The simple fact that any two time series become perfectly anti-correlated when their global signal is regressed from each should give cause for concern when interpreting anti-correlations. If the first time series contains a signal modulation of interest, the second will be negatively correlated with the first after global signal regression, regardless of the signal fluctuations it contains. Extending this concept to multiple time series, the theory demonstrates that global signal regression changes voxel time series such that approximately half become negatively correlated with a seed voxel. Due to the circularity of the technique (i.e., deriving a nuisance regressor from the data itself), all voxels could have similar interesting signal fluctuations but will display a range of seed voxel correlation values from highly positive to highly negative after its implementation. These findings alone should cause fMRI researchers to question the efficacy of this technique as a correction tool.
Resting state data are unique in that the researcher does not have a priori knowledge of task signal modulations. The simulations and breath holding data yield an insight into the effect global signal regression has on known fluctuations. For example, the spatial extent simulations show that time series in noise voxels outside an ROI containing resting state fluctuations become negatively correlated with those fluctuations when global signal regression is implemented. Not only does global signal regression reduce correlations in areas containing fluctuations, it introduces negative correlations in pure noise voxels. The degree of negative correlation depends on the extent of the ROI and the signal-to-noise ratio of the fluctuations. These simulations demonstrate that if there are large scale resting state networks in the brain, their influence on the global signal will force purely noise voxels to become negatively correlated with the resting network (e.g. the PCC region). When the SNR of the fluctuations is suitably high, only ~ 10% of the brains voxels need contain these signal modulations for the remaining voxels to become negatively correlated. The information in suggests that in resting state data the task-negative network is large enough for this situation to occur.
The purpose of global signal regression is to remove any confounds that may mask neuronally-induced fluctuations. When confounds and resting state fluctuations are of similar frequency, as in the Breath Holding and Visual Data, their relative phases can severely affect the detectability of activation. In seed connectivity analyses where an explicit breathing confound exists, if global signal regression was completing the intended correction properly, one would expect the resulting connectivity measure distributions to resemble those of the VisOnly condition. However, this is not the case: global signal regression introduces negatively correlated voxels into the visual cortex. Even when no relationship between the global confounds and the fluctuations-of-interest exist (as in the RandVis condition), global signal regression does not sharpen the connectivity measure distributions as it should. These data demonstrate that global signal regression does not perform a correction that reveals the underlying neuronally-induced fluctuations.
In the Breath Holding and Visual Data, since the visual cortex represents such a small proportion of voxels it is expected that the seed voxels drawn from this area should bear little relation to most other voxels in the brain. When the breathing task introduces a global confound, whole brain connectivity measure distributions are skewed. Removing the global confound with regression results in distributions that are bell-shaped. This is unsurprising since the time series resulting from global signal regression are the residuals from a GLM analysis that assumes a Gaussian noise model. However, the spatial pattern of activations and deactivations varies depending on the breathing manipulation (see ). This indicates that global signal regression does not remove the global breathing confound successfully. Although the visual cortex remains the most positively correlated area (as it should), negatively correlated areas can be situated in vastly different regions after global signal regression, suggesting that, in this case, the negative correlations are not neuronal in origin but an artefact of the global signal regression method.
The task-positive network is not evident in resting state data until the global signal is regressed from each time series. This is not a thresholding artefact; and demonstrate that lowering the threshold in the uncorrected map would not reveal negatively correlated voxels in the task-positive network. If it is possible to see positive correlations to the PCC before global signal regression, why are the negative correlations not visible? The standard answer is that the uninteresting, confounding fluctuations which are removed by the technique overshadow the underlying neuronally-induced fluctuations. However, removal of low-frequency confounds due to breathing depth changes using RVT correction barely alters correlation values. Even if RVT correction does not remove all global signals of interest, it is a global confound that is known to overlap well with the default mode network and correlates significantly with the global signal at CC = −0.5±0.13 (Birn et al., 2006
). One would expect the RVT technique to somewhat reduce correlation values in the task-positive network.
There also exists a large amount of variability across subjects in the correlation values in the task-positive areas before any correction is performed. Comparing these values with the histograms in shows that subjects with the lowest average correlation values in task-positive areas (see Subjects 4 and 11) have distributions that extend the furthest into negative values. Voxels that become the most strongly anti-correlated after global signal regression are the voxels that were least correlated prior to the regression. This suggests that when global signal regression distorts the distribution to become bell-shaped and centred around zero (as shown experimentally), voxels in the task-positive network always remain on the negative tail. Depending on the shape of this distribution, their average correlation value before correction can be both positive and negative. After global signal regression, the variability in these values is removed since all distributions are forced to be bell-shaped (thus satisfying the theoretical prediction that correlation values sum to less than zero). This implies that the drastic reductions of the correlation values in the task-positive network are due to the mathematics of converting a skewed distribution into a bell-shaped distribution centred on zero. Task-positive areas may be converted into negative correlations simply because they are the least correlated with the PCC to begin with.
If the global signal obscures fluctuations related to neuronal firing, why does the regression of this signal not uncover other positively correlated areas? Large areas of the brain are significantly positively correlated with the PCC before removal of the global signal. The task-negative network produced after global signal regression is always a subset of these positive areas. The areas that subsequently comprise the task-negative network can largely be determined by raising the threshold on the correlation maps without global signal regression (see ). The global correction does not reveal any new areas that are positively correlated with the PCC. If the neurons firing in the PCC produced fluctuations that were not correlated to the global confound but were overshadowed by such a confound, we would not expect the positively correlated areas to be identical before and after global signal regression. This suggests that either the global signal is highly correlated to the PCC neuronal fluctuations or that fluctuations due to neuronal firing in the PCC are visible above the global signal confound. If the former were true then neuronal fluctuations in the PCC would be removed by global signal regression. If the latter were true, then anti-correlated networks should be visible above the global signal confound also. Since the task-negative network remains highly correlated after global signal regression and anti-correlated networks are not visible before, this suggests that a shifting of distributions by the technique is the most likely explanation for negatively correlated regions.
