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Neurobiology of Aging 70 (2018) 59e69

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Neurobiology of Aging

journal homepage: www.elsevier .com/locate/neuaging

Frequency and amplitude modulation of resting-state fMRI signalsand their functional relevance in normal aging

Albert C. Yang a,b,c,*, Shih-Jen Tsai b,c,d, Ching-Po Lin d, Chung-Kang Peng a,Norden E. Huang e

aDivision of Interdisciplinary Medicine and Biotechnology, Beth Israel Deaconess Medical Center/Harvard Medical School, Boston, MA, USAbDepartment of Psychiatry, Taipei Veterans General Hospital, Taipei, Taiwanc Institute of Brain Science, National Yang-Ming University, Taipei, TaiwandDivision of Psychiatry, School of Medicine, National Yang-Ming University, Taipei, TaiwaneCenter for Dynamical Biomarkers and Translational Medicine, National Central University, Chungli, Taiwan

a r t i c l e i n f o

Article history:Received 22 December 2017Received in revised form 24 May 2018Accepted 4 June 2018Available online 15 June 2018

Keywords:Functional magnetic resonance imagingBlood oxygen leveledependent signalFrequency and amplitudeHilberteHuang transformAging

* Corresponding author at: Division of Interdisciplnology, Beth Israel Deaconess Medical Center/Harvardline Avenue, KS-B26, Boston, MA, USA. Tel.: þ1 617 667

E-mail address: cyang1@bidmc.harvard.edu (A.C. Y

0197-4580/$ e see front matter � 2018 Elsevier Inc. Ahttps://doi.org/10.1016/j.neurobiolaging.2018.06.007

a b s t r a c t

The intrinsic composition and functional relevance of resting-state blood oxygen leveledependent sig-nals are fundamental in research using functional magnetic resonance imaging (fMRI). Using the HilberteHuang Transform to estimate high-resolution time-frequency spectra, we investigated the instanta-neous frequency and amplitude modulation of resting-state fMRI signals, as well as their functionalrelevance in a large normal-aging cohort (n ¼ 420, age ¼ 21e89 years). We evaluated the cognitivefunction of each participant and recorded respiratory signals during fMRI scans. The results showed thatthe HilberteHuang Transform effectively categorized resting-state fMRI power spectra into high (0.087e0.2 Hz), low (0.045e0.087 Hz), and very-low (�0.045 Hz) frequency bands. The high-frequency powerwas associated with respiratory activity, and the low-frequency power was associated with cognitivefunction. Furthermore, within the cognition-related low-frequency band (0.045e0.087 Hz), we discov-ered that aging was associated with the increased frequency modulation and reduced amplitude mod-ulation of the resting-state fMRI signal. These aging-related changes in frequency and amplitudemodulation of resting-state fMRI signals were unaccounted for by the loss of gray matter volume andwere consistently identified in the default mode and salience network. These findings indicate thatresting-state fMRI signal modulations are dynamic during the normal aging process. In summary, ourresults refined the functionally related blood oxygen leveledependent frequency band in a considerablynarrow band at a low-frequency range (0.045e0.087 Hz) and challenged the current method of resting-fMRI preprocessing by using low-frequency filters with a relatively wide range below 0.1 Hz.

� 2018 Elsevier Inc. All rights reserved.

1. Introduction

A trend in recent studies has indicated growing interest in usingblood oxygen leveledependent (BOLD) signals obtained throughfunctional magnetic resonance imaging (fMRI) to measure spon-taneous brain activity (Fox and Raichle, 2007). Approximating aBOLD signal as a measure of neural activity depends largely onneurovascular coupling (Logothetis et al., 2001), that is, the corre-lation between activated neuronal activity and increased cerebralblood flow in the nearby vasculature (Malonek and Grinvald, 1996;Ogawa et al., 1990). Therefore, a BOLD signal is a hemodynamic

inary Medicine and Biotech-Medical School, 330 Brook-4553; fax: þ1 617 667 4894.ang).

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response per se that is potentially influenced by cerebrovasculardynamics.

Cerebrovascular dynamics are not homeostatic processes(Girouard and Iadecola, 2006). Spatially, the density of brain cap-illaries is regionally heterogeneous, varying by regional blood flowand regional metabolic demand (Ward and Lamanna, 2004).Temporally, cerebrovascular dynamics are interconnected withcardiovascular and respiratory activities (Katura et al., 2006).Furthermore, aging is known to affect cerebrovascular dynamicsthrough increased atherosclerosis (Romero et al., 2009), increasedtortuosity of cerebral vessels (Brown and Thore, 2011), alteredcollateral circulation (Duvernoy et al., 1981), lowered resting-statecerebral blood flow (Martin et al., 1991), and reduced cerebralmetabolic rate of oxygen consumption (Marchal et al., 1992) (seeD’Esposito et al., 2003 for a review of relevant the literature).Collectively, these factors may affect the neurovascular coupling

A.C. Yang et al. / Neurobiology of Aging 70 (2018) 59e6960

dynamics, a possibility that inherently implies the alteration ofintrinsic oscillations of BOLD signals during the aging (D’Espositoet al., 1999). Such alteration could be detected in the frequencyand amplitude modulation observed in BOLD signals (Logothetisand Wandell, 2004; Wan et al., 2006).

However, the exact composition of BOLD oscillations and theirfunctional relevance remain controversial. Previous studies haverevealed that BOLD frequencies above 0.1 Hz are influenced bycardiac and respiratory activity, whereas those below 0.01 Hz maybe prone to nonstationarity or low-frequency drift (Smith et al.,1999). Few studies have investigated the divisions of spectralproperties of resting-state BOLD signals (Cordes et al., 2001;Salvador et al., 2008; Zuo et al., 2010). In general, these studiesshow that functional component of a resting-state BOLD signal isdetected typically in the low-frequency range of <0.08 or <0.1 Hz(Biswal et al., 1995; Buckner et al., 2009; Leopold and Maier, 2012;Zou et al., 2008), and the exact frequency component related toneuronal function remains underexplored.

On the other hand, a number of temporal analyses of the BOLDsignal have been proposed, such as standard deviation (SD) (Garrettet al., 2011, 2013), amplitude of low-frequency fluctuations (ALFF)(Zang et al., 2007), or fraction ALFF (Zou et al., 2008). Thesemethods have been applied to investigate the resting-state BOLDsignal in aging (Balsters et al., 2013; Burzynska et al., 2015; Garrettet al., 2013; Niazy et al., 2011; Yan et al., 2011). However, neither SDnor ALFF/fraction ALFF methods consider the intrinsic componentsof the BOLD signal and warrant further investigations.

We hypothesized that cognition-related BOLD signal fre-quencies occurred within a narrow band, and that the frequencyand amplitude modulation of these signals are altered by theaging process. To test this hypothesis, we adopted an adaptivedata analysis method, the HilberteHuang Transform (HHT)(Huang et al., 1998), to decompose the BOLD signal into a set ofintrinsic components and obtain high-resolution images of theinstantaneous time-frequency spectrum. Subsequently, weassessed the frequency and amplitude modulation characteristicsto determine their functional relevance and association withnormal aging based on a large normal-aging cohort includingadults of all ages.

2. Material and methods

2.1. Participants

The cohort in this study comprised 420 healthy Han Chineseparticipants representative of the adult lifespan (age ¼21e89 years; men ¼ 215; women ¼ 205). The participants wererecruited from communities in Northern Taiwan. This study is anongoing healthy aging project (Yang et al., 2013, 2014) conducted inaccordance with the Declaration of Helsinki. Approval for this studywas received from the Institutional Review Board at Taipei VeteransGeneral Hospital. Each participant was evaluated by a trainedresearch assistant who used the Mini-International Neuropsychi-atric Interview to exclude the presence of Axis-I psychiatric disor-ders (Sheehan et al., 1998). The cognitive function of all participantswas assessed using the Mini-Mental State Examination (MMSE)(Folstein et al., 1975) andWechsler Digit Span Task (DST) (Wechsler,1997). Participants who were older than 59 years were furtherassessed using the Clinical Dementia Rating scale (Hughes et al.,1982) to exclude dementia (Clinical Dementia Rating >0). Overall,the exclusion criteria for participants comprised the following: (1)presence of dementia, (2) presence of an Axis-I psychiatric disorder(e.g., schizophrenia, bipolar disorders, or unipolar depression), and(3) a history of neurological conditions (e.g., head injury, stroke, orParkinson disease).

