Dynamic Characteristics of Local Functional Connectivity Revealed by Dynamic Regional Phase Synchrony

Studies on functional connectivity (FC) between remote brain regions or in local brain region have revealed ample statistical associations between the brain activities of corresponding brain units and deepened our understanding of brain. However, the dynamics of local FC were largely unexplored. In this study, we employed the dynamic regional phase synchrony (DRePS) method to investigate local dynamic FC based on multiple sessions resting state functional magnetic resonance imaging (rs-fMRI) data. We observed consistent spatial distribution of voxels with high or low temporal averaged DRePS in some specific brain regions across subjects. To quantify the dynamic change of local FC patterns, we calculated the average regional similarity of local FC patterns across all volume pairs under different volume interval and observed that the average regional similarity decreased quickly as volume interval increased, and would reach different steady ranges with only small fluctuations. Four metrics, i.e., the local minimal similarity, the turning interval, the mean of steady similarity, and the variance of steady similarity, were proposed to characterize the change of average regional similarity. We found that both the local minimal similarity and the mean of steady similarity had high test-retest reliability, and had negative correlation with the regional temporal variability of global FC in some functional subnetworks, which indicates the existence of local-to-global FC correlation. Finally, we demonstrated that the feature vectors constructed with the local minimal similarity may serve as brain “fingerprint” and gained good performance in individual identification. Together, our findings offer a new perspective for exploring the local spatial-temporal functional organization of brain.


