Introduction

Functional connectivity (FC) derived from functional magnetic resonance imaging (fMRI) provides the most insightful correlation between behavior and the brain [1]. FC is traditionally considered a static and trait-level characteristic of individuals [2]. FC alterations have been linked to changes in cognitive performances [3], sex-related differences [4], and many brain diseases [5, 6]. However, this implicit assumption of temporal stationarity of FC has been challenging. A growing body of research believes that the dynamic nature of the brain enables changes in cognition and behavior that allow an individual to adapt to a complex environment [7, 8]. Dynamic FC (DFC) approaches, which consider the fluctuations in FC within a single scan [9, 10], track transient brain organization in a finer timescale. DFC can quantify the time-varying information in cognitive states and task demands [11], providing insights into how FC dynamics are related to cognition and psychiatric problems [12, 13]. These findings suggested the great potential of tapping into the relation between FC dynamics and individuals’ behavior, especially for children, as cognitive problems and mental health are critically important for children at this stage of brain development.

Developmental neuroscience that investigates the associations between neuroimaging and cognitive ability is a rapidly growing field in recent decades [14, 15]. Many functionally-integrated networks emerge in early childhood [14], responsible for the maintenance of cognitive functioning and mental behavior [16, 17]. Studies have found that resting-state FC is a reliable indicator of cognition in children [18, 19], and FC impairments might lead to the worsening of cognitive functioning in early childhood. Mental diseases often first manifest during childhood and adolescence [20, 21], and alterations of FC in neurocognitive networks have been shown to underlie dimensional indices of psychopathology, including internalizing and externalizing psychopathology [22, 23]. Abnormal FC has been identified in children with brain disorders [6], reflecting that dimensions of psychopathology in children may be related to the derangement of functional circuits. More recently, studies have demonstrated the utility of DFC for understanding neurodevelopment in children. Marusak et al. found that the occurrence of a DFC state is related to the content of self-generated thoughts in children [24]. By applying DFC analysis to 28 young children, a study showed that the decreased DFC variance between the posterior cingulate cortex (PCC) and the right precentral gyrus is associated with a decline in social motivation and social relating [25].

Despite such progress, studies focusing on DFC in children have ignored the potential interactive relationships between mental health, cognition, and DFC. Mental health and cognitive performance in children might have an interactive relationship. For example, attention plays a critical role in cognitive and social development, and its deficits affect children with various mental illnesses, such as attention-deficit/hyperactivity disorder (ADHD) [26]. In addition, previous work has used a relatively small number of children and failed to demonstrate the test–retest reliability of the DFC findings, indicating the need for a robust large-scale study such as the present one that included more than 10,000 participants. A comprehensive exploration of the DFC in children can help to draw a full picture of brain dynamics in early life, which might improve our understanding of the neural mechanisms underlying the association between functional brain organization and behavior formation in children.

In this study, we aimed to establish robust DFC patterns in children using large-scale neuroimaging data from Adolescent Brain Cognitive Development (ABCD). This multi-sessional data with a large number of participants provides an unprecedented opportunity to examine reliable DFC and its associations with cognitive and mental behavior in children [27]. We applied a hybrid independent component analysis (ICA) framework to probe the reoccurring DFC patterns during the resting-state. We hypothesized that children’s resting-state FC is highly fluctuated, with reoccurring patterns underlying different information transfer abilities. The connectivity patterns, namely as DFC states, are reproducible across scans and sessions. Cognitive or mental problems in children might be related to the time they spend in distinct states. We also hypothesized that the associations between DFC and cognitive performance might be related to psychiatric problems.

