Elsevier

NeuroImage

Volume 44, Issue 3, 1 February 2009, Pages 893-905
NeuroImage

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

https://doi.org/10.1016/j.neuroimage.2008.09.036Get rights and content

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.

Introduction

Spontaneous fluctuations in blood oxygenation level dependent (BOLD) fMRI signals have recently aroused a large amount of interest in the fMRI literature (Fox and Raichle, 2007). These fluctuations are often correlated between functionally related areas and can occur either on top of task-induced signal modulations (Fox et al., 2006) or in the absence of an explicit task (Biswal et al., 1995). It has been hypothesized that correlated fluctuations reflect synchronized variations in the neuronal activity of discrete brain areas and are representative of functional connections within networks of the brain. Functional connectivity analyses can investigate these coherent signal fluctuations, characterized by their low frequency (∼ 0.1 Hz) (Lowe et al., 1998). By studying fluctuations at rest, researchers have claimed that the brain is intrinsically organized into dynamic, anti-correlated functional networks (Fox et al., 2005, Fransson, 2005, Greicius et al., 2003). The extent to which a commonly used correction method called global signal regression alters functional connectivity maps by introducing anti-correlated time series is the topic of this paper.

Biswal et al. first reported the correlation in fMRI signal fluctuations between the left and right motor cortices when the brain was at “rest” (Biswal et al., 1995). Subsequent studies have identified several consistent resting state networks, including motor, auditory, visual, attention and default mode (Damoiseaux et al., 2006, De Luca et al., 2006, Greicius et al., 2003). The default mode network is of particular interest since it appears to be more active during rest than during task (Raichle et al., 2001). It has been hypothesized that this activation is indicative of internal monitoring, e.g. “day-dreaming” or a “wandering mind” (Buckner et al., 2008, Mason et al., 2007). Early clinical studies have attributed disruptions in the connections between nodes of the default mode network to disorders such as Alzheimer's disease (Greicius et al., 2004), schizophrenia (Garrity et al., 2007), ADHD (Sonuga-Barke and Castellanos, 2007) and autism (Just et al., 2007, Kennedy et al., 2006).

The common assumption in most fMRI investigations of connectivity is that correlated fluctuations in resting state networks are neuronal in origin. However, other sources of fluctuations exist in fMRI data that are not directly related to local neuronal firing and have a largely physiological source. Cardiac pulsations and respiration-related artefacts can cause significant correlated signal changes in the vicinity of large blood vessels and throughout grey matter, obscuring spontaneous neuronal fluctuations (Lund et al., 2006). By measuring cardiac and respiratory traces during acquisition of fMRI data, the influence of the related physiological fluctuations can largely be removed, using retrospective correction techniques (Glover et al., 2000, Hu et al., 1995). Other techniques have been developed that do not require physiological recordings (Beall and Lowe, 2007, Chuang and Chen, 2001, Perlbarg et al., 2007). However, further physiological sources of noise in the fMRI signal remain uncorrected by these methods. In particular, low frequency BOLD fluctuations have been associated with changes in the level of arterial carbon dioxide (CO2) in the frequency range 0–0.05 Hz (Wise et al., 2004) resulting from changes in the breathed-volume (respiration volume over time — RVT) (Birn et al., 2006) and changes in the rate of cardiac pulsation at ∼ 0.08 Hz (Shmueli et al., 2007). These sources of noise can artificially inflate connectivity measures since they introduce global, spatial coherence across the brain.

Global signal regression, otherwise known as orthogonalization to the global signal, is often performed as a processing step in an attempt to account for several potential sources of physiological noise. In this technique, the global signal, calculated by averaging the time series over all voxels in the brain, is used as a regressor in a general linear model (GLM) to remove the associated variance (Desjardins et al., 2001, Macey et al., 2004). This technique assumes that fMRI experiments are concerned with local changes in neuronal activity and that global signals represent uninteresting sources of noise. However, this assumption is only accurate when the global signal and experimental conditions are orthogonal to each other, that is, uncorrelated. The majority of the methodology literature regarding global signal regression examines its effect on task paradigms. Whether findings from such research are applicable to seed-based connectivity studies is unknown.