I. INTRODUCTION
W ITH functional magnetic resonance imaging (fMRI), brain at resting state comes into attention since the seminal discover of highly correlated activities between the brain regions identified by hand movements task and other brain regions associated with motor function in resting state fMRI (rs-fMRI) data [1]. Traditional functional connectivity (FC) analyses of rs-fMRI data generally use the statistical association between the representative fMRI time series of corresponding brain regions as the FC strength [2]. Such FCs are assumed to be stationary, and thus generally called static FC analysis, in which the calculation of FC usually need rs-fMRI data of entire scan or experimental condition. However, brain activity is actually not simply static but with ample temporal information even during resting state [3], [4], [5], [6], [7]. So in recent years, the assessments of regional interactions based on rs-fMRI data draw increasing attention on the time-varying changes of FC, i.e., dynamic FC [8].
The dynamic FC analysis investigates the time-resolved fluctuations in FC, which may index changes in macroscopic neural activity [9]. Various dynamic FC analysis methods have been proposed. Preti et al. summarized these methods into two categories, i.e., sliding window strategy and conceptually innovative extensions [5]. Sliding window approaches segment the total fMRI data into a set of temporal windows and calculate the static FC in each window, and further gather descriptive measures of static FC across the temporal windows to characterize brain dynamics. In each window, the static FC is generally defined as the statistical association, such as Pearson correlation, between the representative fMRI time series of brain regions. Although the sliding window approaches are simple and useful, cautions are needed in selecting the window parameters, such as window length [10], [11], [12], [13]. Improper choice of window length might smooth out important temporal information of FC. To overcome this limitation, joint time-frequency analysis such as wavelet transform coherence (WTC) [3] has been proposed. Beyond sliding window approaches, event related single frame analysis and temporal modeling for a sequence of frames are considered as two directions of conceptually innovative extensions, which include change point analysis [14], point process analysis [15], co-activation patterns (CAPs) [16] and spatiotemporal pattern analysis [17], [18].
From the perspective of spatial scale, FC generally refers to the statistical association between remote brain regions. In contrast, local FC is defined at a local spatial scale within several millimeters [19]. Measures such as regional homogeneity (ReHo) [20], integrated local correlation (ILC) [21], and local FC density [22], were introduced to examine local neuronal function integration. In order to investigate dynamic FC at the local spatial scale, assessing aforementioned measures across sliding windows is a useful strategy. Sliding window ReHo (sw-ReHo) is a representative method of local dynamic FC analysis and considered to reflect the local integration of intrinsic brain activity [23]. Alterations of the variability of sw-ReHo have been reported in various neurological or psychiatric disorders, such as conduct disorder [24], Alzheimer's disease [25], schizophrenia [26], [27], attention-deficit/hyperactivity disorder (ADHD) [28]. However, the temporal resolution of sw-ReHo is also limited by the window. To overcome this limitation, dynamic regional phase synchrony (DRePS) was proposed based on phase synchronization [29]. Synchronization is a simple cooperative phenomenon between dynamic systems due to internal coupling or external forcing [30], [31], [32]. Phase synchronization can be quantified by the mean phase coherence of time series [31], [33], [34], [35], [36]. DRePS quantifies instantaneous mean phase coherence among central voxel and its spatially adjacent neighboring voxels at each time-point, characterizing local dynamic FC with the highest temporal resolution of rs-fMRI. Abnormalities of dynamic property of the voxel-wise DRePS time series have been observed in studies on brain diseases. For examples, neocortical focal epilepsy patients showed increased brain-wide average spectral density of DRePS signals compared with healthy control [37]; generalized anxiety disorder patients exhibited decreased standard deviation of DRePS signals in the bilateral caudate, left hippocampus, and some other brain regions [38]. In total, these studies indicate that DRePS could provide new insights into normal and abnormal local brain dynamic activities.
The dynamic property of DRePS time series has been characterized with average spectral density [37] and standard deviation [38]. These measures only quantified the fluctuations in DRePS time series but discarded its temporal ordering information. In the analysis of dynamic FC states, the occurrence or persistence of FC states, which is usually defined by clustering dynamic FC patterns (i.e., FC matrix obtained at each time point) into a small set of FC states, may provide temporal information [5]. To analyze the dynamic FC states, some studies defined a single matrix named FC dynamics (FCD) matrix, in which the elements denote the similarities between FC matrices (i.e., all FC across all brain regions) across all pairs of time windows [39], [40].
In this study, we extended this strategy to local dynamic FC proxy, i.e., DRePS, and formed local FC dynamics (lFCD) matrix for each brain region. lFCD could gather similarity between the local FC patterns (i.e., the vectors formed by the DRePS values of all voxels within region) at each pair of time points. Instead of defining local FC states through clustering methods, we directly characterized the diagonal texture of lFCD, inspired by the idea of recurrence quantification analy-sis [41], [42]. Each diagonal assembled the spatial correlation between local FC patterns with the same temporal interval. By analyzing the diagonal texture of lFCD, we could quantify how the local FC would stay at a specific states or shift to other state for a specific brain region. In our previous study, we have investigated the local FC states in rs-fMRI data based on sw-ReHo and observed recurrence of similar ReHo patterns across sliding windows [23]. By introducing lFCD based on DRePS, we would expect to obtain more information of local dynamic FC fluctuations at high temporal resolution.
The regional DRePS fluctuations depict the local dynamic FC. However, the relationship between local dynamic FC and global dynamic FC has been rarely examined yet. Comprehensively understanding brain activity and cognitive function requires an explanatory framework focus upon multi-scale neural activity [43]. Regional temporal variability was used to measures the interaction between FC profiles of a brain region with other remote brain regions across different time windows, reflecting the dynamic reconfiguration of a brain region across time [44], [45], [46]. Abnormal temporal variability of FC has been found in patients with Parkinson [47], ADHD and schizophrenia [48]. In this study, we also explored the relationship between regional DRePS fluctuations and the regional temporal variability, to provide new information on the relationship between local dynamic FC and global dynamic FC.
The aim of this study is to characterize the local dynamic FC of brain activities in healthy subjects using the DRePS method. We expect that DRePS is reliable both in characterizing static and dynamic properties of local FC. For the local static FC, we compared the spatial distribution of temporal averaged DRePS with ReHo across 100 subjects. For the local dynamic FC, for the first time we characterized the spatial correlation between DRePS patterns of two different time points at regional scale. For a specific brain region, we represented all spatial correlation coefficients between DRePS patterns of any time interval by an lFCD matrix, and further defined several dynamic metrics to depict the notable changes of the diagonal texture of lFCD matrix. Such quantification of local dynamic FC takes the high temporal and spatial resolution advantages of DRePS method. In addition, we examined the test-retest reliability of the extracted dynamic metrics and their relationship to the well-known metric named regional temporal variability. Furthermore, we explored their ability as brain "fingerprint" in individual identification. The findings of this study further support that the local dynamic FC, as a complementary analytical method of other types of FC, is a promising tool for exploring brain activities.