2.2. Image acquisition and processing

The fMRI scanning was performed at National Yang-Ming Uni-versity by using a 3T Siemens MRI scanner (Siemens Magnetom TimTrio, Erlangen, Germany) equipped with a 12-channel head coil. Thescanning protocol was consistent with that in our previous studies(Yang et al., 2013, 2014). For the resting-state imaging, T2*-weightedimages with BOLD contrast were measured using a gradient echo-planar imaging (EPI) sequence (repetition time (TR) ¼ 2500 ms;echo time ¼ 27 ms; field of view ¼ 200 mm; flip angle ¼ 77; matrixsize ¼ 64 � 64; voxel size ¼ 3.44 � 3.44 � 3.40 mm). For eachsequence, 200 EPI volumes were acquired along the anteriorcommissure e posterior commissure plane. Structural T1 imageswere acquired using a 3D magnetization-prepared rapid gradientecho sequence (TR ¼ 2530 ms, echo time ¼ 3.5 ms, TI ¼ 1100 ms,field of view ¼ 256 mm, flip angle ¼ 7). T1 images were segmentedto estimate the total gray matter volume of each participant.

Resting-state fMRI data were preprocessed and analyzed usingSPM8 (Wellcome Department of Imaging Neuroscience, London,UK), which was implemented in MATLAB (MathWorks Inc, Sher-born, MA). The fMRI images were slice-timing corrected, realigned,and normalized into the standard stereotaxic space of a MontrealNeurological Institute EPI template and resampled to a 3-mmisotropic voxel. Covariates of the BOLD time-series data wereregressed out, including the time courses of 6 head motions, whitematter, and cerebrospinal fluid. No global signal regression wasperformed to avoid introducing distortions into the time-seriesdata (Anderson et al., 2011; Murphy et al., 2009). The participantsincluded in this study exhibited a maximal displacement of lessthan 1.5 mm at each axis, and an angular motion of less than 1.5� foreach axis. The first 5 data points (12.5 seconds) in the BOLD time-series data were discarded because the initial fMRI scanning wasunstable, and 195 data points remained in the final data. Becausethe HHT method was used to estimate the time-frequency spec-trum of the BOLD signal, we did not perform temporal low-passfiltering, which is typically used when investigating the resting-state BOLD signal.

2.3. Respiratory signal analysis

Respiratory activity was recorded simultaneously with theresting-state fMRI scans by using a pneumatic belt tension trans-ducer for 393 of the participants. The signal of respiratory effort wassampled at 50 Hz. The respiratory rate and power were estimatedthrough a power spectrum analysis of signal between 0.1 and 0.4 Hz(Malik, 1996).

2.4. Empirical mode decomposition and the HHT

Empirical mode decomposition (EMD), which is the core of theHHT (Huang et al., 1998), was developed to decompose andidentify intrinsic oscillations, called intrinsic mode function(IMF), which are embedded in time-series data, and has beenapplied widely to multiple disciplines. Unlike Fourier-based time-series data analysis, EMD involves no a priori assumptionregarding the underlying structure of the time-series data, and itis therefore an adaptive method for analyzing nonlinear andnonstationary signal comprising multiple periodic components(Wu et al., 2007).

Decomposition was conducted using a sifting process todecompose the original time-series data into a finite set of IMFs. Insummary, the sifting process comprised the following steps: (1)connecting the local maxima or minima of a targeted signal to formthe upper and lower envelopes by natural cubic spline lines, (2)extracting the first prototype IMF by estimating the difference

A.C. Yang et al. / Neurobiology of Aging 70 (2018) 59e69 61

between the targeted signal and the mean of the upper and lowerenvelopes, and (3) repeating these procedures to produce a set ofIMFs that were represented by a certain frequency-amplitudemodulation at a characteristic time scale. The decomposition pro-cess was completedwhen nomore IMFs could be extracted, and theresidual component was treated as the overall trend of the rawdata. Although IMFs are empirically determined, they remainorthogonal to one another and may therefore contain independentphysical meanings (Lo et al., 2009; Wu et al., 2007).

To mitigate mode mixing during the decomposition (i.e., theexistence of drastically disparate wave periods), a noise-assistedmethod (i.e., the ensemble EMD) was used to improve the EMD(Wu and Huang, 2004; Wu et al., 2009). This method defines thetrue IMF components as the average of an ensemble of trials (N ¼1000 in the present study), each consisting of the signal plus thewhite noise of finite amplitude. The added noise in each trial iscanceled out in the ensemble mean of large trials. In this study, theadded white noise was 0.1 of the SD of the original BOLD time-series data (Wu et al., 2007). The uniformly added white noisefacilitated projecting the decomposition of the IMFs onto compa-rable scales, independent of the nature of original signal, therebymitigating the problem ofmode-mixing and enabling the time scaleof each IMF decomposed frommultiple time-series observations tobe mutually comparable. The MATLAB-based ensemble EMD algo-rithm was available publicly at http://rcada.ncu.edu.tw/FEEMD.zip(Wang et al., 2014). Fig. 1A shows the ensemble EMD decomposi-tion of a BOLD signal.

Fig. 1. Illustration of the HHT of BOLD signal obtained from a single participant. (A) EMD of aan example, the Hilbert transformwas applied to the IMF to determine the instantaneous freyielded, a HilberteHuang spectrum that showed a higher resolution in time-frequency-pofrom FFT. Four quantitative frequency and amplitude statistics were derived from the HHT. Fmean weighted frequency, mean amplitude, variability of the frequency modulation (i.e., ththe SD of the instantaneous amplitude). Abbreviations: BOLD, blood oxygen level dependent;transform; IMF, intrinsic mode function; SD, standard deviation.

2.5. Frequency and amplitude analysis of IMFs of BOLD signal

The IMFs were decomposed using the EMD method to enablecalculating the instantaneous frequency by using the Hilberttransform (Fig. 1B). The IMF decomposed from EMD overcomes thelimitation as imposed by Hilbert transform to derive physicallymeaningful instantaneous frequency (Huang et al., 1998, 2009). Foreach IMF, they represent narrow-band amplitude and frequency-modulated signal S(t) and can be expressed as

s ðtÞ ¼ AðtÞcos fðtÞ (1)

where instantaneous amplitude A and phase f can be calculated byapplying the Hilbert transform, defined as SH ¼ 1

p

RSðt’Þ=t� t’dt’,

AðtÞ ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiS2ðtÞ þ S2HðtÞ

q, and fðtÞ ¼ arctanðSHðtÞ=SðtÞÞ. The instan-

taneous frequency is then calculated as the derivative of the phasefunction uðtÞ ¼ dfðtÞ=dt.

Thus, the original BOLD signal X can be expressed as the sum-mation of all IMFs and residual, r

XðtÞ ¼Xkj¼1

AjðtÞexp�iZ

ujðtÞdt�þ r (2)

Where k is the total number of IMFs, Aj(t) is the instantaneousamplitude of each IMF; and uj(t) is the instantaneous frequency ofeach IMF.

BOLD signal. The decomposition yielded 6 IMFs and a residual trend. (B) Using IMF 2 asquency and amplitude. (C) Combining the results of the Hilbert transform from all IMFswer characteristics compared with the conventional power spectrum density derivedor instantaneous frequencies and amplitudes derived from each IMF, we calculated thee SD of the instantaneous frequency), and variability of the amplitude modulation (i.e.,EMD, empirical mode decomposition; FFT, fast Fourier transform; HHT, HilberteHuang

A.C. Yang et al. / Neurobiology of Aging 70 (2018) 59e6962

The instantaneous frequency and amplitude derived from Hil-bert transform (Equation 2) of each IMF decomposed from theBOLD signal enable to present the amplitude and the instantaneousfrequency as functions of time in a three-dimensional plot, inwhichthe power density (squared amplitude) can be color-coded on thefrequency-time plane. Thus, combining the results of Hilberttransform of all IMFs, the frequency-time distribution of the powerof the BOLD signal is designated as the HilberteHuang spectrum(Fig. 1C).

Furthermore, with the HilberteHuang spectrum defined, we canalso define the marginal spectrum by estimating the cumulatedpower over the entire time span in a frequency domain (see HHTmarginal spectrum in Fig. 1C). The marginal spectrum is a measureof total power contribution from each frequency and can becomparedwith conventional power spectrum derived using Fouriertransform (FT) (see FT spectrum in Fig. 1C).

