The power of spectral density analysis for mapping endogenous BOLD signal fluctuations

Abstract

FMRI has revealed the presence of correlated low‐frequency cerebro‐vascular oscillations within functional brain systems, which are thought to reflect an intrinsic feature of large‐scale neural activity. The spatial correlations shown by these fluctuations has been their identifying feature, distinguishing them from fluctuations associated with other processes. Major analysis methods characterize these correlations, identifying networks and their interactions with various factors. However, other analysis approaches are required to fully characterize the regional signal dynamics contributing to these correlations between regions. In this study we show that analysis of the power spectral density (PSD) of regional signals can identify changes in oscillatory dynamics across conditions, and is able to characterize the nature and spatial extent of signal changes underlying changes in measures of connectivity. We analyzed spectral density changes in sessions consisting of both resting‐state scans and scans recording 2 min blocks of continuous unilateral finger tapping and rest. We assessed the relationship of PSD and connectivity measures by additionally tracking correlations between selected motor regions. Spectral density gradually increased in gray and white matter during the experiment. Finger tapping produced widespread decreases in low‐frequency spectral density. This change was symmetric across the cortex, and extended beyond both the lateralized task‐related signal increases, and the established “resting‐state” motor network. Correlations between motor regions also reduced with task performance. In conclusion, analysis of PSD is a sensitive method for detecting and characterizing BOLD signal oscillations that can enhance the analysis of network connectivity. Hum Brain Mapp 2008. © 2008 Wiley‐Liss, Inc.

INTRODUCTION

The presence of synchronized low‐frequency cerebrovascular oscillations within functional brain systems has been a major discovery of fMRI, providing insight into the large scale functional organization of the brain [Biswal et al., 1995; Raichle and Snyder, 2007; Xiong et al., 1999]. Up to 10 functional networks can be reliably identified within BOLD signal resting‐state recordings [Damoiseaux et al., 2006]. The oscillations appear to be an intrinsic component of neural activity, persisting even during anesthesia [Kiviniemi et al., 2005]. Many properties of these networks have been studied, including their stability across sessions and subjects [Damoiseaux et al., 2006; Fox et al., 2006], the frequency composition of correlations [Cordes et al., 2001], their relationship to task‐performance [Arfanakis et al., 2000; Fox et al., 2005c; Raichle et al., 2001], the effects of pathology [Fox et al., 2005b; Greicius et al., 2003; Quigley et al., 2003], the effects of physiological perturbations [Biswal et al., 1997; Peltier et al., 2005], and interactions between different networks [Fox et al., 2005a; Greicius et al., 2003]. Recent studies have found that low frequency oscillations may in fact reveal a more detailed hierarchical organization of functional connectivity that parallels known anatomical connectivity [Achard et al., 2006; Salvador et al., 2005].

Correlations in BOLD signal between brain regions has been the primary identifying feature of endogenous resting‐state networks, and has served to distinguish these oscillations from those associated with other processes. Correlation‐based analysis approaches including seed‐region regression [Biswal et al., 1995; Fox et al., 2006; Hampson et al., 2002; Xiong et al., 1999], ICA [Arfanakis et al., 2000; Calhoun et al., 2001; Damoiseaux et al., 2006], coherence analysis [Sun et al., 2004, 2007], cluster analysis [Cordes et al., 2002], partial correlation analysis [Salvador et al., 2005], and wavelet correlation analysis [Achard et al., 2006] have been applied to identify networks and to characterize connectivity differences across different conditions.

While correlation‐based techniques have been the dominant class of methods for analyzing fMRI fluctuations, they do not fully characterize the system dynamics. Potential confounds exist for any study of systematic changes in connectivity across conditions. Cardiac pulsations, respiration effects, and fluctuations associated with blood CO₂ levels may all change across experimental conditions and are likely to affect correlations between voxels [Giardino et al., 2007; Wise et al., 2004]. Factors such as anxiety, breath‐holding, and age can affect baseline cerebral blood flow and change the amplitude of BOLD signal effects, potentially affecting the size of correlations [Abbott et al., 2005; Giardino et al., 2007]. Correlation‐based techniques are not able to directly distinguish the effects of these phenomena on inter‐regional correlations from those associated with changes in neural dynamics. While a variety of methods such as band‐pass filtering, global signal regression, and cardiac signal regression have been used to suppress the effects of specific signal confounding factors, these methods remain heuristic and are not applicable to all fMRI studies [Biswal et al., 1996; Deckers et al., 2006]. Studies focused primarily on inter‐regional correlation properties within a particular network, focusing on a narrow frequency band, will inadequately characterize changes in dynamics that occur across a broader range of frequencies or affect correlations within multiple networks.

The power spectral density (PSD) characterizes the frequency distribution of signal variance in a time series. The PSD of BOLD signal in gray matter shows a distinct frequency dependence, with greatest power at low‐frequencies (<0.10 Hz). Sources of oscillations in this band include endogenous network fluctuations, low frequency cardiovascular fluctuations, autoregulatory vasomotion, and uncontrolled cognitive processes [Wise et al., 2004]. In activation studies, switches in task conditions often fall into this frequency band. The PSD can also exhibit peaks at higher frequencies, associated with cardiac and respiratory pulsations, some of which are aliased at standard acquisition rates [Cordes et al., 2001; Mitra et al., 1997]. White matter tends to exhibit a flatter frequency spectrum, with relatively less power at low frequencies.