A. Dataset and Preprocessing
The "100 Unrelated Subjects" dataset of Human Connectome Project [49], [50], which is available through the data management platform Connectome DB (https://db. humanconnectome.org/), was used in this study. This dataset includes 100 unrelated subjects (54 females and 46 male adults, mean age=29.1±3.7 years). All the subjects are not family relatives, thus family-structure co-variables were excluded and the general population characteristics could be well represented. For the rs-fMRI data, each subject received four runs of scan on two different days (filename: rfMRI_RSET1, rfMRI _REST2), with two runs each day through opposing phase encoding in the left-to-right (LR) and right-to-left (RL) directions. The four resting state runs were all collected under eye-open condition, and each run lasted about 14 min (TR: 0.72s, 1200 volumes). For presentation convenience, these rs-fMRI runs were named as Session 1 (S1, rfMRI_RSET1_LR), Session 2 (S2, rfMRI_RSET1_RL), Session 3 (S3, rfMRI_ RSET2_LR), and Session 4 (S4, rfMRI_RSET2_RL) respectively in this study. S1 data were used for main analysis and other three Sessions data were used for the results reliability validation and individual identification analysis.
The preprocessed rs-fMRI data that were downloaded has been processed with the minimal preprocessing pipelines [51], and motion time series and artifact ICA components were regressed out using the FMRIB group's ICA-based Xnoiserifer (FIX) [52]. Further preprocessing was conducted with our home made Matlab codes, including scanner drift detrending and temporal band-pass filtering (0.01-0.1 HZ).
The spatial scope of local brain regions were defined according to the Schaefer atlas in MNI space [53]. Considering the trade-off between the within-region homogeneity and the signal-to-noise ratio (SNR), the Schaefer atlas recommends to divide the gray matter into 200 regions [54]. So in this study, the local dynamic FC for the 200 regions defined by the Schaefer-200 atlas was investigated and presented in the main text, while the local dynamic FC for the 400 regions defined by the Schaefer-400 atlas was examined to validate the results of the case of 200 regions. The so-defined brain regions were assigned to seven functional subnetworks, i.e., visual (Vis), somatomotor (SMN), dorsal attention (DAN), saliency/ventral attention (VAN), limbic (LIM), control (Cont), and default mode subnetworks (Default), which were defined by seven Yeo Networks [55].

B. Dynamic Regional Phase Synchrony
The DRePS approach was proposed to measure local mean instantaneous phase coherence of a center voxel with its adjacent voxels [29]. First, the instantaneous phase (IP) sequences of the center voxel and its adjacent voxels were calculated from their fMRI time series respectively based on Hilbert transform [32]. Let us take the No.144 region of the Schaefer-200 atlas as an example to illustrate the process to calculate IP sequence and DRePS sequence of a selected center voxel x (Fig. 1). For the fMRI time series x (t) of voxel x (blue point in Fig. 1a) and the fMRI time series y i (t) of its 26-connected neighboring voxels y i , i= 1, 2, . . . , 26,t= 1, 2, . . . , 1200, their IP sequences were denoted by ϕ x (t) and ϕ y i (t) respectively. For x (t), its analytic signal is defined as where A x (t) and ϕ are the instantaneous amplitude and IP of x (t), respectively, and is the Hilbert transform of x(t), where P.V. implies that the integral in Eq. (1) is taken in the sense of Cauchy principal value. In calculation, the analytic signal z (t) is obtained by manipulating the Fourier transform of x (t) in the frequency domain rather than directly through Eq. (1) [32], [34]. Similarly, the IP sequence of each neighboring voxel y i can be calculated from its fMRI time series respectively. Then the DRePS ψ x (t) of x (t) is defined as in (2), shown at the bottom of the page, to quantify the instantaneous mean phase coherence between center voxle x and all its M-connected neighbors y i at any given time t. Note that the concept of IP coherence has been used in phase synchronization analysis, which quantifies the phase synchronization level of two variables by the mean phase coherence of the IP sequences of two variables in a time window rather than at a given time [32], [34].

C. Local DRePS Dynamics
For a given time t, we defined the DRePS values of all voxels in a brain regions as the DRePS vector to represent the pattern of local FC in the brain region at that time. Then to characterize the dynamic changes and occurrence of local FC pattern, we defined a lFCD matrix S(t i , t j ), in which the element in ith row and jth column represents the Pearson correlation coefficient between the local FC patterns at the ith volume and the jth volume (Fig. 1g). From Fig. 1h, we could observe that the similarity of local FC patterns decreases quickly as it departs from the main diagonal, which implies that the similarity of local FC patterns decreases quickly as the time interval of the volume pair increases, and the local FC patterns stay at a certain state for only a short period. To quantify the dynamic changes of local FC patterns in a certain brain region, we calculated the average regional similarity of local FC patterns across all volume pairs under different volume intervals, that is, where L = 1200 denotes the total volume number, k denotes the volume interval (i.e., the difference of volume index between two volumes) (Fig. 1i). R (k) is actually the average of all elements in the kth diagonal lines which is off the main diagonal k units. Then the R (k) of all brain regions with respect to k could reveal the spatiotemporal dynamics from the perspective of the regional state occurrence of local FC patterns. To characterize of average regional similarity curves with respective to volume interval k, four dynamic metrics were defined (Fig. 1i). The first minimum value of the curve of the average regional similarity was defined as the local minimal similarity, and the volume interval that corresponds to the local minimal similarity was defined as the turning interval. After the turning interval, the curve of the average regional similarity stays at a steady stage with only small fluctuations. So the mean and variance of the curve of the average regional similarity from the turning interval to 1000 volume interval were defined as the mean of steady similarity and the variance of steady similarity. Note that the mean and variance of steady similarity in two other volume interval ranges, i.e., from the turning interval to 600 or to 1190 volume interval, have also been calculated, and the mean of steady similarities calculated from the three different volume interval ranges are highly correlated with each other, so do the variance of steady similarities calculated from the three different volume interval ranges. So in the following context, only the results calculated from the range from the turning interval to 1000 volume interval were presented.

