Age-Related Differences in Test-Retest Reliability in Resting-State Brain Functional Connectivity

Resting-state functional MRI (rs-fMRI) has emerged as a powerful tool for investigating brain functional connectivity (FC). Research in recent years has focused on assessing the reliability of FC across younger subjects within and between scan-sessions. Test-retest reliability in resting-state functional connectivity (RSFC) has not yet been examined in older adults. In this study, we investigated age-related differences in reliability and stability of RSFC across scans. In addition, we examined how global signal regression (GSR) affects RSFC reliability and stability. Three separate resting-state scans from 29 younger adults (18-35 yrs) and 26 older adults (55-85 yrs) were obtained from the International Consortium for Brain Mapping (ICBM) dataset made publically available as part of the 1000 Functional Connectomes project www.nitrc.org/projects/fcon_1000. 92 regions of interest (ROIs) with 5 cubic mm radius, derived from the default, cingulo-opercular, fronto-parietal and sensorimotor networks, were previously defined based on a recent study. Mean time series were extracted from each of the 92 ROIs from each scan and three matrices of z-transformed correlation coefficients were created for each subject, which were then used for evaluation of multi-scan reliability and stability. The young group showed higher reliability of RSFC than the old group with GSR (p-value = 0.028) and without GSR (p-value <0.001). Both groups showed a high degree of multi-scan stability of RSFC and no significant differences were found between groups. By comparing the test-retest reliability of RSFC with and without GSR across scans, we found significantly higher proportion of reliable connections in both groups without GSR, but decreased stability. Our results suggest that aging is associated with reduced reliability of RSFC which itself is highly stable within-subject across scans for both groups, and that GSR reduces the overall reliability but increases the stability in both age groups and could potentially alter group differences of RSFC.

section_content: Since the discovery that the human brain at rest consists of spatially distributed but functionally connected regions in which coherent patterns of low-frequency fluctuations in the blood oxygen level-dependent (BOLD) signal are temporally correlated [1], resting-state functional MRI (rs-fMRI) has been used extensively for investigating brain functional connectivity (FC). Resting-state functional connectivity (RSFC) provides insight into the large scale structure of interactions between brain regions that support the integrated deviations of disease states from normally observed human health. These deviations may be a fundamental causative factor in both neuropathologic and neurodevelopmental conditions such as dementia [2] [3], autism [4] [5] [6], schizophrenia [7] [8] [9], depression [10] [11] and other conditions. 

The reliability and stability of the RSFC method is critical to establish in normals as well as in normal development and normal aging so that deviations from these healthy states can be assigned to a particular disease state with certainty. Here, reliability is defined as the reproducibility of functional connections for a given subject across scan sessions, quantified with Intraclass Correlation coefficients (ICC). Reliability of RSFC has been evaluated in healthy young adults [12], and in healthy children as well as adolescents [13]. Stability is defined as the consistency of functional connections for a given subject across scans (withinsubject) or in a given scan session across subjects (between-subject), quantified with Kendall's coefficient of concordance (W). Spatial consistency of RSFC has been demonstrated on young normal adults [14] [15] [16]. Although these results are encouraging, much more work needs to be done in order to explore normal agerelated differences in RSFC. Previous studies on functional brain networks indicated that cost efficiency was reduced significantly in older normal people based on analyses of network efficiency [17], and that normal aging was associated with changes in modular organization of functional networks based on a graph theoretical analysis [18]. Furthermore, the modular organization of structural brain networks was similar between the young and middle age groups, but quite different from the old group based on an analysis of topological organization of structural brain networks in healthy individuals [19]. Another recent study found significant grouplevel variance in FC maps between young and old groups [20]. However, to our knowledge, test-retest reliability and stability in RSFC has not yet been explicitly quantified in older adults. The main purpose of this study is to investigate test-retest reliability and stability of the RSFC parameters in both young and old groups. 

In the present study, we divided all healthy subjects into two extreme groups by age. Study participants were selected from the ICBM dataset. The functional connectivity in the human brain consisting of 92 regions (Figure S1 ) was constructed by computing the correlation matrices across subjects and across each of the three scans. Similar to the method demonstrated in a recent study by Shehzad et al. [12] in which they assessed intersession (between-scan time-interval. 5 months), intrasession (between-scan time interval,1 hour), and multi-scan (across all 3 scans) reliability and stability on 26 young adults, we measured multi-scan reliability and stability on both young and old adults based on region-of-interest (ROI) analyses. Our first goal was to compare test-retest reliability and stability of RSFC across scans between the young and old group. 