The ability of the BOLD signal power spectrum to resolve changes in brain dynamics has not been well established. Power spectrum estimation ideally requires long blocks in which the subject is in a stable task‐state. Most analyses of such data have focused on measures of connectivity. A recent fMRI study by Fukunaga et al. [ 2006] found steady increases in average low frequency (<0.05 Hz) signal power over the extended periods of rest, which appeared to be associated with drowsiness or sleep. A subsequent ICA analysis determined that these amplitude increases occurred across multiple networks of correlated activity. This study did not, however, determine whether the changes in fluctuations significantly affected inter‐regional correlations. In another recent study, Yang et al. [ 2007] compared the amplitude of low frequency fluctuations during eyes‐open rest to eyes‐closed rest, finding increased in BOLD signal fluctuations in visual cortex, and reductions in the right paracentral lobule (PCL).

Continuous task‐performance is likely to alter the spectral characteristics of the BOLD signal. Studies have reported both increases and decreases in functional connectivity during continuous task performance, however few have characterized changes in the PSD. Fransson [ 2006] studied properties of the task‐negative default‐mode network, which they had previously identified to include the precuneus, posterior, and anterior parts of the cingulate cortex, medial prefrontal cortex, lateral parietal cortex, anterolateral temporal cortex, and the parahippocampal gyri [Fransson, 2005]. They found a reduction in spectral power in the 0.012–0.1 Hz band in this network during a sustained working memory task. These changes were not significant in all ROIs in the network, such as medial prefrontal cortex. Fransson did not assess changes in BOLD signal power outside of this network. The working memory task also produced reductions in the amplitude of signal in many parts of the default network and reductions in the strength of correlations between its component regions. In a near infra‐red spectroscopy study, Obrig et al. [ 2000] found fluctuations in deoxyhemoglobin in visual cortex to decrease in amplitude during visual stimulation. Leopold et al. [ 2003] assessed fluctuations of band‐limited power measurements from electrode recordings in monkey visual cortex, finding low‐frequency (<0.1 Hz) fluctuations to be coherent over extended distances. The measured local field potential signal, known to be correlated with BOLD signal, also showed reduced power during task periods, particularly at frequencies of 1 Hz and below [Logothetis et al., 2001].

The above results suggest that analysis of PSD can resolve changes in oscillatory BOLD signal dynamics associated with changes in neural activity. Our aim in the present work was to determine whether a full‐band voxel‐wise characterization of PSD changes over the course of experimental sessions can reveal effects that are lost or misinterpreted in multivariate, correlation‐based approaches. We analyzed scanning sessions that contained extended periods of motor performance and rest. Our aim was to verify the previously reported dynamics of the BOLD signal PSD, determine the spatial and frequency distribution of these effects and investigate the relationship between PSD changes and inter‐regional correlations.

METHODS

Experimental Paradigm

Fourteen right‐handed volunteers (7 M, 7 F), ranging from 18‐ to 45‐years‐old, with no known neurological disorders, were recruited, trained, and imaged. An informed consent statement was obtained for each subject before participation. The study was approved by the Institutional Review Board of the Research Imaging Centre, San Antonio. Subjects underwent three scanning sessions over a one month training period, with six scans acquired in each session. The results presented here are derived from an analysis of the first session, which was recorded prior to any training.

Figure 1a shows the design of each session. In the first and final scan of each session subjects were asked to remain as still as possible, resting with their eyes open (“resting‐state scans”). These scans were 280 s in duration, and were recorded with a fast acquisition rate, TR = 0.7 s. The second through fifth scans lasted 8 min each, during which two 2‐min finger tapping periods were interposed with 2 min rest periods (“task‐performance scans”). During task‐periods, fingers of the left hand were repetitively tapped upon the thumb in a specific ordered sequence. One of two tapping orders were performed, 4‐2‐3‐1 and the reverse, 1‐3‐2‐4 in a randomized fashion. Subjects were instructed to maintain a steady 2 Hz finger tapping rate paced by the noise of the regular gradient shifts. The scans within each session were separated by periods of no longer than 1 min, during which subjects were advised of the upcoming task and were instructed to rest.

Figure 1.

(a) Experimental sessions: the first and final 4‐min scan of each session were resting‐state scans with an acquisition rate of 1.4 Hz, and a reduced field of view (green box). The second through fifth scans recorded alternating 2 min periods of task performance and rest, at an acquisition rate of 0.5 Hz, with full brain coverage (white box). Task performance was randomized between two simple, untrained, left handed thumb‐to‐finger tapping sequences. (b) Spatial distribution of the average estimated spectral power at frequencies 0.03, 0.10, 0.23, and 0.35 Hz in a single slice from the first resting‐state scan [position shown in red in (a)]. (c) Regions showing significant group‐level differences in spectral density in the second resting‐state scan, compared to the first, at the frequencies shown. There were significant increases in average spectral density at higher frequencies across the cortex.

