Frequency-specific age-related decreased brain network diversity in cognitively healthy elderly: A whole-brain data-driven analysis

2.1 Participants

The participants in this study is part of a larger community sample from the Risk Index for Subclinical brain lesions in Hong Kong study, which is used to investigate the risk index for screening subclinical brain lesions (Wong et al., 2015). The participants were recruited from the local community centers, and screened by a battery of neuropsychological tests, including the Hong Kong version Montreal Cognitive Assessment (HK-MoCA) (Wong et al., 2009) for the global cognitive function evaluation, and the Barthel Index (BI) (Mahoney & Barthel, 1965) and Lawton's Instrumental Activity of Daily Living (IADL) (Lawton & Brody, 1969) scales for the functional independence test. The inclusion criteria were: (a) aged 65–80 years; (b) right-handed; (c) intact daily life activities, BI = 20 and IADL <2; (d) cognitively healthy defined by the age and education corrected HK-MoCA (Wong et al., 2015). Participants with any history of clinical stroke/transient ischemic attack/large cerebral infarcts, history of psychiatric and/or neurological disorders, or evidence of brain tumors were excluded. Supine blood pressure was also assessed at study enrollment. Approval was given by the Joint Chinese University of Hong Kong-New Territories East Cluster Clinical Research Ethics Committee (CUHK-NTEC CREC), and written informed consent was obtained from all the participants.

A total of 219 cognitively healthy elderly were included in this study. Twenty-eight subjects were excluded due to excessive head motion, and one subject was excluded due to bad image quality. Two subjects missing blood pressure information were also excluded. Thus, 188 subjects were retained in the further analysis. The demographic and neuropsychological characteristics of the retained elderly are shown in Table 1.

2.2 Data acquisition

All participants were scanned using a 3 T Philips MRI scanner (Achieva TX, Philips Medical System, Best, the Netherlands) with an eight-channel SENSE head coil. The high-resolution T1-wieghted anatomical image up to 305 sagittal slices were first obtained with the following parameters: repetition time (TR) = 7.5 ms, echo time (TE) = 3.5 ms, flip angle = 8°, field of view (FOV) = 250 × 250 mm², and voxel size = 1.04 × 1.04 × 0.6 mm³. Functional MRI images were acquired as a series of 210 continuous resting state volumes using a T2-weighted gradient echo-planar imaging sequence: TR = 2,050 ms, TE = 25 ms, flip angle = 90°, FOV = 205 × 205 mm², voxel size = 3.2 × 3.2 × 3.2 mm³, slices = 47. All participants were instructed to keep their eyes open at a cross on the screen.

2.3 Data preprocessing

Conventional data preprocessing procedures were performed using Statistical Parametric Mapping software (SPM12, http://www.fil.ion.ucl.ac.uk/spm/). The preprocessing procedures included the following steps: discarding the first 10 volumes, slice-timing, realignment for head motion correction, coregistering the anatomical scan to the mean realigned functional image. The coregistered T1 and T2-FLAIR images were combined to segment into various tissue classes including gray matter, white matter, and cerebrospinal fluid, then a study-specific anatomic template was created using the Diffeomorphic Anatomical Registration Exponentiated Lie algebra toolbox (Ashburner, 2007), and the corrected functional images were nonlinearly spatial normalized to the standard Montreal Neurological Institute (MNI) space. The normalized functional images were resampled to 3 × 3 × 3 mm³ and spatially smoothed using a Gaussian kernel of full-width half maximum = 8 mm.

The pre-processed functional images were further detrended, and high-pass filtered (0.008 Hz, 128 s cutoff period) to remove the possible effect of low-frequency drifts. The nuisance signals, which included the six head-motion parameters, averaged signals of the ventricle, white matter, and the whole brain, along with their first derivatives, were also regressed out from the time series of each voxel by using a general linear model (GML), and a first-order autoregressive AR (1) model was applied to account for the autocorrelation in fMRI time series. The whole brain signal regression was performed in this study to better reduce the physiological noise of aging as used in previous studies (Geerligs et al., 2015; Ng et al., 2016). Moreover, previous simultaneous fMRI-electrophysiology study has reported that the global signal would be a confounding factor rather than neural-related activity for the sliding window functional connectivity analysis (Thompson et al., 2013). The residual series were yielded for further dynamic functional connectivity analysis.

To further minimize spurious changes in dynamic functional connectivity estimation due to motion, the volumes with frame-wise displacement (FD) larger than 0.5 mm, as well as one preceding and two succeeding of those volumes were flagged (Leonardi et al., 2013; Power et al., 2014). During the dynamic functional connectivity estimation, a sliding-window approach was used, and the windows with more than 30% of flagged volumes would also be flagged. Subjects with more than 30% flagged windows were considered as extensive head motion and would be excluded from the further analysis. This led to exclusion of 28 subjects. One subject with bad image quality and two subjects without blood pressure information were also excluded, and leaving a total of 188 subjects retained in the analyses.

