## Abstract

Recent studies have revealed spatial and functional relations in the temporal dynamics of resting-state functional magnetic resonance imaging (rs-fMRI) or electroencephalography (EEG) signals recorded in the adult brain. By modeling the frequency power spectrum of resting-state brain signals with a power-law function $O(f)∝1fα$, the power-law exponent α has been shown to relate to the connectivity patterns of spontaneous brain activity that forms so-called rs-fMRI networks in the human adult brain. Here, we present an analysis of the dynamic properties of rs-fMRI and EEG signals acquired both in the newborn and adult brain, and we demonstrate frequency scaling of a power-law kind for orders of magnitude in the hemodynamic (0.01–0.15 Hz) and the electrical (0.2–30 Hz) domain. We show that the spatial segregation of resting-state dynamics of intrinsic fMRI signals in terms of the power-law exponent α is closely related to previously delineated resting-state neuronal architecture that encompasses primary sensory cortices and associate cortex in newborns. Moreover, the spatial profiles of differences in temporal dynamics for rs-fMRI signals could also be observed in EEG measurements in the newborn brain, albeit at a coarser spatial scale, with larger power-law exponents in occipital and parietal cortices compared with signals from the frontal brain.

## Introduction

Scientific interest in the properties of large-scale dynamics of spontaneous brain activity has rapidly increased. Recent studies on interdependencies and connectivity between brain regions have found that functional patterns to a large extent reflect the underlying structural connectivity (Honey et al. 2009). Functional networks have been shown to operate at a wide range of temporal and spatial scales (Sporns 2010), and they also show a remarkable spatial and temporal overlapping between functionally relevant entities. Such characteristics of brain organization have requested development of research techniques that, when appropriately combined, can capture and quantify the full range of activity at all scales in the living brain.

Much of the advancement in the field has been made possible with the advent of resting-state functional magnetic resonance imaging (rs-fMRI) (Fox and Raichle 2007), which together with tractography techniques have opened up avenues to noninvasively map the spatial topology of structural and functional circuits in the brain, collectively named “the human brain connectome” (Sporns et al. 2005). By employing concepts and analytical tools originally developed within graph theory (Bullmore and Sporns 2009), recent network analyses of MRI data have revealed a so-called “small-world” network architecture in the brain, which is shown to strike a balance between needs to support both functional integration as well as functional segregation (Achard et al. 2006).

Brain function is not, however, adequately described with spatial patterns alone. There has been an intensive development of paradigms that capture dynamics in the temporal domain, including temporal frequency scales much wider than those conventionally ascribed to magnetic resonance (MR)-related techniques (Achard et al. 2006; Bullmore and Sporns 2009). Most studies in that area have employed electroencephalography (EEG) or magnetoencephalography (MEG) methodology, and they have repeatedly demonstrated how temporal dynamics of spontaneous neural oscillations appear to follow power-law scaling (power-law distribution, $O(f)∝1fα$) behavior with remarkable invariance across adult subjects (Freeman et al. 2000; Linkenkaer-Hansen et al. 2001; Miller et al. 2009). Such temporal organization is ubiquitously found in complex systems with rapid adaptation to new situations and robustness to failure, and it is compatible with the underlying spatial organization into small-world networks (Linkenkaer-Hansen et al. 2001; Achard et al. 2006; Miller et al. 2009). Frequency scaling of a power-law kind is reported when frequency power spectra are shown to follow power-law distribution (i.e., linear in log–log coordinates) over a given frequency range. An interesting novel dimension to this field was brought by recent studies of He et al. (2010) who combined analysis of temporal dynamics of fMRI with that of invasive EEG (electrocorticogram) signals and reported distinct spatial specificity in frequency scaling across the cortex (see also He 2011).

From a multitude of theoretical work, it has become obvious that such characteristics in temporal behavior can only arise with a foundation in the underlying structural connectivity (Rubinov et al. 2009). The development of major structural networks in human brain is known to take place over an extended time window from midgestation to early postnatal life (Kostovic and Jovanov-Milosevic 2006). It is also known that the structural and functional maturation proceeds spatially from the primary sensory cortices to parietal areas and finally to frontal cortical areas (Lagercrantz et al. 2010). Intriguingly, such spatial advance in relative maturation in primary sensorimotor brain areas was recently shown also with rs-fMRI measurements in newborns (Fransson et al. 2011). This is in sharp contrast with adults who have more mature default mode and task-positive networks, as well as their underlying cortical hubs (Fair et al. 2008, 2009; Buckner et al. 2009; Fransson et al. 2011). The early development of the link between the spatial topology of rs-fMRI networks, their power spectrum profiles, and arrhythmical brain activity as measured with EEG is unknown. In the present study, we hypothesized that such marked spatial differences in brain maturation should also be reflected onto the temporal domain such that the spatial characteristics of frequency scaling of rs-fMRI and EEG signals would change significantly after the neonatal period. rs-fMRI and EEG data from newborns as well as adults were analyzed in the temporal domain with respect to the scaling of their frequency power spectra and spatial topology.