Global signal, the spatial average of local signals from all cerebral voxels, has been suggested as a nuisance regressor for artifact reduction as it reflects coherent signal fluctuations across the brain [21]. While some studies indicate improved fMRI results after global signal regression [22], others suggest to avoid global scaling in fMRI analysis as it may decrease statistical power [23] and cause anti-correlations [24]. Our second goal in this study was to investigate how global signal regression (GSR) affects RSFC and the test-retest reliability and stability.
section_name: Introduction

section_name: Results

section_content: To investigate the between-group differences of RSFC reliability, we calculated multi-scan ICCs for each correlation across all 3 scans for each group (Table 1 ). A reasonable criterion for interpreting ICC is that an ICC value of $0. 75 is considered to be excellent/high reproducibility, ICC values in the range of 0. 4 to 0. 75 indicate fair to moderate reproducibility, and an ICC value of less than 0. 4 indicates low to poor reproducibility [25]. In the present study, a threshold of an ICC value = 0. 5 was used in order to confine our age-and GSR-related analyses to functional connections that were reasonably reliable. Within each group, multi-scan ICC values for specific correlations were variable, ranging from effectively zero to moderate/high. Some multi-scan ICC measures are negative, theoretically, due to relatively lower between-subject variability compared with within-subject variability. However, the reasons for negative ICC values are still unclear [26] and our analysis was based on all positive ICCs. 

Age-related differences in reliability of RSFC. Using Binomial proportion test, significant (i. e., correlation is significant at the group level for each of the 3 scans, p-value,0. 05 adjusted by FDR correction) and reliable (multi-scan ICC. 0. 5) correlations was compared between the two groups (Figure 1 ; Table 2 ). We found that significantly higher proportion of reliable correlations from the young group than from the old group with GSR (p-value = 0. 028; Figure S2 ) and without GSR (p-value,0. 001; Figure S3 ). The young group also showed significantly higher proportion of positive correlations as compared to the old group (p-value,0. 001) both with and without GSR (Table 3 ). 

Significant versus non-significant correlations. Within each group, we tested the differences between significant and nonsignificant correlations using Wilcoxon rank-sum test, and we found that significant correlations were significantly more reliable than non-significant correlations (p,0. 0001 for both groups with GSR (Figure S4 a-b ). The Wilcoxon rank-sum test was also used to test multi-scan ICCs without GSR and it showed that significant correlations were significantly more reliable than non-significant correlations only for the old group (p,0. 0001), and there was no significant difference between them in the young group (p = 0. 36). 

Positive versus negative correlations. Based on binomial proportion tests, we found significantly higher proportion of positive correlations than negative correlations in both groups with and without GSR (p,0. 001 for all comparisons) (Figure 2 ). Negative correlations were found in both groups with GSR but none of them survived after FDR correction without GSR (Figure S4 c-d ). The Wilcoxon rank-sum test suggested that multi-scan ICCs for positive correlations were significantly greater than for negative correlations (p,0. 0001 for all comparisons) in both groups with GSR.
section_name: Reliability of Functional Connectivity

section_content: and magnitude of functional connections. For each functional connection that was significant both with and without GSR, its magnitude (i. e., groupaveraged multi-scan correlation coefficients) was Fisher z-transformed and plotted against the corresponding ICC value shown in Figure 3 and 4 for each group. Linear fitting revealed a trend of higher correlations leading to higher ICC measures (Figure 3 (Figure 3b and Figure 4b ), indicating reduced magnitude of correlations due to GSR. 

Global signal regression factor in reliability of RSFC. Across all the connections between ROIs, using Binomial proportion test, we found significantly more reliable correlations without GSR than with GSR in both groups (p-value,0. 001, Figure 1, S2-S3; Table 2 ), and significantly more positive correlations without GSR than with GSR (p-value,0. 001, Figure 2 ; Table 3 ). Within default and fronto-parietal network, we found significantly more reliable correlations with GSR than without GSR in both groups. However, it also showed significantly less reliable correlations between-network with GSR than without GSR in both groups (p-value,0. 001, Figure 5 ; Table 4 ). A direct comparison of ICC values with vs. without GSR was shown in Figure 6. ICC values for those reliable correlations (ICCs. 0. 5) were reduced after GSR (i. e., regression lines were underneath the y = x line for ICCs. 0. 5. ). 