The instantaneous modulation of the BOLD signal creates thepossibility for measuring the static or dynamic coupling betweentwo comparable IMFs in BOLD time-series data, warranting aseparate study of the functional connectivity obtained by using theHHT. In this study, we focused on modulating the frequency andamplitude of BOLD data and the following HHT-based measures.First, for given IMF Si, we calculated the weighted mean of theinstantaneous frequency and normalized power as follows:

uSl ¼XNj¼1

uSi

�tj�A2Si

�tj�,XN

j¼1

A2Si

�tj�

(3)

~P ¼XNj¼1

A2Si

�tj�,Xk

i¼1

XNj¼1

A2Si

�tj�

(4)

where u and A, respectively, denote frequency and amplitudederived from the Hilbert spectrum of the ith IMF Si, k is the totalnumber of IMFs, and N is the number of time points. Second, weused the SD of the instantaneous frequency and amplitude overtime (Fig. 1B) to determine the variability (or spread) of theinstantaneous frequency and amplitude modulations. Although themean and variance were used, these metrics represented the globalproperties of the instantaneous BOLD signal modulation unac-counted for by the conventional FT, which generates coarse fre-quency and amplitude estimations in the short and noisy BOLDsignal (Fig. 1C).

2.6. Statistical analysis

The HHT was applied to the BOLD signal of every gray mattervoxel (3 � 3 � 3 mm) by using a group-specific gray matter maskthresholding for partial volume estimates at 0.25. The decomposi-tion of the BOLD signal yielded a set of IMFs that were used sub-sequently to estimate the power spectrum density at the voxelwiselevel. The statistics of the instantaneous frequency and amplitude of

Table 1Normal aging cohort characteristics

Age group(year)

Number ofparticipants

Females (%) MMSE DST-F

20e29 80 41 (51.2) 29.3 � 1.1 15.3 � 1.030e39 60 32 (53.3) 29.2 � 1.1 15.3 � 1.940e49 52 29 (55.8) 28.6 � 1.3 13.6 � 2.050e59 71 43 (60.6) 28.6 � 1.3 13.7 � 2.460e69 73 43 (58.9) 27.8 � 2.2 13.6 � 2.070e79 36 14 (38.9) 27.1 � 3.1 12.4 � 2.680e89 48 3 (6.3) 26.2 � 2.6 11.7 � 2.6

Key: DST-F, digit span forward test; DST-B, digit span backward test; MMSE, mini-ment

each IMF were used to generate parametric images. To preserve theoriginal frequency and amplitude characteristics of the BOLD data,no spatial image smoothing was applied. The statistical analysescomprised the following steps.

First, we assessed the spectrum characteristics of the BOLDsignal and compared the spectrum derived from the HHT with thatobtained using the conventional FT. Subsequently, we assessed thefunctional relevance of the BOLD frequency band by calculating thepartial correlation of the cognitive scores and respiratory metricswith the power spectrum density at each frequency bin, therebycontrolling the effect of age. This procedure facilitated identifyingwhich BOLD frequency band was related to cognitive function orrespiration while excluding the effect of age on these functional orphysiologic metrics.

Second, having determined the cognition-related BOLD fre-quency band, we investigated the association of age with BOLDfrequency and amplitude statistics in major functional networks(Shirer et al., 2012), which provided a decoding of 14 cognitive-related brain networks (see nomenclature of these networks athttp://findlab.stanford.edu/functional_ROIs.html). Among thesenetworks, we choose 10 representative networks to be tested in ourstudy, including anterior and posterior salience networks, dorsaland ventral default mode network (DMN), precuneus, basal ganglia,sensorimotor, auditory, visual-spatial, and language networks. Thefrequency and amplitude measures were averaged across all voxelswithin the functional network masks (Shirer et al., 2012), and thepartial correlation was controlled according to sex and total graymatter volume. The partial correlation was considered statisticallysignificant if the p value was less than 0.0013 using Bonferronicorrection for multiple comparisons (i.e., significance cutoff wascalculated by 0.05 divided by all 40 partial correlation testsd10functional networks multiplied by 4 BOLD frequency or amplitudemeasures).

Finally, the regional effect of age on the frequency-amplitude ofthe BOLD signal was assessed using a general linear model at thevoxelwise level while controlling for the effect of sex and total graymatter volume. Significant peak coordinates in the MontrealNeurological Institute space were reported if the p value correctedfor the false discovery rate was less than 0.05 at the peak level.

3. Results

3.1. Participants

Table 1 shows the demographic characteristics of the normalaging cohort. As expected, age was negatively correlated withMMSE (Pearson’s r ¼ �0.46, p < 0.001), DST forward (r ¼ �0.48,p < 0.001), DST backward (r ¼ �0.64, p < 0.001), and the total graymatter volume (r ¼ �0.77, p < 0.001). Age was not correlated withthe respiratory rate or power. A one-way analysis of variancerevealed no between-group difference in the respiratory rate(F ¼ 1.99, p ¼ 0.07) or power (F ¼ 0.72, p ¼ 0.64).

DST-B Respiratoryrate (/min)

Respiratory power Total gray mattervolume, cm3

11.0 � 3.0 15.9 � 2.5 381 � 84 645 � 5810.5 � 2.8 14.7 � 3.4 365 � 95 618 � 599.0 � 2.6 15.0 � 2.4 347 � 83 575 � 478.0 � 3.1 15.0 � 2.5 355 � 109 571 � 607.9 � 3.1 15.3 � 2.3 357 � 85 525 � 485.0 � 2.6 15.4 � 2.5 375 � 130 474 � 513.5 � 2.3 15.9 � 2.7 366 � 114 450 � 48

al state examination.

A.C. Yang et al. / Neurobiology of Aging 70 (2018) 59e69 63

3.2. Power spectrum characteristics of BOLD signal

Fig. 2A shows a comparison of the power spectrum densityderived from the HHT and FT. The power spectrum density wasaveraged from all graymatter voxels among the entire study cohort.The HHT spectrum yielded a more favorable signal-to-noise ratiothan did the FT spectrum, exhibiting an identifiable pattern of BOLDfrequency bands at the boundary of 0.045 and 0.087 Hz, whichweredetermined by the localminima of the spectral density curve of HHTmarginal spectrum. The BOLDoscillations at frequencies higher than0.087 Hz (as high as 0.2 Hz) were derived from IMF 1, those between0.045 and 0.087 Hz were derived from IMF 2, and those lower than0.045 Hz were derived from the remaining IMFs (Fig. 1A and C).

Supplementary Fig. S1 and Table S1 show the normalized his-togram of the central frequency of each IMF of BOLD signals andfrequency range of each IMF across the entire study participants,respectively. The data suggest that the central frequency of eachIMF is narrow banded and is consistent across different individuals,thus supporting the validity of spectral boundary seen in theaveraged HHT marginal spectrum of the BOLD signals (Fig. 2A).

Using frequency boundaries derived from HHT, we categorizedthe BOLD spectrum into bands of high (0.087e0.2 Hz), low(0.045e0.087 Hz), and very-low (<0.045 Hz) frequencies. Thefractional power of these frequency bands relative to the total po-wer was 54.8%e71.1% (95% confidence interval) in high-frequencypower, 9.2%e14.0% in low-frequency power, and 19.0%e32.0% invery-lowefrequency power.

3.3. Functional relevance of BOLD frequency band

Figures 2BeF show the partial correlations of the cognitive orrespiratory metrics with the BOLD power spectrum density at each

Fig. 2. (A) Comparison of the mean power spectrum density derived from (left) the HHT andfrequency. The vertical dashed lines indicate the boundary of the frequency bands according(left) and FT (right) power spectrum at each frequency bin with (B) scores of the MMSE, (C)(DST-B), (E) respiratory rate, and (F) respiratory signal power. All partial correlations were coof correlation when p < 0.001). Respiratory signal was recorded simultaneously with themagnetic resonance imaging; FT, Fourier transform; HHT, HilberteHuang transform; MMSE

frequency bin after adjustment to control for the effects of age. TheMMSE and DST forward scores indicated an increased positivecorrelation with HHT power spectrum in the low-frequency band(0.045e0.087 Hz); the correlation between the HHT power and DSTbackward scores exhibited a similar pattern but did not achievestatistical significance. The respiratory rate was not correlated withHHT power in any frequency band, although the respiratory powerwas correlatedwith the HHT spectrum in the high-frequency powerrange (0.087e0.2 Hz). The FT-based power spectrum was notassociated with any cognitive score, respiratory rate, or respiratorypower.