## Materials and Methods

### fMRI Acquisition

rs-fMRI images were acquired in both adults and newborns. The adult cohort consisted of 17 subjects (age 22–41 years, mean 29 years) with no history of neurological and psychiatric illness as previously published (Fransson 2006). All newborns in the cohort of 18 subjects were all born via a planned caesarean section at full term, with a normal Apgar score (Fransson et al. 2009). Furthermore, all newborn subjects were scanned during normal sleep and their anatomical MR scans were found to be normal without any visible signs of brain abnormalities. Additional information regarding age, age at scanning, head circumference is found in Fransson et al. (2009). All MR examinations were carried out according to the ethical guideline and declarations of the Declaration of Helsinki (1975). The study was approved by the local ethics committee in Stockholm, and parental consent was given prior to examination. fMRI data in adults were acquired at 1.5 T (General Electric Twin-Speed Signa Horizon) using an echoplanar imaging (EPI) sequence (time repetition [TR]/time echo [TE]/flip = 2000 ms/40 ms/80°, matrix size = 64 × 64, field-of-view = 220 × 220 mm2, 29 axial slices, slice thickness = 5 mm, spatial resolution = 3.4 × 3.4 × 5 mm3). The rs-fMRI scan lasted for 10 min (300 image volumes acquired) during which the adult subjects were instructed to rest and fixation on a black crosshair centered on a white screen. Newborns were scanned during natural sleep at 1.5 T (Philips Intera, 6-channel receive-only coil). EPI data (TR/TE/flip = 2000 ms/50 ms/80°, matrix size = 64 × 64, field-of-view = 180 × 180 mm2, 20 axial slices, slice thickness = 4.5 mm, spatial resolution = 2.8 × 2.8 × 4.5 mm3) of the newborn brain were acquired during 10 min (300 image volumes).

### Frequency Spectrum Analysis of fMRI Data

After regressing out spurious signal variance, the normalized power spectrum of the fMRI signal was computed for all 39 ROIs in both adults and newborns using the Welch method for power spectrum density estimation as implemented in the Signal Processing Toolbox in Matlab. Lastly, the frequency spectrum functions were fitted with a power-law function $O(f)∝1fα$ using least-square estimation (in a log frequency by log power plot) in the frequency range of 0.01–0.15 Hz. The lower frequency limit was chosen to avoid signal contributions from scanner drift, whereas the higher limit was set slightly lower than the Nyquist frequency to avoid contamination from aliasing effects. Notably, least-square estimation of the slope of the power spectrum is prone to give too much weight to the highest density of data-points in the high end of the frequency spectrum (see, for example, Miller et al. 2009). To circumvent this potential bias, we used a logarithmically distributed sampling of the power spectrum function, giving equal weight to all frequency ranges in the power spectrum estimation. The average power density for each ROI was obtained by averaging across subjects, and density estimates for homologous areas were averaged together, resulting in power spectrum density estimates for 22 brain regions. The fMRI signal variance and power-law slope α for all 22 brain regions are given in Supplementary Table 2. Finally, the slope α was entered into an analysis of variance (ANOVA) with network as the main factor.

### EEG Acquisition and Preprocessing

All EEG data were collected in the Department of Children’s Clinical Neurophysiology (Helsinki University Central Hospital) using a NicoOne EEG amplifiers (Cardinal Healthcare, Madison, WI) or a Cognitrace amplifier (ANT B.V., Enschede, the Netherlands, www.ant-neuro.com) amplifier. Further details of newborn EEG recordings of this kind are shown in http://www.nemo-europe.com/en/educational-tools.php and Stjerna et al. (2011). Sampling rate was 256 or 512 Hz, but the data were resampled at 256 Hz during the offline analysis. Electrodes (sintered Ag/AgCl) were placed according to the international 10-20 standard. In the babies, we used either individual attachment or an electrode cap (Waveguard, ANT-Neuro, Germany; www.ant-neuro.com; see also Vanhatalo et al. 2008; Stjerna et al. 2011, and http://www.nemo-europe.com/en/educational-tools.php). Adult recordings were ambulatory, and the electrodes were individually fixed according to the full 10-20 system. Informed consent was obtained from the parents of the babies that participated in prospective studies. Use of archived anonymized EEG recordings in our present study was approved by the Ethics Committee of the Hospital for Children and Adolescents, Helsinki University Central Hospital.

Newborn EEG data were obtained from 15 babies at mean conceptional age of 42.1 (range 39–44) weeks. Most recordings were collected from control groups recruited for other ongoing studies (see e.g., Vanhatalo et al. 2009). All recordings included succession of vigilance states from awake to active sleep and quiet sleep. For the present analysis, we chose relatively artifact free epochs with duration of 5 min (except in one case with only 4 min), from the “most active” and the “most quiet” sleep periods. While these definitions do not strictly comply with the official neonatal sleep scoring criteria (Grigg-Damberger et al. 2007), this was considered as the most plausible proxy (see also Vanhatalo et al. 2005) for our present study for 2 reasons: First, some recordings did not include polygraphic channels that would be needed for a strict sleep staging, so their use in only part of the data set would not have been helpful. Second, for the purpose of the present study, it was more important to obtain sufficiently long and equal lengths of data from EEG-wise comparable epochs rather than to use the conventional fragmenting sleep scoring based on short epochs.

The adult EEG data (7 data sets, mean age 26, age range 14–53 years) were collected from EEG archives from overnight recordings with ambulatory EEG, which is used in our hospital for outpatient studies of various neurological symptoms. An epoch of 5 min was selected from the stage 2 sleep (defined from EEG: spindles, vertex waves, and K complexes). These EEG recordings were selected from a larger group on the basis that they were not directly suggestive of any acute major neurological disorder: differential diagnosis of syncope/fainting spells or panic disorders (3 patients), déjà vu feelings (1 patient), or other feelings of various parts of the body (2 patients), as well as differential diagnosis of clinical seizure symptoms (1 patient).