Network analysis of significant and reliable correlations. Among 92 ROIs, 17 in the fronto-parietal network, 19 are in the default-mode network, 23 in the cinguloopercular network and 33 in the sensorimotor network (Figure S1 ; Table S1 ). We found 1) highest number of significant and reliable correlations between regions in the sensorimotor network (Figure 5 ; Table 5 ), 2) least number of significant and reliable correlations between regions in the cingulo-opercular network in both groups with and without GSR (Figure 5 ; Table 5 ), 3) the old group had significantly less number of reliable correlations between-network than the young group with and without GSR (pvalue,0. 001, Figure 5 ; Table 6 ), 4) the old group had significantly more reliable correlations within fronto-parietal and sensorimotor networks without GSR than the young group (pvalue,0. 006, Figure 5 ; Table 6 ). Group-level consistency across scans. We also assessed the consistency of group-averaged functional connectivity across scans. Group-level correlation matrices were obtained by averaging all z-transformed correlation coefficients across all subjects for each scan and each group. The reverse transformation was run on each resulting mean correlation coefficient, resulting in the creation of three 1 by 4186 matrices of correlation coefficients for each group. Group-averaged correlations for all three scans were then plotted against each other and the results exhibited high consistency between any two of them for both groups (Figure 7 ).
section_name: Reliability

section_content: To investigate the stability of RSFC, we measured the consistency of correlations within and between subjects using Kendall's W. More specifically, within each subject the rank order of correlations was evaluated across scans and within each scan session the rank order of correlations was evaluated across subjects. Within-subject across scans, Kendall's W measures were variable, ranging from moderate to high (Table 7 ). Between subjects within each scan, the measures were variable and much lower than the measures within-subject Kendall's W (Table 8 ). 

Significant versus non-significant RSFC within subjects across scans. We compared the Kendall's W for significant and non-significant correlations within each subject across all three scans (Figure S6 ). The Wilcoxon rank-sum test demonstrated that significant correlations were significantly more stable than nonsignificant correlations for both groups with and without GSR (pvalue,0. 0001 for all comparisons). 

Positive versus negative RSFC within subjects across scans. The Wilcoxon rank-sum test demonstrated that positive correlations were significantly more stable than negative correlations for both groups with GSR (p-value,0. 0001 for all comparisons). No negative correlations were observed without GSR. 

Age-related differences in stability of RSFC. Using Wilcoxon rank-sum test, we found no significant difference in stability of significant correlations between the two groups (pvalue = 0. 572 with GSR and p-value = 0. 136 without GSR, Figure 8 ). Similarly, no significant differences in positive correlations were found between groups (p-value = 0. 794 with GSR and p-value = 0. 115 without GSR). 

Global signal regression factor in stability of RSFC. The Wilcoxon rank-sum test suggested that Kendall's W within-subject across-scan for significant correlations with GSR was significantly greater than without GSR for both groups (p-value,0. 0001; Figure 8 ). For positive correlations, the old group showed significantly higher stability with GSR than without GSR (pvalue = 0. 024) but no significant differences in the young group (pvalue = 0. 768). 

Stability between subjects within scan. We found the stability of RSFC for each scan was highly similar between subjects within scan (Figure 9 ) but much lower as compared to the stability of RSFC within subject across scans (Table 7 8 ). Higher stability of RSFC between subjects within scan was observed with GSR than without GSR (Figure 9, Figure S7 ; Table 8 ).
section_name: Stability of Functional Connectivity

section_content: Growing evidence suggests that human brains undergo dynamic functional reorganizations during the lifespan. Resting-state functional connectivity provides insight into this large scale structural interaction between brain regions. The goal of the current study was to investigate age-related differences in re- liability and stability of resting-state functional connectivity across scan sessions. We found that RSFC is more reliable for the young group and highly consistent for both groups, and that, consistent with previous studies [12, 24, 27, 28], regressing the global signal altered group differences of between-region functional connections. Age-related differences in reliability of RSFC. Using the Binomial proportion test, we found significantly higher proportion of reliable correlations in the young group than in the old group across 92 ROIs. To further examine this difference in each correlation, we compared the RSFC within-and between-network and found that pronounced decreases in the proportion of reliable correlations between-network in the old group with and without GSR (p-value,0. 001, Table 5 6 ). However, the old group also showed pronounced increases in the proportion of reliable correlations within-network especially without GSR (p-value,0. 006, Table 5 6 ). 