3.4. Correlation between age and BOLD frequency-amplitudestatistics in major functional networks

Because low-frequency power exhibited functional relevance tocognitive function, and the low-frequency range was contributedmainly from the IMF 2, we opted to use IMF 2 to investigate thecorrelation between age and BOLD instantaneous frequency-amplitude modulations in the major functional networks (Table 2and Fig. 3).

The mean frequency of BOLD IMF 2 was positively correlatedwith age in all of the major functional networks. After controllingfor the effects of sex and total gray matter volume, the strongestcorrelation between age andmean BOLD frequencywas observed inthe dorsal DMN, r ¼ 0.33, followed by the precuneus (r ¼ 0.30) andposterior salience networks (r ¼ 0.30). By contrast, the normalizedpower of BOLD IMF 2 was negatively correlated with age in theventral and dorsal DMNs and in the posterior salience network aftercontrolling for the effects of sex and total gray matter volume (allr ¼ �0.24). The variability of instantaneous frequency modulationwas positively correlated with age in all of the major functional

(right) FT among all 420 patients. Gray line indicates the SD of spectral density in eachto the HHT spectrum (0.045 and 0.087 Hz). (BeF) Partial correlations between the HHTscores of the digit span forward test (DST-F), (D) scores of the digit span backward testntrolled to account for the effects of age (the horizontal dashed lines indicate the levelfMRI scans by using a chest-belt tension transducer. Abbreviations: fMRI, functional, Mini-Mental State Examination; SD, standard deviation.

Table 2Correlations between age and frequency/amplitude modulation at low frequency of BOLD signal in major functional networks

Network Anterior salience Posteriorsalience

Dorsal DMN Ventral DMN Precuneus Basalganglia

Sensorimotor

Auditory Visual-spatial

Language

Mean frequencyPearson’s r 0.34 0.41 0.39 0.38 0.37 0.36 0.41 0.29 0.39 0.32Partial r 0.28 0.30 0.33 0.25 0.30 0.26 0.32 0.28 0.29 0.26

Normalized power (%)Pearson’s r �0.17 �0.31 �0.25 �0.31 �0.24 �0.30 �0.26 �0.24 �0.28 �0.28Partial r �0.18 �0.24 �0.24 �0.24 �0.22 �0.23 �0.23 �0.22 �0.21 �0.22

Variability of frequency modulationPearson’s r 0.18 0.36 0.33 0.29 0.33 0.37 0.34 0.38 0.38 0.34Partial r 0.22 0.29 0.31 0.27 0.28 0.30 0.29 0.38 0.32 0.29

Variability of amplitude modulationPearson’s r �0.13 �0.16 �0.15 �0.23 �0.09 �0.14 �0.14 �0.04 �0.18 �0.10Partial r �0.16 �0.17 �0.17 �0.16 �0.14 �0.13 �0.17 �0.09 �0.13 �0.11

Low-frequency range: 0.045e0.087 Hz. Correlation r values with boldface indicate a uncorrected p value of less than 0.001.Partial correlation following adjustment to control for the effects of sex and total gray matter volume.Key: BOLD, blood oxygen level dependent; DMN, default mode network.

A.C. Yang et al. / Neurobiology of Aging 70 (2018) 59e6964

networks; the strongest correlation was observed in the auditorynetwork (r¼ 0.38), followed by the dorsal DMN (r¼ 0.31), and thenthe basal ganglia (r ¼ 0.30). All of the reported partial correlationshad an uncorrected p value of less than 0.001. No significant cor-relation was observed between age and the amplitude modulationvariability. In addition, we observed that the correlations betweenage and HHT spectral characteristics of the BOLD signal were linear(Fig. 3) and were not explained better by the exponential or seconddegree of polynomial models (data not shown).

To compare with results derived from HHT, we derived power-weighted mean frequency between the 0.045 and 0.087 Hz thatwe identified in HHT marginal spectrum. No significant correlationwas found between age and FT mean frequency.

Fig. 3. Scatter plots of the correlations between age and amplitude-frequency modulation obecause low-frequency power exhibited functional relevance to cognitive function, and the looxygen level dependent; IMF, intrinsic mode function. *Indicates partial correlations with u

3.5. Regional correlation between age and BOLD frequency-amplitude statistics

Figs. 4 and 5 show the regional patterns of correlations betweenage and the BOLD frequency-amplitude measures of each IMF.Increased age was associated with increased mean frequency inIMFs 1e5 (Fig. 4, left panel). In addition, it was associated withincreased normalized power in IMF 1 but with reduced normalizedpower in the other IMFs (Fig. 4, right panel). For the variability ofinstantaneous frequency-amplitudemodulation of the BOLD signal,increased age was associated with reduced variability of frequencymodulation in IMF 1 and with increased variability of frequencymodulation in IMFs 2 and 3 (Fig. 5, left panel). By contrast, increased

f the IMF 2 of the BOLD signal in the major functional networks. The use of IMF 2 wasw-frequency range was contributed mainly from the IMF 2. Abbreviations: BOLD, bloodncorrected p value of less than 0.001.

Fig. 4. Voxelwise correlations among age, mean frequency, and normalized power for each IMF. Abbreviation: IMF, intrinsic mode function

A.C. Yang et al. / Neurobiology of Aging 70 (2018) 59e69 65

age was associated with the increased variability of amplitudemodulation in IMF 1 but with reduced variability of amplitudemodulation in IMFs 2e5 (Fig. 5, right panel).

Table 3 shows a summary of the regional regression statisticsbetween age and the frequency-amplitude statistics afteradjustment to control for the effects of sex and total gray mattervolume. We focused on and reported exclusively the results ofIMF 2 because of its functional relevance. Generally, increasedage was associated with increased mean frequency and itsmodulation, as well as reduced normalized power and the vari-ability of amplitude modulation. Specifically, positive correlationsbetween age and the mean BOLD frequency modulation weresignificant in the left-middle temporal (peak t ¼ 7.12), right-middle cingulum (t ¼ 6.86), left-inferior parietal (t ¼ 6.86),right-superior temporal pole (t ¼ 6.77), and right-posterior

Fig. 5. Voxelwise correlations among age, variability of frequency, and amplit

cingulum (t ¼ 6.75). Negative correlations between age andnormalized power were observed in the right-middle temporal(t ¼ �5.95), right cuneus (t ¼ �5.92), right postcentral(t ¼ �5.89), right-middle frontal (t ¼ �5.75), and left-middletemporal cortices (t ¼ �5.74).

Positive correlations between age and the variability offrequency modulation occurred in the right caudate (t ¼ 6.80), left-superior occipital (t ¼ 6.46), left-middle frontal (t ¼ 6.38),right-middle temporal (t ¼ 6.25), and right-anterior cingulum(t ¼ 6.02). Negative correlations between age and the variability ofamplitude modulation were observed in the left and right post-central (t ¼ �5.78 and �5.34, respectively), left-middle temporal(t ¼ �4.66), left lingual (t ¼ �4.65), and right-superior occipitalcortices (t ¼ �4.61). All of the reported brain regions had falsediscovery rateecorrected p value of less than 0.05.

ude modulation for each IMF. Abbreviation: IMF, intrinsic mode function

Table 3Top 5 brain regions with significant correlations between age and frequency/amplitude modulation in low frequency of BOLD signal

Brain region BA MNI coordinates Peak t

x y z

Mean frequencyMid. Temporal L 22 �57 �48 12 7.12Mid. Cingulum R 32 3 27 36 6.86Inf. Parietal L 40 �45 �48 51 6.86Sup. Temporal Pole R 38 48 18 �18 6.77Post. Cingulum R 23 6 �36 27 6.75

Normalized power (%)Mid. Temporal R 37 51 �66 6 �5.95Cuneus R 19 12 �90 36 �5.92Postcentral R 3 48 �18 57 �5.89Mid. Frontal R 10 24 57 27 �5.75Mid. Temporal L 37 �54 �69 0 �5.74

Variability of frequencymodulationCaudate R 12 3 12 6.80Sup. Occipital L 7 �9 �81 42 6.46Mid. Frontal L 10 �30 60 18 6.38Mid. Temporal R 37 51 �69 6 6.25Ant. Cingulum R 32 3 36 24 6.02

Variability of amplitudemodulationPostcentral L 40 �45 �39 60 �5.78Postcentral R 3 48 �21 57 �5.34Mid. Temporal L 37 �54 �69 0 �4.66L. Lingual L 18 �12 �81 �6 �4.65Sup. Occipital R 19 15 �93 30 �4.61

Low-frequency range: 0.045e0.087 Hz.Correlation was conducted using general linear model covarying with sex and totalgray matter volume.Key: BOLD, blood oxygen level dependent; BA, Brodmann Area; L, left; MNI, Mon-treal Neurological Institute; R, right.