The global signal correction technique has been widely used in the PET imaging literature to remove global blood flow fluctuations with some debate as to the appropriate removal method (Andersson et al., 2001, Arndt et al., 1996, Fox et al., 1988, Friston et al., 1990, Ramsay et al., 1993). It has been suggested that defining the global signal as the average over all voxels can introduce a bias since the resulting time course will not be orthogonal to the task-induced activations (Andersson, 1997, Strother et al., 1995). Given that voxels responding to the experimental task are included in the global regressor, this correction technique will significantly influence the results by underestimating true activation levels and by introducing deactivations.

The global signal explains a large proportion of spatial variance in PET imaging (Fox and Mintun, 1989, Friston et al., 1990). Whether removal of this global signal is prudent in fMRI studies of task-related activity is a matter of debate. In spatially smoothed fMRI data, the global signal was shown to be strongly influenced by the performance of a behavioural task but inclusion of this signal as a covariate did not reduce sensitivity (Aguirre et al., 1997). Also, including the global signal covariate in a general linear model reduced spatial coherence and subsequently stabilised false-positive rates (Zarahn et al., 1997). However it has also been demonstrated that if the global signal is strongly correlated with experimental manipulations, considerably different results may be obtained. Aguirre et al. analysed an fMRI dataset in which subjects made button presses to brief intermittent stimuli both with and without covariation for the global signal and found that global signal regression reduced the spatial extent and intensity of positively activated regions whilst introducing spurious negatively activated areas (Aguirre et al., 1998a). Interestingly, these negative regions map out what is now known as the default mode network, a network shown to be anti-correlated with attentional tasks (i.e., deactivated during attention demanding tasks). Although the authors state that these areas “did not have a significant relationship with the task”, global signal regression may have helped bring these true deactivations to light.

Five different methods of global normalization in fMRI were compared by Gavrilescu et al., namely grand mean session scaling, proportional scaling, ANCOVA, a masking method and an orthogonalization method (Gavrilescu et al., 2002). The orthogonalization method, first proposed by Desjardins et al. (2001), was shown to perform better than other methods and is essentially the same as the global signal regression technique. However, it can, nonetheless, decrease the sensitivity of statistical analyses and induce artefactual task deactivations. Using both a high and low arousal emotional task, Junghofer et al. showed that the validity of proportional global signal scaling varied as a function of the emotional arousal of the stimuli (Junghofer et al., 2005). The high arousal condition violated the assumption of orthogonality between the global regressor and the experimental condition leading to a reduction in positively activated areas and “widely distributed artificial deactivations”, none of which made sense in terms of known emotional and default mode areas.

It is clear that global signal regression can cause reductions in sensitivity and can introduce false deactivations in studies of task activation since the assumption of orthogonality can be violated when the experimentally-induced activations contaminate the global signal. By definition, the experimental condition in resting state data is undefined. Although it is known that resting state fluctuations are low-frequency, the exact timing, spatial extent and relative phase between areas are unknown and may vary from session to session. The degree of correlation between the global signal and the resting state fluctuations cannot therefore be determined, and thus global signal regression could lead to spurious results in seed voxel correlation analyses of resting state data.

In a seed voxel analysis, a common method for computing functional connectivity, a time series is chosen in the brain that is hypothesized to represent fluctuations-of-interest. The correlation value between this time series and every other voxel indicates the extent of functional connectivity between the voxels. Using this connectivity analysis, previous studies have claimed that the brain is intrinsically organized into dynamic, anti-correlated networks (Fox et al., 2005, Fransson, 2005, Greicius et al., 2003, Kelly et al., 2008). These studies, however, have all used global signal regression as a pre-processing step. The default mode network is termed the task-negative network since it deactivates during a wide range of tasks. Its anti-correlated network is termed the task-positive network since it represents regions that increase in activity when default mode areas decrease. If the global signal is uncorrelated with the resting state fluctuations as represented by the seed voxel, then the finding of a task-positive network (anti-correlated with the task-negative network) at rest is valid. If, on the other hand, this is not the case, the interpretation that the brain is organized into anti-correlated networks may be brought into question since it is based on results that are contaminated by the global signal regression pre-processing step.