Materials and methods

Participants and preprocessing

This study was based on the ABCD release 3.0 downloaded from the National Institute of Mental Health Data Archive (NDA, https://nda.nih.gov/), containing over 11,800 children aged 9-11 years old. The 3.0 release is suitable for our current investigation, and we also validated the results using the latest release of the ABCD data (Fig. S9), which can ensure that our results are not impacted by using the 3.0 release. The resting-state data were collected by three 3 T scanner platforms, including Siemens Prisma, Philips, and GE 750 3 T scanners. The imaging protocols are similar across scanners [27], which are listed below: repetition time (TR)/echo time (TE) = 800/30 ms, voxel spacing size = 2.4 × 2.4 × 2.4 mm, number of slices = 60, flip angle (FA) = 52°, field of view (FOV) = 216 × 216 mm, %FOV phase = 100%, and multiband acceleration = 6. We preprocessed the raw data using a combination of the FMRIB Software Library (FSL) v6.0 and Statistical Parametric Mapping (SPM) 12. After the preprocessing, we performed a quality control (QC) to select scans for further analysis. We examined the correlations between the individual mask and the group mask and excluded those scans with correlations lower than the given thresholds. For the replication purpose, we also required the included subjects with at least two scans from a session passing the QC, and all these criteria yielded the final sample for the investigation. More detailed preprocessing and QC are provided in the supplementary material, sections “fMRI Preprocessing” and “Quality Control And Subject Selection”.

Cognitive and mental health assessments

To investigate the relationships between DFC and cognition, we used the uncorrected raw scores from the National Institutes of Health Cognition Battery Toolbox (NIHTBX) [28, 29]. We used the raw scores from the parent-rated Child Behavior Checklist (CBCL) to investigate the associations between DFC and children’s mental health. We also validated our results using other cognitive and mental health batteries, including the ABCD Pearson Scores (PS: abcd_ps01) as the measurements of cognition and the ABCD Parent Diagnostic Interview for DSM-5 Full (KSADS-5: abcd_ksad01) and ABCD Parent General Behavior Inventory-Mania (PGBI: abcd_pgbi01) as the measurements of mental health, as shown in Tables S13–S16.

NeuroMark framework to extract regions of interest

A methodological flowchart of the DFC analysis is provided in Fig. S1. We first implemented the NeuroMark framework via the group ICA of fMRI toolbox (GIFT) [30]. NeuroMark can address the issues in previous atlas- and decomposition-based methods [30, 31]. By incorporating a robust template with spatially constrained ICA, this framework extracts individual-level features comparable across scans, subjects, and datasets, which can avoid the discrepancy that might hinder the validation of results. On the other hand, NeuroMark retains the benefits of data-driven strategies that can optimize the network extraction according to the single-scan properties [30]. Our recent study has demonstrated the generalizability of NeuroMark by showing that the templates are highly reproducible from infants to aging populations [31]. More details of NeuroMark and its application to the children dataset are described in the supplementary material, section “NeuroMark Framework”.

Dynamic functional connectivity and clustering

Time-courses (TCs) of components underwent additional post-processing to remove the remaining noise. These procedures included: (1) detrending linear, quadratic, and cubic trends, (2) multiple regression of six realignment parameters and their derivatives, (3) removal of detected outliers, and (4) band-pass filtering with a cutoff frequency of 0.01–0.15 Hz. DFC was estimated by a sliding window approach with a window size of 40 TRs. A tapered window, created by convolving a rectangle (width = 40 TRs = 32 s) with a Gaussian (σ = 3 TRs), was used for segmenting the TCs. Existing evidence has shown that window size between 30 s to 1 min produces reliable DFC estimates [32, 33]. To show the robustness of our findings, we also used different window sizes and Gaussians in the DFC estimation. The overall results are consistent, as shown in Fig. S10 and S11. For each segment, we estimated covariance from the regularized precision matrix [34], which was obtained by the graphical LASSO method [35] with an L1 penalty to promote sparsity. The regularization parameter lambda was optimized for each scan by evaluating the log-likelihood of unseen data [10]. The FC estimate of each window was concatenated to form a final DFC array representing the changes of FC between regions as a function of time.