All EEG data were processed further offline in the BESA software (MEGIS GmbH, Gräfelfing, German, Scherg et al. 2002). Possible bad channels were replaced with a spatially interpolated signal (a built-in feature in BESA software), then the signal was filtered with a combination of high-pass filter at 0.05 Hz (3 dB) and a low-pass filter at 40 Hz (24 dB), remontaged into 27 Laplacian derivations (see Supplementary Fig. 3), and exported into a .foc format with a resampling at 256 Hz. Finally, all signals were converted with BESA from .foc to .edf format, which could be read into the Matlab environment. The aim of all the above processing was to make EEG signals technically similar so that further analysis could be carried out in an identical manner irrespective of little differences in the EEG sampling process.

### Frequency Spectrum Analysis of EEG Data

Power spectrum estimates and respective power-law exponents for all 27 EEG derivations (see Supplementary Fig. 3) were computed from 0.2 to 30 Hz using similar methods to those used for the fMRI data. The slope of the power spectrum was estimated for each individual EEG signal and subsequently pooled across subjects. This frequency range was selected to cover as wide frequency range as possible with genuine brain activity. The lower end of the range is limited by 2 factors: First, our NicOne amplifier has a conventional AC coupling that results in high-pass filtering at around this limit. Second, potential artifacts, such as sweating or movements, would show up with high amplitudes at the lowest frequencies, which could seriously confound the analysis. The upper end of the spectrum was extended to the highest frequencies reliably recorded from a spontaneous neonatal EEG (Vanhatalo et al. 2005). Notably, inspection of frequency power spectra from this frequency range in log–log coordinates show remarkable linearity (see also Supplementary Figs 1, 2A,B).

## Results

### Spatial Distribution of the Power-Law Exponent of the Frequency Spectra in Newborn and Adult rs-fMRI Data

The normalized power spectrum was computed for each of the 39 ROI (34 of which were pairs of ROIs located in homologous brain areas and thus analyzed and presented together, see also Supplementary Table 1), averaged across subjects, and shown in a log–log diagram in Figure 1. The spatial topology of the dynamics of resting-state brain activity in the neonate and adult brain was then assessed after grouping the data into 7 networks (sensory, auditory, vision, default, attention, saliency, and subcortical similar to previous work [He et al. 2010; He 2011]). When plotted in logarithmic scale, the power spectra of spontaneous, rs-fMRI signal intensity time-courses showed a linear decrease as a function of frequency, which suggests a power-law behavior of brain dynamics (see also Discussion), both in the newborn as well as in the adult brain (Fig. 1). The mean slope of frequency power spectra (power-law exponent, α, was found to be 0.60 and 0.41 in newborns and adults, respectively. When grouped within network, the power-law exponents displayed in Figure 2 showed a significant dependence on brain network when tested in an ANOVA with network as the main factor (newborns: F17,6 = 10.13, P < 0.0001; adults: F16,6 = 11.53, P < 0.0001).

Figure 1.

Power-law dynamics in intrinsic fMRI signals recorded in newborns (A) and adults (B). Normalized power spectrum of intrinsic rs-fMRI signals plotted in a log–log plot for 39 ROIs (17 pairs of homologous regions were averaged together, see Supplementary Tables 1 and 2). Line colors are grouped by cortical network (Green = default, red = attention, sensory = blue, auditory = yellow, vision = black, saliency = magenta, subcortical = cyan).

Figure 1.

Power-law dynamics in intrinsic fMRI signals recorded in newborns (A) and adults (B). Normalized power spectrum of intrinsic rs-fMRI signals plotted in a log–log plot for 39 ROIs (17 pairs of homologous regions were averaged together, see Supplementary Tables 1 and 2). Line colors are grouped by cortical network (Green = default, red = attention, sensory = blue, auditory = yellow, vision = black, saliency = magenta, subcortical = cyan).

Figure 2.

Network-specific differences in power-law exponents in newborns (A) and adults (B) estimated from rs-fMRI data. Each power density spectrum shown in Figure 1 was fit with a power-law function $O(f)∝1fα$ in a log–log diagram and fitted with a straight line in the frequency range 0.01–0.15 Hz. The exponent α was entered into an ANOVA with brain network (sensory, auditory, vision, default, attention, subcortical, saliency) as a main factor. The main effect of network was significant in both newborns (F17,6 = 13.32, P < 0.0001) and adults (F16,6 = 11.53, P < 0.0001).

Figure 2.

Network-specific differences in power-law exponents in newborns (A) and adults (B) estimated from rs-fMRI data. Each power density spectrum shown in Figure 1 was fit with a power-law function $O(f)∝1fα$ in a log–log diagram and fitted with a straight line in the frequency range 0.01–0.15 Hz. The exponent α was entered into an ANOVA with brain network (sensory, auditory, vision, default, attention, subcortical, saliency) as a main factor. The main effect of network was significant in both newborns (F17,6 = 13.32, P < 0.0001) and adults (F16,6 = 11.53, P < 0.0001).

The power-law exponents for rs-fMRI data in newborns were typically larger in primary sensory regions than higher order associative brain areas (Figs 1A and 2A). Interestingly, the situation seemed to be reversed in adults for which the power-law exponents were generally larger in networks that encompass higher order association cortices (default, attention) compared with primary sensory regions (sensory, auditory) with the exception of the visual system (Figs 1B and 2B). We tested this dichotomy of power-law characteristics in both age cohorts by collapsing the exponents belonging to the default and attention network into one group and the sensory and auditory networks into a second group.

