EEG functional connectivity as a Riemannian mediator: An application to malnutrition and cognition.

Mediation analysis assesses whether an exposure directly produces changes in cognitive behavior or is influenced by intermediate "mediators". Electroencephalographic (EEG) spectral measurements have been previously used as effective mediators representing diverse aspects of brain function. However, it has been necessary to collapse EEG measures onto a single scalar using standard mediation methods. In this article, we overcome this limitation and examine EEG frequency-resolved functional connectivity measures as a mediator using the full EEG cross-spectral tensor (CST). Since CST samples do not exist in Euclidean space but in the Riemannian manifold of positive-definite tensors, we transform the problem, allowing for the use of classic multivariate statistics. Toward this end, we map the data from the original manifold space to the Euclidean tangent space, eliminating redundant information to conform to a "compressed CST." The resulting object is a matrix with rows corresponding to frequencies and columns to cross spectra between channels. We have developed a novel matrix mediation approach that leverages a nuclear norm regularization to determine the matrix-valued regression parameters. Furthermore, we introduced a global test for the overall CST mediation and a test to determine specific channels and frequencies driving the mediation. We validated the method through simulations and applied it to our well-studied 50+-year Barbados Nutrition Study dataset by comparing EEGs collected in school-age children (5-11 years) who were malnourished in the first year of life with those of healthy classmate controls. We hypothesized that the CST mediates the effect of malnutrition on cognitive performance. We can now explicitly pinpoint the frequencies (delta, theta, alpha, and beta bands) and regions (frontal, central, and occipital) in which functional connectivity was altered in previously malnourished children, an improvement to prior studies. Understanding the specific networks impacted by a history of postnatal malnutrition could pave the way for developing more targeted and personalized therapeutic interventions. Our methods offer a versatile framework applicable to mediation studies encompassing matrix and Hermitian 3D tensor mediators alongside scalar exposures and outcomes, facilitating comprehensive analyses across diverse research domains.

Improved fMRI-based pain prediction using Bayesian group-wise functional registration.

In recent years, the field of neuroimaging has undergone a paradigm shift, moving away from the traditional brain mapping approach towards the development of integrated, multivariate brain models that can predict categories of mental events. However, large interindividual differences in both brain anatomy and functional localization after standard anatomical alignment remain a major limitation in performing this type of analysis, as it leads to feature misalignment across subjects in subsequent predictive models. This article addresses this problem by developing and validating a new computational technique for reducing misalignment across individuals in functional brain systems by spatially transforming each subject's functional data to a common latent template map. Our proposed Bayesian functional group-wise registration approach allows us to assess differences in brain function across subjects and individual differences in activation topology. We achieve the probabilistic registration with inverse-consistency by utilizing the generalized Bayes framework with a loss function for the symmetric group-wise registration. It models the latent template with a Gaussian process, which helps capture spatial features in the template, producing a more precise estimation. We evaluate the method in simulation studies and apply it to data from an fMRI study of thermal pain, with the goal of using functional brain activity to predict physical pain. We find that the proposed approach allows for improved prediction of reported pain scores over conventional approaches. Received on 2 January 2017. Editorial decision on 8 June 2021.

Associations between neighborhood socioeconomic status, parental education, and executive system activation in youth.

Socioeconomic status (SES) can impact cognitive performance, including working memory (WM). As executive systems that support WM undergo functional neurodevelopment during adolescence, environmental stressors at both individual and community levels may influence cognitive outcomes. Here, we sought to examine how SES at the neighborhood and family level impacts task-related activation of the executive system during adolescence and determine whether this effect mediates the relationship between SES and WM performance. To address these questions, we studied 1,150 youths (age 8-23) that completed a fractal n-back WM task during functional magnetic resonance imaging at 3T as part of the Philadelphia Neurodevelopmental Cohort. We found that both higher neighborhood SES and parental education were associated with greater activation of the executive system to WM load, including the bilateral dorsolateral prefrontal cortex, posterior parietal cortex, and precuneus. The association of neighborhood SES remained significant when controlling for task performance, or related factors like exposure to traumatic events. Furthermore, high-dimensional multivariate mediation analysis identified distinct patterns of brain activity within the executive system that significantly mediated the relationship between measures of SES and task performance. These findings underscore the importance of multilevel environmental factors in shaping executive system function and WM in youth.

Three Dimensions of Association Link Migraine Symptoms and Functional Connectivity.