The extent to which global signal regression affects seed voxel functional connectivity analyses was investigated. This paper is organized into four sections (theory, simulations, breathing and visual data, and resting state data), each of which addresses a different aspect of resting state fluctuations and how they are influenced by global signal regression. The theory demonstrates that mathematically, regardless of the characteristics of the resting state fluctuations, global signal regression will always result in a negative mean correlation value during a seed voxel functional connectivity analysis. Three sets of simulations were performed. The first is an empirical demonstration of the theory. The second reveals that if similar resting state fluctuations (represented by a sine wave) are present in all voxels, functional connectivity analyses will determine that approximately half are anti-correlated with a seed after global signal regression. The relative phase of fluctuations in the seed voxel and other regions can bias those regions to become anti-correlated, serving as a possible explanation for the clustering of anti-correlated areas in the brain. The third simulation investigated the behaviour of these anti-correlations as the spatial extent of voxels containing resting state fluctuations increases from zero voxels to the entire brain. The challenge in resting state functional connectivity studies is that the timing and location of spontaneous neuronal activation and global nuisance fluctuations (such as respiration) are unknown. Since it is impossible to systematically alter resting fluctuations, visual task activation was used in the breathing and visual data section to create localisable connectivity maps similar to those generated in resting state correlation studies. A comparatively global fluctuation was introduced into the data using a breath-holding challenge. The relative phase of the two tasks were varied to examine how the influence of global signal regression on connectivity measures is dependent upon the relationship between resting state fluctuations and the global signal, a quantity which, by definition, is unknown. Finally, task-negative and task-positive regions were defined in resting state data and changes in correlation measure with global signal regression were examined in depth.

Section snippets

Theory

This mathematical proof demonstrates that after global signal regression, the sum of correlation values with a seed voxel across the entire brain is less than or equal to zero.

Let each Si(t) be a column vector representing a ith voxel's time series, i = 1,...,N. Since the mean of each voxel's time series can be removed during regression, assume that each voxel has a mean of zero. Let the corresponding time series after global signal regression be represented by the column vector xi(t).

Regression

Simulations

Simulations were performed to test the conclusions of the theory and to examine its practical implications. Two voxel and three voxel simulations were carried out using Matlab (MathWorks, Inc.). One thousand sets of time series were generated, each consisting of two and three time courses respectively. Resting state fluctuations were represented in each time series using a sine wave with a randomly chosen frequency between 0.1 Hz and 0.2 Hz and randomly chosen amplitude between 0 and 1. To

Simulations

All 1000 sets of time courses in both the two voxel and the three voxel simulations demonstrate that Eq. (3) is true: the beta weights from the GLM average to exactly 1 (±  10 15) in all cases. Each time point summed across all time series in the set after regression of the global signal is exactly zero (±  10 13), demonstrating Eq. (5). The final correlation between the time courses after global signal removal in the two voxel case is exactly − 1 (±  10 15) in all 1000 simulations. In the three

Discussion

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

Conclusions

In this paper we have shown using theory, simulations, task and resting state data that anti-correlated networks in the brain may be a consequence of the global signal regression pre-processing step. Mathematically, this technique forces approximately half the voxels in the brain to become anti-correlated with a seed voxel. Global signal regression of data containing a known neuronal oscillation corrupted by a known respiration confound demonstrated that this technique is not successful in

Acknowledgments

This study was supported by the Intramural Research Program, National Institute of Mental Health, NIH. Thanks go to Phil Reiss and Clare Kelly for helpful discussions.

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