A.C. Yang et al. / Neurobiology of Aging 70 (2018) 59e6966

4. Discussion

Using the HHT, we explored the frequency and amplitudecharacteristics of the BOLD signal and their functional relevance innormal aging. Compared with the BOLD signal estimated using theFT, the HHT was more effective at differentiating among the BOLDsignal with a clear separation of frequency bands. According to theHHT spectrum, BOLD frequencies can be categorized into high(0.087e0.2 Hz), low (0.045e0.087 Hz), and very-low (<0.045 Hz)frequency bands. The low-frequency power of the BOLD signal wasassociated with cognitive function, whereas the high-frequencypower was related to respiratory activity. The low-frequencyrange was consistent with that reported in previous studies onresting-state fMRI, indicating the functional relevance of the BOLDsignal at frequencies below 0.1 Hz (Biswal et al., 1995; Buckner et al.,2009; Zou et al., 2008). In this study, we advanced the frequencyresolution of the resting-state fMRI signal into more precise andnarrower frequency bands and subsequently applied this feature tostudy the effect of age on the cognition-related BOLD oscillations.

The cognition-related BOLD low-frequency band indicated thatage was associated with increased mean frequency and the vari-ability of its modulation, as well as with reduced normalized powerand amplitude modulation, implying that the modulation of theBOLD oscillations was inconstant throughout the aging process.This finding is particularly pertinent because previous studies onresting-state fMRI have assumed a relatively fixed spectral distri-bution in BOLD oscillations among all participants, and the linearPearson’s correlation has been used to investigate the dependenceof the BOLD signal among the various regions of the brain. However,using the Pearson’s correlation cannot account for the frequencyand amplitude modulation of the BOLD signal, a modulationthat could contribute to inaccurate estimations of functional

connectivity (Bullmore and Bassett, 2011; Kayser et al., 2009; Siegelet al., 2012). The findings presented in this article can be used toaccount for these frequency and amplitude modulations of theBOLD signal in future functional connectivity studies.

In addition, we observed the largest power in the very-low fre-quency band. BOLD signals have been known to have 1/f frequencydistribution that its power spectral density is inversely proportionalto the frequency of the BOLD signal (Fox et al., 2007; Zarahn et al.,1997). 1/f frequency distribution is an ubiquitous feature of thecomplex system (Goldberger et al., 2002; Schlesinger, 1987) and hasbeen observed in other neurophysiologic signal (Linkenkaer-Hansenet al., 2001; Stam and de Bruin, 2004). In a complex system, this 1/fdistribution is likely to arise from the underlying oscillatory com-ponents operating at multiple time scale and frequencies(Goldberger et al., 2002; Hausdorff and Peng, 1996), thus delineatingthese diverse frequency components are crucial for understandingthe physiologic nature of the BOLD signal (Buzsaki and Draguhn,2004; Cordes et al., 2001; Niazy et al., 2011; Salvador et al., 2008;Zuo et al., 2010). Furthermore, the present article used SD to assessthe distribution of frequency and amplitude modulation and war-rants future study of the complexity of IMFs of the resting-state fMRIsignal, which may extend our previous findings of assessing thecomplexity of the resting-state fMRI signal at multiple time scales(Hager et al., 2017; Yang et al., 2013, 2014, 2015).

4.1. The association of normal aging with frequency and amplitudeof resting-state BOLD signal

Aging is invariably associated with declined cerebrovascularfunction, leading to changes in neurovascular coupling and subse-quent measures of BOLD activity (D’Esposito et al., 2003). Previoustask-based studies have shown that compared with younger peo-ple, older people were associated with a decreased signal-to-noiseratio in the BOLD signal (D’Esposito et al., 1999) and with a reducedBOLD signal intensity (Hesselmann et al., 2001), indicating a changein the coupling between neuronal activity and BOLD responsesthroughout the aging process.

A number of studies have investigated the association of normalaging with the variability (Garrett et al., 2011, 2013) or spectralproperties of the resting-state fMRI signal, such as ALFF (Biswalet al., 2010; Hu et al., 2014; Yan et al., 2011). Generally, thesestudies have reported that increased age was associated withdecreased amplitude and variability of the BOLD signal. Forexample, Garrett et al., 2011 showed that older adults haddecreased SD in the BOLD signal than younger participants, andBurzynska et al., 2015 showed that greater BOLD SD was associatedwith better fluid abilities and memory in older adults. Yan et al.,2011, however, did not find difference in ALFF between arelatively small sample of older and younger participants. Hu et al.,2014 found that reduced fractional ALFF was associated with agingin the supplementary motor area, anterior cingulate cortex, bilat-eral dorsal lateral prefrontal cortex, right inferior parietal cortex,and posterior cingulate cortex. Our results correspond with theaforementioned observations that normalized power was reducedwith increased age in the low-frequency band, particularly in theDMN and posterior salience network (Table 3). Moreover, wepostulated that such changes were associated with the shift inpower and amplitude modulation toward the high-frequency band,as characterized in IMF 1 (Figs. 4 and 5).

Of note, SD measures the variability of the BOLD signal (Garrettet al., 2010, 2011) but does not consider any intrinsic componentsthat are mixed up from different sources. On the other hand, ALFF isdefined as the total power within the frequency range between 0.01and 0.1 Hz, thus capturing the variability in low-frequency fluctua-tions not revealed by SD of the BOLD signal. We expect that ALFF is

A.C. Yang et al. / Neurobiology of Aging 70 (2018) 59e69 67

comparable with the total power of combined IMFs within 0.01 and0.1 Hz, but because we found a functional association with a morenarrow-band signal in IMF 2, our results may capture more preciselythe amplitude of narrow-band low-frequency signal than ALFF.

Our findings on the aging-related shift in the mean and vari-ability of frequency modulation are novel because such high-resolution spectrum and the estimation of instantaneous fre-quency are poorly quantified in the short BOLD signal according tothe FT method. In our study, 3 functional networks receivedparticular attention: the dorsal DMN (i.e., the posterior cingulateand medial prefrontal cortices), ventral DMN (i.e., the retrosplenialand medial temporal cortices), and posterior salience network (i.e.,the posterior insula). These networks consistently exhibited anincreased mean and variability in frequency modulation anddecreased power associated with older age.

4.2. Functional relevance of BOLD frequency band

Since the inception of resting-state fMRI (Biswal et al., 1995),determining the frequency and functional relevance of the seem-ingly noisy spontaneous BOLD oscillations has been critical (Buzsakiand Draguhn, 2004; Cordes et al., 2001; Niazy et al., 2011; Salvadoret al., 2008; Zuo et al., 2010). Previous studies have determined thatthe resting-state BOLD signal at a frequency below 0.1 Hz (or0.08 Hz) were related to functional brain activity (Biswal et al.,1995; Buckner et al., 2009; Zou et al., 2008), whereas BOLD fre-quencies above 0.1 Hz were vulnerable to cardiac (Shmueli et al.,2007) and respiratory activities (Birn et al., 2008; Cordes et al.,2001). However, the lower region of this functionally related fre-quency band has remained largely underexplored. Zuo et al. (2010)investigated the ALFF in the resting-state BOLD signal by using theFT method (Zang et al., 2007), revealing that the slow-3(0.073e0.198 Hz) and slow-2 (0.198e0.25 Hz) bands were associ-ated with the white matter regions, whereas the slow-4(0.027e0.073 Hz) and slow-5 (0.01e0.027 Hz) bands were pri-marily associated with gray matter; prominent and reliable pat-terns were observed in the slow-4 band.

