The Temporal Dedifferentiation of Global Brain Signal Fluctuations During Human Brain Aging

The variation of brain organization as healthy aging has been discussed widely using resting-state functional magnetic resonance imaging. Previous conclusions may be misinterpreted without considering the effects of global signal (GS) on local activities and the variation of GS as age is still unknown. To ll this gap, we systematically examined the correlation between GS uctuations and age. Correlations were evaluated between age and parameters of GS uctuations including power at each frequency point, spectral centroids, and trends of power spectra. Data with hemodynamic response function (HRF) de-convolution and head motion parameter were further analyzed to test whether the age effect of GS uctuations has neural origins. GS uctuations varied as age in three ways. First, general GS power reductions were found in both time and frequency dimensions. Second, the GS power at lower frequencies transferring to higher frequencies was observed. Third, more evenly distributed power across frequencies was showed in aging brain. These trends were partly impacted by HRF de-convolution, but not by head motion. These results suggest that GS uctuations are weaker and more evenly distributed across frequencies in elderly brain. It may indicate the temporal dedifferentiation hypothesis of brain aging from the global signal level.


Introduction
Resting-state functional magnetic resonance imaging (rs-fMRI) provides abundant information for largescale brain bases of age-related cognitive changes 1 . Numerous studies have documented altered almost all functional networks with age in functional organization with rs-fMRI 1,2 . The global signal (GS) of rs-fMRI, as the average signal of the whole brain, has a great impact on the functional brain organization from local neural activities to inter-regional connections 3,4 . The characteristics of GS varying with age, therefore, is a key to understanding the age-related functional brain organization, which has not yet been elucidated.
The debate about whether the GS is signal or noise has lasted for over two decades 3 . Although early studies have found prominent artifacts (i.e. head motion, respiration) in the GS 5,6 , numerous recent studies have tied GS uctuations to vigilance 7 , behavioral traits 8 , brain states 9 , and mental disorders 4,10 , suggesting that the GS conveys particular physiological, psychological, and pathological information 11 . A recent study found a close relationship between the GS of rs-fMRI and the global EEG signal at multiple frequency bands 12 . By contrast, another study causally demonstrated that the GS could be regulated by signals from the basal forebrain 13 . Besides, Tsvetanov et al. suggested that the age effect of blood oxygen level-dependent (BOLD) signal variability could be fully explained by cardiovascular and cerebrovascular factors 14 . Since the GS has both neural and non-neural origins, it is worth exploring whether the neural and vascular factors contribute differently to the variation of GS with age.
In the current study, we aimed to investigate the age effect of GS uctuations during the adult lifespan, using a large-sample of rs-fMRI data. Because local BOLD signal uctuations have been reported to be increased and decreased with age in different regions and frequencies 15,16 , we expected to nd frequency-dependent rise and fall of GS uctuations with age.

Participants
A total of 492 volunteers (307 females, aged 19 to 80 years) were recruited from Southwest University (SWU, China) 17 . All participants reported no psychiatric disorder, substance abuse, or MRI contraindications. The project was approved by the Research Ethics Committee of the Brain Imaging Center of Southwest University, following the Declaration of Helsinki. Written informed consent was obtained from each participant.

Imaging acquisition and preprocessing
All rs-fMRI data were obtained from a 3T Siemens Trio MRI scanner (Siemens Medical, Erlangen, Germany) at the Brain Imaging Center of SWU. Subjects were asked to close their eyes, rest without thinking about any in particular, but refrain from falling asleep. Two hundred and forty-two volumes were acquired for each subject using the T2-weighted gradient echo planar imaging (EPI) sequence: 32 slices of 3 mm, slice gap = 1 mm, TR/TE = 2000/30 ms, ip angle = 90°, eld of view = 220 mm × 220 mm, resulting in a voxel with 3.4 × 3.4 × 4 mm 3 . The MRI data used in this study are available to the public from the International Data-sharing Initiative (http://fcon_1000.projects.nitrc.org/indi/retro/sald.html).
Image preprocessing was conducted using the Data Processing Assistant for Resting-State fMRI package (DPARSF, http://www.restfmri.net) 18 according to steps in previous studies 5,19 : removing the rst 12 volumes, slice timing and realignment. Subjects whose translational and rotational displacement exceeded 2.0 mm or 2.0° or mean frame-wise displacement (FD) exceeded 0.2 were excluded. The remaining sample included 322 subjects (194 females; mean age = 41.48, SD = 17.36). Images were then normalized to the standard EPI template, resampled to a 3 × 3 × 3 mm 3 cube, and spatially smoothed (6mm FWHM Gaussian kernel). Linear detrend, white matter, cerebrospinal uid signals, and Friston 24 motion parameters were used as regressors to reduce head movement and non-neuronal information 20 .