Acquisition

Scanning was performed on an Elscint Prestige 2 Tesla whole body scanner. During the task‐performance scans, 240 16‐slice whole‐brain volumes were acquired using a T2*‐weighted gradient‐echo, echo‐planar‐imaging sequence (TR = 2,000 ms; TE = 45 ms; flip angle = 70°; slice thickness = 6 mm; 3.19 × 3.21 mm² in‐plane voxel resolution; 128 × 72 image matrix, FOV 411 × 229 mm²). In the resting‐state scans, 400 six‐slice brain volumes were acquired with a TR of 700 ms. The resting‐state images consisted of the superior six slices of the task‐performance scans, which reliably covered the sensory‐motor strip, supplementary motor area (SMA), cingulate, superior frontal and parietal cortices. Other acquisition settings were as specified for the task‐performance scans. The first four volumes were discarded from all scans to ensure stable magnetization was reached.

At the end of the fMRI data collection, spin‐echo, T1‐weighted anatomical images (TR = 33 ms; TE = 12 ms; flip angle = 60°; slice thickness = 5 mm; 1 × 1 mm² voxel resolution; 256 × 256 image matrix) were acquired in the same slice positions to facilitate the precise determination of the structures corresponding to the functional activation foci. For registration, a high resolution 3D image was also acquired (TE = 6 ms, TR = 33 ms, flip angle = 35°, 256 × 256 image matrix, 1 × 1 × 0.5 mm³ voxel resolution).

Preprocessing

BOLD signal time series preprocessing and GLM activation analysis was performed using the FSL tool, FEAT (FMRI Expert Analysis Tool, http://www.fmrib.ox.ac.uk/fsl). Rigid body motion correction was applied to all functional time series, with estimates of head motion retained for assessment with the voxel data [Jenkinson et al., 2002]. Gaussian spatial filtering (5 mm FWHM) was applied to all images.

Spatial normalization was performed with the FSL tool FLIRT, by first registering each subject's individual EPI data to their high resolution T1 image, and registering this image to the MNI template brain using an affine transformations with 12 degrees of freedom [Jenkinson et al., 2002]. Spatial normalization of the resting‐state data was achieved by first registering a whole‐brain EPI scan to the resting‐state data, using a rigid‐body transformation. The whole‐brain EPI scan was then used to generate the required spatial normalization transforms.

Data Extraction and Assessment

In our study we were interested in signal fluctuations during periods of continuous task performance and rest. The 280‐s resting‐state scans were investigated in their entirety, except for four scans at onset removed to avoid magnetization artefacts. In the task‐performance scans, 90‐s blocks of the EPI images were extracted, starting 30 s after transitions between conditions to avoid the nonstationary transients at task transitions reported previously [Duff et al., 2007]. The data were checked for major artefacts. Linear trends were removed using MATLAB by fitting a linear function to the data and removing it. Estimated head motion parameters were regressed from the BOLD data, and analyzed for changes correlated with the experimental paradigm.

Estimation and Modeling of Power Spectral Densities

Spectral analysis was performed utilizing the Chronux spectral analysis MATLAB toolkit (http://www.chronux.org) [Mitra and Pesaran, 1999; Mitra et al., 1997]. This implements multitaper spectral estimation, which utilizes a sequence of orthogonal taper functions to produce multiple tapered data samples from which independent spectral estimates can be obtained. These are averaged to produce a final spectral estimate. The multitaper procedure reduces variance and bias in PSD estimation, enabling the assessment of small, noisy datasets. The discrete‐spherical‐proloid sequence of functions (Slepian functions) are employed as taper functions, being the set of orthogonal functions that have a maximal concentration of spectral power within a given frequency band. An integer parameter NW for these functions determines the spectral smoothing their use will entail, with N specifying the number of time points, and W being the bandwidth parameter that determines the frequency band within which the Slepian functions are concentrated. The choice of the bandwidth parameter should be based on visual assessment of the spectral estimates, to ensure variance reduction is achieved without the introduction of distortion [Mitra and Pesaran, 1999]. We were interested in average spectral effects significant at the group level, so our analysis involved smoothing across multiple runs. Therefore, we chose a relatively low level of spectral smoothing, W = 0.03 Hz, to maintain spectral resolution. The leading 2NW Slepian functions contain almost all of the spectral power of the sequences. Slightly less than 2NW tapers are typically employed for spectral estimation, as the final tapers have worsening spectral concentration properties. We therefore used 13 tapers for the resting‐state scans, and five for the task‐performance blocks. This estimation procedure reduced the effect of isolated signal spikes on the spectral estimates for individual runs, but did not distort the overall shape of the spectra.