The power-law exponents in newborns were significantly higher in primary sensory networks compared with higher associative networks (P < 0.0001, Z = 6.17, Wilcoxon rank sum test), whereas in adults, the power-law exponents were higher in associative networks compared with primary sensory networks (P < 0.0001, Z = 5.02, Wilcoxon rank sum test). Additionally, we found a significant correlation between variance in spontaneous fMRI signals and power-law exponents in newborns as shown in Figure 3 (R2 = 0.435, P < 0.0008). The corresponding correlation in the adult cohort was found to be nonsignificant, due to the very large signal variance detected in the hippocampus formation (HF) (R2 = 0.137, P < 0.09). However, if the single outlier was omitted from the correlation analysis, the correlation between fMRI signal variance and power-law exponent was significant (R2 = 0.474, P < 0.0004) in adults (Fig. 3). It is of interest to note that the high signal variance found here for the hippocampus in adults replicates a previous observation by He et al. (2010), which provides further support for the notion that this finding reflects a true anatomical and/or physiological property of the hippocampus rather than an artifact due to a low signal to noise ratio. Moreover, the signal variance in spontaneous fMRI signals was found to be dependent on network (tested with an ANOVA with network as a main factor) in both infants (F(17,6) = 3.07, P < 0.008) and adults (F(16,6) = 2.68, P < 0.018). Power-law exponents and signal variance for all ROIs are given in Supplementary Table 2.

Figure 3.

Correlation between power-law exponent (α) and total fMRI signal variance in newborns (A) and adults (B). The correlation was found to be significant in newborns (R2 = 0.434, P < 0.0008) but not in adults (R2 = 0.137, P < 0.09). However, the variance detected in the adult hippocampus formation (HF) was in comparison with all the remaining ROIs very high. When this single outlier was excluded from the analysis, the correlation between signal intensity variance and power-law exponent was indeed significantly correlated also in adults (R2 = 0.587, P < 0.0001). Symbols used in figure: circles = sensory, diamonds = auditory, triangle pointing downwards = vision, x-marks = default, plus signs = attention, asterisk = saliency, squares = subcortical.

Figure 3.

Correlation between power-law exponent (α) and total fMRI signal variance in newborns (A) and adults (B). The correlation was found to be significant in newborns (R2 = 0.434, P < 0.0008) but not in adults (R2 = 0.137, P < 0.09). However, the variance detected in the adult hippocampus formation (HF) was in comparison with all the remaining ROIs very high. When this single outlier was excluded from the analysis, the correlation between signal intensity variance and power-law exponent was indeed significantly correlated also in adults (R2 = 0.587, P < 0.0001). Symbols used in figure: circles = sensory, diamonds = auditory, triangle pointing downwards = vision, x-marks = default, plus signs = attention, asterisk = saliency, squares = subcortical.

The usage of regressing out the global brain mean signal has previously been debated in the literature (Fox et al. 2009; Murphy et al. 2009), and it has been suggested that the mean global fMRI signal to some extent is related to neuronal activity (Schölvinck et al. 2010), but it has been shown not to qualitatively affect the spatial patterns of power-law frequency scaling in adults (He et al. 2010; He 2011). Our own complimentary analysis performed without regression of the global mean signal confirmed that this is the case in newborns as well (see Supplementary Figs 4–6). In agreement with the previous studies in adults (He et al. 2010; He 2011), there were only slight increases in power-law exponents (newborns: mean(α) = 0.66; adults: mean(α) = 0.46), but this step did not produce any qualitative change in the spatial pattern of power-law exponents. Identical statistical tests (ANOVA and Wilcoxon rank sum tests) were performed on the data for which the global mean regression step was omitted and yielded similar results (see also legends to Supplementary Figs 4–6).

### Spatial Distribution of the Power-Law Exponent of the Frequency Spectra in Newborn and Adult EEG Data

The estimated power-law exponents for the frequency spectra for all 27 EEG signals are shown in Figure 4. Two features of the spatial distribution of power-law exponents are immediately apparent. First, there seems to be a gross difference in the steepness of the frequency spectra between newborns and adults, where the average power-law exponent obtained in newborns (Fig. 4A, mean(α) = 2.07, standard deviation [SD(α)] = 0.22) is larger than in adults (Fig. 4B, mean(α) = 1.86, SD(α) = 0.45). Indeed, the average (across EEG signals and subjects) power-law exponent is significantly higher in the newborn cohort compared with the adult cohort (P < 0.0001, Z = 8.15, Wilcoxon sign rank test), akin to the difference across age for the rs-fMRI data described above. Second, the variability in power-law exponent estimates is significant across EEG signals but also across subjects in each cohort. An example of the variability within subjects as well as across subjects is given for a representative subject and a representative EEG signal in Supplementary Figs 1 and 2, respectively. Despite of the intersubject variability, a closer inspection of the exponents shown in Figure 4 suggests a tendency for slightly lower power-law exponents in frontal areas compared with EEG signals covering more posterior and occipital regions in newborns, whereas the opposite pattern with slightly larger exponents for frontal areas compared with parietal/occipital areas is found in adults.

Figure 4.

Estimated power-law exponents (α) for the power frequency spectra of EEG recordings in newborns (A) and adults (B). A total of 27 EEG signals were recorded in 5 min epochs of nonrapid eye movement sleep (quite sleep in newborns, S2 stage in adults) from 15 to 7 subjects in newborns and adults, respectively.

Figure 4.

Estimated power-law exponents (α) for the power frequency spectra of EEG recordings in newborns (A) and adults (B). A total of 27 EEG signals were recorded in 5 min epochs of nonrapid eye movement sleep (quite sleep in newborns, S2 stage in adults) from 15 to 7 subjects in newborns and adults, respectively.