We performed the k-means clustering with Euclidean distance on the DFC to identify FC patterns. DFC between meaningful regions (53 components in the NeuroMark template) were used in the clustering, resulting in (53 × (53 − 1))/2 = 1378 features. Before clustering, subject DFC estimates were subsampled along the window dimension, which helped reduce redundancy between windows. We selected subject exemplars according to their FC variance across pairs (local maximum variance). The k-means clustering was performed on the exemplars and repeated 500 times with random initialization of centroids. We then used the resulting centroids to cluster all data. The optimal number of states was estimated using the elbow criterion [36]. As shown in Fig. S6, the number of clusters was k = 5, within a reasonable range consistent with previous DFC studies [37,38,39]. To show the reliability of our results, we replicated the findings by using a different number of clusters (3~6), as shown in Fig. S12. The fractional rate is calculated as the percentage of windows clustered to each state to measure the state occurrence. Additional reliability analyses [40, 41] based on the DFC states were performed to demonstrate the stability of the subject-specific states (Fig. S5). We also implemented two null models, the vector autoregressive model [32, 42] and the phase randomization model [43], to demonstrate that the fluctuations in DFC reject the null hypothesis of stationary (Figs. S3–S4).

Associations between DFC states and children’s behavior

A linear mixed-effect model (LMM) was implemented to investigate the associations between the state occurrence and the cognition/psychiatric problems. The LMM can model family nested within the site to take account of the correlated observations. In this model, the fractional rate of each state was modeled as the dependent variable, while each cognitive/mental health score was modeled as a fixed effect. Age, sex, race/ethnicity, height, and weight were the confounding effects, modeled as other fixed effects. We used the birth sex measured by the PhenX toolkit, which is the assignment as male or female based on the biological attribute. The race/ethnicity information is provided in the American Community Survey post-stratification weights and family relationships measures (acspsw03). More detailed information is provided in Table 1. The family structures and sites were modeled as random effects [44]. The correlation r-value, t-statistic, and Cohen’s d were calculated for each association analysis. The results were corrected by false discovery rate (FDR) correction [45]. Results were replicated by controlling the head motions and excluding the large head motions subjects, as shown in Tables S2–S5. Other potential confounding effects were also considered in the LMM analyses, including the scanner information, parents’ education level, and medications, as shown in Tables S6–SS12.

Table 1 Basic demographics of subjects.
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Test–retest reliability

We first split the discovery data in half, one half included data from randomly picked 10 sites, and the other half included data from the remaining 11 sites. We performed identical analyses for each half and matched the states to the state centroids obtained from all 21 sites. We then replicated the associations between DFC states and cognitive/mental scores. Additionally, we repeated the analysis by selecting the same number of subjects from each site. 294 subjects were randomly selected for each site, resulting in a total of 6174 subjects for the analysis. We performed the same analysis to explore the relationships between DFC states and cognition/mental scores. These results have been summarized in Figs. S7 and S8.

To further show the reliability of our findings, we ran the analysis using the second scan from the baseline session. We also replicated the results using two scans from the second-year session. The resulting states were matched to the centroids from discovery data. The associations between DFC states and cognition/mental scores were investigated using LMM.

Mental health mediates the relationship between DFC states and cognition

We performed a standard mediation analysis using the Mediation Toolbox (https://github.com/canlab/MediationToolbox). We used a standard three-variable path model. The fractional rate of a DFC state was the independent variable, and the cognitive score was the dependent variable. The mental problem score was the mediator. Confounding variables were regressed in the mediation model. The significance of the mediation was estimated by a bias-corrected bootstrap approach with 10000 random samplings.

Graph analysis demonstrates topological difference between DFC states

We calculated the graphic measures of DFC states and examined their differences between states. Node strength and efficiency were estimated based on the DFC within each state using the brain connectivity toolbox (https://sites.google.com/site/bctnet/). For each subject, we averaged the DFC estimates assigned to each state to obtain the mean state-based DFC. Then we used the positive FC, negative FC, and absolute FC of the state-based DFC to construct three graphs. The graphic measures were calculated based on the three graphs and were compared between states using a pair-wise t-test for each region.

