Resting-state Functional Magnetic Resonance Imaging Correlates of Sevoflurane-induced Unconsciousness

ANESTHETIC agents induce profound derangements of consciousness and cognition. The neural mechanisms underlying sedation and general anesthesia include potentiation and inhibition of target receptors and ion channels¹  and modulation of subcortical arousal circuitry.²  Electrophysiological recordings have also implicated disrupted signaling between distant brain regions.^3,4  At the systems level, functional magnetic resonance imaging (fMRI) provides a means of elucidating mechanisms whereby humans rendered unconscious fail to perceive, attend, or react to the external world.

fMRI is based on the measurement of blood oxygen level–dependent (BOLD) signals⁵  that indirectly reflect neural activity.⁶  Task-based fMRI has been extensively used to localize sensory, motor, and cognitive functions to specific patterns of activated brain regions.⁷  More recently, task-free (“resting-state”) fMRI has been used to probe this neural architecture in diverse cognitive states.⁸  Resting-state fMRI exploits the fact that intrinsic activity is temporally coherent within widely distributed functional systems.⁹  This phenomenon is referred to as functional connectivity (FC); the associated topographies comprise resting-state networks (RSNs).¹⁰  RSNs are associated with specific functions based on the observation that their topographies recapitulate fMRI responses to task paradigms.^11,12 

Reports describing human resting-state fMRI effects of sedation date back to 2000¹³  and now number several dozen, listed as a table with study parameters in Supplemental Digital Content 1, https://links.lww.com/ALN/B159. Loss of purposeful responses to verbal or painful stimulation has been associated with reversible disruption of FC within RSNs.^14–16  Most previous studies in this field used intravenous agents, primarily propofol. In contrast, sevoflurane has been less often used, and some of the reported effects are inconsistent with the rest of the literature. For example, although reduced FC within the default mode network (DMN) is a commonly observed correlate of propofol-induced unconsciousness,^14,16  Martuzzi et al.¹⁷  studied 1% sevoflurane and did not observe this effect. It is unclear whether this discrepancy reflects pharmacologic differences between anesthetic agents or technical confounding factors such as motion artifact. The extent to which micromovements of the head contribute to spurious FC findings has been recognized only recently.^18–22  Because the bulk of fMRI investigations on anesthetic-induced unconsciousness were conducted before quantitative censoring of motion artifact, it is unknown what effect this potential confound has had on the body of knowledge in this field.

Herein, we report a resting-state fMRI study of the unconsciousness induced by sevoflurane, incorporating scrupulous attention to minimizing the impact of head motion–related artifact. We hypothesized that sevoflurane-induced unconsciousness would reduce FC, particularly within the DMN.^15,23–25  We also demonstrate that head motion is a significant source of artifact in studies of this type and can produce false effects in both the correlation and the covariance structure of resting-state fMRI.

All aspects of this study were supervised by the Washington University Human Research Protection Office, including regular review by a data monitoring and safety board. Inclusion criteria included 18 to 40 yr of age, American Society of Anesthesiologists physical status class I, and body mass index of 18 to 30 kg/m². Exclusion criteria included use of over-the-counter antihistamines, antiemetics, herbal supplements, ethanol, or illicit drugs within a week of the study; known auditory or physical impairments; known family history of malignant hyperthermia; sedation, general anesthesia, or upper respiratory infection in the past 30 days; disturbance in normal sleep pattern within the past 14 days; or implanted magnetic resonance imaging (MRI)–incompatible metal or prosthetic. In total, 224 applicants were screened. Of these, 43 participants were enrolled in the study. Eligible study volunteers underwent a history and physical examination. Preparation for sedation involved overnight fasting. Female participants underwent urine pregnancy testing. All participants gave written informed consent and were paid for their participation. Functional imaging was initiated in 21 participants but aborted in 5 because of agitation manifesting as gross motion, vocalization, tachycardia, or hypertension.