Power spectrum analysis of GS uctuations
The GS was obtained by averaging signals over all gray matter voxels constrained by the binary automated anatomical labeling (AAL) 90 mask 21,22 . The Welch method with hamming window (window width 0.031 Hz, overlap rate 50 %) was applied to transform time series into frequency domain 23 . Data were cutoff within 0.007 ~ 0.25 Hz for de-noising 24 . The power-law function y = a × x b was applied to separate the fractal trend from oscillations because the original BOLD signal consisted of a scale-free trend and multiple oscillations 25 . Frequency boundaries of oscillations were determined by the local minima on the mean power density curve of all subjects 16 . The spectral centroid (SC) of each oscillation was calculated with Eq. (1), representing the center of gravity of the power spectrum within the given range of oscillation 26 .
Where f = 0.25/256 Hz, representing the width between two successive frequency points, P(i) indicates the power at the i th frequency point within i 1 ~ i 2 Hz.

Hemodynamic response function (HRF) de-convolution
The basic hypothesis underlying the BOLD signal is the convolution of neural events and neurovascular coupling 27 . In order to determine whether the relationship between the power of GS and age is resulted from neural activity, the blind hemodynamic response function (HRF) de-convolution approach was performed. According to our previous studies 22,28 , the following steps were conducted. After noise regression, the point process analysis was adopted to detect spontaneous neural events 29 . BOLD signals larger than mean plus one SD were detected and the onsets of neural events were extracted for HRF reconstruction 30 . The HRF in each voxel was evaluated by matching BOLD signal with the canonical HRF and its time derivative. After that, neural level signals were recovered by Wiener de-convolution (http://users.ugent.be/,dmarinaz/HRF_deconvolution.html) 31 .

Contributor detection for the relationship between GS uctuations and age
The same analysis as the original data was performed for de-convolved data. The only difference was that the linear function y = ax + b is used to separate the trend from oscillations because the power-law trend disappeared after HRF de-convolution (see Fig. 1).
Using Pearson's correlation, we evaluated the relationship between age and relative indices, including the mean and SD of GS, GS power at each frequency point, SCs of two oscillations, coe cients (a, b) of power-law and linear functions. Paired-samples t tests on SCs were performed to examine the effect of neurovascular coupling on the frequencies of two oscillations. Lastly, the correlation between the FD and age was calculated to evaluate the contribution of head motion to our results. Multiple comparisons were corrected with the false discovery rate (FDR) method (q < 0.05).

Results
There was no correlation between the mean of GS and age (r = 0.04, p = 0.530 for original data, r = 0.06, p = 0.282 for de-convolved data) because the residual of GS is close to 0 after noises regression. Negative correlations between the SD of GS and age, and between the range of GS power and age were found for original data (r = -0.47, p < 0.001; r = -0.26, p < 0.001), but the age effect was not signi cant for de-convolved data (r = -0.06, p = 0.312; r = -0.11, p = 0.06), suggesting that the decline of GS variability with age is mainly contributed by neurovascular coupling.
The frequency range of oscillation 1 was 0.007 ~ 0.047 Hz and of oscillation 2 was 0.047 ~ 0.149 Hz for the original data. The SCs of the two oscillations tended to shift to higher frequencies with age ( Fig. 2A, middle and right panels). For de-convolved data, oscillation 1 and oscillation 2 were located at 0.007 ~ 0.043 Hz and 0.043 ~ 0.195 Hz, respectively. Similar shifting to higher frequencies of their SCs was observed (Fig. 2B, middle and right panels). In addition, the SC of oscillation 1 was moved to lower frequencies (t = -43.3, p < 0.0001, Cohen's d = -2.42) whereas that of oscillation 2 was moved to higher frequencies (t = 46.0, p < 0.0001, Cohen's d = 2.56) by HRF de-convolution. These results suggested that oscillations shifting to higher frequencies is a general feature of brain aging, irrespective of the in uence of neurovascular coupling on the middle frequency range.
The power-law trend of the original GS power spectrum was reduced with age ( Fig. 3A, left panel), which was mainly determined by decreased coe cient a (the height of the power-law function; Fig. 3A, middle panel) rather than b (the curvature of the function; Fig. 3A, right panel), indicating that brain aging does not change the scale-free curve of GS power spectrum, but reduces the overall power especially in the lower frequency end. For the de-convolved data, the slope of linear trend (coe cient a) increased with age from negative to positive (Fig. 3B, left and middle panels), while the intercept (coe cient b) decreased with age (Fig. 3B, right panel), suggesting that the power of GS transfers from lower frequency to higher frequency as brain aging.
Finally, a signi cant positive correlation between the power of FD and age was found at 0.007 ~ 0.025 Hz. It was found both positive and negative and mainly negative correlation between the power of GS and age for the original data while no correlation for the de-convolved data within this frequency range, indicating that correlations between the power of GS and age are not determined by head motion.