Migraine is a heterogeneous disorder with variable symptoms and responsiveness to therapy. Because of previous analytic shortcomings, variance in migraine symptoms has been inconsistently related to brain function. In the current analysis, we used data from two sites (n = 143, male and female humans), and performed canonical correlation analysis, relating resting-state functional connectivity (RSFC) with a broad range of migraine symptoms, ranging from headache characteristics to sleep abnormalities. This identified three dimensions of covariance between symptoms and RSFC. The first dimension related to headache intensity, headache frequency, pain catastrophizing, affect, sleep disturbances, and somatic abnormalities, and was associated with frontoparietal and dorsal attention network connectivity, both of which are major cognitive networks. Additionally, RSFC scores from this dimension, both the baseline value and the change from baseline to postintervention, were associated with responsiveness to mind-body therapy. The second dimension was related to an inverse association between pain and anxiety, and to default mode network connectivity. The final dimension was related to pain catastrophizing, and salience, sensorimotor, and default mode network connectivity. In addition to performing canonical correlation analysis, we evaluated the current clustering of migraine patients into episodic and chronic subtypes, and found no evidence to support this clustering. However, when using RSFC scores from the three significant dimensions, we identified a novel clustering of migraine patients into four biotypes with unique functional connectivity patterns. These findings provide new insight into individual variability in migraine, and could serve as the foundation for novel therapies that take advantage of migraine heterogeneity.SIGNIFICANCE STATEMENT Using a large multisite dataset of migraine patients, we identified three dimensions of multivariate association between symptoms and functional connectivity. This analysis revealed neural networks that relate to all measured symptoms, but also to specific symptom ensembles, such as patient propensity to catastrophize painful events. Using these three dimensions, we found four biotypes of migraine informed by clinical and neural variation together. Such findings pave the way for precision medicine therapy for migraine.

A machine learning based approach towards high-dimensional mediation analysis.

Mediation analysis is used to investigate the role of intermediate variables (mediators) that lie in the path between an exposure and an outcome variable. While significant research has focused on developing methods for assessing the influence of mediators on the exposure-outcome relationship, current approaches do not easily extend to settings where the mediator is high-dimensional. These situations are becoming increasingly common with the rapid increase of new applications measuring massive numbers of variables, including brain imaging, genomics, and metabolomics. In this work, we introduce a novel machine learning based method for identifying high dimensional mediators. The proposed algorithm iterates between using a machine learning model to map the high-dimensional mediators onto a lower-dimensional space, and using the predicted values as input in a standard three-variable mediation model. Hence, the machine learning model is trained to maximize the likelihood of the mediation model. Importantly, the proposed algorithm is agnostic to the machine learning model that is used, providing significant flexibility in the types of situations where it can be used. We illustrate the proposed methodology using data from two functional Magnetic Resonance Imaging (fMRI) studies. First, using data from a task-based fMRI study of thermal pain, we combine the proposed algorithm with a deep learning model to detect distributed, network-level brain patterns mediating the relationship between stimulus intensity (temperature) and reported pain at the single trial level. Second, using resting-state fMRI data from the Human Connectome Project, we combine the proposed algorithm with a connectome-based predictive modeling approach to determine brain functional connectivity measures that mediate the relationship between fluid intelligence and working memory accuracy. In both cases, our multivariate mediation model links exposure variables (thermal pain or fluid intelligence), high dimensional brain measures (single-trial brain activation maps or resting-state brain connectivity) and behavioral outcomes (pain report or working memory accuracy) into a single unified model. Using the proposed approach, we are able to identify brain-based measures that simultaneously encode the exposure variable and correlate with the behavioral outcome.

Enhanced hyperalignment via spatial prior information.

Functional alignment between subjects is an important assumption of functional magnetic resonance imaging (fMRI) group-level analysis. However, it is often violated in practice, even after alignment to a standard anatomical template. Hyperalignment, based on sequential Procrustes orthogonal transformations, has been proposed as a method of aligning shared functional information into a common high-dimensional space and thereby improving inter-subject analysis. Though successful, current hyperalignment algorithms have a number of shortcomings, including difficulties interpreting the transformations, a lack of uniqueness of the procedure, and difficulties performing whole-brain analysis. To resolve these issues, we propose the ProMises (Procrustes von Mises-Fisher) model. We reformulate functional alignment as a statistical model and impose a prior distribution on the orthogonal parameters (the von Mises-Fisher distribution). This allows for the embedding of anatomical information into the estimation procedure by penalizing the contribution of spatially distant voxels when creating the shared functional high-dimensional space. Importantly, the transformations, aligned images, and related results are all unique. In addition, the proposed method allows for efficient whole-brain functional alignment. In simulations and application to data from four fMRI studies we find that ProMises improves inter-subject classification in terms of between-subject accuracy and interpretability compared to standard hyperalignment algorithms.