Sessions were carried out in the Center for Clinical Imaging and Research within Barnes- Jewish Hospital. At least one advanced cardiac life support– certified anesthesiologist, research nurse, and magnetic resonance technologist were present throughout each imaging session. A forearm intravenous catheter provided fluid and drug access. A radial arterial catheter was placed for blood gas sampling. Invasive blood pressure, temperature, oxygen saturation, and end-tidal carbon dioxide and sevoflurane concentration were measured using a Medrad Veris monitoring system (Medrad, Inc., USA). An airtight facemask allowed administration of sevoflurane and exhaled gas monitoring during spontaneous breathing. Mask leaks were inferred from large gradients in inspired and expired oxygen percentages, capnographic traces, or noises from the masks. The radio frequency coil and padding in front of the mask was used to secure the mask to the face of the participant. Gas administration was controlled through a Dräger Narkomed MRI-2 machine (Dräger, North America). A mixture of 2 l/min air:2 l/min oxygen was delivered throughout the study.

The experimental protocol involved stepwise changes in inhaled sevoflurane concentration, from 0 to 1.2% and back to 0%, in 0.6% increments, with a goal of deep sedation at 0.6% sevoflurane and unconsciousness at 1.2% sevoflurane (0.6 to 0.7 minimum alveolar concentration²⁶ ). After each step, 15 min of anesthetic equilibration were allotted before functional BOLD imaging data were acquired. Excessive subject motion at 0.6% sevoflurane precluded analysis of fMRI data acquired at this concentration. Hence, we report only fMRI data acquired at baseline (0%) and 1.2% sevoflurane. Arterial blood gases, for measuring Paco₂, were sampled after at least 20 min of equilibration and were analyzed using a portable I-Stat and G3+ cartridges (Abbott Point of Care, Inc., USA). Behavioral assessments were based on the modified Observer’s Assessment of Alertness/Sedation Scale²⁷  (OAA/S) and the Ramsay Sedation scale.²⁸  If verbal responses were not elicited, noxious pressure was applied to fingernail beds (the trapezius muscles were not accessible in the MRI environment).

All volunteers were awake and cooperative at baseline (modified OAA/S of 5 and Ramsay of 2) but were unresponsive at 1.2% sevoflurane (modified OAA/S of 0 and Ramsay of 6), consistent with the definition of general anesthesia.²⁹  The modified OAA/S and Ramsay scores were different between the two groups (P < 0.001, Mann–Whitney U test). The mean ± SD end-tidal sevoflurane concentrations were 0 ± 0 and 1.2 ± 0.1%. There was a small but significant change in mean Paco₂, from 42.1 ± 4.7 to 48.3 ± 6.0 mmHg (P = 0.03, Mann–Whitney U test). Controls for carbon dioxide retention are included in the present analyses (see Results).

We used a Siemens 3T Trio scanner (Siemens, Germany) equipped with a standard 12-channel head coil. Structural imaging included one T1-weighted magnetization-prepared rapid gradient echo (field of view [FOV], 256 mm; repetition time [TR], 2,400 ms; echo time [TE], 3.16 ms; flip angle [FA], 8°; voxel size, 1 mm isotropic; 176 slices) and one T2-weighted scan (FOV, 256 mm; TR, 6,280 ms; TE, 88 ms; FA, 120°; voxel size, 1 × 1 × 4 mm; 36 slices). At least two 7.5-min, T2*-weighted fMRI runs (FOV, 256 mm; TR, 2,200 ms; TE, 27 ms; FA, 90°; 4-mm isotropic voxels; 36 slices/volume; 200 volumes/run) were acquired in each anesthetic condition. Participants were instructed to remain still and awake with eyes closed during fMRI.

Image preprocessing proceeded as previously described,³⁰  with the addition of fMRI image distortion correction using the FUGUE module in FSL.³¹  Field maps were approximated using the technique described by Gholipour et al.³²  Distortion correction and motion correction were combined in one resampling step to generate volumetric time series in Talairach atlas space (3 × 3 × 3-mm cubic voxels). Each fMRI run was intensity normalized (one multiplicative constant applied to all voxels and frames) to obtain a whole brain mode value of 1,000.³³  Because of this normalization, BOLD signal amplitudes were interpretable for both purposes of frame censoring and evaluation of time series covariance values.