Results

Brain parcellation

Our QC yielded 10988 subjects with two good scans for the baseline session and 3622 subjects with two good scans for the second-year session. Assuming moderate observational errors (~5% of the mean) in neuroimaging data and weak effects (r = 0.1), the sample size of n = 10988/3622 subjects is enough to achieve power equal to 0.80 and a Type I error equal to 0.05 in the correlation analysis. The first scan from the baseline session was the discovery data and the remaining three scans were the replication data. The NeuroMark framework parcellated the brain into 53 components as the regions of interest (ROIs), as shown in Table S1 and Fig. S2. The 53 ROIs were arranged into seven networks according to their presumed functional properties. Specifically, there are five ROIs in the subcortical network (SC), two ROIs in the auditory network (AUD), nine ROIs in the sensorimotor network (SM), nine ROIs in the visual network (VS), 17 ROIs in the cognitive-control network (CC), seven ROIs in the default-mode network (DM), and four ROIs in the cerebellar network (CB).

Highly reproducible DFC states

Figure 1 displays the clustering results. The first row (Fig. 1A) shows the centroid patterns of each state for the discovery data and the second to fourth rows (Fig. 1B) show the centroid patterns for the replication data. The brain states from the replication data were matched to the states from the discovery data by evaluating the correlation between their centroids. 4 out of 5 states are highly replicated among scans with averaged r values > 0.8. State 1 from the discovery data has matched states from the replication data (r = 0.9960, 0.9224, and 0.9830, respectively). It shows strongly positive FC within the sensory networks (AUD, SM, and VS) and the most negative connectivity of the SM network with VS and CB networks. It has the lowest occurrence across the five states (fractional rate [the percentage of windows that is assigned to a given state] is around 8% ~13% windows). State 2 is a sparsely connected state replicated across scans (r = 0.9757, 0.9710, and 0.9684) and has the highest occurrence during the resting-state (fractional rate is around 39% ~48% windows). State 4 shares similar FC patterns with state 1, but has weaker connectivity, especially within the SM network. State 5 is the only state with positive FC between SM and VS networks, positive FC between CC and CB networks, and negative FC between VS and CB networks.

Fig. 1: Reproducible brain states across resting-state scans and between longitudinal sessions.
figure 1

Five DFC states are identified by the k-means clustering for each scan, respectively. A the FC patterns of DFC states for scan 1 of the baseline session (discovery data). B the FC patterns of DFC states for replication data, including scan 2 of the baseline session, scan 1 of the second-year session, and scan 2 of the second-year session. Brain states are matched by evaluating the correlation coefficient between the centroid patterns. Four DFC states (columns 1, 2, 4, and 5) are highly replicable between the discovery and replication data (r > 0.8).

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DFC states are associated with children’s cognitive performance

The cognitive scores were negatively correlated with the fractional rates of the DFC states with strong connectivity (e.g., states 1 in Fig. 2A). 10 out of 10 cognitive scores were negatively correlated with the fractional rate of state 1, with correlation r values ranging from −0.0446 to −0.0919 (FDR corrected, q < 0.05). The cardsort score, fluid composite score, and total composite score were the scores most significantly negatively correlated with the fractional rate of state 1 (r = −0.0687, p = 7.97 × 10−13; r = −0.0906, p = 4.52 × 10−21; and r = −0.0919, p = 1.30 × 10−21). In contrast, the cognitive scores were positively correlated with the fractional rates of the states with weak and sparsely connected patterns (e.g., state 5). 10 out of 10 cognitive scores were positively correlated with the fractional rate of state 5, with correlation r values ranging from 0.0208 to 0.0567. Similarly, the cardsort score, fluid composite score, and total composite score were the scores most significantly positively correlated with the fractional rate of state 5 (r = 0.0567, p = 3.44 × 10−9; r = 0.0553, p = 3.13 × 10−8; and r = 0.0490, p = 3.72 × 10−7). The associations between DFC states 1 and 5 and cognitive scores were replicated using replication data (Fig. 2B).

Fig. 2: DFC states are correlated with children’s cognitive performance.
figure 2

A Significant correlations between DFC states and cognitive scores are identified using the discovery data (FDR corrected, q < 0.05). Strongly connected DFC states are negatively associated with cognitive scores and sparsely connected DFC states are positively associated with cognitive scores. Children with good cognitive performance tended to have fewer occurrences in the strongly connected states and more in the weak connected states. B Significant correlations between DFC states and cognitive scores are replicated using scan 2 from the baseline session, and two scans from the second-year session. Reproducible brain states show consistent associations with children’s cognitive performance.