Given the previous study of stronger rs-fMRI functional connectivity in primary sensory areas compared with higher associative cortex in newborns (Fransson et al. 2011), we wanted to test our a priori hypothesis that maturation progress in rs-fMRI network connectivity is reflected in the temporal dynamics of EEG activity. Hence, we conducted an a priori sorting (see also Supplementary Fig. 3) of the EEG signals into 2 groups, a posterior/occipital group that included signals that foremost sample EEG activity in primary sensory areas and a second group that represented an average of frontal activity. Since previous rs-fMRI studies have shown in most cases a bilateral symmetry in functional connectivity between hemispheres (Damoiseaux et al. 2006), we as a control test created EEG signal groups from the left and right hemispheres without midline derivations. Power-law exponent estimates were pooled across subjects and EEG signal groups for adults and newborns separately. The mean power-law exponent for the parietal/occipital and the frontal group is shown in Figure 5. Consistent with our prior hypothesis, the average power-law exponent for the EEG power spectra was significantly higher in the parietal/occipital group compared with the frontal group in newborns (P < 0.0001, Z = 5.489, Wilcoxon sign rank test). The opposite was found in adults, for which power-law exponent for the frontal group was significantly higher compared with the occipital/parietal group (P < 0.0105, Z = 2.56, Wilcoxon sign rank test). A similar comparison for the power-law exponents between the left and right hemispheres (Fig. 5C,D) was nonsignificant (P > 0.1) in both adults and newborns.

Figure 5.

The bars show the average power-law exponents (pooled over subjects within each group) for posteriorly versus frontally located EEG signals in newborns (A) and adults (C). The average power-law exponent was significantly larger in the posterior group compared with the frontal group in newborns (P < 0.0001, Z = 5.49), whereas the frontal group was significantly larger than the posterior ensemble of EEG signals in adults (P < 0.0105, Z = 2.56). As a control, signals for the left and right hemisphere (midline derivations excluded) were pooled in separate groups, and no significant differences between groups were found in newborns (B) nor in adults (D) (P > 0.1). Error bars displayed are the standard error of the mean.

Figure 5.

The bars show the average power-law exponents (pooled over subjects within each group) for posteriorly versus frontally located EEG signals in newborns (A) and adults (C). The average power-law exponent was significantly larger in the posterior group compared with the frontal group in newborns (P < 0.0001, Z = 5.49), whereas the frontal group was significantly larger than the posterior ensemble of EEG signals in adults (P < 0.0105, Z = 2.56). As a control, signals for the left and right hemisphere (midline derivations excluded) were pooled in separate groups, and no significant differences between groups were found in newborns (B) nor in adults (D) (P > 0.1). Error bars displayed are the standard error of the mean.

## Discussion

To the best of our knowledge, this is the first study to compare the dynamics of rs-fMRI and EEG signals in the newborn brain. We could observe a network dependence on the power-law exponent for the rs-fMRI frequency spectrum in newborns as well as in adults. In adults, our results corroborate the findings by He et al. (2010), in that the power-law exponents for the default network and the visual system were significantly larger than the exponents for sensory, subcortical, and areas belonging to the saliency and attentional networks (He et al. 2010; He 2011). Our study shows further that the highest power-law exponents for rs-fMRI data in the adult brain are localized to the default mode network that previously has been shown to have the strongest low-frequency spontaneous fMRI signal fluctuations, namely in the precuneus/posterior cingulate cortex, left parietal cortex, and the medial-prefrontal cortex (see for reference Figs 2 and 3 in Fransson 2005). The newborn brain exhibits a completely different pattern of dynamical properties of resting-state signals, with the highest power-law exponents obtained for primary sensory areas (auditory, vision, sensorimotor) and lower values found in the default, attention, and subcortical networks. The main observation from rs-fMRI data was intriguingly substantiated by EEG findings, which also showed age-dependent spatial distribution in temporal dynamics. While the spatial resolution available to us from newborn EEG (see also below) did not allow for a more detailed assessment, we could clearly demonstrate higher power-law exponents in primary sensory cortices compared with frontal areas, whereas the opposite relationship was found in adults.

While the presence of power-law scaling has been shown to imply properties of the underlying dynamical processes (He et al. 2010; He 2011), the significance of any particular value of the power-law exponent of the frequency power spectra in terms of neuronal processing and human behavior is as yet elusive. There exists evidence, however, that power law–like dynamical processes are relevant for temporal organization of the brain, in that task performance has been shown to modulate scale free brain activity (He et al. 2010). Speculatively, relatively larger values of the power-law exponent might signify neuronal processes with longer internal memory. Hence, a neuronal network, which displays larger power-law exponents, might support a temporal structure that allows a flow and/or storage of information that spans larger time durations compared with networks that harbor dynamics that are characterized by significantly lower power-law exponents. Such speculations gain mechanistic support from the EEG domain, where higher power-law exponents in the newborns are likely due to the low-frequency power from spontaneous activity transients (Vanhatalo et al. 2005) that are the electrophysiological underpinnings of the brain activity responsible for the establishment of the first neuronal networks in the human brain (Khazipov and Luhmann 2006; Vanhatalo and Kaila 2006).

The spatiotemporal properties of power-law brain activity reported here are in line with our previous investigations regarding different developmental trajectories for rs-fMRI networks in the human brain. We have previously shown that in the newborn brain, primary sensorimotor cortices mature before associative cortex in terms of forming resting-state network hubs (Fransson et al. 2011). The current results provide support for the notion that differences in the relative maturation of resting-state brain networks play an important role for the dynamical properties of EEG and fMRI signals in the human brain. Moreover, our results suggest a link between the development of the spatial topology of resting-state network activity, including an early formation of sensory networks compared with associative networks, and local changes in scale-free brain dynamics activity.