Our study, which included a large aging cohort, complementedthe aforementioned studies because we determined that high-frequency BOLD power was associated with respiratory activity,and only a narrow low-frequency band at 0.045e0.087 Hz wasrelated to cognitive function, indicating a tight neurovascularcoupling at this frequency band. Although we did not observe anycognitive or respiratory correlates at very-low frequencies(<0.045 Hz), a previous study indicated that BOLD frequencies at0.05 Hz and belowwere influenced by the spontaneous fluctuationsin the arterial carbon dioxide level at rest, which was not accountedfor by the respiratory activity (Wise et al., 2004). A recent review onthe frequency characteristics of the BOLD signal determined thatBOLD frequencies between 0.04 and 0.07 Hz may be used to avoidartifactual results in phase-synchronization calculations (Glereanet al., 2012). In summary, our findings combined with evidencefrom the literature may challenge the current understanding ofresting-state fMRI preprocessing that involves using a band-passfilter at frequencies below 0.1 Hz (or 0.01e0.08 Hz). According tothe HHT power spectrum, we assert that BOLD oscillations at fre-quencies between 0.045 and 0.087 Hz are the primary componentsassociated with functional brain activity, a topic that warrantsfurther studies of functional connectivity that focus on this specificmode of BOLD oscillations.

4.3. Applications of EMD and HHT in neuroscience

The decomposition of neurophysiologic signal is critical inidentifying the source and components underlying the complex

networks of the brain. Accordingly, independent component anal-ysis (ICA) has dominated the field of neuroscience (Fox and Raichle,2007; Salimi-Khorshidi et al., 2014). In particular, ICA decomposi-tion is based on maximizing the statistical independence of esti-mated components, whereas EMD is based on separating distinctmodes of frequency and amplitude modulations in the timedomain. Without resorting to frequency-domain decomposition,EMD bypasses the limitation imposed on data characteristics (as isthe case in Fourier analyses), thereby yielding a more precisedefinition of frequencies (Huang et al., 2009). Therefore, EMD ispotentially more suitable than ICA for delineating complex time-varying structures embedded in neurophysiologic signal, particu-larly at low signal-to-noise ratios.

Recent evidence indicated that EMD could be used in denoisingelectroencephalogram data (Safieddine et al., 2012) and improvedsource localization when combing EMD with ICA (Mijovic et al.,2010). Currently, only a few studies have explored using EMD inthe BOLD signal analysis. For example, Zheng et al., 2010 showedthat EMD can be used to detect BOLD activation and investigateregional homogeneity in various IMFs of the BOLD signal (Songet al., 2014). Because EMD is an adaptive method for nonlinearand nonstationary signal, we propose that the EMDmay be used infMRI studies to delineate the complex brain function according toboth temporal and spatial dimensions.

4.4. Limitations

This study was subject to certain limitations. First, we omittedexamining the effect of sex and the interactive effect of sex and ageon the HHT spectral measures because the sex effect was not theprimary focus of this study. Second, neuronal activity is notnecessarily associated with changes in cerebral blood flow (Huoet al., 2014); thus, the BOLD fMRI data may omit certain brain re-gions unaccounted for by neurovascular coupling. Third, the TR was2.5 seconds (sampling rate¼ 0.4 Hz) in this study; consequently, wecould not examine the effect of cardiac activity on the BOLD signal.Forth, the dip at 0.087 Hz is possibly associated with respiration-related artifacts, which needs to be further verified in futurestudies. Fifth, the applicability of the new approach to single-subject analysis remains to be evaluated. Finally, it is possible thatinformation reported in this article requires resting-state fMRI of alonger scan session (e.g., 8 minutes), and it remains unknown ifshorter fMRI scan duration (e.g., 5 minutes; potentially with fewerdynamic signal changes) may provide the same information.

5. Conclusion

Using the HHT, we narrowed the functionally related BOLDfrequency band to the range of 0.045e0.087 Hz. In addition, werevealed that normal aging was associated with the shift toward ahigh frequency in the BOLD signal and the reduced power andamplitude modulation in the DMN and salience network. The HHTapproach may be applied to other fMRI studies on neuropsychiatricillness to identify specific brain regions exhibiting pathologicchanges in frequency and amplitudemodulation in the BOLD signal.

Disclosure statement

The authors have no actual or potential conflicts of interest.

Acknowledgements

This work was supported by Taipei Veterans General Hospital,Taiwan (grants V106C-013 and V105D17-002-MY2-2); Taipei Vet-erans General Hospital-National Yang-Ming UniversityeExcellent

A.C. Yang et al. / Neurobiology of Aging 70 (2018) 59e6968

Physician Scientists Cultivation Program, No.103-V-A-002, and theMinistry of Science and Technology (MOST) of Taiwan (grantMOST 101-2314-B-075-041-MY3; MOST 103-2320-B-008-001; MOST104-2314-B-075-078-MY2; MOST 104-2745-B-075-002; MOST107-2634-F-075-002), and the MOST support for the Center forDynamical Biomarkers and Translational Medicine, National CentralUniversity, Taiwan (grant MOST 104-2911-I-008-001). Approval forthis study was received from the Institutional Review Board at TaipeiVeterans General Hospital, and the studywas conducted in accordancewith the Declaration of Helsinki.

Appendix A. Supplementary data

Supplementary data associated with this article can be found, inthe online version, at https://doi.org/10.1016/j.neurobiolaging.2018.06.007.

References

Anderson, J.S., Druzgal, T.J., Lopez-Larson, M., Jeong, E.K., Desai, K., Yurgelun-Todd, D., 2011. Network anticorrelations, global regression, and phase-shiftedsoft tissue correction. Hum. Brain Mapp. 32, 919e934.

Balsters, J.H., Robertson, I.H., Calhoun, V.D., 2013. BOLD frequency power indexesworking memory performance. Front. Hum. Neurosci. 7, 207.

Birn, R.M., Murphy, K., Bandettini, P.A., 2008. The effect of respiration variations onindependent component analysis results of resting state functional connectivity.Hum. Brain Mapp. 29, 740e750.

Biswal, B., Yetkin, F.Z., Haughton, V.M., Hyde, J.S., 1995. Functional connectivity inthe motor cortex of resting human brain using echo-planar MRI. Magn. Reson.Med. 34, 537e541.

Biswal, B.B., Mennes, M., Zuo, X.N., Gohel, S., Kelly, C., Smith, S.M., Beckmann, C.F.,Adelstein, J.S., Buckner, R.L., Colcombe, S., Dogonowski, A.M., Ernst, M., Fair, D.,Hampson, M., Hoptman, M.J., Hyde, J.S., Kiviniemi, V.J., Kotter, R., Li, S.J., Lin, C.P.,Lowe, M.J., Mackay, C., Madden, D.J., Madsen, K.H., Margulies, D.S.,Mayberg, H.S., McMahon, K., Monk, C.S., Mostofsky, S.H., Nagel, B.J., Pekar, J.J.,Peltier, S.J., Petersen, S.E., Riedl, V., Rombouts, S.A., Rypma, B., Schlaggar, B.L.,Schmidt, S., Seidler, R.D., Siegle, G.J., Sorg, C., Teng, G.J., Veijola, J., Villringer, A.,Walter, M., Wang, L., Weng, X.C., Whitfield-Gabrieli, S., Williamson, P.,Windischberger, C., Zang, Y.F., Zhang, H.Y., Castellanos, F.X., Milham, M.P., 2010.Toward discovery science of human brain function. Proc. Natl. Acad. Sci. U. S. A.107, 4734e4739.

Brown, W.R., Thore, C.R., 2011. Review: cerebral microvascular pathology in ageingand neurodegeneration. Neuropathol. Appl. Neurobiol. 37, 56e74.

Buckner, R.L., Sepulcre, J., Talukdar, T., Krienen, F.M., Liu, H., Hedden, T., Andrews-Hanna, J.R., Sperling, R.A., Johnson, K.A., 2009. Cortical hubs revealed byintrinsic functional connectivity: mapping, assessment of stability, and relationto Alzheimer’s disease. J. Neurosci. 29, 1860e1873.

Bullmore, E.T., Bassett, D.S., 2011. Brain graphs: graphical models of the human brainconnectome. Annu. Rev. Clin. Psychol. 7, 113e140.