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DFC states are associated with children’s mental health

Children’s mental scores were positively correlated with the strongly connected states (e.g., state 1 in Fig. 3A) and negatively correlated with the sparsely connected states (e.g., state 5 in Fig. 3A). Specifically, 18 out of 20 psychiatric scores were positively correlated with the fractional rate of state 1, with correlation r values ranging from 0.0310 to 0.0778 (FDR corrected, q < 0.05). These mental scores were negatively correlated with the fractional rate of state 5, with correlation r values ranging from −0.0232 to −0.0818. Among these scores, the attention score and the Diagnostic and statistical manual of mental disorders (DSM-5) ADHD score were the most significantly correlated with the fractional rate of DFC states (state 1: r = 0.0778, p = 3.36 × 10−16; r = 0.0742, p = 7.36 × 10−15; state 5: r = −0.0818, p = 9.58 × 10−18; r = −0.0736, p = 1.16 × 10−14). The psychiatric relevance of DFC states was validated using the replication scans (Fig. 3B).

Fig. 3: DFC states are correlated with children’s mental health.
figure 3

A Significant correlations between DFC states and psychiatric scores are identified using the discovery data (FDR corrected, q < 0.05). Strongly connected DFC states are positively associated with the psychiatric scores and sparsely connected DFC states are negatively associated with the psychiatric scores. Children with high mental problem scores tended to have more occurrences in the strongly connected states and fewer occurrences in the weak connected states. B Significant correlations between DFC states and psychiatric scores are replicated using scan 2 from the baseline session, and two scans from the second-year session. Reproducible DFC states show consistent associations with children’s mental health.

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In this work, we highlighted states 1 (Fig. 4A) and 5 (Fig. 4D) because of the following reasons. Firstly, these two states reveal distinct FC patterns that might indicate topological changes in functional networks during rest. Secondly, these two states show the most robust associations with children’s cognition and mental health. Thirdly, these two states are most reproducible across scans and analysis parameters (e.g., consistently identified from low-order clustering to high-order clustering). DFC state 1 was reproducible across multiple scans with inter-correlations higher than 0.89 (Fig. 4B). The fractional rate of this state was negatively correlated with children’s cognitive performance and positively correlated with children’s mental scores (Fig. 4C). DFC state 5 was also replicable across scans with inter-correlations higher than 0.94 (Fig. 4E). The fractional rate of this state was positively correlated with the cognitive scores and negatively correlated with the mental scores (Fig. 4F).

Fig. 4: Two DFC states show robust associations with children’s cognitive performance and mental health.
figure 4

A Brain state 1 showing the most within-network synchrony and the most anticorrelations between networks is reproducible across multiple scans. B Reproducible brain states show high inter-correlations >0.85. C The fractional rate of state 1 shows negative correlations with cognitive scores and positive correlations with mental problem scores. D Brain state 5 showing strong integration of sensory networks and antagonism between default-mode and sensorimotor networks but revealing weak segregation of the cerebellum is reproducible across multiple scans. E Reproducible brain states show high inter-correlations >0.9. F The fractional rate of state 5 shows positive correlations with cognitive scores and negative correlations with mental problem scores.

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Mental health mediates effects Of DFC states on cognition

The baseline data was used for the mediation analysis. We selected the attention score and DSM-5 ADHD score as the mediators for the following reasons. First, attention is a prerequisite for performing most cognitive tasks [46]. The attention problems and the developmental syndrome of ADHD can significantly impact academic achievement and life adaptation. Second, the attention and ADHD scores show the most significant correlations with DFC states. We believed that the larger effect size might be beneficial for exploring the mediation effects [44]. The fractional rate of states is the independent variable, and the fluid composite score is the dependent variable. The mediation analysis shows that the attention score mediated the effect of the occurrence of state 1 on the fluid composite score (Fig. 5A). The attention also mediated the effect of the occurrence of state 5 on the fluid composite score (Fig. 5B). Similar results were found for the ADHD score. The ADHD score mediated the effect of the occurrence of state 1 on the fluid composite score (Fig. 5C). In addition, the ADHD score mediated the effect of the occurrence of state 5 on the fluid composite score (Fig. 5D).