Separate spectral estimates are obtained for each tapered sample and averaged to provide a smoothed spectral estimate [Percival and Walden 1993; Thompson, 1982]. This procedure controls variance and bias in the estimation of the PSD of noisy time‐series, enabling the assessment of small, noisy datasets. An integer bandwidth parameter for the Slepian functions, NW, determines the spectral resolution. For both scan‐types, we chose this parameter so as to provide a spectral smoothing bandwidth of ∼0.03 Hz. We used 15 tapers for the 280 s resting‐state scans, and five for the shorter ninety second blocks of task‐performance or rest from the task‐performance scans. This procedure reduced the effect of isolated signal spikes for the spectral estimation of individual scans.

Power spectra were calculated in native space for individual scans, for all brain voxels. The resulting 4D spectral image files were spatially normalised and averaged across subjects to provide an indication of the average PSD function. We performed statistical analysis on the power estimates at a number of frequencies, 0.03, 0.10, and 0.23 Hz. For the resting‐state scans we also assessed power at 0.35 Hz. These frequencies were chosen to enable us to assess two separate components of the traditional low‐frequency spectral band, and to assess the higher frequency band often assumed to be dominated by physiologic artefacts.

Linear modeling and statistical analysis of the data was performed using MATLAB, FEAT, and additional tools provided in the FSL package. Systematic change in spectral power over the course of the experimental sessions was assessed by fitting separate linear models to the power estimates at each selected frequency. The rapid acquisition part‐brain resting state runs (scans 1 and 6) were modeled separately from the motor‐task runs (scans 2–5), because of their different acquisition rates, which affect high‐frequency aliasing and the total spectral power of the series. The resting‐state scan analysis modeled changes between the resting‐state scan at the start of the sessions, and the resting‐state scan at the end of the sessions, across all subjects. The task‐performance scan analysis modeled differences between the task‐performance and rest periods of these scans. The model accounted also for changes in task and rest spectral power over time. All linear models included regressors accounting for subject‐to‐subject variation in spectral density. Contrasts were defined that tested for both increases and decreases in power across conditions. For the task‐performance scans, the GLM included regressors accounting for linear change over time for both the rest and task periods, as well as the differences between task and rest conditions. As the spectral power estimates at the analyzed frequencies were well above zero for all samples, the data were not skewed and an assumption of Gaussian variability across samples was reasonable. A z‐score cut‐off of 2.3 was employed to identify clusters, and a cluster probability was estimated using Gaussian Random Field theory [Worsley et al., 1992]. Clusters with P‐values of less than 0.05 were retained. Results were compared with a GLM activation analysis of the task‐performance scans, performed using FEAT [Duff et al., 2007].

ROI Assessment

We utilized the REX toolbox [Duff et al., 2007] to visualize regional spectra and to generate time‐plots of signal power over time. Three ROIs in the SMA, and left and right motor cortex were derived from a GLM activation analysis of the dataset [Duff et al., 2007]. A fourth ROI in the left middle frontal gyrus was defined manually, based on a standard labeling of the MNI standard brain, to enable assessment of signal in a nonmotor region [Tzourio‐Mazoyer et al., 2002]. A jack‐knife procedure, performed over all tapered data samples, was employed to generate error bars in the spectral plots. Assuming local smoothness in the spectrum, the orthogonality of tapers ensures that the spectra estimated from the tapered time series are independent of each other. The jack‐knife procedure generates estimates of variance at each point, which were converted to 95% confidence intervals [Mitra and Pesaran, 1999]. Moving average plots of the spectra within the ROIs were generated to determine visually if there was any evidence of consistent changes in spectra within the resting‐state scans. These used a 60‐s moving window with a 5‐s step. Time plots showing changes in average spectral power over the task‐performance scans of the experiment were generated, for the same frequencies used for the spatial mapping. The correlation between the signal from each of the ROIs were calculated for individual scans, and also visualized as time plots.

RESULTS

Training and Preprocessing

Subjects were able to perform the task in the scanning sessions at the required pace. Difficulties in spatial normalization of the part‐brain resting‐state images led to two subjects being excluded from the analysis of the resting‐state scans. During data assessment, two resting‐state scans were removed from a further subject due to excessive motion. Head motion levels were typical for an fMRI experiment, with estimated displacements during scans typically less than 2 mm. In the Y‐plane there was a consistent linear drift due to hardware instabilities, resulting in image displacement of up to 3 mm over the course of scans.

Resting‐State Scans

We first assessed the spectral properties of the resting‐state scans recorded at the start and end of sessions, as these volumes were acquired at the higher acquisition rate. Spectral power was strongest at frequencies below 0.05 Hz (Fig. 1b) and reduced markedly over the frequency band 0.05–0.2 Hz. In many regions there was increased spectral power between 0.2 and 0.4 Hz.

The overall spatio‐temporal distribution of power was consistent with previous reports [Fukunaga et al., 2006; Mitra et al., 1997]. Low frequency power was strongest in the gray matter, particularly posteriorly and along the midline. High frequency signal power showed little contrast across grey and white matter compared to lower frequency signal. BOLD signal power at the lower end of the 0.2–0.4 Hz band was strongest around major sinuses, suggesting cardiovascular effects. There was a clear peak medio‐posteriorly around the sinus confluens, another medially near the SMA and cingulate, and bilaterally at the junction of the parietal and temporal lobes, near the inferior sagittal sinus (Fig. 1b, 0.23 Hz). At 0.35 Hz there was less power at the sinus confluens and saggital sinus.

