Aberrant Functional Connectivity in Core–Periphery Structure Based on WSBM in ADHD

Abstract

Objective:

Brain network studies have revealed that the community structure of ADHD is altered. However, these studies have only focused on modular community structure, ignoring the core–periphery community structure.

Method:

This paper employed the weighted stochastic block model to divide the functional connectivity (FC) into 10 communities. And we adopted core score to define the core–periphery structure of FC. Finally, connectivity strength (CS) and disruption index (DI) were used to evaluate the changes of core–periphery structure in ADHD.

Results:

The core community of visual network showed reduced CS and a positive value of DI, while the CS of periphery community was enhanced. In addition, the interaction between core communities (involving the sensorimotor and visual network) and periphery community of attention network showed increased CS and a negative valve of DI.

Conclusion:

Anomalies in core–periphery community structure provide a new perspective for understanding the community structure of ADHD.

Keywords

ADHD community detection core–periphery structure functional connectivity

Introduction

ADHD is one of the most common neurodevelopmental disorders (Fair et al., 2010; Shaw et al., 2013), which appears in childhood and usually persists into adolescence and adulthood. The main persistent symptoms are inattention, hyperactivity, and inappropriate impulsiveness(Lui et al., 2013; Park et al., 2017). Resting-state functional magnetic resonance imaging (rs-fMRI) and complex network theory provide a new approach to studying brain networks (Thilaga et al., 2018; Yeo et al., 2011). A large number of studies have shown that ADHD occurs in functional brain networks with dysfunctional brain network organization and functional connectivity (Henry & Cohen, 2019; Qian et al., 2019; Zhu et al., 2023). Therefore, it is essential to deeply explore the cause of ADHD and the related cognitive neural mechanisms on functional networks.

Community structure is an important feature of brain networks (Sporns & Betzel, 2016; Tooley et al., 2022), and there is growing evidence that community structure is associated with specialized information processing and cognitive behavior (Baniqued et al., 2019; Ding et al., 2022). Research based on ADHD has found some abnormalities in community structure. Kyeong et al. (2017) used the Louvain algorithm to analyze the modular organization of the ADHD functional network and observed altered functional connectivity within several large-scale brain networks in ADHD. Qian et al. (2019) used the Louvain algorithm to extract the modular structure of brain functional networks and used the modularity coefficient (Q) to find that the connectivity within the ADHD modules in functional networks was reduced. Yin et al. (2022) utilized the GenLouvain algorithm to find that ADHD patients exhibit changes in dynamic module structure. These studies have shown a weakening of intra-module connectivity and an increase in inter-module connectivity in ADHD. However, these studies have only focused on the modular community structure identified by Louvain and GenLouvain algorithms, namely tightly connected within modules and sparsely connected between modules, ignoring the interaction between communities. Therefore, research on the structure of the ADHD community is incomplete.

Recently, research has shown that the community structure of the brain network contains different characteristics such as modular, core–periphery, and disassortative (Betzel and Bassett, 2017). Among them, the core–periphery community structure supports two strictly interconnected principles of mesoscale brain organization: local segregation and functional integration (Sporns, 2016). The core–periphery structure encompasses the characteristics of a module, while at the same time valuing the interaction between the core and the periphery (Betzel et al., 2018). As a result, the core–periphery structure is an important topological feature of the brain network, and a growing number of studies are focusing on core–periphery community structures. Faskowitz et al. (2018) found that the entire human life cycle has a type of community structure that goes beyond modularity. Gu et al. (2020) revealed the core–periphery pair structure of the functional network of the human brain, and the core–periphery pair interaction is closely related to human cognitive function. Iandolo et al. (2021) studied the community structure in different frequency bands, revealing that the most representative of all frequency bands is the core–periphery structure. However, it is not clear how the core–periphery structure of ADHD has changed. In conjunction with the existing studies of ADHD modular community structure, we hypothesize that ADHD core–periphery community structure is also abnormal.

Here, to investigate the anomalies of ADHD in the core–periphery structure, we employed a model-based community detection algorithm, the Weighted Stochastic Block Model (WSBM) (Aicher et al., 2015). WSBM explicitly considers pattern interactions between communities to describe the broader community structure topology, sensitively capturing the core–periphery community structure. Firstly, this paper constructed static and dynamic functional connectivity, applying WSBM to the average functional network of healthy controls (HC) to obtain consistent community segmentation results. Further, we combined the identified core–periphery pairs with the core score to define the core–periphery structure. Next, we used the connectivity strength (CS) and disruption index (DI) to quantify changes in the core–periphery structure. In addition, we used correlation analysis to analyze the relationship between this abnormality and the clinical characteristics of ADHD. In conclusion, this study aims to describe ADHD from the perspective of a new community structure using both static and dynamic functional brain network approaches.

