The nuisance of nuisance regression: Spectral misspecification in a common approach to resting-state fMRI preprocessing reintroduces noise and obscures functional connectivity

Highlights

• Bandpass filtering and nuisance regression are intended to reduce noise in RS-fMRI.

• When RS-fMRI data are filtered, but regressors are not, noise is poorly controlled.

• In addition, this approach reintroduces synchronous noise into RS-fMRI data.

• Such noise leads to systematically inflated estimates of functional connectivity.

• Simultaneous bandpass filtering and regression eliminates this source of bias.

Abstract

Recent resting-state functional connectivity fMRI (RS-fcMRI) research has demonstrated that head motion during fMRI acquisition systematically influences connectivity estimates despite bandpass filtering and nuisance regression, which are intended to reduce such nuisance variability. We provide evidence that the effects of head motion and other nuisance signals are poorly controlled when the fMRI time series are bandpass-filtered but the regressors are unfiltered, resulting in the inadvertent reintroduction of nuisance-related variation into frequencies previously suppressed by the bandpass filter, as well as suboptimal correction for noise signals in the frequencies of interest. This is important because many RS-fcMRI studies, including some focusing on motion-related artifacts, have applied this approach. In two cohorts of individuals (n = 117 and 22) who completed resting-state fMRI scans, we found that the bandpass–regress approach consistently overestimated functional connectivity across the brain, typically on the order of r = .10–.35, relative to a simultaneous bandpass filtering and nuisance regression approach. Inflated correlations under the bandpass–regress approach were associated with head motion and cardiac artifacts. Furthermore, distance-related differences in the association of head motion and connectivity estimates were much weaker for the simultaneous filtering approach. We recommend that future RS-fcMRI studies ensure that the frequencies of nuisance regressors and fMRI data match prior to nuisance regression, and we advocate a simultaneous bandpass filtering and nuisance regression strategy that better controls nuisance-related variability.

Introduction

Resting-state functional connectivity magnetic resonance imaging (RS-fcMRI) is a dominant method for characterizing the human functional connectome (Cole et al., 2010, Van Essen and Ugurbil, 2012). In RS-fcMRI, the blood-oxygen-level-dependent (BOLD) contrast is measured for several minutes in an MR scanner while the subject remains passive (Biswal et al., 2010). The BOLD signal measures metabolic changes that result from neural activity (Magri et al., 2012), and during resting-state fMRI, BOLD fluctuations reflect spontaneous neural activity, which are strongest in the .009 Hz–.08 Hz frequency range (He et al., 2008, Schölvinck et al., 2010). Correlations of RS-fcMRI time series across brain regions reflect intrinsic functional connectivity (i.e., interactivity among functionally related populations of neurons; Van Dijk et al., 2010), and numerous studies on this topic have contributed greatly to the elucidation of the functional architecture of the human brain (Buckner et al., 2011, Fair et al., 2007, Fox et al., 2005). The RS-fcMRI method has also stimulated research investigating the development of brain networks in children and adolescents (Dosenbach et al., 2010, Fair et al., 2007, Stevens et al., 2009, Supekar et al., 2009), as well as potentially maladaptive network differences in individuals with psychiatric disorders (Church et al., 2009, Cole et al., 2011, Seeley et al., 2009).

Relative to task-based fMRI studies, signal processing in seed-based correlation analyses of resting-state fMRI data typically includes two additional steps: 1) bandpass filtering of voxel time series into the low-frequency range, typically 0.009–0.08 Hz (but see Jo et al., 2010); and 2) regression of additional sources of noise, including estimates of individual head motion, average BOLD signals in the white matter and ventricles, and controversially, the average BOLD signal across all brain voxels (Murphy et al., 2009). These steps are often performed in the above order and are intended to reduce or eliminate temporally synchronous artifacts in resting-state fMRI time series that could be mistaken for neural activation and functional coupling. Nuisance regression seeks to attenuate non-neural BOLD fluctuations from measurable noise sources such as scanner drift and head motion, as well as periodic physiological signals (e.g., heartbeat and respiration; Birn et al., 2008, Chang et al., 2009), whereas bandpass filtering suppresses all variability in a range of frequencies that are a priori not of interest.