Fig. 5: The mediation effects among DFC states, children’s cognition and mental health.
figure 5

A The mediation implemented by attention problems from the state 1 on the fluid composite score is significant (beta = −0.7979, p = 2.49 × 10−4, 14.08% of the total effects). B The mediation implemented by attention problems from the state 5 on the fluid composite score is significant (beta = 0.8732, p = 1.70 × 10−4, 23.79% of the total effects). C The mediation implemented by ADHD scores from the state 1 on the fluid composite score is significant (beta = −0.6982, p = 2.79 × 10−4, 12.29% of the total effects). D The mediation implemented by ADHD scores from the state 5 on the fluid composite score is significant (beta = 0.7121, p = 1.68 × 10−4, 19.35% of the total effects). The indirect paths A, B and AB show that mental health mediates part of the effect of DFC states on the fluid composite score. Path A: effect of the fractional rate of DFC states on the mediator, mental health scores; Path B: effect of the mediator on cognitive performance; Path C′: direct effect of the fractional rate of DFC states on cognitive performance; Path AB: effect of DFC states on cognition explained by the mental health problems.

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We performed additional analyses using other CBCL scores as the mediators. 18 of 20 CBCL scores mediated the effect of the occurrence of state 1 on the fluid composite score (FDR corrected, q < 0.05), contributing 0.84–14.08% of the total effects. Consistently, 16 out of 20 CBCL scores mediated the effect of the occurrence of state 5 on the fluid composite score (FDR corrected, q < 0.05), contributing 2.03%–23.79% of the total effects. In addition to these analyses, we performed the mediation analysis using the crystal and the total composite scores as the dependent variable. The overall results show that the mental scores mediated the effect of the DFC states on the cognitive scores. Specifically, 14 of 20 CBCL scores mediated the effect of the occurrence of state 1 on the crystal score (FDR corrected, q < 0.05), contributing 1.15–16.86% of the total effects (Fig. S13). 14 CBCL scores also mediated the effect of the occurrence of state 5 on the crystal score (FDR corrected, q < 0.05), contributing 5.07–41.21% of the total effects. For the total composite score, 16 of 20 CBCL scores mediated the effect of the occurrence of state 1 on the total score (FDR corrected, q < 0.05), contributing 0.73–14.86% of the total effects (Fig. S14). 15 out of 20 CBCL scores mediated the effect of the occurrence of state 5 on the total score (FDR corrected, q < 0.05), contributing 1.88–28.18% of the total effects.

DFC states show distinct network topologies

Figure 6A displays the connectogram maps of states 1 and 5. The pair-wise t-test results of node strength are displayed in Fig. 6B. For the positive graph, most ROIs had larger node strength in state 1 (compared to state 5, FDR corrected, q < 0.05), except for the VS network. For the negative graph, ROIs from VS and CB networks had larger node strength in state 1, while superior parietal lobule (SPL) and PCC had larger node strength in state 5 (FDR corrected, q < 0.05). The results for the absolute graph show that most ROIs had larger node strength in state 1, while SPL and PCC had larger node strength in state 5.

Fig. 6: FC profile of DFC states and graph analysis on the centroid topologies.
figure 6

Graph is constructed using positive FC, negative FC or absolute FC respectively. A The functional connectogram and brain mapping of FC centroids of states 1 and 5. FC of states’ centroids are divided into positive and negative values and thresholded to retain only strong connectivity for displaying (|FC| > 0.2). B Pair-wise t-test results on node connectivity strength of ROIs between state 1 and state 5. C Pair-wise t-test results on local efficiency of ROIs between state 1 and state 5.