Differences in functional connectivity distribution after transcranial direct-current stimulation: A connectivity density point of view.

In this manuscript, we consider the problem of relating functional connectivity measurements viewed as statistical distributions to outcomes. We demonstrate the utility of using the distribution of connectivity on a study of resting-state functional magnetic resonance imaging association with an intervention. The method uses the estimated density of connectivity between nodes of interest as a functional covariate. Moreover, we demonstrate the utility of the procedure in an instance where connectivity is naturally considered an outcome by reversing the predictor/response relationship using case/control methodology. The method utilizes the density quantile, the density evaluated at empirical quantiles, instead of the empirical density directly. This improved the performance of the method by highlighting tail behavior, though we emphasize that by being flexible and non-parametric, the technique can detect effects related to the central portion of the density. To demonstrate the method in an application, we consider 47 primary progressive aphasia patients with various levels of language abilities. These patients were randomly assigned to two treatment arms, transcranial direct-current stimulation and language therapy versus sham (language therapy only), in a clinical trial. We use the method to analyze the effect of direct stimulation on functional connectivity. As such, we estimate the density of correlations among the regions of interest and study the difference in the density post-intervention between treatment arms. We discover that it is the tail of the density, rather than the mean or lower order moments of the distribution, that demonstrates a significant impact in the classification. The new approach has several benefits. Among them, it drastically reduces the number of multiple comparisons compared with edge-wise analysis. In addition, it allows for the investigation of the impact of functional connectivity on the outcomes where the connectivity is not geometrically localized.

Single-index models with functional connectivity network predictors.

Functional connectivity is defined as the undirected association between two or more functional magnetic resonance imaging (fMRI) time series. Increasingly, subject-level functional connectivity data have been used to predict and classify clinical outcomes and subject attributes. We propose a single-index model wherein response variables and sparse functional connectivity network valued predictors are linked by an unspecified smooth function in order to accommodate potentially nonlinear relationships. We exploit the network structure of functional connectivity by imposing meaningful sparsity constraints, which lead not only to the identification of association of interactions between regions with the response but also the assessment of whether or not the functional connectivity associated with a brain region is related to the response variable. We demonstrate the effectiveness of the proposed model in simulation studies and in an application to a resting-state fMRI data set from the Human Connectome Project to model fluid intelligence and sex and to identify predictive links between brain regions.

Mode decomposition-based time-varying phase synchronization for fMRI.

Recently, there has been significant interest in measuring time-varying functional connectivity (TVC) between different brain regions using resting-state functional magnetic resonance imaging (rs-fMRI) data. One way to assess the relationship between signals from different brain regions is to measure their phase synchronization (PS) across time. However, this requires the a priori choice of type and cut-off frequencies for the bandpass filter needed to perform the analysis. Here we explore alternative approaches based on the use of various mode decomposition (MD) techniques that provide a more data driven solution to this issue. These techniques allow for the data driven decomposition of signals jointly into narrow-band components at different frequencies, thus fulfilling the requirements needed to measure PS. We explore several variants of MD, including empirical mode decomposition (EMD), bivariate EMD (BEMD), noise-assisted multivariate EMD (na-MEMD), and introduce the use of multivariate variational mode decomposition (MVMD) in the context of estimating time-varying PS. We contrast the approaches using a series of simulations and application to rs-fMRI data. Our results show that MVMD outperforms other evaluated MD approaches, and further suggests that this approach can be used as a tool to reliably investigate time-varying PS in rs-fMRI data.

A functional mixed model for scalar on function regression with application to a functional MRI study.

Motivated by a functional magnetic resonance imaging (fMRI) study, we propose a new functional mixed model for scalar on function regression. The model extends the standard scalar on function regression for repeated outcomes by incorporating subject-specific random functional effects. Using functional principal component analysis, the new model can be reformulated as a mixed effects model and thus easily fit. A test is also proposed to assess the existence of the subject-specific random functional effects. We evaluate the performance of the model and test via a simulation study, as well as on data from the motivating fMRI study of thermal pain. The data application indicates significant subject-specific effects of the human brain hemodynamics related to pain and provides insights on how the effects might differ across subjects.

