The impact of global signal regression on resting state correlations: are anti-correlated networks introduced?

Abstract

Low-frequency fluctuations in fMRI signal have been used to map several consistent resting state networks in the brain. Using the posterior cingulate cortex as a seed region, functional connectivity analyses have found not only positive correlations in the default mode network but negative correlations in another resting state network related to attentional processes. The interpretation is that the human brain is intrinsically organized into dynamic, anti-correlated functional networks. Global variations of the BOLD signal are often considered nuisance effects and are commonly removed using a general linear model (GLM) technique. This global signal regression method has been shown to introduce negative activation measures in standard fMRI analyses. The topic of this paper is whether such a correction technique could be the cause of anti-correlated resting state networks in functional connectivity analyses. Here we show that, after global signal regression, correlation values to a seed voxel must sum to a negative value. Simulations also show that small phase differences between regions can lead to spurious negative correlation values. A combination breath holding and visual task demonstrates that the relative phase of global and local signals can affect connectivity measures and that, experimentally, global signal regression leads to bell-shaped correlation value distributions, centred on zero. Finally, analyses of negatively correlated networks in resting state data show that global signal regression is most likely the cause of anti-correlations. These results call into question the interpretation of negatively correlated regions in the brain when using global signal regression as an initial processing step.

Figures

Fig. 1

The results of the phase simulation are shown. Each panel displays correlation values on 64×64 voxel grid. The time series for each voxel consisted of a sine wave representing resting state fluctuations with a frequency of 0.1 Hz and a phase that varied for voxels progressively from 0 to π/4 along the x-axis. Random Gaussian noise with a mean of 0 and a standard deviation varying from 0 to 10 along the y-axis was added. The first column shows correlations to a 0.1 Hz sine wave with zero phase. The remaining columns depict correlation values to a time series averaged over the ROIs shown. This figure demonstrates that small phase differences between time series can lead to negative correlations after global signal regression.

Fig. 2

The spatial extent simulations show how correlation values vary after global signal regression as a function of the percentage of voxels that contain resting state fluctuations. Red lines represent the average correlation over voxels that contain a sine wave (representing a resting state oscillation) whereas blue lines depict the average correlation over the remaining noise voxels. Both low SNR (amplitude of sine wave equals standard deviation of noise) and high SNR (amplitude of sine wave 10 times greater) simulations are shown, in solid and dashed lines respectively. Significance lines showing P<0.001 are depicted. These simulations demonstrate that the reduction of correlation values due to global signal regression is dependent on the number of voxels containing resting state fluctuations with greater spatial extent leading to a greater decrease. Voxels containing purely random noise become more negatively correlated as spatial extent increases.

Fig. 3

Correlation values averaged over the visual cortex and over subjects are shown for the combined breath holding and visual task. Each of the five conditions demonstrate how the relative phase of global (breath hold) and “resting state” (visual) signal changes affects the correlation measure with and without global signal regression (red and blue lines respectively). The significance levels for all comparisons were determined using paired t-tests: VisOnly P = 0.42, Synch P = 0.23, Synch + 10 s P = 8.9×10−6, Asynch P = 7.7×10−4, RandVis P = 0.045. When the phase of the breath hold and visual responses are the same (Synch + 10s condition), global signal regression causes a large reduction in correlation value in the visual cortex.

Fig. 4

The distributions of correlation values in the seed region correlation analyses are shown with each subject represented by a different colour. Each of the five rows displays one of the five breath holding and visual task conditions. Distributions drawn from only the visual cortex are displayed on the left with whole brain distributions on the right, for data with and without global signal regression. The distributions from the visual areas show that global signal regression is not revealing underlying neuronally-related BOLD signal changes as we would like it to. Distributions in the visual cortex are broadened instead of sharpened by this technique and negative correlations are introduced. The whole brain distributions on the right demonstrate that global signal regression forces a bell-shaped curve, centred on zero, regardless of the relative phase of global and “resting state” changes.

Fig. 5

Three axial slices of correlations with the PCC region averaged across subjects are shown for each of the Breath Holding and Visual Task conditions. Without global signal regression, correlation values can be high across the entire brain. The Asynch condition shows that this is not the case when global signal and “resting-state” fluctuations are out of phase. If global signal regression performed the intended correction, one would expect all resulting maps to be similar. Large variation exists in the pattern of activated and deactivated regions across the conditions.

Fig. 6

Correlations to a seed region in the PCC averaged across all subjects using a Fisher transform are shown with and without correction for the global signal. The task-positive network is visible only after global signal regression. Since global signal regression changes the distribution of correlation values (see Fig. 8), it would be incorrect to use the same threshold for both maps. To enable a fair comparison, we chose a correlation value such that all voxels that positively correlate to the PCC and that passed threshold would comprise 15% of the total number of voxels. Using these thresholds, the default mode network is visible both with and without global signal regression, but negatively correlated voxels are only visible after the global correction. Fig. 7 and the distributions in Fig. 8 demonstrate that lowering the threshold in the map that retains the global signal would not reveal negatively correlated voxels in the task-positive network.

Fig. 7

Average correlation values across the task-negative (top panel) and task-positive (bottom panel) regions are shown for all subjects. Three conditions are depicted: 1) without any global signal or RVT correction, 2) with RVT correction to remove low-frequency fluctuations related to breathing depth and 3) with global signal regression. RVT correction has little impact on correlation values in both the task-negative and task-positive areas. Before global signal regression, task-positive areas can be highly correlated with the PCC region with only two subjects showing small negative correlations. Global signal regression causes all task-positive areas to become negatively correlated and reduces the variability across subjects.

Fig. 8

The distribution of correlation values to the PCC across all voxels in the brain for each subject are shown before (top panel) and after (bottom) global signal regression is performed. As with the results shown in Fig. 4, global signal regression causes the distributions to become bell-shaped and centred on zero.