2.4 Dynamic functional brain network construction

In this study, a commonly used automated anatomical labeling atlas was used (Tzourio-Mazoyer et al., 2002), and the brain was divided into 90 ROIs. The averaged time series over voxels within each ROI were estimated and resulting 90 sets of time-series for each subject. Then, the maximum-overlap discrete wavelet decomposition (MODWT) was used to decompose the fMRI time series to different frequency intervals (Percival & Walden, 2000). The wavelet decomposition has been demonstrated to be an effective way to detect small changes in nonstationary time series and was widely used in investigating dynamic functional connectivity and denoising (Bassett et al., 2011; Bassett, Yang, Wymbs, & Grafton, 2015; Patel et al., 2014). The number of wavelet scale J was selected based on the largest integer which satisfying, where L is the length of time-series and l_w is the length of wavelet filter. In this study, L = 200, and the Daubechies least asymmetric wavelet filter, that is, “la8” ( l_w = 8), was used, thus the number of wavelet scales was set to 4. For the time-series of each ROI X _t, the wavelet coefficients of the four scales W _{X, s, t} were estimated using MODWT, where s indicates the wavelet scale, and t represents time point. The wavelet coefficients of the s scale would provide information of the frequency interval Hz. With the TR of 2.05 s ( f _s = 1/2.05 Hz), the wavelet coefficients of the four scales would provide information of different frequency intervals (wavelet Scale 1: 0.12–0.24 Hz, Scale 2: 0.06–0.12 Hz, Scale 3: 0.03–0.06 Hz, and Scale 4: 0.015–0.03 Hz).

Similar as the wavelet coherence/correlation analysis used in previous studies (Bassett et al., 2011; Bassett et al., 2015), the wavelet coefficients at each scale were used for the dynamic functional connectivity estimation. The dynamic functional connectivity of the whole brain network was estimated using the pairwise interregional distance correlation between the wavelet coefficients at each scale with a sliding window approach. In this study, the distance correlation was used to evaluate the pairwise correlation since it could evaluate both the linear and nonlinear dependencies of two signals (Szekely, Rizzo, & Bakirov, 2007), and has been demonstrated to be an effective measure to evaluate both the static and dynamic functional connectivity (Geerligs et al., 2016; Geerligs, Tsvetanov, & Henson, 2017; Rudas et al., 2015). For a pair of signals (X, Y) with L time points, the distance matrix of X is defined as Euclidean distance of all pairwise of time points of signal X,

(1)

and a double-centering was applied to the Euclidean distance matrix, yields

(2)

where is the average distance value of i-th row, is the average distance value of j-th column, and is the grand mean of the distance matrix for signal X. Similar double-centering matrix B _{i, j} is obtained for signal Y.

The distance covariance between X and Y is defined as

(3)

and distance variance is defined as

(4)

The squared distance correlation is defined as

(5)

In this study, the squared distance correlation was used to evaluate the dynamic functional connectivity since it was thought to provide a well definition for dissimilarities (Szekely & Rizzo, 2014). The distance correlation ranges between 0 and 1. It will equal 0 if and only if X and Y are independent, and equal 1 when Y = a + b X C for existing vector a, nonzero real number b and orthogonal matrix C.

For each participant and each window, a whole-brain network correlation matrix was generated in different frequency interval separately. The correlation matrixes were then transformed to a normal distribution using Fisher's z transformation. To make sure capture the low-frequency band components of the signal, at least one period of the low frequency band should be used for the time-varying correlation estimations (Leonardi & Van De Ville, 2015). In this study, two times of the low frequency period were served as window length with one time point shift step was used for each frequency band (i.e., Scale 1: 8 time points [16 s], Scale 2: 16 time points [33 s], Scale 3: 32 time points [66 s], Scale 4: 64 time points [131 s]). To eliminate the selection of window length, we also estimate the dynamic functional connectivity with 2.5 times of low frequency period. The results showed similar results as shown in Supporting Information. To minimize spurious changes in dynamic functional connectivity due to motion, the flagged windows (with more than 30% of flagged volumes in that window) would be excluded in further analysis.

2.5 Singular value decomposition

In this study a data-driven approach based on k-means clustering and two-step SVD is proposed to capture the time-varying dynamics of the whole-brain (as shown in Figure 1). The upper triangular part of each functional connectivity matrix would be unfolded and concatenated across all the windows for each subject in each scale. Thus, for each subject, a M × T _s dynamic functional connectivity matrix X is obtained in each scale s, where , N = 90 is the number of ROIs, and T _s is the window number in the scale s. The dynamic functional connectivity matrix was then normalized by using the mean value of each window.