Materials and Methods

Participants

The resting-state fMRI data for HC and patients diagnosed with ADHD came from the University of California LA Consortium for Neuropsychiatric Phenomics study. We used a total of 97 subjects, including 40 patients with ADHD and 57 HC. Firstly, we exclude healthy individuals with head movements that exceed 1 mm in translation or 1° in rotation. Secondly, the gender ratio of ADHD patients is male/female = 21/19, with an age of 32.05 ± 10.41 years. We selected 57 healthy individuals from the remaining healthy individuals. The gender ratio of 57 healthy individuals is male/female = 30/27, with an age of 32.88 ± 9.12 years, to exclude the influence of gender and age on the experimental results. Specific sample information is shown in Table 1. The neuroimaging data set was obtained via the public database openfMRI (https://www.openfmri.org/). The Wechsler Adult Intelligence Scale (WAIS) is an intelligence quotient (IQ) test aimed to measure intelligence and cognitive abilities in adults and older adolescents. The matrix reasoning task in the WAIS (WAIS_MR) is aimed to measure inductive reasoning abilities, and the Vocabulary task in the WAIS (WAIS_VOC) is designed to measure verbal comprehension and expression ability.

Table 1.

Sample Demographic Details in this Study.

Group	ADHD	HC	p-Value
Number of subjects	40	57	—
Age (mean ± SD)	32.05 ± 10.41	32.88 ± 9.12	.68
Gender (M/F)	21/19	30/27	.98
WAIS_MR	20.98 ± 3.92	20.56 ± 3.86	.94
WAIS_VOC	43.68 ± 9.58	44.58 ± 9.16	.48

Note. SD= standard deviation; The WAIS_MR and WAIS_VOC scores were used to assess intelligence and cognitive ability in adults with and without ADHD.

Data Acquisition and Preprocessing

The neuroimaging data were obtained on a 3T Siemens Trio scanner. During the collection of fMRI data, the subjects were not stimulated, asked to stay relaxed, opened their eyes, and thought nothing. Functional MRI data were collected using T2* weighted echo plane imaging (EPI) sequences with the following parameters: slice thickness = 4 mm, slices = 34, repetition time (TR) = 2 seconds, echo time (TE) = 30 ms, flip angle = 90°, the field of view (FOV) = 192 mm, and matrix = 64 × 64. The resting fMRI scan lasted a total of 304 seconds.

Data preprocessing was carried out by the DPABI toolbox. Considering the adaptability of the subjects to the environment, the first 10 volumes of the signal were discarded, and the remaining data were first slice timing-corrected and head-motion-corrected. Then, the resulting data were normalized to Montreal Neurological Institute (MNI) standard space. Spatial smoothing was accomplished by using a Gaussian kernel with 6 mm fullwidth at half-maximum (FWHM). Next, bandpass filtering (0.01 ≤ f ≤ 0.1 Hz) was performed on the image. Finally, the covariates were removed, and the brain was divided into 90 regions using the automatic anatomical marker template (AAL).

Functional Brain Network Construction

First, the network nodes are defined by 90 brain regions of interest predefined by the AAL template. In the static network, the Pearson’s correlation coefficient of each pair of regions is calculated for the average time series of 90 regions and defined as the edge of the network.

Second, the sliding window method is used to construct the dynamic network. We divided the fMRI time series of each subject into smaller time windows with a length of 100 seconds (50 time points) by using sliding time window technology. This window size was chosen because it was suggested that the window length used in dynamic network studies should not be less than the reciprocal of the minimum frequency of the data (Leonardi & Van De Ville, 2015). Each window moves one time point, each subject obtains 93 windows, each window constructs a 90 × 90 functional connection matrix.

Finally, we extract the upper triangular elements of the matrix as clustering features for further analysis. Compared with other distance functions (Euclidean), the Manhattan distance function has a better similarity measure for high-dimensional data (Allen et al., 2014). Subsequently, we adopted the Manhattan distance function as the index, using the clustering algorithm k-means for the cluster analysis.