Relatively little research has explored the optimal approach for applying bandpass filtering and nuisance regression to RS-fcMRI data (cf. Weissenbacher et al., 2009). In our study, we considered three possibilities: 1) bandpass filtering followed by nuisance regression (BpReg); 2) regression followed by bandpass filtering (RegBp); and 3) simultaneous bandpass filtering and regression (Simult). Bandpass filtering and nuisance regression can be both conceptualized as linear filters of the data—that is, the filtered signal, y, is a linear transformation of the original signal, x: $y_t={\mathcal{T}}_t\left\{x\right\}$, where the transformation operator $\mathcal{T}$ linearly maps every value of x to a transformed value of y at each time t. When two linear filters are orthogonal to each other, the output signal is the same regardless of which filter is applied first (Jenkins and Watts, 1968). Nuisance regressors (e.g., motion parameters) and bandpass filter coefficients, however, are unlikely to be orthogonal because noise sources typically include power at frequencies in the stopband (i.e., the frequencies to be suppressed), leading to statistical dependency between the spectral filter and nuisance regressors. Thus, the manner in which bandpass filtering and nuisance regression are applied to RS-fcMRI data may affect the quality of noise in RS-fcMRI data, as well as estimates of functional connectivity.

Using simulated time series and empirical RS-fcMRI data, we demonstrate that the nuisance regression model is misspecified in the frequency domain when the fMRI time series are bandpass filtered but one or more regressors are unfiltered, resulting in the reintroduction of temporally synchronous nuisance-related variation into frequencies previously suppressed by the bandpass filter, as well as suboptimal correction for nuisance signals in the frequencies of interest. This paradoxical reintroduction of nuisance variation is contrary to the underlying goal of the regression, yet our review of the RS-fcMRI literature below indicates that the bandpass–regress (BpReg) approach is common, although not universal. By contrast, there is no frequency mismatch in the nuisance regression for bandpass filtering after regression (RegBp) and simultaneous filtering (Simult), so these approaches do not suffer from the same flaw.

The potential for ill effects of nuisance regression on connectivity estimates is topical in light of compelling evidence from three contemporaneous papers demonstrating that head motion during RS-fcMRI acquisition confounds estimates of functional connectivity (Power et al., 2012, Satterthwaite et al., 2012, Van Dijk et al., 2012). Specifically, the relationship between head motion magnitude and connectivity estimates was spatially structured such that greater head motion was associated with increased estimates of short-range connectivity and potentially suppressed estimates of long-range connectivity. However, two of these studies used the BpReg approach for the head motion regressors such that the fMRI data were bandpass filtered, whereas motion parameters were not (K. Van Dijk, personal communication, December 18, 2012; Van Dijk et al., 2012; J.D. Power, personal communication, June 26, 2012; Power et al., 2012); the other report conducted nuisance regression prior to bandpass filtering (i.e., RegBp; T. Satterthwaite, personal communication, November 13, 2012; Satterthwaite et al., 2012). This raises the possibility that the effects of head motion on connectivity estimates may partially reflect nuisance variability reintroduced by BpReg.

In addition, Power and colleagues observed that motion-related fluctuations in the overall BOLD signal contaminated RS-fcMRI time series despite bandpass filtering and nuisance regression (see also Friston et al., 1996), potentially biasing connectivity estimates. To attenuate motion-related artifacts, they suggested censoring volumes surrounding periods of large head motion prior to computing correlations among brain regions. As our results suggest, however, motion-related fluctuations using the BpReg approach may reflect the inadvertent reintroduction of nuisance variation into the RS-fcMRI time series. Conversely, the appropriate application of bandpass filtering and nuisance regression using the RegBp or Simult approach may help to mitigate motion-related artifacts.

Our study sought to characterize the effects of bandpass filtering and nuisance regression on estimates of functional connectivity using seed-based correlational analyses, as well as differences among processing approaches in the quality and magnitude of noise in RS-fcMRI signals, particularly motion-related artifacts. In order to develop best-practice recommendations and to quantify the prevalence of the BpReg approach, we also reviewed the use of bandpass filtering and nuisance regression in a subset of RS-fcMRI studies. A secondary goal was to characterize whether the Simult and BpReg approaches differed with respect to the interregional distance-dependent effects of head motion on connectivity estimates. To address these questions, we analyzed resting-state fMRI data from two cohorts, one collected at the University of Pittsburgh that included children, adolescents, and young adults; and a smaller cohort of children collected at Washington University in which motion-related changes in connectivity estimates were previously described by Power et al. (2012).