If negatively correlated voxels are an artefact of the correction technique, why are they in spatially contiguous areas and not randomly scattered throughout the brain? We have shown experimentally that global signal regression forces a skewed distribution to become bell-shaped, centred on zero and that voxels on the negative tail of this skewed distribution become the most negatively correlated. The reason that the task-positive network becomes anti-correlated after global signal regression is because it is the least correlated before. But why is it the least correlated? One possibility is that the correlation is reduced by a spatial heterogeneity in the “global” respiration related signal changes. Studies have shown that fMRI signal induced by variations in breathing depth (also reflected in variations in the end-tidal CO2
) have spatial structure and are most prominent in areas associated with the default mode network (Birn et al., 2006
; Wise et al., 2004
). When seed voxels are chosen from the PCC, an area in the default mode network that is highly contaminated with breathing rate related confounds, areas outside the default mode network such as the task-positive regions will likely be the least correlated with the seed voxels. Also, phase differences can exist between time series drawn from the task-negative and task-positive areas and that these time series can have a low correlation value between them even though both are highly correlated with the global signal (see ). This could be due to differences in vascular supply or haemodynamic properties that are unrelated to neuronal firing. The phase simulations show that this technique can introduce negative correlations between time series that display identical resting state fluctuations that are slightly shifted in time. The largest phase change in these simulations corresponds toa time delay of between 1.25 s and 12.5 s for frequencies between 0.01 Hz and 0.1 Hz. Although values on the upper end of this range are unlikely to be accounted for by haemodynamic delays alone, values on the lower end are within range of natural haemodynamic delay variation (Aguirre et al., 1998b
; Handwerker et al., 2004
; Saad et al., 2001
) suggesting that areas whose neurons fluctuate simultaneously but whose haemodynamics vary temporally could display anti-correlations after global signal regression. Furthermore, underlying neuronal delays in low-frequency fluctuations on the order of seconds between networks would display high correlations with each other neuronally but would be deemed anti-correlated after global signal regression. (It should also be noted that pi/4 was an arbitrarily chosen phase delay and that if the maximum delay was smaller, similar correlation maps would be obtained). Spatial smoothing tends to increase the correlation of voxel time series with the global signal (Aguirre et al., 1997
) and could also help consolidate sparsely positioned negatively correlated voxels into contiguous regions.
If global signal regression is a poor choice of correction method, which techniques should be used to remove noise confounds, be they physiologically related or not? The circularity of choosing a noise regressor from the data itself leads to the problems identified in this study. Confounding regressors derived from external measures, such as pulse oximeter, respiration belt and end-tidal CO2
readings, should not suffer from this problem. There exist other techniques that derive regressors from regions in the fMRI data, such as the ventricles, white matter, blood vessels and CSF, that may cause less of a problem. Studies have shown that anti-correlated networks do not exist after regression of movement, ventricle and white matter signals (Fox et al., 2008
; Weissenbacher et al., 2008
) and therefore these correction methods may not cause the same artefact as global signal regression. If a regressor is uncontaminated by the task in which we are interested (in this case the resting state fluctuations), then it may not introduce anti-correlations. However, the greater the correlation with the global signal, the larger a problem such a regression may cause by reducing true neuronally-related correlations and by increasing numbers of anti-correlated voxels. Using global signal regression to remove physiological noise clearly has confounding factors. While the optimal way to remove physiological noise isn’t clear, many of the best current methods require collection of cardiac and respiration time courses. Collecting such data should become a standard part of resting state connectivity studies.
This study has concentrated on correlation-based analyses, the most popular method employed to detect resting state networks. Other methods have been used to support the idea that the brain is organized into independent neuronal networks, for example, k
-means clustering (Golland et al., 2008
) or ReHo analysis (Long et al., 2008
). However, removing the global signal is often included as a preprocessing step. An alternative technique that is now frequently used to study functional connectivity is independent component analysis or ICA (Birn et al., 2008
; Calhoun et al., 2005
; Kiviniemi et al., 2003
; Kiviniemi et al., 2004
; Long et al., 2008
; McKeown et al., 2003
; McKeown et al., 1998
; McKeown and Sejnowski, 1998
). With ICA, statistically independent maps and their associated time courses are extracted from the data. If the global signal is not removed before this technique is employed, it must be assigned to one or more components. Therefore, ICA may have an inherent global signal regression built into it. The time course for each component determines the behaviour of the network beyond all other components, including those that represent the global signal. Therefore, task-negative and task-positive networks determined by ICA may have associated time courses that artificially appear to be anti-correlated.
Global signal regression not only introduces anti-correlated regions in the brain, it also reduces positive correlation values. If such a simple mathematical process used as a pre-processing step affects correlation values so drastically, can we trust correlation techniques to give a true measure of connectivity in the brain? What do correlation values actually mean? In a clinical context, do small differences in connectivity measures between patient groups and controls really reflect deficits in neuronal connectivity? More importantly, can the global signal regression introduce false differences between these two groups? These questions must be taken into account before we can truly understand resting state neuronal networks in the brain, their relationships to each other and their importance in clinical conditions.