For a M × T _s dynamic functional connectivity matrix , the k-means clustering approach was first applied to separate the dynamic functional connectivity into distinct state patterns [X¹, X², ⋯, X ^k]. The number of clusters k was determined by using the elbow criterion (Allen et al., 2014). Due to the dynamic connectivity patterns of resting-state were considered to be better described by multiple overlapped patterns (Leonardi et al., 2014), the SVD was then applied in each state separately. For each state-pattern X ^k with windows, it could be factorized as

(6)

where L is the rank of X ^k (typically, L = min(M,) = in this study), is a set of orthonormal vectors ( M × 1) corresponding to the spatial singular vectors of X ^k, is a set of orthonormal vectors () corresponding to the temporal singular vectors of X ^k, is diagonal with positive real entries, is the singular values of X ^k. Thus, is the spatial component that captures most of the energy of the state pattern k, and similarly captures the second largest part of energy of that sate pattern (Mahyari, Zoltowski, Bernat, & Aviyente, 2017).

In order to remove the components determined by noise, a permutation test was used to assess whether the effect of a given spatial singular vector is strong enough to be different from noise. The permutation was accomplished using randomize the sate-pattern of each connectivity matrix. SVD was recalculated for each new sate-pattern, and the number of times the new singular values larger than the raw singular values was estimated and expressed as a probability. The permutation was repeated 500 times, and only the spatial singular vectors corresponding to a probability <0.05 were retained. This permutation approach is similar to the method used to determine the number of retained latent variables in partial least squares (McIntosh, Chau, & Protzner, 2004). In this case, only the first R _k spatial components determined by the permutation approach were retained, and each state could be represented by low-rank spatial components separately.

To unify the spatial components across state patterns, a second level SVD was applied to the retained spatial components of each state. The reduced-rank spatial components of each state weighted with their respective singular values were concatenated to establish a M × N _R matrix W _R = [W¹, W², ⋯, W ^k], where and . We could transform these sate-specific spatial components to a common spatial space as

(7)

The spatial singular vectors represent the common spatial space across the state patterns. Similarly, the first subspace U₁ captures the largest amount of energy across all states, and the second subspace U₂ captures the second largest amount of energy across all states, and so forth.

Finally, the functional connectivity matrix X would be projected to the common spatial space as:

(8)

where W = X ^TU is the weights of N _R common spatial spaces. In this case, the functional connectivity matrix could be represented as a linear combination of N _R common orthonormal spatial components U _l with time-varying weights w _tl. The first common spatial component captures the most part of the power (around more than 70% in this study) across the collection of the dynamic functional connectivity matrix and would correspond to the stationary connectivity as estimated in static connectivity(Alter, Brown, & Botstein, 2000; Mahyari et al., 2017). Similar as the eigenconnectivities used in (Leonardi et al., 2013), these common spatial components would correspond to the basic building blocks of dynamic connectivity. Thus, the time-varying functional connectivity matrix could be represented as a linear combination of the stationary component and the dynamic component with time-varying weights. The positive weight of the dynamic component indicates a positive effect of that component relative to the stationary component, while a negative weight shows a negative effect (i.e., relative to the positive weight) of that component relative to the stationary component.

The relative power of each component across the collection of dynamic functional connectivity matrix could be expressed as

(9)

Since the sign of the time-varying weights for dynamic components represent different effects of that component to the stationary component, they are considered as different dynamic states, and the relative power of positive and negative time-varying weights would be estimated, respectively.

2.6 Relationship between stationary component and static connectivity

By using two-step SVD, the time-varying functional connectivity matrix is represented as a linear combination of the stationary component and the dynamic components with time-varying weights. In order to evaluate relationship between the stationary component extracted from the dynamic functional connectivity and static connectivity derived from the overall time series, the static distance correlations in each frequency interval were also estimated by using the time series extracted from the un-flagged volumes. Then, the relationship between stationary component and the static connectivity in each frequency interval would be evaluated by using Pearson correlation.

2.7 Whole-brain network diversity

The Shannon entropy, which is derived from information theory and has been used as a measure of diversity, was used to quantify the diversity of the whole brain network (Shannon, 1997). Specially, the diversity of the whole brain dynamic functional connectivity is defined as

(10)

The entropy values between 0 and log(N _R), the larger of entropy value, the more diversity of brain states would be. The entropy equals 0 indicates only one common spatial component is found across the dynamic functional connectivity ( P₁ = 1). The entropy equals log(N _R) corresponds to a flexibility connectivity pattern where the power of all the N _R spatial components were uniform distributed. In fact, similar measure has been proposed and used to capture the dynamic of gene expression (Alter et al., 2000).