Evaluating phase synchronization methods in fMRI: A comparison study and new approaches.

In recent years there has been growing interest in measuring time-varying functional connectivity between different brain regions using resting-state functional magnetic resonance imaging (rs-fMRI) data. One way to assess the relationship between signals from different brain regions is to measure their phase synchronization (PS) across time. There are several ways to perform such analyses, and we compare methods that utilize a PS metric together with a sliding window, referred to here as windowed phase synchronization (WPS), with those that directly measure the instantaneous phase synchronization (IPS). In particular, IPS has recently gained popularity as it offers single time-point resolution of time-resolved fMRI connectivity. In this paper, we discuss the underlying assumptions required for performing PS analyses and emphasize the importance of band-pass filtering the data to obtain valid results. Further, we contrast this approach with the use of Empirical Mode Decomposition (EMD) to achieve similar goals. We review various methods for evaluating PS and introduce a new approach within the IPS framework denoted the cosine of the relative phase (CRP). We contrast methods through a series of simulations and application to rs-fMRI data. Our results indicate that CRP outperforms other tested methods and overcomes issues related to undetected temporal transitions from positive to negative associations common in IPS analysis. Further, in contrast to phase coherence, CRP unfolds the distribution of PS measures, which benefits subsequent clustering of PS matrices into recurring brain states.

Moderated t-tests for group-level fMRI analysis.

In recent years, there has been significant criticism of functional magnetic resonance imaging (fMRI) studies with small sample sizes. The argument is that such studies have low statistical power, as well as reduced likelihood for statistically significant results to be true effects. The prevalence of these studies has led to a situation where a large number of published results are not replicable and likely false. Despite this growing body of evidence, small sample fMRI studies continue to be regularly performed; likely due to the high cost of scanning. In this report we investigate the use of a moderated t-statistic for performing group-level fMRI analysis to help alleviate problems related to small sample sizes. The proposed approach, implemented in the popular R-package LIMMA (linear models for microarray data), has found wide usage in the genomics literature for dealing with similar issues. Utilizing task-based fMRI data from the Human Connectome Project (HCP), we compare the performance of the moderated t-statistic with the standard t-statistic, as well as the pseudo t-statistic commonly used in non-parametric fMRI analysis. We find that the moderated t-test significantly outperforms both alternative approaches for studies with sample sizes less than 40 subjects. Further, we find that the results were consistent both when using voxel-based and cluster-based thresholding. We also introduce an R-package, LIMMI (linear models for medical images), that provides a quick and convenient way to apply the method to fMRI data.

Children with attention-deficit/hyperactivity disorder spend more time in hyperconnected network states and less time in segregated network states as revealed by dynamic connectivity analysis.

Previous studies in children with attention-deficit/hyperactivity disorder (ADHD) have observed functional brain network disruption on a whole-brain level, as well as on a sub-network level, particularly as related to the default mode network, attention-related networks, and cognitive control-related networks. Given behavioral findings that children with ADHD have more difficulty sustaining attention and more extreme moment-to-moment fluctuations in behavior than typically developing (TD) children, recently developed methods to assess changes in connectivity over shorter time periods (i.e., "dynamic functional connectivity"), may provide unique insight into dysfunctional network organization in ADHD. Thus, we performed a dynamic functional connectivity (FC) analysis on resting state fMRI data from 38 children with ADHD and 79 TD children. We used Hidden semi-Markov models (HSMMs) to estimate six network states, as well as the most probable sequence of states for each participant. We quantified the dwell time, sojourn time, and transition probabilities across states. We found that children with ADHD spent less total time in, and switched more quickly out of, anticorrelated states involving the default mode network and task-relevant networks as compared to TD children. Moreover, children with ADHD spent more time in a hyperconnected state as compared to TD children. These results provide novel evidence that underlying dynamics may drive the differences in static FC patterns that have been observed in ADHD and imply that disrupted FC dynamics may be a mechanism underlying the behavioral symptoms and cognitive deficits commonly observed in children with ADHD.

Identification of the Somatomotor Network from Language Task-based fMRI Compared with Resting-State fMRI in Patients with Brain Lesions.