In the present study, we describe the frequency scaling of arrhythmic brain activity measured with fMRI or EEG to follow a power-law distribution, which is characteristic of a scale-free behavior (Clauset et al. 2009). However, it should be noted that a power spectrum alone is suggestive but not conclusive of genuine scale invariance in the system. There are other statistical distributions that may show power law–like scaling (“scale free”–like) behavior over limited range, such as the log-normal or Poisson distribution (Clauset et al. 2009; Stumpf and Porter 2012). It would be challenging, if not unattainable, to perform a tour de force testing of scale invariance in an empirical data set with limited sample sizes, such as those available from naturally sleeping healthy human babies. Therefore, our usage of the terms scale-free and power-law exponents should be interpreted as provisory until more stringent statistical tests have been performed using larger quantities of data. An important feature of scale free behavior is, however, it’s spanning over orders of magnitude (Clauset et al. 2009). We report orders of magnitude in both the fMRI (0.01–0.15 Hz) and the EEG data (0.2–30 Hz), and the range of analysis in both signals was limited by physical (noise and time window of the measurement) rather than analytical reasons.

It might be speculated that the adult subjects in our study were not completely normal because the data sets were extracted from ambulatory EEG recordings performed for clinical indications. The subjects in our study were selected on the basis that their EEG study was reported normal, none of them had clinical symptoms during the EEG epoch analyzed, the symptoms were mainly subjective, and they were not suggestive of any acute major neurological dysfunction. Notably, our earlier studies on infraslow activity and its nesting (phase–amplitude modulation) with other EEG frequencies were carried out with healthy controls and severely epileptic patients, and we found no qualitative differences between these subjects (Vanhatalo et al. 2004). We feel it hence reasonable to assume that the quality of our finding was not affected by the fact that we used data obtained from recent clinical archives (see also He et al 2010). Finally, we would like to propose that the mechanisms studied in our present work are so fundamental properties of brain function that any effect from potential brain disorders would be quantitative rather than qualitative.

The present results constitute a first step toward an understanding of the relationship between the early phases of maturation of human rs-fMRI brain networks and the shaping of the dynamical properties of brain activity. Indeed, a recent study that examined power-law behavior of EEG data obtained in a large cohort of individuals from spanning childhood to adulthood could show an influence of development on scale-free EEG activity (Smit et al. 2011). Moreover, the idea that scale-free dynamics of EEG activity are related to the topography of resting-state networks has recently gained support from several studies that have exploited the nonstationary property of EEG and MEG signal traces (Britz et al. 2010; Musso et al. 2010). To this end, it has been shown that so-called EEG microstates lasting about 100 ms are spatially tied to the default mode network in adults (de Pasquale et al. 2010; Van de Ville et al. 2010).

The findings reported here call for further investigations in several aspects. First, by examining the properties of the $O(f)∝1fα$ function fitted to the power frequency spectra, only the coarse aspects of the fine temporal scaling properties of resting-state activity can be probed. An obvious extension would be to investigate further the nesting properties of phase and frequency in neonatal EEG signals (Vanhatalo et al. 2005) and their potential link to the structure of rs-fMRI activity. Furthermore, the gross dichotomy between posterior and frontal EEG activity described here would benefit from a spatially more detailed investigation of the dynamics of the individual EEG signals at the level of individual rs-fMRI networks. However, a spatial division of EEG activity at this resolution requires analyses in the source domain (Schoffelen and Gross 2009) that implies EEG source localization with inverse solutions. Realistic newborn head models suitable for such investigations are unfortunately as yet not available.

A relevant issue when studying the temporal dynamics of EEG brain activity would be to extend the frequency range to cover infraslow brain activity (infraslow oscillations/fluctuations, ISO/ISF, « 0.5 Hz) that recently has been shown to contribute to brain function in multiple ways (Vanhatalo et al. 2011). The infraslow frequency range in the EEG power spectra seems especially intriguing because it overlaps with the frequency range studied in rs-fMRI. However, reliable recordings of ISO/ISF with EEG recordings require a perfectly DC-stable setting (Vanhatalo et al. 2004, 2005), free of movements and with a very high spatial resolution. Unfortunately, such measurements are not available for newborns. Another approach to infraslow electrical brain dynamics would be to study EEG fluctuations in a frequency band–specific manner (Britz et al. 2010), which do only partially associate with the genuine ISO/ISF (Vanhatalo et al. 2004). Compared with adults, the qualitative difference in the nature of spontaneous neonatal EEG activity at the level of individual oscillations and their underlying intracortical mechanisms (de Pasquale et al. 2010; Van de Ville et al. 2010) makes interpretation of findings between rs-fMRI and EEG in newborns very challenging. Before this attractive pathway is explored, there is hence a need for more work in parceling EEG activity with respect to its potential contributions to hemodynamical changes in the newborn brain.

In sum, we have shown that the newborn brain dynamics follow an apparently scale-free frequency power distribution across orders of magnitude in both rs-fMRI and EEG signals. Moreover, we have shown that the spatial segregation of dynamics of newborn brain activity, in terms of the power-law exponent, follows differential patterns of maturation in networks previously discovered using functional connectivity rs-fMRI. In newborns, primary sensory brain areas exhibit a larger power-law exponent than higher associate brain areas, in stark contrast to the dynamical characteristics of rs-fMRI signals in the adult brain for which associative cortex typically displays the largest power-law exponents. The present findings call for future studies to assess the clinical relevance of the dynamical properties of spontaneous EEG and rs-fMRI signal activity, as well as to search for mechanisms that translate the maturation of these dynamic features into the development of human cognitive abilities.