Weighted Stochastic Block Model

SBM is an unsupervised learning algorithm used to describe how groups of nodes in a network interact with each other. Importantly, a community as defined by a WSBM is a group of nodes that connect to the rest of the network in a similar pattern. Here, we applied a recent extension of this method to weighted graphs, commonly referred to as the WSBM (Aicher et al., 2015). Formally, we follow the notation in (Aicher et al., 2015), which describes the generative model for weighted pairwise interactions among n vertices, with an exponential family distribution $F$ and a block structure R. An important parameter is the vector of nodes assignment $Z = [z_{1}, . . ., z_{N}]$ where $z_{j} \in {1, . . ., k}$ , with $n$ the number of nodes and k the number of communities the algorithm must learn. For a given adjacency matrix A and the likelihood is given by:

\Pr (A | {z_{i}}, {θ_{r s}}, ℳ_{ℱ, ℛ}) = \prod_{i \leq j} f (A_{i j} | θ_{ℛ (z_{i}, z_{j})})

(1)

where ${z_{i}}$ is the set of community assignments, ${θ_{r s}}$ is the matrix of edge bundle parameters $θ$ . For an estimated model $ℳ_{ℱ, ℛ}$ , the log-Evidence score

ℒ_{ℳ_{ℱ, ℛ,}} = \log \Pr (A | ℳ_{ℱ, ℛ})

(2)

is used to quantify the goodness of fit and to inform model selection. Thus, the best approximation of the posterior is obtained through a procedure aimed at maximizing the log-Evidence score. We selected 250 independent trials to find the best log-Evidence value. Within this limit, the algorithm searches for the best log-Evidence value. Every time a better log-Evidence value (i.e., a better solution) is obtained, the algorithm updates the solution. We selected the community’s assignment with the greatest log-Evidence value. We run the WSBM model for different values of $k$ (ranging from 2 to 15) and we performed 250 WSBM fits per each value of $k$ .

Definition of Core–Periphery Block Structure

Next, because WSBM aggregates nodes into communities, and for the block set $B_{r}$ of the subject $h$ , we can quantify the inter-block CS $ω_{r s}$ and the intra-block CS $ω_{r r}$ and $ω_{s s}$ , the block average strength between block $r$ and $s$ is defined as:

ω_{r r} = \frac{\sum_{i \in C_{r}, j \in C r, i \neq j} A_{i j}^{s}}{| B r | \cdot | B r | - | B r |}

(3)

ω_{s s} = \frac{\sum_{i \in C_{s}, j \in C s, i \neq j} A_{i j}^{s}}{| B s | \cdot | B s | - | B s |}

(4)

ω_{r s} = \frac{\sum_{i \in C_{r}, j \in C s} A_{i j}^{s}}{| B r | \cdot | B s |}

(5)

We can describe interactions between communities based on the strength of paired community connections. Consider a given pair of blocks $r$ , $s$ with associated within-block mean strengths $ω_{rr}$ and $ω_{ss}$ and with associated between-block mean strength $ω_{r s}$ . We say that this pair forms a “core–periphery pair” when $| ω_{r r} | \leq | ω_{r s} | \leq | ω_{s s} |$ (or $| ω_{s s} | \leq | ω_{r s} | \leq | ω_{r r} |$ ).

Further, we investigated which block is more like the core block. Specifically, we used the core score defined by (Borgatti & Everett, 1999) to perform our core–periphery analysis. In a Euclidean representation, the core score would correspond to the distance from the centroid of a single point cloud. We calculated the core score of each node in the network using the continuous heuristic MINRES method, and then we averaged these values over nodes in a block to obtain a core score for the block. For the core score $C_{r}$ of block r and the core score $C_{s}$ of block $s$ , we define a sign variable $ε$ , $ε = 1$ denotes the block $r$ is the core block (block $s$ is the periphery block), $ε$ = 0 denotes the block $r$ is the periphery block (block $s$ is the core block):

ε = {\begin{cases} 1 & i f C_{r} > C_{s} \\ 0 & i f C_{r} < C_{s} \end{cases}}

(6)

In order to better understand the anomaly of ADHD in core–periphery interactions between blocks, we identify the core–periphery interactions of each individual at a finer topological scale. Focusing on core–periphery pairs, we first wanted to determine whether their locations were consistent between ADHD and HC. Here, we confine ourselves to considering the pairs that are core–periphery pairs in at least one-third the sample of participants in both groups. That is, block $r$ and block $s$ display at least 33% in both groups in a core–periphery pair relationship.

Having identified the core–periphery pair interactions, we next explored the possibility of complex connections between multiple core–periphery pairs. Specifically, by integrating core–periphery pairs with common blocks, we recognize a way of connecting what we call the “core–periphery pattern,” that is, different core blocks are connected by the same periphery block. We will only focus on the consistent core–periphery pairs in ADHD and HC and do not consider the isolated core–periphery pairs in the two groups.

Analysis of Core–Periphery Block Structure

First, we analyze the difference in the CS of the core–periphery block structure according to equations (3), (4), and (5), and explore whether ADHD patients have abnormalities in the core block or periphery block, or between the core block and the periphery block.