These findings suggest between-network connections may be more vulnerable to aging effects than within-network connections. This is consistent with our recent work using support vector machines which showed that between-network connections best differentiated older adults from younger adults based on their resting state functional connectivity [33]. Other studies have shown aging is associated with decreased functional connectivity in the DMN involving the superior and middle frontal gyrus, posterior cingulate cortices, and the superior parietal region [2, 20, [34] [35]. Interestingly, we observed a significant increase in reliable connections in the DMN in the old group with GSR, whereas no significant differences were found in terms of the proportion of reliable correlations between the young and the old group without GSR. This further confirmed that group differences could be altered, or perhaps misinterpreted, after GSR [28]. 

GSR-related differences in reliability of RSFC. Binomial proportion test showed that the proportion of significant and reliable connections is significantly decreased with GSR in both groups (Figure 1, S2-S3; Table 2 ). Similarly, we observed significantly more positive correlations without GSR than with GSR in both group (Figure 2, Table 3 ). We also found that negative correlations were only present with GSR, exhibiting relatively low reliability (mean multi-scan ICCs,0. 3) and stability (multi-scan Kendall's W within subjects,0. 6 and between subjects within scan #0. 06). These findings not only suggest higher reliability of RSFC without GSR than with GSR but also further confirms the observations in previous studies that GSR reduces the sensitivity for detecting true correlations [27] as well as negatively biases the correlations [24] and could fundamentally alter interregional correlations [28], especially when examining group differences.
section_name: Discussion

section_content: Age-related differences in stability of RSFC. We examined all connections between ROIs across the pre-defined 92 seed regions using Wilcoxon rank-sum test. A high degree of multi-scan stability of RSFC within subjects was found in both groups and no significant difference between groups was observed (p-value = 0. 572 with GSR and p-value = 0. 136 without GSR). This suggests that functional connectivity observed from each subject is highly stable or consistent from scan to scan and this stability/ consistency remains independent of aging effects. We also observed relatively lower Kendall's W scores across all correlations within each scan between subjects (Table 8 ), suggesting high individual variability exists in RSFC. 

GSR-related differences in stability of RSFC. Although GSR significantly reduced the number of reliable connections in both groups (Figure S2 -S3; Table 2 -3) especially those between-network connections (Table 4 ), it elevated the observed stability of RSFC both within-subject across scans (Figure 8 ; Table 7 ) and between subjects within scan (Figure 9 ; Table 8 ). A left shift of data points indicates a reduction in the magnitude of functional connections when GSR is applied. The Wilcoxon signed-rank test shows reduced ICC values when GSR is applied (p-value,0. 0001). Each data point represents a correlation that is significant both with and without GSR. Linear regression fits were overlaid on the data. doi:10. 1371/journal. pone. 0049847. g004 These findings suggest GSR could potentially alter the pattern of RSFC in each observation from each subject and each scan and enhance the agreement/stability within subject from scan to scan or within scan from subject to subject. Furthermore, our results showed highly stable RSFC within each individual across scan sessions (Age-related differences in stability of RSFC), suggesting highly consistent measurements of RSFC independent of aging factor. However, measures between subjects within each scan were relatively low, indicating the existence of individual variation. It may imply that variations of RSFC between individuals need further examination in order to discriminate from neuropathological changes.
section_name: Stability

section_content: Normal aging is associated with anatomical and functional changes as well as cognitive decline [34, 36]. However, the effect of aging on brain functional connectivity remains largely unknown. In the present study, we found fewer significant connections between ROIs from 92 pre-defined seed regions in the old group than in the young group. This is consistent with the observation made by Wu et al. [19], who investigated changes in small-world and modular organization of structural brain network with normal aging, demonstrating a notable decrease in the connector ratio and the intermodule connections in the old group. 

Conversely, we observed concomitant age-related increases in reliable functional connections within sensorimotor and frontoparietal networks. The old group showed significantly higher proportion of reliable connections than the young group without GSR within these two networks (Figure 5 ; Table 5 6 ). This could be potentially explained by a compensation mechanism that the decline of reliable functional connections between regions with aging, especially the long range connections between networks, is compensated by increased functional connections within networks. 