## Supplementary Material

Supplementary material can be found at: http://www.cercor.oxfordjournals.org/

## Funding

P.F. was supported by The Swedish Research Council, S.V. was supported by Helsinki University Hospital, Juselius Foundation, Foundation of Pediatrics (Lastentautien tutkimussäätiö), European Community's Seventh Framework Programme (FP7-PEOPLE-2009-IOF, grant agreement no. 254235), M.M. was supported by the Finnish Medical Foundation.

Conflict of Interest: None declared.

## References

Achard
S
R
Whitcher
B
Suckling
J
Bullmore
E
A resilient, low-frequency, small-world human brain functional network with highly connected association cortical hubs
J Neurosci
,
2006
, vol.
26
(pg.
63
-
72
)
Britz
J
Van De Ville
D
Michel
CM
BOLD correlates of EEG topography reveal rapid resting-state network dynamics
Neuroimage
,
2010
, vol.
52
(pg.
1162
-
1170
)
Buckner
RL
Sepulcre
J
Talukdar
T
Krienen
FM
Liu
H
Hedden
T
Andrews-Hanna
JR
Sperling
RA
Johnson
KA
Cortical hubs revealed by intrinsic functional connectivity: mapping, assessment of stability, and relation to Alzheimer's disease
J Neurosci
,
2009
, vol.
29
(pg.
1860
-
1873
)
Bullmore
E
Sporns
O
Complex brain networks: graph theoretical analysis of structural and functional systems
Nat Rev Neurosci
,
2009
, vol.
10
(pg.
186
-
198
)
Clauset
A
Shalizi
CR
Newman
MEJ
Power-law distributions in empirical data
Siam Rev
,
2009
, vol.
51
(pg.
661
-
703
)
Damoiseaux
JS
Rombouts
SA
Barkhof
F
Scheltens
P
Stam
CJ
Smith
SM
Beckmann
CF
Consistent resting-state networks across healthy subjects
Proc Natl Acad Sci U S A
,
2006
, vol.
103
(pg.
13838
-
13853
)
de Pasquale
F
Della Penna
S
Snyder
AZ
Lewis
C
Mantini
D
Marzetti
L
Belardinelli
P
Ciancetta
L
Pizzella
V
Romani
GL
, et al.  .
Temporal dynamics of spontaneous MEG activity in brain networks
Proc Natl Acad Sci U S A
,
2010
, vol.
107
(pg.
6040
-
6045
)
Fair
DA
Cohen
AL
Dosenbach
NU
Church
JA
Miezin
FM
Barch
DM
Raichle
ME
Petersen
SE
Schlaggar
BL
The maturing architecture of the brain’s default network
Proc Natl Acad Sci U S A
,
2008
, vol.
105
(pg.
4028
-
4032
)
Fair
DA
Cohen
AL
Power
JD
Dosenbach
NU
Church
JA
Miezin
FM
Schlaggar
BL
Petersen
SE
Functional brain networks develop from a “local to distributed” organization
PLoS Comput Biol
,
2009
, vol.
5
pg.
e1000381

Fox
MD
Raichle
ME
Spontaneous fluctuations in brain activity observed with functional magnetic resonance imaging
Nat Rev Neurosci
,
2007
, vol.
8
(pg.
700
-
711
)
Fox
MD
Zhang
D
Snyder
A
Raichle
ME
The global signal and observed anticorrelated resting state brain networks
J Neurophysiol
,
2009
, vol.
101
(pg.
3270
-
3283
)
Fransson
P
Spontaneous low-frequency BOLD signal fluctuations: an fMRI investigation of the resting-state default mode of brain function hypothesis
Hum Brain Mapp
,
2005
, vol.
26
(pg.
15
-
29
)
Fransson
P
How default is the default mode of brain function? Further evidence from intrinsic BOLD signal fluctuations
Neuropsychologia
,
2006
, vol.
44
(pg.
2836
-
2845
)
Fransson
P
Åden
U
Blennow
M
Lagercrantz
H
The functional architecture of the infant brain as revealed by resting-state fMRI
Cereb Cortex
,
2011
, vol.
21
(pg.
145
-
154
)
Fransson
P
Åden
U
Lagercrantz
H
Blennow
M
Spontaneous brain activity in the newborn brain during natural sleep—an fMRI study in infants born at full term
Pediatr Res
,
2009
, vol.
66
(pg.
301
-
305
)
Freeman
WJ
Rogers
LJ
Holmes
MD
Silbergeld
DL
Spatial spectral analysis of human electrocorticograms including the alpha and gamma bands
J Neurosci Methods
,
2000
, vol.
95
(pg.
111
-
121
)
Grigg-Damberger
M
Gozal
D
Marcus
CL
Quan
SF
Rosen
CL
Chervin
RD
Wise
M
Picchietti
DL
Sheldon
SH
Iber
C
The visual scoring of sleep and arousal in infants and children
J Clin Sleep Med
,
2007
, vol.
3
(pg.
210
-
240
)
He
BJ
Scale-free properties of the functional magnetic resonance imaging signal during rest and task
J Neurosci
,
2011
, vol.
31
(pg.
13786
-
13795
)
He
BJ
Zempel
JM
Snyder
AZ
Raichle
ME
The temporal structures and functional significance of scale-free brain activity
Neuron
,
2010
, vol.
66
(pg.
353
-
369
)
Honey
CJ
Sporns
O
Cammoun
L
Gigandet
X
Thiran
JP
Meuli
R
Hagmann
P
Predicting human resting-state functional connectivity from structural connectivity
Proc Natl Acad Sci U S A
,
2009
, vol.
106
(pg.
2035
-
2040
)
Kazemi
K
HA
Grebe
R
Gondry-Jouet
C
Wallois
F
A neonatal atlas template for spatial normalization of whole-brain magnetic resonance images of newborns: preliminary results
Neuroimage
,
2007
, vol.
37
(pg.
463
-
473
)
Khazipov
R
Luhmann
HJ
Early patterns of electrical activity in the developing cerebral cortex of humans and rodents
Trends Neurosci
,
2006
, vol.
29
(pg.
414
-
418
)
Kostovic
I
Jovanov-Milosevic
N
The development of cerebral connections during the first 20-45 weeks’ gestation
Semin Fet Neonat Med
,
2006
, vol.
11
(pg.
416
-
422
)
Lagercrantz
H
Hanson
MA
Ment
LR
Peebles
DM
The newborn brain: neuroscience & clinical applications
,
2009
2nd ed
Cambridge (UK): University Press
K
Nikouline
VV
Palva
JM
Ilmoniemi
RJ
Long-range temporal correlations and scaling behavior in human brain oscillations
J Neurosci
,
2001
, vol.
21
(pg.
1370
-
1377
)
Miller
KJ
Sorensen
LB
Ojemann
JG
den Nijs
M
Power-law scaling in the brain surface electric potential
PLoS Comput Biol
,
2009
, vol.
5
pg.
e1000609