Burzynska, A.Z., Wong, C.N., Voss, M.W., Cooke, G.E., McAuley, E., Kramer, A.F., 2015.White matter integrity supports BOLD signal variability and cognitive perfor-mance in the aging human brain. PloS One 10, e0120315.

Buzsaki, G., Draguhn, A., 2004. Neuronal oscillations in cortical networks. Science304, 1926e1929.

Cordes, D., Haughton, V.M., Arfanakis, K., Carew, J.D., Turski, P.A., Moritz, C.H.,Quigley, M.A., Meyerand, M.E., 2001. Frequencies contributing to functionalconnectivity in the cerebral cortex in "resting-state" data. AJNR Am. J. Neuro-radiol. 22, 1326e1333.

D’Esposito, M., Deouell, L.Y., Gazzaley, A., 2003. Alterations in the BOLD fMRI signalwith ageing and disease: a challenge for neuroimaging. Nat. Rev. Neurosci. 4,863e872.

D’Esposito, M., Zarahn, E., Aguirre, G.K., Rypma, B., 1999. The effect of normal agingon the coupling of neural activity to the bold hemodynamic response. Neuro-image 10, 6e14.

Duvernoy, H.M., Delon, S., Vannson, J.L., 1981. Cortical blood vessels of the humanbrain. Brain Res. Bull. 7, 519e579.

Folstein, M.F., Folstein, S.E., McHugh, P.R., 1975. “Mini-mental state”. A practicalmethod for grading the cognitive state of patients for the clinician. J. Psychiatr.Res. 12, 189e198.

Fox, M.D., Raichle, M.E., 2007. Spontaneous fluctuations in brain activity observedwith functional magnetic resonance imaging. Nat. Rev. Neurosci. 8, 700e711.

Fox, M.D., Snyder, A.Z., Vincent, J.L., Raichle, M.E., 2007. Intrinsic fluctuations withincortical systems account for intertrial variability in human behavior. Neuron 56,171e184.

Garrett, D.D., Kovacevic, N., McIntosh, A.R., Grady, C.L., 2010. Blood oxygen level-dependent signal variability is more than just noise. J. Neurosci. 30, 4914e4921.

Garrett, D.D., Kovacevic, N., McIntosh, A.R., Grady, C.L., 2011. The importance ofbeing variable. J. Neurosci. 31, 4496e4503.

Garrett, D.D., Kovacevic, N., McIntosh, A.R., Grady, C.L., 2013. The modulation ofBOLD variability between cognitive states varies by age and processing speed.Cereb. Cortex. 23, 684e693.

Girouard, H., Iadecola, C., 2006. Neurovascular coupling in the normal brain and inhypertension, stroke, and Alzheimer disease. J. Appl. Physiol. (1985) 100,328e335.

Glerean, E., Salmi, J., Lahnakoski, J.M., Jaaskelainen, I.P., Sams, M., 2012. Functionalmagnetic resonance imaging phase synchronization as a measure of dynamicfunctional connectivity. Brain Connect. 2, 91e101.

Goldberger, A.L., Amaral, L.A., Hausdorff, J.M., Ivanov, P., Peng, C.K., Stanley, H.E.,2002. Fractal dynamics in physiology: alterations with disease and aging. Proc.Natl. Acad. Sci. U. S. A. 99 (Suppl 1), 2466e2472.

Hager, B., Yang, A.C., Brady, R., Meda, S., Clementz, B., Pearlson, G.D., Sweeney, J.A.,Tamminga, C., Keshavan, M., 2017. Neural complexity as a potential translationalbiomarker for psychosis. J. Affect Disord. 216, 89e99.

Hausdorff, J.M., Peng, C., 1996. Multiscaled randomness: a possible source of 1/fnoise in biology. Phys. Rev. E Stat. Phys. Plasmas. Fluids Relat. Interdiscip. Topics54, 2154e2157.

Hesselmann, V., Zaro Weber, O., Wedekind, C., Krings, T., Schulte, O., Kugel, H.,Krug, B., Klug, N., Lackner, K.J., 2001. Age related signal decrease in functionalmagnetic resonance imaging during motor stimulation in humans. Neurosci.Lett. 308, 141e144.

Hu, S., Chao, H.H., Zhang, S., Ide, J.S., Li, C.S., 2014. Changes in cerebral morphometryand amplitude of low-frequency fluctuations of BOLD signals during healthyaging: correlation with inhibitory control. Brain Struct. Funct. 219, 983e994.

Huang, N.E., Shen, Z., Long, S.R., Wu, M.L.C., Shih, H.H., Zheng, Q.N., Yen, N.C.,Tung, C.C., Liu, H.H., 1998. The Empirical Mode Decomposition and the HILBERTSpectrum for Nonlinear and Non-Stationary Time Series Analysis. Proceedingsof the Royal Society of London SeriesA-Mathematical Physical and EngineeringSciences 454(1971), pp. 903e995.

Huang, N.E., Wu, Z., Long, S.R., Arnold, K.C., Chen, X., Blank, K., 2009. On instanta-neous frequency. Adv. Adaptive Data Anal. 1, 177e229.

Hughes, C.P., Berg, L., Danziger, W.L., Coben, L.A., Martin, R.L., 1982. A new clinicalscale for the staging of dementia. Br. J. Psychiatry 140, 566e572.

Huo, B.X., Smith, J.B., Drew, P.J., 2014. Neurovascular coupling and decoupling in thecortex during voluntary locomotion. J. Neurosci. 34, 10975e10981.

Katura, T., Tanaka, N., Obata, A., Sato, H., Maki, A., 2006. Quantitative evaluation ofinterrelations between spontaneous low-frequency oscillations in cerebral he-modynamics and systemic cardiovascular dynamics. Neuroimage 31,1592e1600.

Kayser, A.S., Sun, F.T., D’Esposito, M., 2009. A comparison of Granger causality andcoherency in fMRI-based analysis of the motor system. Hum. Brain Mapp. 30,3475e3494.

Leopold, D.A., Maier, A., 2012. Ongoing physiological processes in the cerebralcortex. Neuroimage 62, 2190e2200.

Linkenkaer-Hansen, K., Nikouline, V.V., Palva, J.M., Ilmoniemi, R.J., 2001. Long-rangetemporal correlations and scaling behavior in human brain oscillations.J. Neurosci. 21, 1370e1377.

Lo, M.T., Novak, V., Peng, C.K., Liu, Y., Hu, K., 2009. Nonlinear phase interactionbetween nonstationary signals: a comparison study of methods based onHilbert-Huang and Fourier transforms. Phys. Rev. E Stat. Nonlin. Soft MatterPhys. 79 (6 Pt 1), 061924.

Logothetis, N.K., Pauls, J., Augath, M., Trinath, T., Oeltermann, A., 2001. Neurophys-iological investigation of the basis of the fMRI signal. Nature 412, 150e157.

Logothetis, N.K., Wandell, B.A., 2004. Interpreting the BOLD signal. Annu. Rev.Physiol. 66, 735e769.

Malik, M.E.A., 1996. Task force of the European society of cardiology: heart ratevariability. Standards of measurement, physiological interpretation, and clinicaluse. Task force of the European society of cardiology and the North Americansociety of pacing and electrophysiology. Eur. Heart J. 17, 354e381.

Malonek, D., Grinvald, A., 1996. Interactions between electrical activity and corticalmicrocirculation revealed by imaging spectroscopy: implications for functionalbrain mapping. Science 272, 551e554.

Marchal, G., Rioux, P., Petit-Taboue, M.C., Sette, G., Travere, J.M., Le Poec, C.,Courtheoux, P., Derlon, J.M., Baron, J.C., 1992. Regional cerebral oxygen con-sumption, blood flow, and blood volume in healthy human aging. Arch. Neurol.49, 1013e1020.

Martin, A.J., Friston, K.J., Colebatch, J.G., Frackowiak, R.S., 1991. Decreases in regionalcerebral blood flowwith normal aging. J. Cereb. Blood FlowMetab. 11, 684e689.

Mijovic, B., De Vos, M., Gligorijevic, I., Taelman, J., Van Huffel, S., 2010. Sourceseparation from single-channel recordings by combining empirical-modedecomposition and independent component analysis. IEEE Trans. Biomed.Eng. 57, 2188e2196.