BOLD signal fluctuations were increased in the second resting‐state scan, which followed the task‐performance scams. Figure 1c maps regions in which power was significantly greater in the second scan compared to the first, for the four different frequencies assessed in our analysis. Extended regions of the brain showed increases in BOLD signal power around 0.23 Hz, in both gray and white matter regions. Investigation of the data at a slightly lower z‐score cluster threshold (z > 1.7, cluster P‐value < = 0.05), and assessment of similar results from subsequent sessions of the experiment, showed widespread tendency for BOLD signal power increases at 0.35 Hz, and for signal at 0.03 Hz to increase bilaterally across motor‐sensory cortices.

Group‐averaged spectra from the SMA, left and right primary motor cortex and the left middle frontal gyrus were compared for the first and second resting‐state scans separately (Fig. 2a, green and red respectively). In the group‐averaged data, increases in power could be seen across the 0.2–0.4 Hz band in all regions. In some regions, such as the right motor cortex, new spikes appeared in the spectra. The significant change in lower‐frequency spectral power in the left motor cortex is clearly separated from the 0.2–0.4 Hz band effects by a middle band that shows little change across the two scans. Moving average power spectrograms of the first and second resting‐state scans, averaged over all subjects, indicated that there were no consistent changes in spectra over the course of either of the resting‐state scans (Fig. 2b).

Figure 2.

(a) Average spectral properties of the SMA, right and left motor cortices, and the left middle frontal gyrus for the two resting‐state scans. Dashed lines show 95% confidence intervals for the mean, determined by a jack‐knife procedure. (b) Group‐average spectrograms of the SMA ROI for the first and second resting‐state scans, using a 60‐s window.

Average BOLD signal correlations between all ROIs were increased in the second resting‐state scan, although the increase was only significant (P < 0.05) for correlations between right motor cortex and left medial frontal gyrus.

We calculated the PSD of the estimated head motion parameters. These data showed a similar PSD structure to the BOLD signal, with strong low frequency power, and higher frequency peaks 0.2–0.4 Hz (results not shown). The PSDs of estimated y‐plane motion and roll around the y‐axis showed small but significant increases in power above 0.2 Hz. Comparison of the BOLD ROI spectra before and after regression of motion parameters showed no apparent effect of the regression on the changes in across spectral power scans (results not shown).

Task Performance Scans

The task performance scans (2–5) were assessed for power spectral differences between task and rest conditions. Low frequency BOLD signal fluctuations decreased during the performance of the motor task (Fig. 3a). At 0.03 Hz these changes were widespread in the gray matter, with particular strength in bilateral motor and sensory cortices, the SMA, temporal and parietal lobes, insula, and the cerebellar hemispheres. At 0.10 Hz, voxels showing statistically significant reductions in spectral power during the task condition were less widespread, with no significant voxels at the midline. At 0.23 Hz only small clusters showed significant reductions in power. The symmetric distribution of decreases in signal oscillations across the cortex contrasted with the increases in sustained signal amplitude that also occurred during task periods, which exhibited some right‐hemisphere lateralization [Fig. 3b, Duff et al., 2007].

Figure 3.

(a) Regions showing changes in spectral power during task periods compared to the spectral power during the rest periods, at frequencies 0.03, 0.10, and 0.23 Hz. (b) Regions showing sustained increases in BOLD signal amplitude during the task periods, compared to the rest periods (activation).

Figure 4a shows ROI time‐plots of average spectral power across scans 2–5, at three frequencies. The differences between task and rest periods can be seen for the SMA and motor cortices at 0.03 Hz. At 0.23 Hz a consistent increase in signal power over the course of the session can be seen in motor regions, affecting both task and rest periods. The nonmotor ROI, the left middle frontal gyrus, showed some change in low frequency power, but no change in high frequency signal.

Figure 4.

(a) Time plots of average BOLD signal power in ROIs over the four task‐performance scans (scans 2–5). Task periods are shaded. Error bars show standard errors. (b) Time plots of changes in correlation between ROIs over the four task scans.

Figure 4b tracks correlations between SMA and the three remaining regions, and between right M1 and the two regions, left M1, and left middle frontal gyrus. The pattern evident in the correlations between motor regions mirrors that of spectral power at low frequency, with correlation higher in the rest periods than during task periods. A trend over time was not evident. The medial frontal gyrus signal showed limited correlation with motor regions.

Finally, the PSD of task performance scan motion parameters showed no consistent differences in task periods compared to rest (results not shown). Average low frequency Y‐plane motion and roll was greater in the initial rest period of the first task performance scan, however we found no other significant changes over time.