D. Test-Retest Reliability
We further examined the test-retest reliability of the four metrics defined above, i.e., the local minimal similarity, the turning interval, the mean of steady similarity, and the variance of steady similarity, across four Sessions with intraclass correlation coefficient (ICC). There are some different forms of ICC, which are applicative for different situations. Following the guideline [56] and our former research [57], we selected ICC(A,1) [58] in this study, in which σ p , σ s and σ e represent the variance components associated with person, session, and residual error respectively.

E. Individual Identification
Previous studies on local FC mainly investigated the common patterns across subjects, but paid few attentions to their individual variability. In recent years, studies have revealed that brain activation patterns during cognitive tasks and intrinsic FC at resting state contain ample individual information [59], [60]. Specially, feature vectors constructed by static FC can serve as brain "fingerprint" in individual identification with rs-fMRI data recorded from a group of subjects in repeated experiments of multiple sessions [61]. To further explore the reliability and potential applications of the metrics defined from the curve of the average regional similarity (i.e., R (k)), we constructed feature vectors from the metrics extracted from each session rs-fMRI data of each subject, and performed individual identification for the so constructed feature vectors.
We took local minimal similarity as an example to describe how to perform individual identification. For the lth session of nth subject, we could calculate the local minimal similarity for each brain region, and further used the 200 local minimal similarities for the 200 brain regions to construct a feature vector denoted by W nl . Then for the so constructed 400 feature vectors for all the 400 sessions (4 sessions/subject times 100 subjects), we could get a discrimination matrix D r s , in which the element of r th row and sth column represent the Pearson correlation between the feature vectors of r th session and sth session. In the discrimination matrix D r s , the session index is r = l + 4(n−1), that is, the four sessions of one subject were arranged in one block and then the four sessions of the next subject. The discrimination matrix D r s is a 400 by 400 symmetrical matrix, with the values of the elements in the main diagonal are 1. On the main diagonal, if there are many 4-by-4 blocks (each block corresponding to one subject), in which elements would have higher values than other elements that are off the main diagonal, the feature vector would have good performance in individual identification. The higher values in the 4-by-4 blocks on the main diagonal imply that the within-subject similarities of feature vectors are greater than the between-subject similarities of feature vectors.
We took two measures, i.e., the identification success rate (ISR) and the perfect separability rate (PSR) [57], [61], [62], to quantify the performance of feature vectors in individual identification. Considering each row of discrimination matrix as an identification process, it is a successful identification if the maximal similarity appeared between two feature vectors from one same subject. The measure ISR quantifies the total rate of successful identification for all rows of discrimination matrix. For the identification process of each subject, perfect separability is obtained if the within-subject similarities of the feature vectors of the four sessions from the subject are all greater than all the similarities between the feature vectors of the subject and the feature vectors of all other subjects. The measure PSR quantifies the total rate of perfect separability for all subjects. Note that in individual identification for a cohort of subjects with multiple session data, PSR would have lower value than ISR since it requires all within-subject similarities of feature vectors greater than all between-subject similarities of feature vectors across all sessions.

F. Regional Temporal Variability
The DRePS analysis focuses on the dynamic changes of local FC. Zhang et al. and his colleagues proposed a measure named temporal variability of a brain region which characterizes the temporal variability of all the FCs that link the brain region with all other remote brain regions in functional brain network [44], [63]. To calculate this measure, the representative fMRI time series of each brain region were obtained by averaging the fMRI time series of all voxels in the brain region, and then the representative fMRI time series of all brain regions were segmented into windows with no overlapping. For a given window w, the Pearson correlation of the representative time series of two brain regions in the window was defined as the strength of the FC between the two brain regions, and all the FCs of brain region m to all other brain regions could construct a vector named the FC profile of brain region m and denoted by F w,m . Then the temporal variability of brain region m is defined as where N is the number of windows, corr (·, ·) denotes the Pearson correlation between the FC profiles of the brain region m in window w and window q. The measure V m could evaluate the temporal variability of the functional architecture specifically associated with brain region m at network level. The window length was set as 25 volumes, and thus there were 48 windows with no overlapping in total for the fMRI data of 1200 volumes. Note that previous study indicated that the regional temporal variability was little affected by the choice of window length [44], and the window with 25 volumes length was appropriate [47].