Discussion
The current results revealed GS uctuations varied as age in three aspects: general power reduction, power transferring to higher frequencies, and more even power distribution across frequencies, which indicate the correlation between GS uctuations and age directly during the adult lifespan for the rst time. More importantly, they argue a temporal dedifferentiation interpretation of brain aging. Age-related variations of GS uctuations have both neural and vascular origins. Elucidating the variation of GS uctuations with age is essential to understand altered functional organization as brain aging.
To begin with, these ndings are consistent with the general decline of local BOLD signal uctuations as age in extensive regions 15,16 , which suggested to represent a less complex neural system capable of smaller dynamic range, as well as an attenuated ability to e ciently process ever-changing external stimuli 32 . The present ndings demonstrated that the GS, as an average of local signals, shows the same trend as local signals. Garrett and colleagues have demonstrated that local BOLD signal uctuations are generally declined with age and predict age by more than four times over the mean BOLD signal 32 . The same trend also appeared from new born children to adults 33 . Combined with current ndings, we suggest a general trend of low frequency power decline across human lifespan.
Secondly, frequencies of the two oscillations increased with age, as was showed in the rst year of life 34 . But we do not know for sure if this trend persists throughout life for evidence of lifespan development is lacking. Furthermore, age-related frequency transfer was found in both power-law and linear trends. It is also known that frequency transfer occurred during the transition of the brain from resting-state to taskstate, suggesting the brain expends more effort on immediate tasks 35 . These ndings may indicate that low frequency brain organizations tend to run faster with age to maintain normal functions.
Thirdly, the GS power was more evenly distributed in aging brain, showing by (1) increased power with age at frequency bands with lower power and decreased power with age at frequency bands with higher power and (2) power transferring from lower frequencies with higher power to higher frequencies with lower power. These phenomena were much similar to the spatial dedifferentiation of brain aging, which argued that brain functions recruit more distributed rather than specialized brain regions in the elderly brain 36 . Analogously, we interpret the more evenly distributed power in elderly brain as temporal dedifferentiation. The spatiotemporal dedifferentiation may be of importance for preserving brain functions and preventing functional degeneration during brain aging 37 .
Finally, we demonstrated that the decline and temporal dedifferentiation of GS uctuations with age are primarily contributed by neural activity, less contributed by vascular factors, and almost unaffected by head motion. Grinband  respiratory and cardiac signals) should be tested directly in future studies. Second, head motion parameters were strictly restricted and regressed out, which may eliminate motion-related physiological activities 40 . Thus, the contribution of head motion to brain aging warrants further studies. Third, the cognitive relevance of our results cannot be determined because there is no cognitive measurement in this dataset. Given the close relationship between brain signal uctuations and cognition in particular frequency bands 16 , our ndings in multiple frequency bands may be associated with various cognitions which deserves in-depth studies. Finally, there were more females (n = 194) than males (n = 128) in the nal analysis. We regressed out sex information and did not test the sex effect because it was outside the scope of this study. However, the in uence of sex on brain aging is inconclusive and deserves further investigations 43 .

Conclusion
We investigated GS uctuations across the adult lifespan. The decline and temporal dedifferentiation of GS power with age were con rmed to be general patterns of brain aging. These patterns may be driven by various physiological and psychological components. The temporal dedifferentiation extends the classical theory of spatial dedifferentiation in aging brain and requires further veri cation.

Declarations
Author contributions Y.W. designed the study. Y.W., Y.A., and X.C. analyzed the data. Y.W., Y.A., X.C., and J.K. wrote the manuscript. All authors reviewed and edited the manuscript. All authors read and approved the manuscript.
42. Mosher, C. P. et al. Cellular classes in the human brain revealed in vivo by heartbeat-related modulation of the extracellular action potential waveform. Cell Reports, 30, 3536-3551 (2020).
43. Joel, D. Beyond the binary: Rethinking sex and the brain. Neuroscience & Biobehavioral Reviews, 122, 165-175 (2021). Figure 1 The power spectra of GS for original data (A) and de-convolved data (B), showing in multiple age ranges. Figure 2