DISCUSSION

The aim of the present work was to investigate whether the PSD of BOLD signal shows significant changes across the brain over the course of fMR scanning sessions. We were interested to determine if the analysis of PSD changes could provide an informative characterization of BOLD signal oscillations complimentary to correlation‐based analyses. A key potential strength of the approach was that it could provide a characterization of BOLD signal oscillations at each voxel. A second potential strength was that it could identify the frequency band over which changes in signal dynamics occur. Our analysis assessed spectral power across a wide frequency band to ensure that the investigation would identify any aspect of signal oscillations that showed changes over the course of the experiment.

Substantial changes in PSD were detected over the course of the scanning sessions. The analysis localized in frequency and space systematic changes in BOLD signal dynamics, providing a characterization of these changes that would not be provided by standard techniques. The increase in correlations over time were found to occur across a wide frequency band, with low and high frequency bands showing different patterns of changes. The reductions in BOLD signal oscillations observed during task performance were notable for occurring within both activated and nonactivated brain regions, and across regions associated with a number of different resting‐state connectivity networks. Parallel changes in inter‐regional correlations were observed, indicating that the dynamics causing changes in the PSD are likely to affect connectivity analyses.

In the following we discuss the implications of our observations, and ways that PSD analysis can be implemented as a routine component of fMRI analyses. While this study did not aim to isolate the different physiological components underlying the BOLD signal dynamics, we also discuss of the possible sources of the observed effects.

Changes in Power Spectral Density Over Time

Changes in high frequency power

The strongest and most widespread changes in fluctuations over time were at high frequencies. High frequency signal power (0.23 Hz) was significantly higher in the second resting‐state scan compared to the first in many areas. Time‐plots of the task‐performance scans indicated that high frequency BOLD signal power rose during the task‐performance scans, in both task and rest conditions, particularly over the last two scans of the sessions. Spectrograms of brain signal during the resting‐state scans indicated that the high frequency power did not start to normalize to baseline levels over the 4 min of the final resting‐state scan.

Fukunaga et al. [ 2006] tracked BOLD signal power changes over extended scanning periods but did not find increases in high‐frequency signal. Their paradigm did not involve repeated task performance, suggesting that the present results could be associated with the performance of a motor task. A number of studies have reported changes in resting‐state signal dynamics following task performance, but these studies did not investigate high‐frequency signal effects [Peltier et al., 2005; Waites et al., 2005]. Increases in signal power could reflect changes in ongoing neural activity following motor performance, or changes in the sensitivity of the vasculature to physiological pulsations following activation. However, as there was no significant immediate effect of task performance on high frequency signal, and the signal changes were not strongly localized to activated regions, these possibilities appear unlikely.

The changes in high frequency BOLD signal activity are likely to be associated with the cardiovascular and respiratory processes that form a major component of signal variation in this frequency band [Birn et al., 2006; Cordes et al., 2001; Mitra et al., 1997]. These processes are known to be sensitive to levels of arousal [Giardino et al., 2007; Wise et al., 2004]. The repeated task performance, or changing levels of relaxation, anxiety, or discomfort over the course of the scan, could have directly affected these physiological processes, causing the increase in the BOLD signal fluctuations.

Respiration and cardiac pulsations may cause head movement, which showed a spectral profile with high frequency peaks similar to those of the BOLD signal spectrum. Head motion parameters also showed some increase in power above 0.23 Hz for the resting‐state scans. As the spatial distribution of regions showing power increases did not show the edge effects typically associated with motion artefacts, it may be that a common respiratory or cardiovascular source contributed to both brain and head‐motion signals. However, the regression of motion parameters from the brain data did not affect the observed changes in power. Hardware instabilities, perhaps related to the heating of electronic components, are another potential source for the changes in signal oscillations. The specificity of the observed effects to brain tissue suggests this is unlikely.

Changes in low frequency power

The left motor cortex showed significantly increased low‐frequency spectral power in the second resting‐state scan, compared to the first. An assessment of the modeling at a slightly lower cluster z‐score cutoff found such a tendency was more widespread, occurring bilaterally across much of the sensory‐motor cortices. An increase in low‐frequency spectral power over time was also apparent in the task‐performance scan time plots. The limited increase in spectral power around the 0.10 Hz band suggests that the low‐ and high‐frequency increases could have separate sources.

The low‐frequency power spectral increases in motor regions may reflect a phenomenon related to previous observations of changes in low‐frequency functional connectivity following task performance [Peltier et al., 2005; Waites et al., 2005]. Following the performance of a language task, Waites et al. found complex changes in the patterns of connectivity of a set of regions that were highly activated during the task. Peltier et al. [ 2005] focused on changes in resting‐state functional connectivity between the motor cortices subsequent to the performance of a fatiguing motor task, finding a significant reduction in correlation. They proposed two potential sources for the observed change: a persistent intrinsic adaptation of the motoneurons as a result of the sustained stimulation, or fatigue‐related inhibition of the neurons from sensory afferent neurons. Our task was not highly fatiguing, but involved intensive performance of an attention‐demanding motor task which could cause persistent intrinsic neural adaptation, or activity associated with consolidation of the practiced motor skill. Whereas we found no significant changes in correlation between motor cortices in the final resting‐state scan, both of the processes discussed by Peltier et al. could conceivably produce changes in the BOLD signal dynamics of individual regions that could be directly detected by spectral power analysis.