A. The Spatial Distribution of Temporal Averaged DRePS
For a typical subject, the averaged DRePS of each voxel in gray matter was calculated as temporal average of the voxel's DRePS sequence ψ x (t) (Fig. 2a), and the averaged DRePS of all voxels were mapped to brain surface (Fig. 2b). Any voxel with the temporal averaged DRePS value exceeded the predetermined thresholds (above or below the mean±SD of temporal averaged DRePS across all voxels) was considered to have extreme high or low temporal averaged DRePS (Fig. 2c). At the group level, the frequency (i.e., number) of subjects who had extreme high or low averaged DRePS was calculated for each voxel among all 100 subjects, and the surface maps of the frequency that the voxels with extreme high or low averaged DRePS in Session 1 were given in Figs. 2d and 2f respectively. To show the location of voxels that were with high frequency to have extreme high or low averaged DRePS at group level, the voxels with frequency value no less than 10 were displayed in Figs. 2e and 2g respectively. In Fig. 2e, voxels with high frequency of extreme high averaged DRePS appeared mainly in lateral occipital cortex, angular gyrus and occipital pole. In Fig. 2g, voxels with high frequency of extreme low averaged DRePS mainly distributed in frontal orbital cortex and temporal fusiform cortex. For comparison, the surface maps of the frequency that the voxels with extreme high or low ReHo in Session 1 were shown in Figs. 2h-2k respectively, which were similar with those of the averaged DRePS respectively. Furthermore, we examined the relationship between temporal averaged DRePS and ReHo across voxels, and observed significant positive linear correlation between temporal averaged DRePS and ReHo in individual subjects and at group level (supplemental Fig. S4). Figure 3a showed the average regional similarity of all 200 brain regions for a typical subject. For all brain regions, their average regional similarity decreased quickly as volume interval increased, and would reached different steady ranges with only small fluctuations when volume interval greater than the turning interval (about 12 to 17 volumes). The values of the average regional similarity of all 200 brain regions at volume interval 2, 5, 10, 15, 60 were mapped on brain surface (b)-(e) The brain surface mappings (from left to right) of the four metrics, i.e., the local minimal similarity, the mean of steady similarity, the variance of steady similarity, and the turning interval, extracted from the curves of the average regional similarity of the typical subject. (f)-(i) The boxplots (from left to right) of local minimal similarity, mean of steady similarity, variance of steady similarity, and turning interval for 200 brain regions in seven functional subnetworks respectively. Each point represents a brain region. The colors of box assigned according to subnetworks. (Fig. 3a), which indicated that the brain regions in postcentral gyrus, superior parietal lobule, lateral occipital cortex had greater average regional similarity than other brain regions.

B. The Average Regional Similarity of Local FC Patterns
To characterize the local dynamic FC in different brain regions, four local DRePS dynamic metrics, i.e., the local minimal similarity, the mean of steady similarity, the variance of steady similarity, and the turning interval, were calculated for each brain region. Figs. 3b-3e showed the surface maps of these four metrics of all 200 brain regions for a typical subject respectively. For this subject, the local minimal similarity and the mean of steady similarity had similar surface maps (Figs. 3b and 3c), and their values were highly correlated across brain regions (the Pearson correlation: r=0.987, p<0.001) (supplemental Fig. S1a). The high correlation between local minimal similarity and mean of steady similarity also consistently appeared in other subjects and sessions (supplemental Fig. S1c). The variance of steady similarity had a weak negative correlation with the local minimal similarity (the Pearson correlation: r=-0.13, p=0.06; supplemental Fig. S1b). However, this weak negative correlation in the typical subject did not consistently appear in other subjects and sessions (supplemental Fig. S1d). Furthermore, Figs. 3f-3i showed the boxplots of the four metrics for 200 brain regions in the seven functional subnetworks (i.e., DAN, Cont, SMN, Default, Vis, VAN, and LIM subnetwoks) respectively. For this typical subject, DAN has significantly greater local minimal similarity than Vis (two-sample t-test, t=3.948, p<0.001), SMN (t=2.128, p=0.037), VAN (t=3.192,p=0.002), and Default (t=4.552, p<0.001) subnetworks respectively. DAN also had significantly greater mean of steady similarity than Vis (t=4.178, p<0.001), SMN (t=2.149, p=0.036), VAN (t=3.164,p=0.003), Limbic (t=2.537, p=0.016), Cont (t=2.099, p=0.040), and Default (t=4.711, p<0.001) subnetworks respectively. Vis had significantly greater variance of steady similarity than DAN (t=2.4, p=0.019), VAN (t=3.159,p=0.003) and Limbic (t=6.146, p<0.001) respectively. For the turning interval, all regions fluctuated between 12 and 17 and the median of all subnetworks kept at interval 15. The average regional similarity of all regions almost turned around 15 volume interval (15.37 ± 1.24), about 10.8s (10.8 ± 0.89s, TR=0.72s). Note that we also performed similar analysis for the 400 brain regions defined by the Schaefer-400 atlas, and the results (supplemental Fig. S2) were consistent with those obtained from the 200 brain regions defined by the Schaefer-200 atlas.