Additional preprocessing in preparation for FC analyses included motion censoring based on the delta variation signal (DVARS) (temporal derivative of RMS BOLD signal across voxels) measure.^18,34  Motion censoring was computed before denoising to avoid FC analyses of frames (volumes) with “cosmetically” improved DVARS values but retained artifact.²²  The DVARS censoring threshold was set at 0.4% root-mean-square frame-to-frame BOLD signal change²²  following 20-mm spatial preblur in each direction. Epochs containing less than 10 contiguous frames meeting the DVARS criterion were excluded from the FC computations. Of the 21 participants for whom BOLD fMRI was acquired, 15 were imaged at both 0% and after loss of consciousness induced by 1.2% sevoflurane. Of these, 10 and 9, respectively, provided useable fMRI data in the 0 and 1.2% sevoflurane conditions. Only six contributed useable data in both conditions. The fraction of uncensored data from each participant is listed as a table in Supplemental Digital Content 2, https://links.lww.com/ALN/B160. Rigorous quality assurance criteria resulted in a severe winnowing of the useable data, but there was no statistically significant difference in the DVARS measures between the 0 and 1.2% sevoflurane data sets (P = 0.62, Student t test). The distributions of these DVARS values are shown in Supplemental Digital Content 3, https://links.lww.com/ALN/B161. The fraction of uncensored frames in the analyzed data was 72.0 ± 18.9 and 56.7 ± 28.4%, respectively, in the 0 and 1.2% sevoflurane conditions. Head movement statistics (translation + rotation in units of root-mean-square mm), averaged over retained frames, were 0.35 ± 0.15 and 0.39 ± 0.18, respectively, for the 0 and 1.2% sevoflurane conditions.

After motion censoring, the mean of retained frames were made 0 within each voxel but the data were not otherwise temporally or spatially filtered. Denoising was accomplished using a strategy similar to component based noise correction method.³⁵  Nuisance regressors were derived from white matter and ventricle masks, segmented in each individual using FreeSurfer,³⁶  then spatially resampled in register with the functional data. Nuisance regressors also were extracted from voxels in the extra-axial cerebral spinal fluid space exhibiting high (>2.5%) temporal SD. Additional nuisance regressors were derived from rigid body head motion correction, the global signal averaged over the whole brain, and the global signal temporal derivative.

Our analysis includes conventional computation of FC using Pearson correlation.³⁷  The Pearson correlation coefficient is a unitless quantity not sensitive to signal amplitude. Previous observations suggest that anesthetic agents affect the amplitude of intrinsic activity more than its correlation structure.^38,39  Accordingly, we also report covariance analyses of BOLD time series, in which sensitivity to the amplitude of BOLD fluctuations is retained. Algebraic formulae are given in the appendix.

FC was computed in terms of region of interest (ROI) pairs. ROIs were defined by dividing gray matter regions in atlas space into 9 × 9 × 9-mm cubes, discounting any cubes containing less than 50% gray matter voxels.⁴⁰  Each ROI was assigned to one of seven RSNs.⁴¹  Only ROIs with more than 95% probability of belonging to one of these networks were retained in the analysis. A map of the ROIs and their network assignments is shown in Supplemental Digital Content 4, panel A, https://links.lww.com/ALN/B162. These network assignments were used to evaluate sevoflurane effects within particular functional systems. Additional FC analyses were computed in terms of voxelwise Pearson correlations with time series extracted from specific regions of interest, e.g., the whole thalamus region in Supplemental Digital Content 4, panel B, https://links.lww.com/ALN/B162. Pearson correlations were Fisher z-transformed before averaging and statistical significance testing.

Two-tailed t tests were used to compare behavioral, physiologic, and FC analyses. Nonparametric Mann–Whitney U tests were used for hypothesis testing of covariance estimates. These statistical tests, as well as correlation and covariance analyses, were performed using custom-written scripts implemented on MATLAB (MathWorks, USA). As only six participants provided usable data in both conditions, all group-level significance testing reported in the main text was based on unpaired comparisons. Bonferroni corrections were applied to correct for multiple comparisons.