In a recent study, Tomasi et al. [37] evaluated age-related effects on functional brain networks based on a sample of 913 healthy subjects using functional connectivity density mapping. In their study, global signal intensity was normalized across time points. They found that aging was associated with increases in long-range functional connectivity density in somatosensory and subcortical networks and pronounced decreases in the DMN and dorsal attention network. In our study, we also found that aging was associated with significant increases in proportion of functional connections in the sensorimotor network, whereas no significant differences were found in DMN between the two age groups without GSR (Figure 5 ; Table 5 6 ). Interestingly, with GSR, there was increased proportion of reliable connections in DMN but no significant difference in the somatosensory network in the old group. This further draws attention to the issue of how global signal should be handled in data pre-processing in order to avoid the potential misinterpretation of group differences at functional network level. Research has shown an age-related reduction in occipital activity coupled with increased frontal activity, which is known as posterior-anterior shift in aging (PASA) [38], and age-related increases and correlations with parietal activity. In our study, occipital was not covered by the pre-defined seed regions, however, we observed increases in reliable connections in fronto-parietal network with aging without GSR (Figure 5 ; Table 5 6 ). The frontal-parietal network is engaged by a wide range of higher level cognitive tasks and is thought to be involved in active and adaptive task control [39]. This increase in reliable connections within frontal-parietal network might compensate the age-related decline in adaptive task control. The cingulo-opercular network is engaged in a variety of tasks and thought to contribute to the flexible control of human goaldirected behavior and affect downstream sensorimotor processing through the stable task-set maintenance [39]. We observed the least number of reliable connections within cingulo-opercular network in both groups without age-related differences (Table 5- 6), suggesting dynamic changes in functional connections within this network throughout adults' lifespan. 

Additionally, GSR plays a significant role in the observed RSFC. We conclude that GSR reduces the overall reliability of RSFC (Figure 1 2 ; Table 1, 2, 3) but increases the stability in both age groups (Figure 8 -9; Table 7 8 ), and that GSR affects the interpretation of group differences, especially, in each brain network presented in this study (Figure 5 ; Table 4 ). 

Several alternatives to global signal regression have been proposed such as applying principal components analysis (PCA) to resting-state fMRI time-series in order to regress out the component most correlated with signal of interest [40] [41]. Our future work will determine the test-retest reliability of connectivity measures using PCA.
section_name: Functional Brain Network with Normal Aging

section_content: The age-related differences between young and old groups, presented in this study, were based on resting-state functional connectivity among 92 pre-defined seed regions. The axial slice acquisition of the fMRI data prevented the inclusion of the occipital and cerebellar networks in our analysis, as several subjects included in the ICBM dataset did not have coverage in these regions. The use of ROIs across the whole brain would have been ideal in that we would be able to assess the reliability of each correlation drawn from an even larger sample, however, the statistical tests presented in our study still showed significant agerelated differences in RSFC. 

Group differences in head movement have been shown by Van Dijk et al. [42] to significantly affect correlations between seed regions. Given our recent work [33], using the same ICBM dataset, showing that significantly more motion in the old group, it should be noted that the motion in older subjects was fairly constant from time to time point with no large spikes of motion present. Interestingly, after removal of motion-sensitive correlations, more than 70% of total correlations were preserved, suggesting that motion may account for some of the differences in connectivity observed in this study but the overall results should be robust based on Binomial proportion test and Wilcoxon ranksum test. 

In the present study, we examined how GSR affects RSFC primarily due to the ongoing debate on the use of GSR when studying RSFC. We found GSR reduces the overall reliability in young and old groups, reduces the magnitude of correlations and could potentially alter group differences. As shown in Figure 3, 4 and S5, a higher correlation leads to a higher reliability score. Therefore, the reduced reliability score (i. e., ICC value) for a functional connection, when global signal is removed, might be confounded by the reduced correlations due to GSR. But overall, GSR, as a factor of reducing correlation values, reduces ICC measures and thus the reliability of functional connections. Other factors such as the magnitude of noise and/or motion which affect correlation values could also potentially have an impact on ICC measures.
section_name: Limitations