Background Resting-state functional MRI (rs-fMRI) is a potential alternative to task-based functional MRI (tb-fMRI) for somatomotor network (SMN) identification. Brain networks can also be generated from tb-fMRI by using independent component analysis (ICA). Purpose To investigate whether the SMN can be identified by using ICA from a language task without a motor component, the sentence completion functional MRI (sc-fMRI) task, compared with rs-fMRI. Materials and Methods The sc-fMRI and rs-fMRI scans in patients who underwent presurgical brain mapping between 2012 and 2016 were analyzed, using the same imaging parameters (other than scanning time) on a 3.0-T MRI scanner. ICA was performed on rs-fMRI and sc-fMRI scans with use of a tool to separate data sets into their spatial and temporal components. Two neuroradiologists independently determined the presence of the dorsal SMN (dSMN) and ventral SMN (vSMN) on each study. Groups were compared by using t tests, and logistic regression was performed to identify predictors of the presence of SMNs. Results One hundred patients (mean age, 40.9 years ± 14.8 [standard deviation]; 61 men) were evaluated. The dSMN and vSMN were identified in 86% (86 of 100) and 76% (76 of 100) of rs-fMRI scans and 85% (85 of 100) and 69% (69 of 100) of sc-fMRI scans, respectively. The concordance between rs-fMRI and sc-fMRI for presence of dSMN and vSMN was 75% (75 of 100 patients) and 53% (53 of 100 patients), respectively. In 10 of 14 patients (71%) where rs-fMRI did not show the dSMN, sc-fMRI demonstrated it. This rate was 67% for the vSMN (16 of 24 patients). Conclusion In the majority of patients, independent component analysis of sentence completion task functional MRI scans reliably demonstrated the somatomotor network compared with resting-state functional MRI scans. Identifying target networks with a single sentence completion scan could reduce overall functional MRI scanning times by eliminating the need for separate motor tasks. © RSNA, 2021 Online supplemental material is available for this article. See also the editorial by Field and Birn in this issue.

Multiple Brain Networks Mediating Stimulus-Pain Relationships in Humans.

The brain transforms nociceptive input into a complex pain experience comprised of sensory, affective, motivational, and cognitive components. However, it is still unclear how pain arises from nociceptive input and which brain networks coordinate to generate pain experiences. We introduce a new high-dimensional mediation analysis technique to estimate distributed, network-level patterns that formally mediate the relationship between stimulus intensity and pain. We applied the model to a large-scale analysis of functional magnetic resonance imaging data (N = 284), focusing on brain mediators of the relationship between noxious stimulus intensity and trial-to-trial variation in pain reports. We identify mediators in both traditional nociceptive pathways and in prefrontal, midbrain, striatal, and default-mode regions unrelated to nociception in standard analyses. The whole-brain mediators are specific for pain versus aversive sounds and are organized into five functional networks. Brain mediators predicted pain ratings better than previous brain measures, including the neurologic pain signature (Wager et al. 2013). Our results provide a broader view of the networks underlying pain experience, as well as novel brain targets for interventions.

The Pain of Sleep Loss: A Brain Characterization in Humans.

Sleep loss increases the experience of pain. However, the brain mechanisms underlying altered pain processing following sleep deprivation are unknown. Moreover, it remains unclear whether ecologically modest night-to-night changes in sleep, within an individual, confer consequential day-to-day changes in experienced pain. Here, we demonstrate that acute sleep deprivation amplifies pain reactivity within human (male and female) primary somatosensory cortex yet blunts pain reactivity in higher-order valuation and decision-making regions of the striatum and insula cortex. Consistent with this altered neural signature, we further show that sleep deprivation expands the temperature range for classifying a stimulus as painful, specifically through a lowering of pain thresholds. Moreover, the degree of amplified reactivity within somatosensory cortex following sleep deprivation significantly predicts this expansion of experienced pain across individuals. Finally, outside of the laboratory setting, we similarly show that even modest nightly changes in sleep quality (increases and decreases) within an individual determine consequential day-to-day changes in experienced pain (decreases and increases, respectively). Together, these data provide a novel framework underlying the impact of sleep loss on pain and, furthermore, establish that the association between sleep and pain is expressed in a night-to-day, bidirectional relationship within a sample of the general population. More broadly, our findings highlight sleep as a novel therapeutic target for pain management within and outside the clinic, including circumstances where sleep is frequently short yet pain is abundant (e.g., the hospital setting).SIGNIFICANCE STATEMENT Are you experiencing pain? Did you have a bad night of sleep? This study provides underlying brain and behavioral mechanisms explaining this common co-occurrence. We show that sleep deprivation enhances pain responsivity within the primary sensing regions of the brain's cortex yet blunts activity in other regions that modulate pain processing, the striatum and insula. We further establish that even subtle night-to-night changes in sleep in a sample of the general population predict consequential day-to-day changes in pain (bidirectionally). Considering the societal rise in chronic pain conditions in lock-step with the decline in sleep time through the industrial world, our data support the hypothesis that these two trends may not simply be co-occurring but are significantly interrelated.