Correlation and covariance matrices corresponding to 0 and 1.2% sevoflurane are shown in figure 1. All networks showed quantitative reductions of FC at 1.2% sevoflurane, but only differences in the DMN and the ventral attention network (VAN) (fig. 1C) remained significant (P < 0.05, Student t tests) after correction for multiple comparisons. The DMN is associated with social cognition and episodic memory and includes midline frontal and parietal structures.⁴²  In contrast, the VAN is involved in orienting to the external environment and includes anterior insula and anterior cingulate cortex.⁴³  Cognitive functions represented in both the DMN and the VAN are considered in detail in Discussion. Compared with correlation analysis (fig. 1, A and B), covariance analysis revealed marked widespread differences. Sevoflurane generally suppressed BOLD signal covariance and amplitudes within all RSNs (fig. 1F, U test, P < 10⁻⁸ for all comparisons, Bonferroni corrected). We verified that the effects shown in figure 1, C and F are found in a paired statistical analysis of the six subjects from whom data were acquired in both 0 and 1.2% sevoflurane conditions. These results are included for both correlation and covariance as bar graphs in Supplemental Digital Content 5, https://links.lww.com/ALN/B163.

Previous work suggests that both propofol anesthesia¹⁴  and slow-wave sleep^25,44  reduce within-network BOLD correlations along the anterior–posterior brain axis. To examine this effect in our (motion censored) data, FC maps were computed in the 0 and 1.2% sevoflurane conditions using seeds in the posterior cingulate cortex (PCC) node of the DMN and frontopolar nodes of the VAN (fig. 2). The coordinates of these seeds have been previously reported.⁴⁵  A comparison across conditions revealed weakening of FC between anterior (medial prefrontal cortex) and posterior (PCC, fig. 2A) components of the DMN during sevoflurane anesthesia (fig. 2, B and C). FC between the PCC and lateral parietal regions was preserved. Similarly, 1.2% sevoflurane reduced FC between the posterior parietal and the anterior portions of the VAN (fig. 2, E and F).

Altered thalamic activity has been widely associated with changes in arousal state.^2,46,47  To examine the effects of sevoflurane on thalamocortical FC, we computed conventional, Pearson correlation maps using the entire thalamus region in Supplemental Digital Content 4, https://links.lww.com/ALN/B162, as a seed. This analysis showed that the primary effect of sevoflurane-induced unconsciousness was weakening of thalamocortical FC over much of the anterior aspect of the mesial surface of each hemisphere (fig. 3, A and B). This anatomical territory encompasses portions of the DMN and VAN, the RSNs most altered in the analysis of intracortical FC (fig. 1C). Therefore, we checked whether these thalamocortical effects were specific from the perspective of RSN assignment by computing the mean FC between the thalamus and the cortical representation of each RSN. Reduced thalamocortical FC was most pronounced in the DMN and VAN (fig. 3C, P < 0.05, paired t tests).

The effects of 1.2% sevoflurane, assessed in terms of thalamocortical covariance, are shown in figure 4, A and B, the format of which parallels figure 3, A and B. Thalamocortical covariance values were generally reduced at 1.2% sevoflurane, especially over the mesial surface of the cerebral hemispheres. This result mirrors the pronounced reduction in BOLD signal amplitudes reflected in the intracortical covariance matrices (fig. 1F). Significant effects of sevoflurane were observed in ensemble measures (averages over within-RSN voxels) of the DMN, VAN, and dorsal attention network (fig. 4C, all P < 0.05, U test, Bonferroni corrected). This pattern of network specificity is similar to that shown in figure 3C, except that the sensitivity of the covariance-based FC seems to be somewhat greater than the correlation-based FC.