Murphy, K., Birn, R.M., Handwerker, D.A., Jones, T.B., Bandettini, P.A., 2009. Theimpact of global signal regression on resting state correlations: are anti-correlated networks introduced? Neuroimage 44, 893e905.

Niazy, R.K., Xie, J., Miller, K., Beckmann, C.F., Smith, S.M., 2011. Spectral character-istics of resting state networks. Prog. Brain Res. 193, 259e276.

Ogawa, S., Lee, T.M., Kay, A.R., Tank, D.W., 1990. Brain magnetic resonance imagingwith contrast dependent on blood oxygenation. Proc. Natl. Acad. Sci. U. S. A. 87,9868e9872.

Romero, J.R., Beiser, A., Seshadri, S., Benjamin, E.J., Polak, J.F., Vasan, R.S., Au, R.,DeCarli, C., Wolf, P.A., 2009. Carotid artery atherosclerosis, MRI indices of brainischemia, aging, and cognitive impairment: the Framingham study. Stroke 40,1590e1596.

A.C. Yang et al. / Neurobiology of Aging 70 (2018) 59e69 69

Safieddine, D., Kachenoura, A., Albera, L., Birot, G., Karfoul, A., Pasnicu, A.,Biraben, A., Wendling, F., Senhadji, L., Merlet, I., 2012. Removal of muscle artifactfrom EEG data: comparison between stochastic (ICA and CCA) and deterministic(EMD and wavelet-based) approaches. J. Adv. Signal Process. 2012, 127.

Salimi-Khorshidi, G., Douaud, G., Beckmann, C.F., Glasser, M.F., Griffanti, L.,Smith, S.M., 2014. Automatic denoising of functional MRI data: combining in-dependent component analysis and hierarchical fusion of classifiers. Neuro-image 90, 449e468.

Salvador, R., Martinez, A., Pomarol-Clotet, E., Gomar, J., Vila, F., Sarro, S.,Capdevila, A., Bullmore, E., 2008. A simple view of the brain through afrequency-specific functional connectivity measure. Neuroimage 39, 279e289.

Schlesinger, M.F., 1987. Fractal time and 1/f noise in complex systems. Ann. N. Y.Acad. Sci. 504, 214e228.

Sheehan, D.V., Lecrubier, Y., Sheehan, K.H., Amorim, P., Janavs, J., Weiller, E.,Hergueta, T., Baker, R., Dunbar, G.C., 1998. The Mini-International Neuropsy-chiatric Interview (M.I.N.I.): the development and validation of a structureddiagnostic psychiatric interview for DSM-IV and ICD-10. J. Clin. Psychiatry 59(Suppl 20), 22e33 quiz 34e57.

Shirer, W.R., Ryali, S., Rykhlevskaia, E., Menon, V., Greicius, M.D., 2012. Decodingsubject-driven cognitive states with whole-brain connectivity patterns. Cereb.Cortex. 22, 158e165.

Shmueli, K., van Gelderen, P., de Zwart, J.A., Horovitz, S.G., Fukunaga, M., Jansma, J.M.,Duyn, J.H., 2007. Low-frequency fluctuations in the cardiac rate as a source ofvariance in the resting-state fMRI BOLD signal. Neuroimage 38, 306e320.

Siegel, M., Donner, T.H., Engel, A.K., 2012. Spectral fingerprints of large-scaleneuronal interactions. Nat. Rev. Neurosci. 13, 121e134.

Smith, A.M., Lewis, B.K., Ruttimann, U.E., Ye, F.Q., Sinnwell, T.M., Yang, Y., Duyn, J.H.,Frank, J.A., 1999. Investigation of low frequency drift in fMRI signal. Neuroimage9, 526e533.

Song, X., Zhang, Y., Liu, Y., 2014. Frequency specificity of regional homogeneity in theresting-state human brain. PLoS One 9, e86818.

Stam, C.J., de Bruin, E.A., 2004. Scale-free dynamics of global functional connectivityin the human brain. Hum. Brain Mapp. 22, 97e109.

Wan, X., Riera, J., Iwata, K., Takahashi, M., Wakabayashi, T., Kawashima, R., 2006. Theneural basis of the hemodynamic response nonlinearity in human primary vi-sual cortex: implications for neurovascular coupling mechanism. Neuroimage32, 616e625.

Wang, Y.H., Yeh, C.H., Young, H.W., Hu, K., Lo, M.T., 2014. On the computationalcomplexity of the empirical mode decomposition algorithm. Physica A. 400,159e167.

Ward, N.L., Lamanna, J.C., 2004. The neurovascular unit and its growth factors:coordinated response in the vascular and nervous systems. Neurol. Res. 26,870e883.

Wechsler, D., 1997. Wechsler adult intelligence scale, third ed. The PsychologicalCorporation, San Antonio, TX.

Wise, R.G., Ide, K., Poulin, M.J., Tracey, I., 2004. Resting fluctuations in arterial carbondioxide induce significant low frequency variations in BOLD signal. Neuroimage21, 1652e1664.

Wu, Z., Huang, N.E., Long, S.R., Peng, C.K., 2007. On the trend, detrending, andvariability of nonlinear and nonstationary time series. Proc. Natl. Acad. Sci. U. S.A. 104, 14889e14894.

Wu, Z.H., Huang, N.E., 2004. A study of the characteristics of white noise using theempirical mode decomposition method. Proc. R. Soc. Lond. Ser. A MathematicalPhys. Eng. Sci. 460, 1597e1611.

Wu, Z.H., Huang, N.E., Chen, X.Y., 2009. The multi-dimensional ensemble empiricalmode decomposition method. Adv. Adaptive Data Anal 1, 339e372.

Yan, L., Zhuo, Y., Wang, B., Wang, D.J., 2011. Loss of coherence of low frequencyfluctuations of BOLD FMRI in visual cortex of healthy aged subjects. OpenNeuroimag. J. 5, 105e111.

Yang, A.C., Hong, C.J., Liou, Y.J., Huang, K.L., Huang, C.C., Liu, M.E., Lo, M.T.,Huang, N.E., Peng, C.K., Lin, C.P., Tsai, S.J., 2015. Decreased resting-state brainactivity complexity in schizophrenia characterized by both increased regularityand randomness. Hum. Brain Mapp. 36, 2174e2186.

Yang, A.C., Huang, C.C., Liu, M.E., Liou, Y.J., Hong, C.J., Lo, M.T., Huang, N.E., Peng, C.K.,Lin, C.P., Tsai, S.J., 2014. The APOE epsilon4 allele affects complexity and func-tional connectivity of resting brain activity in healthy adults. Hum. Brain Mapp.35, 3238e3248.

Yang, A.C., Huang, C.C., Yeh, H.L., Liu, M.E., Hong, C.J., Tu, P.C., Chen, J.F., Huang, N.E.,Peng, C.K., Lin, C.P., Tsai, S.J., 2013. Complexity of spontaneous BOLD activity indefault mode network is correlated with cognitive function in normal maleelderly: a multiscale entropy analysis. Neurobiol. Aging 34, 428e438.

Zang, Y.F., He, Y., Zhu, C.Z., Cao, Q.J., Sui, M.Q., Liang, M., Tian, L.X., Jiang, T.Z.,Wang, Y.F., 2007. Altered baseline brain activity in children with ADHD revealedby resting-state functional MRI. Brain Dev. 29, 83e91.

Zarahn, E., Aguirre, G.K., D’Esposito, M., 1997. Empirical analyses of BOLD fMRIstatistics. I. Spatially unsmoothed data collected under null-hypothesis condi-tions. Neuroimage 5, 179e197.

Zheng, T., Cai, M., Jiang, T., 2010. A novel approach to activation detection in fMRIbased on empirical mode decomposition. J. Integr. Neurosci. 9, 407e427.

Zou, Q.H., Zhu, C.Z., Yang, Y., Zuo, X.N., Long, X.Y., Cao, Q.J., Wang, Y.F., Zang, Y.F.,2008. An improved approach to detection of amplitude of low-frequency fluc-tuation (ALFF) for resting-state fMRI: fractional ALFF. J. Neurosci. Methods 172,137e141.

Zuo, X.N., Di Martino, A., Kelly, C., Shehzad, Z.E., Gee, D.G., Klein, D.F.,Castellanos, F.X., Biswal, B.B., Milham, M.P., 2010. The oscillating brain: complexand reliable. Neuroimage 49, 1432e1445.