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State 1 had significantly higher global efficiency than state 5 (p < 1.0 × 10−100). As shown in Fig. 6C, DFC states show different local efficiency patterns across ROIs as well. For the positive graph, most of the ROIs had higher local efficiency in state 1, especially for the CB network. Interestingly, SPL and PCC had higher local efficiency in state 5. For the negative graph, ROIs from VS and CB networks had higher efficiency in state 5, while the other networks had higher efficiency in state 1. The results for the absolute graph are similar to the results for the positive graph, where only SPL and PCC had higher local efficiency in state 5.

Discussion

Robust DFC In children

Given the dynamic nature of the brain, there is a strong consensus that dynamics in FC likely have a neuronal origin, and as such, may engender a new understanding of brain organization [42, 47]. Our work is the first study that identified robust DFC states in a large (N > 10,000) children population, which are highly replicable across scans and longitudinal sessions. State 1 shows the most coupling and antagonism across networks. Of note, while DM shows weak FC with the SM and CC in the other states, this state has strong positive FC between DM and SM/CC networks. This finding challenges the notion of a stable DM network, as the DM regions might have significant covariation with the frontal and sensorimotor cortex [10]. In addition, this state also shows strong couplings between VS and CB networks. Such a temporal covariation between visual and cerebellum systems might potentially resolve the confusion and ongoing discussion regarding the organization of cerebrocerebellar circuits in human brains [48, 49]. We noted that SM shows different relationships with VS between states 1 and 5. These two states might capture the departure from the typical resting-state networks, in which brain regions form new functional interactions for a short time [50].

Although state 3 showed fewer similarities across scans, this is a common observation from hierarchical clustering, where many additional states that are not sufficiently frequent to be separated will be combined to signify an average state in the DFC analysis [10]. Because the resting-state is unconstrained and subjects are free to “mind-wander”, it is unlikely that FC representing specific brain states would be the same across scans. In the replication data, state 3 is similar, having the fewest occurrences among states. We speculate that this state might be associated with drowsiness. Firstly, this state might not be frequent enough to be separated in baseline scan 1. In that case, this state shows increased occurrence from scan 1 to scan 2 (baseline: <5.49–7.55%; second-year: 5.49–7.97%), which might indicate that subjects tend to become drowsy throughout runs. A similar pattern was observed in previous studies, where a state resembling this state showed an increasing occurrence over time, which might reflect the reduced vigilance along the scan [10, 51]. Secondly, according to the FC patterns from the replication data, this state shows the strongest FC within the sensory networks, similar to the drowsy “eyes-closed” state observed in [43]. This state also shows the most thalamocortical antagonism, a signature of loss of arousal in the resting condition [52]. Low-frequency signals within the DFC state with thalamocortical anticorrelation show concurrent strong fluctuations in the sensory networks, which might explain the enhanced antagonism between subcortical and cortical regions in this state [51].

DFC states and cognitive development in children

Compared to state 1, state 5 has higher PCC strength and efficiency. This is consistent with a previous finding that the more time participants allocated to a dynamic state with strong DM FC, the better their performance was on executive functioning [53]. Although the precise functions of DM are still far from understood, brain regions comprising DM are largely involved in autobiographical memory, self-referential processes, and social cognitive processes [54, 55]. DM connectivity plays an essential role in human cognition and memory processing [56, 57]. However, there are still controversial findings on the relationship between DM and cognition. Some reported significant associations between changes in DM and cognitive impairment [58, 59] while others found no relationship between them [60]. Our result might explain this discrepancy by pointing out that, (1) cognition might have opposite relationships with different DM regions, and (2) cognition might be associated with the occurrence of states with different topologies, rather than the constant FC. Previous work found that DM undergoes significant developmental changes in FC through adolescence but these changes are not uniform across all DM nodes [61]. Our result might provide further evidence to support this argument by showing that the FC of different DM regions can have different relationships with children’s cognition.

State 1 and state 5 also show differences in cerebellum-involved between-network FC. State 1 has strongly negative FC between the cerebellum and many other networks, including SC, SM, CC, and DM. As a pure motor system previously, the cerebellum has now come to be recognized for its participation in complex cognition [62, 63]. The cerebellum receives information from the sensorimotor system, which might help develop general mechanistic accounts of cerebellar prediction and error processing in cognition [64]. Previous work also shows the contribution of the cerebellum to different states of all investigated large-scale cortical networks [65]. We speculate that the entering of a DFC state (state 1) with negative FC might cause decreased information flow between the cerebellum and sensorimotor/cognitive systems, which further results in temporal constraints on the cognitive capabilities of the cerebellum [64]. In contrast, the entering of a DFC state (state 5) with positive cerebellar to cognitive network FC might promote better cognitive performance.