section_name: Materials and Methods

section_content: Resting-state fMRI data were obtained from 29 younger adults (18-35 years, mean age = 25. 8 years; 13 males/16 females) and 26 older adults (55-85 years, mean age = 64. 7 years; 11 males/15 females). All participants are right-handed.
section_name: Participants

section_content: Three resting-state scans from each subject were acquired using a 3. 0 Tesla scanner. Each scan consisted of 128 gradient-echo EPI functional volumes (TR = 2. 0 seconds; 64664 matrix, 23 axial slices). For 19 out of the 29 younger adults, two scans were acquired with voxel size 46465. 5 mm 3 and the third one was 46464 mm 3, while the other 10 subjects had all three scans with voxel size 46464 mm 3. 20 out of 26 older adults, two scans were acquired with voxel size 46465. 5 mm 3 and the third one was 46464 mm 3, while the other 6 subjects had all three scans with voxel size 46464 mm 3. All individuals were asked to keep their eyes closed during the scan. As stated earlier, resting-state fMRI data presented in our study were obtained from the International Consortium for Brain Mapping (ICBM) dataset which were made publically available in the 1000 Functional Connectomes project www. nitrc. org/projects/fcon_1000. Each contributor's respective ethics committee approved submission of deidentified data. The institutional review boards of NYU Langone Medical Center and New Jersey Medical School approved the receipt and dissemination of the data.
section_name: fMRI Data Acquisition

section_content: Data were preprocessed using scripts slightly adapted from fcon_1000 using a combination of AFNI (version AFNI_2009_12_31_1431, http://afni. nimh. nih. gov/afni) and FSL (version 4. 1. 4, www. fmrib. ox. ac. uk/fsl). Data were first deobliqued and reoriented to RPI orientation for use in FSL. AFNI was then used to perform the initial preprocessing steps of 1) slice time correction for interleaved acquisition using Fourierspace time series phase-shifting, 2) motion correction to the average of the time series by aligning each volume to the mean image using Fourier interpolation, 3) skull stripping, and 4) selecting the eighth image for subsequent use in co-registration of BOLD images to the high resolution anatomic image. Further data preprocessing was carried out using FSL and comprised 5) spatial smoothing using a Gaussian kernel with FWHM = 6 mm, and 6) normalizing all volumes by a single scaling factor. Bandpass filtering (0. 005-0. 1 Hz) and detrending to remove linear and quadratic trends for each subject were then performed using AFNI. Masks of preprocessed data for each subject were generated using FSL. Functional data were then transformed into MNI152 (Montreal Neurological Institute 152-brain template; voxel size = 36363 mm 3 ) space using a three-step process: First, a 6 degree of freedom linear affine transformation was carried out using FLIRT [43] [44] to align the functional data into structural space. The anatomical image was then aligned to the standard MNI152 space using a 12 degree of freedom linear affine transformation using FLIRT. The resulting transformation was then applied to each subject's functional dataset.
section_name: fMRI Data Preprocessing

section_content: Signal associated with nuisance covariates consisting of global signal, white matter (WM), CSF and 6 motion parameters obtained during the motion correction step were removed from the resulting preprocessed fMRI time-course data. WM and CSF masks were created by segmentation of each subject's structural images and then applied to functional images to extract the WM and CSF signals. The global signal was calculated by averaging across all voxels in the brain. Following the regression of nuisance covariates, the residual signals were demeaned and re-sampled to the standard MNI-152 space (voxel size = 36363 mm 3 ). 

One goal of the current study was to examine how global signal regression (GSR) affected the reliability and stability of RSFC; therefore we pre-processed the data in two parallel analyses, with and without global signal regression (GSR).
section_name: Nuisance Signal Regression

section_content: Regions of interest. 92 spherical ROIs with radius 5 mm (Figure S1 ; Table S1 ), derived from several meta-analyses of task-related fMRI studies previously defined by Dosenbach et al. [45], were selected in our study. Dosenbach et al. extracted time series from 160 seed regions covering several networks. Due to axial slice selection, not all subjects from ICBM datasets had EPI coverage of the occipital lobe and cerebellum, which resulted in 92 seed regions mainly consisting of default-mode, cingulo-opercular, fronto-parietal and sensorimotor networks. Some subjects had no signal in these areas and therefore were not included in our study.
section_name: Resting-state Functional Connectivity

section_content: Functional connectivity. Mean time series from each ROI were extracted, imported into MATLAB (R2010a, Mathworks), and correlated with that from every other ROI. Pearson correlation coefficients were calculated for each pair of regions for each subject and each scan. The resulting correlation coefficients were then z-transformed for calculations of multi-scan intraclass correlation coefficient (ICCs), or transformed into a distance measure in order to calculate Kendall's coefficient concordance (Kendall's W). 