C. The Reproducibility and Reliability of Local DRePS Dynamic Metrics
Similar analyses were performed on other three rs-fMRI Sessions, i.e., Session 2, Session 3, and Session 4 respectively. To evaluate whether the pattern of local minimal similarity is reproducible across subjects and sessions, we concatenated the local minimal similarity patterns of all the 400 sessions data (Fig. 4a) and calculated the mean of the local minimal similarity patterns across all the 400 sessions data as a group reference pattern (Fig. 4b). The reproducibility of local minimal pattern was quantified by the Pearson correlation coefficient between the pattern of each session and the group reference pattern. The results showed that the patterns of all sessions had significant positive correlation with the group reference pattern respectively (minimal r=0.37, p<0.001, Bonferroni corrected) (Fig. 4c).
The test-retest reliabilities of the four local dynamic metrics were assessed with ICC across all four Sessions for each brain region, and the results were summarized for each functional subnetwork respectively (Fig. 4d). The ICCs of local minimal similarity and mean of steady similarity were higher than those of variance of steady similarity and tuning interval across all functional subnetworks. DAN had the highest ICC of local minimal similarity (0.819±0.135) and mean of steady similarity (0.819±0.144). Furthermore, we also performed similar analyses for the 400 brain regions defined by the Schaefer-400 atlas, and observed similar results (supplemental Fig. S3) as those of the 200 brain regions defined by the Schaefer-200 atlas.

D. Correlation Between the Local Minimal Similarity and the Regional Temporal Variability
The temporal variability of each brain region (Eq. 5) was calculated for each rs-fMRI Session data. In Session 1, the brain surface mapping of group means local minimal similarity of 100 subjects (Fig. 5a) seems anti-correlated with Authorized licensed use limited to the terms of the applicable license agreement with IEEE. Restrictions apply. metrics (i.e., the local minimal similarity, the mean of steady similarity, the variance of steady similarity, and the turning interval) across the 100 subjects and four sessions for brain regions grouped by functional subnetworks. the brain surface mapping of group mean regional temporal variability of 100 subjects (Fig. 5b). The correlation between local minimal similarity and regional temporal variability across 100 subjects were analyzed for each brain region respectively, and significant correlation values were mapped to the corresponding regions (Fig. 5c). Result showed that the brain regions with significant negative correlation mainly distributed in Vis subnetwork (Fig. 5c). Furthermore, the correlation between the group mean local minimal similarity of 100 subjects (Fig. 5a) and the group mean regional temporal variability of 100 subjects (Fig. 5b) were analyzed for whole brain network and each functional subnetworks respectively. Significant correlations appeared in whole brain network (r=-0.47, p<0.001; Fig. 5d) and subnetworks including SMN (r=-0.47, p=0.004; Fig. 5e), DAN (r=-0.57, p=0.003; Fig. 5f), Cont (r=-0.73, p<0.001; Fig. 5g), and Default (r=-0.63, p<0.001; Fig. 5h). Considering the high test-retest reliability of the local minimal similarity and the mean of steady similarity (Fig. 4d) and the positive linear correlation between them (supplemental Figs. S1a and S1c), we mainly present the results of the local minimal similarity in the  5. The correlation between regional temporal variability and local minimal similarity in Session 1. (a) Brain surface mapping of group mean local minimal similarity. (b) Brain surface mapping of group mean regional temporal variability. (c) Brain surface mapping of significant correlation coefficients between local minimal similarity and regional temporal variability across 100 subjects in Session 1 for each brain region. (d)-(i) The scatter plots of group mean local minimal similarity with respect to group mean regional temporal variability in whole brain (d) and subnetworks including SMN (e), DAN (f), Cont (g), and Default (h). Each dot represents one brain region. main text, but summarized the results of the other three local dynamic metrics in supplemental Tables S1 and S2.

E. Individual Identification by the Local Minimal Similarity
To give a reference for the performance of feature vectors constructed by the local minimal similarity, we also performed individual identification with the feature vectors constructed by static FC [61]. From the discrimination matrixes constructed by the feature vectors formed with whole brain local minimal similarity (Fig. 6a) and static FC (Fig. 6b), we could observe that there were prominent small blocks along the diagonal. Generally, the within-subject correlations between feature vectors (i.e., the elements in the small blocks along the diagonal) from the same subject were greater than the between-subject correlations between feature vectors (i.e., the elements outside of the small blocks along the diagonal) from different subjects. Two measures, i.e., ISR and PSR, were used to quantify the performance of individual identification with the feature vectors constructed by the local minimal similarity and static FC from the whole brain and functional subnetworks respectively. Results showed that feature vectors constructed by the local minimal similarity generally gained comparable or even better performance than those constructed by static FC (Fig. 6c and Fig. 6d). We also performed individual identification with the feature vectors constructed by the other three local dynamic metrics, and the results showed that the feature vectors constructed by the mean of steady similarity could gain good performance in individual identification (supplemental Table. S2). Furthermore, the ISR and PSR indicated that the Individual identification by the local minimal similarity and static FC. (a) Discrimination matrix constructed with whole brain local minimal similarity feature vectors (left) and the partial enlargement of discrimination matrix for 10 subjects (right). (b) Discrimination matrix constructed with whole brain static FC feature vectors (left) and the partial enlargement of discrimination matrix for 10 subjects (right). (c) The ISR of individual identification using the local minimal similarity and static FC at whole brain network and the seven functional subnetworks respectively. (d) The PSR of individual identification using the local minimal similarity and static FC at whole brain network and the seven functional subnetworks respectively. feature vectors constructed by the local minimal similarity and by the mean of steady similarity had the same level performance in individual identification.