Intracortical FC analyses without quantitative motion censoring are demonstrated for BOLD signal correlation (fig. 5, A–C) and covariance (fig. 5, D–F), the format of which parallels figure 1. Without motion censoring, the matrices are dominated by positive values reflecting widely shared artifactual variance.²²  No significant sevoflurane-related differences in within-network FC were revealed by the correlation analyses. Covariance analyses showed artifactual increases at 1.2% sevoflurane. These results stand in marked contrast to the results obtained with motion censoring (fig. 1), which include many more values near zero. Thus, scrupulous motion censoring is essential in studies of this type.

The BOLD signal is sensitive to changes in retained carbon dioxide.⁴⁸  As sevoflurane anesthesia induces carbon dioxide retention,^49–51  we analyzed the extent to which changes in Paco₂ account for the effects shown in figure 1, C and F. This estimation was accomplished by the regression of Paco₂ from FC measures in each condition. Paco₂ explained less than 1% of the variance in (Fisher z-transformed) Pearson r values. Regression of Paco₂-dependent effects did not change the statistical significance of the sevoflurane effects in the correlation measures. Similarly, in the covariance analysis, Paco₂ explained less than 2% of the variance, also without affecting the statistical significance of the sevoflurane effects.

We report a resting-state fMRI study of humans rendered unresponsive by sevoflurane. The primary findings are that sevoflurane induces both a spatially widespread reduction in BOLD signal amplitude and also modest but specific reductions in intracortical and thalamocortical FC within the DMN and VAN. Our study differs from previous similar work in two principal characteristics: (i) scrupulous attention to the problem of head motion artifact constitutes a major feature of the methodology and (ii) covariance-based FC measures, which reflect BOLD signal amplitudes, are contrasted against conventional, correlation-based measures. We also demonstrate that, unless the artifacts attributable to head motion are adequately addressed, sevoflurane effects in correlation-based FC measures are obscured (fig. 5C), and observed changes in the covariance structure of intrinsic activity are in the wrong direction (fig. 5F).

The states of anesthetic-induced unconsciousness seem to resemble natural and pathologic reductions in consciousness. More specifically, disorders of consciousness,²³  absence epilepsy,^52,53  slow-wave sleep,^25,44  and propofol¹⁴  and sevoflurane³⁹  anesthesia are all associated with reduced correlation between the posterior (posterior cingulate/precuneus cortex [PCC]) and anterior (medial prefrontal cortex) components of the DMN. Reduced anterior–posterior FC in the DMN has been related to impairments in memory consolidation,^54,55  which may relate to the amnesic effects of sevoflurane.⁵⁶  Reduced FC along the anterior–posterior axis of the DMN is clearly evident in our results (fig. 2, B and C). This result is concordant with a recent study of sevoflurane anesthesia³⁹  but not others.^17,57  Our results (fig. 5C) indicate that insufficient attention to the problem of head motion artifact may account for these discrepancies.

We also observed significant reduction in FC along the anterior–posterior axis of the VAN (fig. 2, E and F). Similar findings have been observed with propofol.^15,16  The VAN, as originally defined, includes the anterior cingulate, anterior insular, middle inferior frontal, and inferior frontal cortical regions.^43,58  Herein, we also assign to the VAN parts of dorsolateral prefrontal cortex and the temporal-parietal junction.⁴¹  Others have variably assigned these regions to the “external awareness network”⁵⁹  or the frontoparietal control network.⁶⁰  Regardless of nomenclature, there is a wide agreement that these regions mediate the capacity to respond to external events.^23,59–62  Our findings are also consistent with altered frontoparietal FC reported in electroencephalographic studies of humans rendered unresponsive by sevoflurane, propofol, and other anesthetic agents.^4,63,64 

Altered thalamic activity is a well-established correlate of reduced arousal.^2,47,65–67  We observed focal reductions in FC between thalamus and midline cortical regions belonging to the DMN and VAN (fig. 3). In contrast, FC between thalamus and primary sensory areas was preserved (fig. 3). Experiments in rats anesthetized with sevoflurane indicate that pharmacologic excitation of medial (but not lateral) thalamus induces transient awakening.^68,69  Propofol has been reported to reduce cerebral blood flow specifically in the medial part of the thalamus.⁶⁷  Therefore, it is of considerable interest that the thalamic components of the DMN and the VAN are represented predominantly in midline nuclei.⁷⁰  Thus, our results support the hypothesis that sevoflurane preferentially acts on the medial thalamus in humans.