Sparse Principal Component based High-Dimensional Mediation Analysis.

Causal mediation analysis aims to quantify the intermediate effect of a mediator on the causal pathway from treatment to outcome. When dealing with multiple mediators, which are potentially causally dependent, the possible decomposition of pathway effects grows exponentially with the number of mediators. An existing approach incorporated the principal component analysis (PCA) to address this challenge based on the fact that the transformed mediators are conditionally independent given the orthogonality of the principal components (PCs). However, the transformed mediator PCs, which are linear combinations of original mediators, can be difficult to interpret. A sparse high-dimensional mediation analysis approach is proposed which adopts the sparse PCA method to the mediation setting. The proposed approach is applied to a task-based functional magnetic resonance imaging study, illustrating its ability to detect biologically meaningful results related to an identified mediator.

Investigating the impact of autocorrelation on time-varying connectivity.

In recent years, a number of studies have reported on the existence of time-varying functional connectivity (TVC) in resting-state functional magnetic resonance imaging (rs-fMRI) data. The sliding-window technique is currently one of the most commonly used methods to estimate TVC. Although previous studies have shown that autocorrelation can negatively impact estimates of static functional connectivity, its impact on TVC estimates is not well known at this time. In this paper, we show both theoretically and empirically that the existence of autocorrelation within a time series can inflate the sampling variability of TVC estimated using the sliding-window technique. This can in turn increase the risk of misinterpreting noise as true TVC and negatively impact subsequent estimation of whole-brain time-varying FC profiles, or "brain states". The latter holds as more variable input measures lead to more variable output measures in the state estimation procedure. Finally, we demonstrate that prewhitening the data prior to analysis can lower the variance of the estimated TVC and improve brain state estimation. These results suggest that careful consideration is required when making inferences on TVC.

Improved state change estimation in dynamic functional connectivity using hidden semi-Markov models.

The study of functional brain networks has grown rapidly over the past decade. While most functional connectivity (FC) analyses estimate one static network structure for the entire length of the functional magnetic resonance imaging (fMRI) time series, recently there has been increased interest in studying time-varying changes in FC. Hidden Markov models (HMMs) have proven to be a useful modeling approach for discovering repeating graphs of interacting brain regions (brain states). However, a limitation lies in HMMs assuming that the sojourn time, the number of consecutive time points in a state, is geometrically distributed. This may encourage inaccurate estimation of the time spent in a state before switching to another state. We propose a hidden semi-Markov model (HSMM) approach for inferring time-varying brain networks from fMRI data, which explicitly models the sojourn distribution. Specifically, we propose using HSMMs to find each subject's most probable series of network states and the graphs associated with each state, while properly estimating and modeling the sojourn distribution for each state. We perform a simulation study, as well as an analysis on both task-based fMRI data from an anxiety-inducing experiment and resting-state fMRI data from the Human Connectome Project. Our results demonstrate the importance of model choice when estimating sojourn times and reveal their potential for understanding healthy and diseased brain mechanisms.

Modular preprocessing pipelines can reintroduce artifacts into fMRI data.

The preprocessing pipelines typically used in both task and resting-state functional magnetic resonance imaging (rs-fMRI) analysis are modular in nature: They are composed of a number of separate filtering/regression steps, including removal of head motion covariates and band-pass filtering, performed sequentially and in a flexible order. In this article, we illustrate the shortcomings of this approach, as we show how later preprocessing steps can reintroduce artifacts previously removed from the data in prior preprocessing steps. We show that each regression step is a geometric projection of data onto a subspace, and that performing a sequence of projections can move the data into subspaces no longer orthogonal to those previously removed, reintroducing signal related to nuisance covariates. Thus, linear filtering operations are not commutative, and the order in which the preprocessing steps are performed is critical. These issues can arise in practice when any combination of standard preprocessing steps including motion regression, scrubbing, component-based correction, physiological correction, global signal regression, and temporal filtering are performed sequentially. In this work, we focus primarily on rs-fMRI. We illustrate the problem both theoretically and empirically through application to a test-retest rs-fMRI data set, and suggest remedies. These include (a) combining all steps into a single linear filter, or (b) sequential orthogonalization of covariates/linear filters performed in series.