A. Local Static FC Can Be Revealed by Averaged DRePS
We observed that the voxels with extreme high averaged DRePS consistently appeared in lateral occipital cortex and occipital pole across 100 subjects (Figs. 2d-2e). Previous local static FC investigation has showed high ReHo in the default network regions, precuneus and medial visual cortex [19], [64], [65], [66], [67]. The high temporal averaged DRePS in visual cortex is consistent with that. This observation may be due to the high metabolic demands of visual cortex in static brain of healthy people [68]. Voxels with extreme low averaged DRePS frequently distributed in ventral brain areas, especially the frontal orbital cortex and temporal fusiform cortex (Figs. 2f and 2g). These two brain regions are functionally related. The orbitofrontal cortex is involved in a wide range of cognitive functions [69], [70], and plays an important role in emotion and reward raising attention in depression [71], [72]. Fusiform gyrus is considered as a key structure performing high-level vision function [73], [74], such as face perception [75]. The simultaneous activation of and bidirectional connectivity between orbitofrontal cortex and fusiform gyrus has been showed in human emotional scene perception [76]. Low averaged DRePS in these regions may be attributed to that they are not fluctuate synchronously within in the frequency band of DRePS analysis. Previous study reported such frequency dependence of ReHo [77], and it is related in fusiform gyrus [78]. These results together suggest that the extreme high or low averaged DRePS may provide inherent information of local static FC.
We also observed that the spatial distribution of voxels with consistent extreme high/low averaged DRePS was very similar to the defined extreme high/low ReHo (Fig. 2). And significant positive linear correlation between temporal averaged DRePS and ReHo appeared in individual subject and at group level (supplemental Fig. S4), which is consistent with the similar correlation reported in previous study [37]. These results together suggest that the temporal averaged DRePS and ReHo depict same aspect of local static FC, and thus temporal averaged DRePS is a trustworthy analysis method to local static FC investigation.

B. The Local Dynamic FC Revealed by DRePS
The regional dynamic fluctuations of DRePS were represented by the lFCD matric, which captured the switching between local FC patterns. Inspiring by recurrence plot analysis and considering the demand of reducing feature space, we focused on the most prominent diagonal structure of lFCD. The average regional similarity calculated from the diagonal elements of lFCD depicted the resilience of local FC pattern, that is, how long and to what extent the local FC pattern remained in the same configuration. The common trend of average regional similarities in all brain regions (Fig. 3a) and the similar turning interval suggested that the dynamics of local FC patterns in different brain regions followed similar rule. We speculate that the occurrence of turning interval (10.8 ± 0.89s) is associated with previously reported 6-8s lags of hemodynamic signal behind the neural signal [79]. The local minimal similarity and the mean of steady similarity both characterized the minimal remained similarity of local FC pattern after a duration (i.e., the turning interval). Actually, the local minimal similarity and the mean of steady similarity had high positive correlation (supplemental Figs. S1a and S1c), similar spatial distribution (Figs. 3b and 3c), similar correlation with regional temporal variability metric (supplemental Table. S1) and similar individual identification performance (supplemental Table. S2). Furthermore, these results obtained for 200 brain regions defined by the Schaefer-200 atlas were also coherent with the results obtained for the 400 brain regions defined by the Schaefer-400 atlas (Figs. S2 and S3). These findings suggested that the dynamics of local FC revealed by DRePS were not affected by granularity of atlas parcellation.
The high average regional similarity of superior parietal lobule (SPL) can be observed even the turning interval reach 60 volume (Fig. 3a). The surface map of the local minimal similarity also displayed high value in SPL no matter in typical subject or at group level (Fig. 3b, Fig. 4b). The SPL plays a pivotal role in many sensory and cognitive processes, including spatial perception [80], [81], somatosensory and visuomotor integration [82], [83] and visuospatial attention [84]. We speculate that the local minimal similarity reflects the level of intrinsic activity of brain region, and SPL may kept at a high level intrinsic activity in resting state brain. SPL is also an important region of DAN subnetwork. DAN is responsible for endogenous goal-driven and exogenous orienting of attention [85], and its activation commonly reported in taskrelated imaging studies. We also observed the distribution of local minimal similarity showed higher value in some regions of DAN, Cont and SMN subnetworks (Figs. 3b, 3f and 4b).
Previous investigation found that antagonistic activities of DAN and DMN were modulated by Cont [86] and a subsystem of Cont exhibited stronger connectivity with DAN than DMN [87]. DAN also has a close relationship with sensorimotor regions [88]. These results may imp ly that the dynamic properties of local FC depicted by the local minimal similarity are more related to the regulation of visuospatial perceptual attention functioned by DAN rather than the regulation of introspective processes functioned by DMN.
Furthermore, we observed moderate (0.5<ICC<0.75) to almost perfect (0.9<ICC<1.0) test-retest reliabilities of the local minimal similarity and the mean of steady similarity at most brain regions (Figs. 4d and S3c) and well reproducibility of the local minimal similarity pattern (Fig. 4c). Comparing to previous local dynamic FC method [89], [90], [91], DRePS analysis utilizes phase information of fMRI signal and provides the highest temporal resolution of local FC fluctuations. These advantages of DRePS enable it to be a promising tool in exploring local dynamic FC.