2.8 Regional brain diversity

We also try to explore the diversity of each brain region under the framework of whole brain dynamic functional connectivity. For a given node, the sub-spatial-components (the edges connected with that node in each spatial component) of that node are first extracted from state-specific spatial components derived from the first-step whole brain network SVD. Then, the second-step SVD is applied to the sub-spatial-components to project the state-specific node-level connectivity to a common node-level spatial space. The power distribution of the common sub-spatial-components of each node will be estimated, and the regional brain diversity would be estimated as the entropy of the power distributions.

2.9 Age-related changes of brain diversity in elderly

For the diversity values regressed out the effect of head motion (mean FD) and window number, a GLM was introduced to explore the age-related changes of brain diversity in cognitive healthy elderly. The model for detecting the associations between age and brain network diversity in each scale was conducted as follows,

(11)

In this model, H _s is the diversity value in the frequency interval of s-scale, age is the explanatory variable, gender, education years (edu), total intracranial volume (ICV), and mean arterial blood pressure (MABP) are used as covariates. The threshold of statistically significant was set to p < .05 for the whole brain network diversity, and p < .05/90 for the regional brain diversity (Bonferroni corrected for multiple comparisons).

2.10 Relationships between brain diversity and general mental flexibility

Symbol Digit Modalities Test (SDMT) (Smith, 1982) and animal fluency test were used to assess the mental flexibility of each subject. SDMT is a variant of the digit-symbol coding task. Subjects are presented a series of abstract symbols and are asked to fill in as many the corresponding digits as possible in 90 s. The number of correctly filled digits is calculated. This test requires subjects to switch between rules for each abstract symbol and thus is related to mental flexibility and information processing speed (O'Sullivan, Morris, & Markus, 2005). The animal fluency test requires subjects to produce as many animal names as possible in 60 s, and the number of correctly generated animal names measures speed and activation as well as executive processes (Wong et al., 2013). The scores of each test were standardized to T scores with mean = 50 and SD = 10. The sum of these T scores for each subject were used as general mental flexibility score (Ng et al., 2016). For the brain diversity regressed out the effects of head motion, window number and blood pressure, Spearman correlation was used to evaluate the relationships between the brain diversity and general mental flexibility score.

3.1 Extracting stationary connectivity from dynamic functional connectivity

After the two-step SVD analysis, the common spatial components in each scale were obtained for each subject. As determined by the permutation approach, an average of 27.9 ± 3.4 (range: 13–35) components in Scale 1, 12.0 ± 1.5 (range: 8–16) components in Scale 2, 5.8 ± 0.7 (range: 4–7) components in Scale 3, and four components in Scale 4 were retained. The common spatial components of a typical subject were shown in Supporting Information.

The relationships between the first common component, that is, stationary component, derived from SVD analysis and the static functional connectivity across group are shown in Figure 2. The results showed significant correlations between the group-averaged stationary component and static functional connectivity in all frequency intervals. The results indicate the static connectivity patterns could be effectively extracted from the dynamic functional connectivity by using SVD analysis. The SVD analysis showed an excellent performance to factorize the dynamic functional connectivity as a combination of the stationary component and dynamic components.

3.2 Frequency-specific age-related decreased brain diversity

We estimated the age effect of the whole-brain network diversity in each frequency interval separately, and a significantly negative effect (r = −.19, p = .008) was only found in the Scale 2 frequency interval (0.06–0.12 Hz) (Figure 3).

In addition, we also evaluated the age effects of regional brain diversity in each scale. The significant age effects were also only found in the Scale 2 interval. The group averaged regional brain diversity of Scale 2 is illustrated in Figure 4. As shown in Figure 4, the high regional brain diversity values are mainly distributed in the frontal and temporal lobes, while the occipital and parietal regions exhibit a more stable pattern with low diversity values. The results of the age effects on regional brain diversity are shown in Figure 5. Only significantly negative correlations were found between age and regional brain diversity in the right inferior frontal gyrus (r = −.29, p < .0001), left inferior parietal gyrus (r = −.25, p = .0005), right amygdala (r = −.26, p = .0003), right hippocampus (r = −.26, p = .0003), and left parahippocampal cortex (r = −.3, p < .0001). These identified regions with age-related decreased diversity mainly distribute in the DMN and FPCN.

3.3 Whole-brain diversity reflects the general mental flexibility

We also explored whether the brain diversity could reflect the general mental flexibility measured by animal fluency and SDMT. The whole-brain diversity shows a significantly positive correlation with general mental flexibility score (r = .25, p = .0006) in Scale 2 (Figure 6). We also conducted a partial correlation between the brain diversity and general mental flexibility with age, gender, education, and ICV as covariates, the positive correlation is still preserved (r = .15, p = .047). No significant correlation between general mental flexibility and regional brain diversity was found in any scale interval.