DFC states and mental health in children

In line with the existing literature, our results demonstrate that the DFC states can be related to mental behavior even in childhood. We found that children with higher attention problem scores and ADHD scores tend to have more occurrence in state 1, which has higher node efficiency in the frontal gyrus. ADHD is a common childhood disorder characterized by pervasive expressions of inattention and hyperactivity [66]. The more occurrences in state 1 and the fewer occurrences in state 5 may reflect the effort of children with attention problems, who cannot sufficiently compensate for the frontal FC deficit during cognitive tasks [66]. Findings in ADHD individuals provide evidence to support this speculation by showing that the frontal gyrus exhibited significantly increased node efficiency during the resting-state in ADHD children [67].

The psychiatric relevance of DFC states can also be interpreted within the concepts of functional integration and segregation [68]. Increased functional segregation has been observed in numerous mental diseases [69, 70], characterized by a deficit in sustained attention. The DFC state characterized by strongly positive within-network FC and negative between-network FC might reflect high segregation between networks. On the other hand, states comprised weak within-network FC and relatively larger between-network FC, especially between SM and VS networks, which can be interpreted as increased functional integration. We speculate that children spending more time in the functionally-segregated state and less time in the functionally-integrated state can be a potential cause that leads to a decreased capacity for sustained attention.

Furthermore, we showed that mental problems mediate the effect of DFC states on cognition. The attentional process is essential for the formation basis of cognitive development [71]. Various investigations have pointed out that individual differences in early attentional development predict later cognitive functioning [72]. The highly informative behavioral measure of infant attention can also provide insight into memory in early development [73]. Part of what was found in our study was that the occurrence of states was associated with both attention problems and cognition. This is of interest because the DFC patterns have previously been implicated in attention during task conditions [74]. Our finding indicates the covariance between DFC states and cognition is partially related to psychiatric problems, especially attention problems. A possible hypothesis is that if a child’s brain is not well developed as reflected in more occurrences in a functionally segregated state and fewer occurrences in a functionally integrated state, then attention problems will occur, which might impact cognitive performance.

Limitations and future directions

In this study, our focus is the replicable DFC patterns and their associations with cognition and mental health. In Fig. S15, we performed supplementary analyses focusing on the DFC differences between the baseline and the second-year sessions and found longitudinal changes in DFC states. Although investigating the longitudinal changes in the ABCD data can be an interesting topic, it might be outside of the scope of this paper. In future studies, when the ABCD provides more data from multiple time points, we can build a comprehensive longitudinal changes model to investigate developments in DFC and phenotypic measures.

There are differences between our study and some previous studies that found larger effects [75]. First, they used a much smaller sample size than those we used in the present work. In a recent publication [76], Marek and colleagues found that the false negative rates were very high (50~75%) even for samples as large as 2000, where half of the significant relationships were inflated by at least 50%. Indeed, the effect size of our findings is close to the results in many large-scale studies based on a similar sample size, showing brain-phenotype associations around or smaller than 0.1 [44, 77,78,79]. Compared to other neuroimaging features, the fractional rate of DFC is at least showing similar effect sizes for studying cognitive and psychiatric scores.

Another possibility of the small effect size might be because of the univariate analysis used in the present study. The multivariate analysis, which combines multiple features in a whole, might provide a large effect size in predicting brain functions and behaviors, but with results more difficult to interpret [80]. In this study, we focused on the fractional rate using the univariate analysis, which can help us to build a more interpretable bridge between DFC and children’s behaviors and take less risk of overfitting the data and drawing spurious conclusions [76]. In future work, we can combine the univariate and multivariate analyses to study the cognitive and psychiatric relevance of the DFC, which might provide a better explanatory model for understanding brain dynamics.