying reason for this finding. It could be that A and B generally covary in their activity and microvascular differences generally cause a larger hemodynamic response delay in B, delaying its fluctuations in the BOLD signal with respect to A, or vice versa. However, a Granger causal influence in a dGCM can be assigned to interactions between neuronal population, if that influence can be shown to be modulated by experimental conditions. If, for instance, an influence between region A and B is found when the subject has to pay attention to houses in a sequence of house and face stimuli, but is not found in a passive viewing condition, the influence most likely reflects real neural interactions (that presumably have something to do with attentional modulation). The reasoning is simply that structural hemodynamic variations could not vary with attentional condition, and are thus discarded as an underlying reason for the influence. The most rigid an reliable influences in dGCMs are those that vary with experimental condition. This is one of the important reasons for the condition-structure in the computation of GCMs, that allows you to see GCMs from different conditions 'side-by-side'.