C. The Negative Correlation Between the Local Minimal
Similarity and the Regional Temporal Variability Significant negative correlations between group mean local minimal similarity and group mean regional temporal variability across brain regions were observed in the whole brain, SMN, DAN, Cont, and Default subnetworks (Figs. 5d-5h) respectively. The regional temporal variability of a brain region characterized the temporal variability of all the FCs that link the brain region with all other remote brain regions [44]. The spatial pattern of group mean regional temporal variability in Fig. 5b is similar with that reported in previous study [46]. Brain regions with low regional temporal variability usually have greater interactions with other brain regions. The human brain functions as a complex dynamic system, and the organization of brain networks are both modular and hierarchical [92]. The interaction between local FC and global FC is important for understanding principle of brain function organization. Previous study showed that local neural activity was related to long-range FC [93]. In computational neuroscience, studies demonstrated that local feedback inhibition control model can affect global dynamics of largescale brain network [94]. In brain disorder, the local FC alteration revealed by two dimensional ReHo were linked with remote FC alteration across cortical mantle in drug naïve schizophrenia patients [95]. In this study, we further demonstrated the existence of local-to-remote FC correlation from the dynamic perspective.

D. Individual Identification Based on Local Dynamic FC
Previous studies have showed that feature vectors constructed by global static FC may be conceptualized as brain "fingerprint" for subjects and gained good performance in individual identification [57], [61], [96]. However, individual identification with feature vectors constructed with local FC is still rare. In this study, we observed that the feature vectors constructed by the local minimal similarity (Fig. 6) and the mean of steady similarity (supplemental Table S2) gained comparable or even better performance in individual identification compared to those constructed by global static FC. These results suggest that the feature vector based on local dynamic FC has the potential of being brain "fingerprint". Previous clinical studies have showed that the brain "fingerprint" constructed by global static FC could be used as biomarker for brain diseases, such as schizophrenia development delay in adults [97]. Together, we would propose that brain "fingerprint" based on local dynamic FC and DRePS analysis is worthy of further investigation in clinical research for brain diseases.

V. CONCLUSION
In conclusion, we employed DRePS analysis to explore the local dynamic FC based on multiple sessions rs-fMRI data. First, we observed consistent spatial distribution of voxels with high or low temporal averaged DRePS across subjects, which is similar with the spatial distribution of voxels with high or low ReHo respectively. Second, we calculated the average regional similarity of local FC patterns across all volume pairs under different volume interval to quantify the dynamic change of local FC patterns, and observed that the average regional similarity decreased quickly as volume interval increased, and would reach different steady ranges with only small fluctuations when volume interval greater than the turning interval. Third, we defined four metrics to characterize the curve of average regional similarity, and demonstrated that the local minimal similarity and the mean of steady similarity had high test-retest reliability, and condensed the most valuable local dynamic FC information. Fourth, we demonstrated that the local minimal similarity had negative correlation with the regional temporal variability of global FC in some brain regions and functional subnetworks, which indicates the existence of local-to-global FC correlation. Finally, we showed that the feature vectors constructed by the local minimal similarity generally gained comparable or even better performance than those constructed by static FC in individual identification as brain "fingerprint". These results enrich our understanding about local dynamic FC and show that DRePS is trustworthy in characterizing static and dynamic properties of local FC.

ACKNOWLEDGMENT
All the data used in this study were provided by the Human Connectome Project, WU-Minn Consortium (Principal Investigators: David Van Essen and Kamil Ugurbil; 1U54MH091657) funded by the 16 NIH Institutes and Centers that supported the NIH Blueprint for Neuroscience Research; and by the McDonnell Center for Systems Neuroscience at Washington University.