Murphy
K
Birn
RM
Handwerker
DA
Jones
TB
Bandettini
PA
The impact of global signal regression on resting-state correlations: are anti-correlated networks introduced?
Neuroimage
,
2009
, vol.
44
(pg.
893
-
905
)
Musso
F
Brinkmeyer
J
Mobascher
A
Warbrick
T
Winterer
G
Spontaneous brain activity and EEG microstates. A novel EEG/fMRI analysis approach to explore resting-state networks
Neuroimage
,
2010
, vol.
52
(pg.
1149
-
1161
)
Rubinov
M
Sporns
O
van Leeuwen
C
Breakspear
M
Symbiotic relationship between brain structure and dynamics
BMC Neurosci
,
2009
, vol.
2
(pg.
10
-
55
)
Scherg
M
Ille
N
Bornfleth
H
Berg
P
Advanced tools for digital EEG review: virtual source montages, whole-head mapping, correlation, and phase analysis
J Clin Neurophysiol
,
2002
, vol.
19
(pg.
91
-
112
)
Schoffelen
JM
Gross
J
Source connectivity analysis with MEG and EEG
Hum Brain Mapp
,
2009
, vol.
30
(pg.
1857
-
1865
)
Schölvinck
ML
Maier
A
Ye
FQ
Duyn
JH
Leopold
DA
Neural basis of global resting-state fMRI activity
Proc Natl Acad Sci U S A
,
2010
, vol.
107
(pg.
10238
-
10243
)
Smit
DJ
de Geus
EJ
van de Nieuwenhuijzen
ME
van Beijsterveldt
CE
van Baal
GC
Mansvelder
HD
Boomsma
DI
K
Scale-Free modulation of resting-state neuronal oscillations reflects prolonged brain maturation in humans
J Neurosci
,
2011
, vol.
31
(pg.
13128
-
13136
)
Sporns
O
Networks in the brain
,
2010
Cambridge (MA)
MIT Press
Sporns
O
Tononi
G
Kotter
R
The human connectome: a structural description of the human brain
PLoS Comput Biol
,
2005
, vol.
1
pg.
e42

Stjerna
S
Voipio
J
Metsäranta
M
Kaila
K
Vanhatalo
S
Preterm EEG: a multimodal neurophysiological protocol
J Vis Exp
,
2011
, vol.
60
pg.
e3774.

Stumpf
MPH
Porter
MA
Science
,
2012
, vol.
335
(pg.
665
-
666
)
Van de Ville
D
Britz
J
Michel
CM
EEG microstate sequences in healthy humans at rest reveal scale-free dynamics
Proc Natl Acad Sci U S A
,
2010
, vol.
107
(pg.
18179
-
18184
)
Vanhatalo
S
Jousmaki
V
S
Metsaranta
M
An easy and practical method for routine, bedside testing of somatosensory systems in extremely low birth weight infants
Pediatr Res
,
2009
, vol.
66
(pg.
710
-
713
)
Vanhatalo
S
Kaila
K
Ontogenesis of EEG activity: from phenomenology to physiology
Semin Fet Neonat Med
,
2006
, vol.
11
(pg.
471
-
478
)
Vanhatalo
S
Metsaranta
M
S
High-fidelity recording of brain activity in the extremely preterm babies: feasibility study in the incubator
Clin Neurophysiol
,
2008
, vol.
119
(pg.
439
-
445
)
Vanhatalo
S
Palva
JM
S
Rivera
C
Voipio
J
Kaila
K
Slow endogenous activity transients and developmental expression of K+-Cl− cotransporter 2 in the immature human cortex
Eur J Neurosci
,
2005
, vol.
22
(pg.
2799
-
2804
)
Vanhatalo
S
Palva
JM
Holmes
MD
Miller
JW
Voipio
J
Kaila
K
Infraslow oscillations modulate excitability and interictal epileptic activity in the human cortex during sleep
Proc Natl Acad Sci U S A
,
2004
, vol.
191
(pg.
5053
-
5057
)
Vanhatalo
S
Voipio
J
Kaila
K
Schomer
D
Lopes da Silva
F
Infraslow EEG activity
Niedermeyr’s electroencephalography. Basic principles, clinical applications and related fields
,
2011
5th ed
Baltimore-Munich
Williams & Wilkins

Chapter 36, p. 741–747