To determine the significance of each correlation, a one-sample t-test was run on the z-transformed correlation coefficients for both young and old group. Group-level significance of each correlation was defined by a two-sided p-value of 0. 05, which was then adjusted for multiple comparisons using false discovery rate (FDR) correction (total 4186 correlations). More specifically, a significant correlation needs to be significant at the group level for each of the 3 scans with p-value,0. 05 adjusted by FDR correction. Within each group, positive correlations were determined by a right-tailed one-sample t-test with a p-value of 0. 05 adjusted by FDR correction. Similarly, negative correlations were determined by a left-tailed one-sample t-test with a p-value of 0. 05 adjusted by FDR correction. 

Reliability of functional connectivity. We attempted to examine if significant connections observed in a first scan session would be reproducible within-subject in the following sessions and any changes between-subject would be due to subject difference. Intraclass correlation is defined as a ratio of the variance of interest over the sum of the variance of interest plus error [46], and has been frequently used to measure test-retest reliability in fMRI data [12] [13], [47] [48]. We calculated the third ICC values defined by Shrout and Fleiss [46] as follows:

where BMS is between-subjects mean square, EMS is residual/ error mean square, and k is the number of scans per subject, which is 3 in our case. Theoretically, high ICC values suggest that compared to between-subject variability (i. e., BMS), within subject variability (i. e., EMS) across scans is relatively smaller, indicating high consistency or reliability of within-subject RSFC. Given multi-scan ICC for each correlation, we examined the effect of the following factors on the multi-scan reliability of RSFC. 1) Statistically significance: significant correlations were compared with non-significant correlations. 2) Patterns: significantly positive correlations were compared with that of significantly negative correlations. 3) Age: significant and reliable correlations in the young group were compared with those in the old group; 4) GSR: significant correlations obtained with GSR were compared with those without GSR within each group. 

Stability of functional connectivity. We used Kendall's coefficient concordance (Kendall's W) to estimate if overall connections were consistent across subjects and across scans. Kendall's W is a measure of agreement among raters based on ranks rather than values, and has been used to assess the concordance of time courses within an individual using fMRI data [49] [50]. We calculated Kendall's W as follows:

where k is the number ofscans or number of subjects, n is the number of correlations, R i is the sum rank of the ith correlation across scans or subjects, Ris the mean of R i 's. Kendall's W reflects the agreement in the rank order of correlations across subjects or across scans. In other words, it indicates how stable RSFC is within-subject across scans or within-scan across subjects. As with ICCs, we examined the effect of the following factors on the multiscan stability of RSFC: statistically significance, patterns, age, and GSR. 

Statistical tests. With Binomial proportion test, one can test the hypothesis of the equality of two binomial proportions. In our study, it was used to test the proportion of significant correlations versus non-significant, positive versus negative correlations between the young and the old group. Significant and nonsignificant correlations are treated as binomial measures (i. e., 19s and 09s respectively) and we tested the proportion of 19s in one group versus that in the other group (i. e., young vs. old). 

Within each group, we tested the differences between significant and non-significant as well as between positive and negative correlations using Wilcoxon rank-sum test, which is a nonparametric test allowing to test measures of ICC or Kendall's W that are not normally distributed.
section_name: Statistical Methodology

section_name: Acknowledgments

section_content: We would like to thank Yunzhi Lin and Alejandro Munoz-Del-Rio for statistical guidance. We would also like to thank 1000 Functional Connectome Project for providing open access to resting state fMRI datasets and data processing scripts.
section_name: Acknowledgments

section_content: Supported by grants RC1MH090912 NIH-NIMH ARRA Challenge Grant to MEM, UW ICTR NIH/UL1RR025011 Pilot Grant from the Clinical and Translational Science Award (CTSA) program of the National Center for Research Resources (NCRR) and KL2 Scholar Award to VP, NIH 5R01AG032088 to BBB, and National Research Service Award T32EB011434 to SV. The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript.

section_name: Supporting Information