Arguably, the most salient feature of the present results is the pervasive reduction in BOLD signal covariance at 1.2% sevoflurane (fig. 1F). We previously observed similar effects in a heterogeneous sample of pediatric epilepsy patients sedated with a variety of anesthetic agents.³⁸  A similar finding, expressed in terms of voxelwise BOLD signal amplitudes, was recently reported by Huang et al.,³⁹  who tested both sevoflurane and propofol. That these effects have not been heretofore more widely recognized is understandable as the preponderance of resting-state FC studies have been focused on delineating RSN topographies rather than measuring BOLD signal amplitudes.^71,72  Covariance measures have informed studies of stroke⁷³  and white matter injury in premature infants.⁷⁴  The current results indicate that the predominant effects of sevoflurane anesthesia on resting-state fMRI signals are reduced amplitude and, consequently, reduced covariance.

This finding is entirely consistent with well-established results. Intrinsic signaling is the primary driver of spontaneous BOLD signal fluctuations^75,76  and also accounts for most of the brain’s energy utilization.⁷⁷  In humans rendered unresponsive by sevoflurane, similar reductions from baseline have been reported in measures of global cerebral blood flow^78–80  and total cerebral metabolic consumption of glucose^79,81  and oxygen.^79,80  As coupling of global cerebral blood flow and metabolic consumption of oxygen and glucose remain intact,⁷⁹  reduced amplitude of spontaneous resting-state BOLD signal fluctuations can be understood as a correlate of reduced intrinsic activity.

Head motion, even of a submillimeter magnitude, generates significant artifact in fMRI^18,21  by interfering with the physics of echo-planar imaging (“spin-history” effects).⁸²  Such artifacts are relatively inconsequential in task-based fMRI because they are automatically reduced by response averaging.⁸³  However, this advantage does not apply to resting-state fMRI.

We encountered unusually prevalent head motion even at 0% sevoflurane. The most likely explanation is discomfort attributable to respiration through a semiclosed breathing circuit. Anxiety related to anticipation of sedation also may have contributed. Subject motion during 0.6% sevoflurane sedation may be caused by paradoxical excitement⁸⁴  and by the inability of subjects to volitionally inhibit movement, as observed in previous studies of propofol sedation.^85,86  Almost none of the current fMRI data acquired at this state met our stringent quality assurance criteria. Usable data were acquired at 1.2% sevoflurane but data loss likely occurred because of intermittent agitation or partial airway obstruction. Thus, inhaled anesthetics present an especially challenging paradigm for resting-state fMRI. This circumstance probably accounts for the fact that only a minority of reported studies listed in Supplemental Digital Content 1, https://links.lww.com/ALN/B159, used these agents (9 of 48, all sevoflurane).

Strategies for minimizing head motion artifact depend on the FC methodology. With independent components analysis, it is possible to reject selected spatial components identified as artifact.⁸⁷  In seed-based correlation analysis, the principal strategy is regression of nuisance waveforms,³⁵  as in the current work. However, regression of nuisance waveforms, including waveforms derived from retrospective motion correction, may be insufficient in seed-based analyses, depending on the prevalence of head motion. Even exclusion of fMRI data on the basis of millimeter-scale movements may not be sufficient. To obtain meaningful results in high-motion subjects, exclusion of corrupted volumes (frames) from the FC computations may be required.^18,22  Most of the reports listed in Supplemental Digital Content 1, https://links.lww.com/ALN/B159, omit quantitative estimates of the prevalence and magnitude of head motion, thereby making it difficult to determine the reliability of reported FC results.