Alternatively, the change in low‐frequency spectral power could be associated with subjects becoming increasingly relaxed or drowsy during scanning sessions. Combined fMRI/EEG studies have found low‐frequency BOLD signal oscillations in fronto‐parietal and occipital networks to be correlated with measures of power in alpha, beta, and theta EEG bands, which are known to correlate with levels of vigilance and sleep states [Laufs et al., 2006]. Fukunaga et al. [ 2006] found large increases in low frequency (<0.05 Hz) BOLD signal fluctuations in visual cortex in subjects who reported drowsiness or sleep during extended resting‐state fMRI scans. A recent follow‐up study found the amplitude of low‐frequency BOLD signal fluctuations in many regions, including the visual, motor, and auditory cortices, to be negatively correlated with wakefulness, as indexed by a measure derived from EEG alpha band power [Horovitz et al., in press]. All subjects in our study performed the task successfully and none fell asleep. However, the long‐duration task and rest blocks may have resulted in subjects becoming drowsy and closing their eyes, which would cause an increase in α‐band activity and low‐frequency BOLD signal oscillations. The limited FOV of our resting‐state scans did not enable us to assess signal in the visual cortex, where these effects have been found to be strongest [Horovitz et al., in press].

Recent studies have found low‐frequency cardiac [Shmueli et al., 2007], respiratory [Birn et al., 2006], and respiration‐related blood‐CO₂ [Wise et al., 2004] fluctuations as having significant influence on BOLD signal in brain tissue. The mechanisms of these physiological contributions to low‐frequency BOLD signal are not well understood, but may be associated with respiratory feedback mechanisms that modulate blood CO₂ levels, or subtle fluctuations in heart rate and arterial blood pressure [Birn et al., 2006]. Factors affecting these contributions, such as relaxation or anxiety, could be another source of the increases in low frequency signal power.

Changes in spectral density with task performance

Task performance produced a decrease in low‐frequency BOLD signal power, but had no effect at higher frequencies. This result agrees with previous reports of task‐induced reductions in the low frequency spectral power of BOLD signal in ROIs in the default network [Fransson, 2006], and of NIRS signals from the visual cortex [Obrig et al., 2000]. The present analysis provides a spatial characterization of spectral power changes, finding task performance to induce reductions in BOLD signal power across a broad, symmetric network, consisting of both activated and nonactivated regions. This result complements the recent study of Yang et al. [ 2007], which reported increased low frequency BOLD signal fluctuations in the visual cortex, and decreased fluctuations in the PCL, during eyes‐open rest, compared to eyes‐closed rest. Taken together, these results indicate that the characterization of spectral power may be a valuable method for identifying changes in BOLD signal dynamics. The PSD of BOLD signal can change significantly across different conditions, and may show interesting localized variations when two similar conditions are compared.

The differences between low frequency BOLD signal spectral power in the task and rest periods were clearly visible in the mean time‐plots. Interestingly, it was not possible to distinguish those regions that showed concurrent sustained activation (e.g., right M1, SMA), from those that did not (e.g., left M1), based on the BOLD signal power spectral data. This suggests that blood flow responses associated with task‐related responses did not directly affect the BOLD signal oscillations.

The spatial symmetry of the reductions in PSD during task performance, and their specificity to low‐frequencies, suggests that they may be associated with the same phenomena that underlies the correlated low‐frequency fluctuations in resting‐state networks. Inter‐regional correlations were also reduced during the task performance periods of our recordings. Focusing on the default mode network, Fransson [ 2006] found reductions in functional connectivity during performance of their working memory task, using a posterior cingulate cortex (PCC)/precuneus area seed region. Interestingly, there were reductions in the extent of both the network of regions correlated with the seed region (the task‐negative default mode network), and the network anticorrelated with the seed region (task‐positive network). Our results suggest that changes in network correlations during task conditions may be associated with widespread changes in the amplitude of low‐frequency oscillations, rather than specific changes in the connectivity of particular regions or networks. Inter‐regional correlations will be reduced if the amplitude of the correlated oscillatory components of regional BOLD signals decreases relative to components of the signals that do not show spatially extended correlations. Analyses that only assess connectivity patterns within specific networks will not adequately characterize dynamics if they include the spatially widespread changes in oscillations we have identified.

The differences in the amplitude of BOLD signal oscillations between task and rest periods may be related to the known correlation of low‐frequency BOLD signals with α‐band EEG power, which increases during rest and light sleep [Horovitz et al., in press]. The network of regions showing task‐related reductions in BOLD spectral power in our data was similar to the network of regions that showed brief transient signal spikes at task onset, subsequently followed by a dip in signal [Duff et al., 2007]. These transients could not have influenced the spectral power density estimates directly, as the first thirty seconds of data following task transitions was excluded from the spectral estimation. These dynamics may reflect task‐related inhibition of endogenous oscillations across the brain, with the transient BOLD signal increase at onset reflecting an initial response to the inhibitory input.