Carbon dioxide retention during sedation has the potential to alter FC. In this context, it is important to distinguish between moment-to-moment fluctuations in Paco₂, which directly generate artifactual BOLD signal correlations,^48,88  from FC alterations induced by sustained changes in Paco₂.^89,90  Less than one third of the studies listed in Supplemental Digital Content 1, https://links.lww.com/ALN/B159, report surrogate measures of arterial carbon dioxide. Propofol has been reported to induce 6 to 10 mmHg increases in Paco₂¹⁴  or end-tidal carbon dioxide (Etco₂).^37,85,86  These perturbations are comparable with the mild hypercapnia observed in our study (6 mmHg on average). More intense hypercapnia, e.g., 8 to 10 mmHg induced by 5% inhaled carbon dioxide, has been reported to slightly reduce FC and BOLD signal amplitudes in the DMN.⁹⁰  Critically, we determined that run-to-run changes in Paco₂ negligibly accounted for measured changes in FC (2% maximum explained variance).

The primary limitation of the current study is the relatively small sample size (10 and 9 subjects, respectively, at 0 and 1.2% sevoflurane). However, our study is not atypical in this regard compared with those in Supplemental Digital Content 1, https://links.lww.com/ALN/B159. It is worth emphasizing that studies of this type are exceedingly difficult because of the requirement for MRI-compatible ancillary equipment, limited participant tolerance for anesthetic-induced unconsciousness, and the high prevalence of subject motion.

The primary effect of sevoflurane-induced unconsciousness is diffuse reduction in BOLD signal amplitude consistent with widespread attenuation of neural activity. In addition, a modest degree of focality is observed, in particular, reduced FC in distributed brain networks associated with episodic memory and orienting to environmental stimuli.

The authors thank Biyu He, Ph.D. (National Institute of Neurological Disorders and Stroke, Bethesda, Maryland), and Eric Leuthardt, M.D. (Washington University School of Medicine, St. Louis, Missouri), for discussion leading to the development of the project; Jane Blood, B.S., R.N. (Washington University School of Medicine), Danielle Tallchief, R.N. (Washington University School of Medicine), and Kristin Kraus, B.S.N., R.N. (Washington University School of Medicine), for nursing support; Tracy Nolan, B.S. (Washington University School of Medicine), for technical support; and Chris Smyser, M.D., M.Sc. (Washington University School of Medicine), for comments on the manuscript.

This study was supported by Foundation for Anesthesia Education and Research (Schaumburg, Illinois)/Society for Neuroanesthesia and Critical Care (Richmond, Virginia) Mentored Research Training Grant (to Dr. Palanca), National Institute of General Medical Sciences (Bethesda, Maryland) grant UL1 RR024992 (to Dr. Palanca), National Institute of General Medical Sciences grant U25 MH071279-01 (to Dr. Palanca), National Institute of Mental Health (Bethesda, Maryland) grant F30 MH106253 (to Mr. Mitra), National Institute of Neurological Disorders and Stroke (Bethesda, Maryland) grant P30 NS-048056 (to Dr. Snyder), The Washington University Department of Anesthesiology (St. Louis, Missouri) (to Dr. Palanca), Mallinckrodt Institute of Radiology (St. Louis, Missouri) (to Dr. Raichle), and the McDonnell Center for Systems Neuroscience (St. Louis, Missouri) (to Dr. Raichle).

The authors declare no competing interests.

Our resting-state functional magnetic resonance imaging (fMRI) preprocessing stream causes the time average of the signal value at each voxel to be a mean of 0. Thus,

where f_i(t) is the signal averaged over region of interest i. Hence, all signals can be viewed as time-dependent fluctuations about a mean of 0. Standard covariance and correlation formulae⁹¹  are discussed below.

The covariance between time-dependent signals, f_i(t) and f_j(t), is

The Pearson product-moment correlation is

where

Thus, correlation is covariance normalized by root-mean-square deviation (σ). It is to be noted that the signal temporal SD is σ. Correlation becomes undefined as the SD of either of the two involved signals approaches 0. r_ij is a unitless scalar confined to the range (−1, +1). c_ij has units (fMRI signal)² and can assume any value in the range ().