Alternatively, the observed effects could be associated with changes in the cardiac, respiratory, or blood CO₂‐related contributions to low‐frequency BOLD signal fluctuations during task performance. Changes in the contributions of respiration and cardiac cycles to BOLD signal during task performance are expected, but have not been studied in detail. The spatial pattern of regions showing reductions in low‐frequency power during task performance was similar to previously reported patterns of BOLD signal correlations with respiration [Birn et al., 2006] and low‐frequency blood‐CO₂ fluctuations [Wise et al., 2004]. Subtle changes in breathing patterns or heart rate may affect these processes [Birn et al., 2006; Wise et al., 2004]. The fluctuations produced by these processes are spatially correlated, so that any changes are likely to affect inter‐regional correlations. It is interesting that the significant changes in blood flow in activated regions did not affect spectral power at high frequencies, where there are large contributions from physiological sources.

Applications of PSD Analysis

Our results indicate that PSD analyses are able to characterize a variety of changes in BOLD signal oscillations in a voxel‐wise manner, and thus provide a useful additional method for the characterization of oscillatory behavior. Whole brain, full bandwidth characterization of spectral power dynamics will enable accurate assessment of the BOLD signal dynamics underlying changes in connectivity measures, helping to avoid spurious attribution of effects to changes in inter‐regional interactions. Inaccurate modeling of fMRI BOLD signal dynamics can have a significant impact on fMRI analyses [Gavrilescu et al., 2004; Razavi et al., 2003; Zhang et al., 2006]. Changes in BOLD signal power over the course of fMRI sessions could bias investigations of slow neural processes that have an intrinsic temporal ordering, such as sleep, particularly when connectivity analysis methods are employed. Large reductions in the amplitude of low‐frequency fluctuations during task performance could invalidate the noise models used in GLM analysis.

Further investigation is required to accurately identify the source of the effects observed here, determine their prevalence across experimental datasets, and develop modeling or preprocessing approaches that minimize their impact on analyses of other aspects of the BOLD signal. The source of both the time‐ and task‐correlated changes in BOLD signal PSDs could be clarified by performing a study of similar design to the present one that includes concurrent recording of EEG and physiological cycles, enabling a detailed comparison of the different signals. Investigations assessing multiple task‐types will determine whether the changes in BOLD signal dynamics observed both during and after task performance are sensitive to the type of tasks performed. The reductions in low‐frequency BOLD spectral power during task performance may correlate with task‐difficulty or other factors [Fransson, 2006]. PSD analysis could be used to assess methods for removing physiological contributions from BOLD signal activity, by testing whether the methods remove spectral‐power changes that are found in both the BOLD signals and physiological measurements.

In circumstances where spurious changes in connectivity measures can be ruled out, PSD analysis may assist in identifying different modes of inter‐regional coupling. For example, increased coupling between two regions might involve the introduction of a new component to activity into one or both regions, resulting in localized increases in BOLD signal spectral power in a certain frequency band. Alternatively, increased coupling between two regions could reduce concomitant neural activity, reducing the spectral power of BOLD signal.

PSD analysis involves a frequency decomposition of the signal, and is optimally used in conjunction with other methods that are able to isolate specific components of the signal dynamics for modeling and statistical analysis. PSD analysis is most appropriate for studies with extended trial durations that enable the PSD estimates to be calculated separately for each condition. However, the method may also provide some insight for studies with standard task‐switching rates, where the PSD is calculated across the entire scanning run. In addition to BOLD signal, the PSD can provide a useful characterization of ancillary experimental measurements such as physiological measurements and head motion estimates.

A number of methodological developments are required to enable the routine application of PSD analysis. Optimal parameter choices for spectral smoothing and tapering need to be determined. A statistical method that identifies significant changes in power across the full frequency spectrum would enhance the analysis. Simple software tools are required to automate the temporal segmentation of the fMRI data and estimation of the PSD, and convert the results into a form easily analyzed by available tools for GLM estimation. More generally, a software framework for combining multiple characterizations of experimental data, such as GLM‐based activation analysis, PSD analysis, ICA, and connectivity analysis, is needed. Finally, some related analytical approaches warrant investigation. The wavelet PSD is an obvious alternative to the PSD. Analysis of the phase of BOLD signal across the brain, relative to a standard may prove another informative voxel‐wise measure of BOLD signal oscillations.

CONCLUSION

Our examination of changes in BOLD signal power spectra over the course of fMRI sessions containing both fast‐acquisition resting‐state scans and block‐design scans involving long periods of motor performance and rest has uncovered two interesting endogenous signal effects: (1) a widespread, bilateral increase in power during rest after task relative to rest before task, and (2) a widespread, bilateral decrease in low frequency BOLD signal power during task periods relative to rest periods. We have demonstrated the confounding nature of these observations regarding endogenous BOLD signal fluctuations on regional correlation‐based measures, thus highlighting the importance of fully characterizing voxel‐wise signal dynamics prior to computation of multivariate correlational measures. We conclude that whole‐brain mapping of power spectra should form an integral part of the assessment of endogenous BOLD signal oscillations and an informative adjunct to correlation‐based analyses.