Next, to evaluate the alterations of local measures, we defined the local measure DI $a$ based on the study (J. Wang et al., 2016). We performed linear fitting to calculate the DI of the edge within the block (or between block) according to Eq. (7):

\bar{E_{A}} - \bar{E_{c}} = a \times \bar{E_{c}} + b

(7)

where $\bar{E_{A}} \in δ^{N}$ ( $N$ is the number of the edge within the block (or between blocks)) and $\bar{E_{c}} \in δ^{N}$ are the mean CS values of each edge within the block (or between blocks) in the ADHD patient group and the HC group, respectively. The strength of edges within and between communities is defined as follows: the edges within the block or between blocks are sorted according to their strength. Using a threshold of 20%, the top 20% of edges within or between communities are defined as high connectivity edges, and the remaining edges that do not pass the threshold are defined as low connectivity edges.

If $a$ is equal to zero, it means that the patients’ values are linearly dependent on the controls’ values, which suggests that there is no disruption in the patient group. If $a$ is negative, it means that the high connectivity edges in HC turn to low connectivity edges in ADHD patients, while the low connectivity edges in HC turn to high connectivity edges in ADHD patients, that is, the edges within the block (or between blocks) are radically reorganized. If $a$ is positive, it means that some edges are low connectivity in the HC and become lower connectivity in ADHD. A simple pipeline of the analysis strategy in this study is displayed in Figure 1.

Figure 1.

Overview of analysis strategy: (a) Construction of static networks based on a complete time series and dynamic networks built by sliding time window technology. (b) Perform community detection using WSBM. (c) Definition of core–periphery block structure. (d and e) Analyze the abnormal core–periphery block structure in terms of connectivity strength and disruption index.

Statistical Analysis

The independent-sample $t$ -test was used to analyze the differences between the ADHD group and the HC. Partial correlation was used to study the relationship between significant differences in core–periphery structures and ADHD symptoms, controlling for age and sex factors. The results were corrected by FDR, and $p < . 05$ was regarded as the threshold for significant differences. Edge difference detection with $p < . 01$ as the threshold for a significant difference.

Results

Optional Community Structure Based on WSBM

We considered a group-average functional brain network constructed by taking the average of the connection matrices of all participants in the HC group. For this group network, we apply the WSBM method to extract its community structure and map this community division to ADHD. We observed the maximum log-Evidence at $k = 10$ and chose to set $k = 10$ to the number of communities. The results of the community division were shown in Figure 2. Next, we calculated the block-level adjacency matrix, that is, a block connection matrix of 10 × 10 for each subject in the ADHD and HC.

Figure 2.

The optional community structure based on WSBM.

k-Means Clustering Analysis

Using $k$ -means clustering and Elbow method, $k_s$ = 4 is selected as the optimal number of clusters. The correlation matrices of all subjects were divided into four states after clustering. The matrix of brain function connections in each state was shown in Figure 3. States 1 to 4 account for 16%, 28%,34%, and 22% of the sliding window, respectively. To analyze from the perspective of the community structure we divided, we ranked their 90 ROIs according to the communities to which the AAL template belonged. In terms of FC mode, state 1 and state 2 exhibited apparent strong network connection, and state 3 and state 4 exhibited apparent weak network connection. Therefore, we proposed two discrete connectivity states, one with high connectivity (State 1 and State 2) and one with low connectivity (State 3 and State 4).

Figure 3.

Pearson correlation matrices for the four states estimated via the dynamic functional connectivity (DFC). Panel A and Panel B exhibit the high connectivity state, and Panel C and Panel D show the low connectivity state.

Core–Periphery Block Structure

In the distribution of core–periphery pairs, we found that core–periphery pairs did not appear at random locations for each participant but exhibited an almost identical distribution in both groups. As shown in Figure 4, we only showed the core–periphery pairs that co-exist in ADHD and HC. In addition, the core–periphery block structure of both static and dynamic networks is defined by us as a core–periphery pattern. The common periphery block #10 was located mainly in the attention network (AN), including the Middle frontal gyrus, orbital part (ORBmid), Angular gyrus (ANG), right Inferior parietal, but supramarginal and angular gyri (IPL) and right Posterior cingulate gyrus (PCG). In the static network (Figure 4a), the core–periphery structure was represented by five core blocks (module 2, module 3, module 4, module 7, and module 9) connected by the common periphery block #10. Modules 2 and 7 were mainly distributed in the subcortical network. Module 3 included the Cuneus (CUN), Superior occipital gyrus (SOG), right Middle occipital gyrus (MOG), and Superior parietal gyrus (SPG). Module 4 was located mainly in the visual network (VN) and Module 9 was mainly located in the sensorimotor network (SMN).

Figure 4.

The core–periphery block structure: (a) Core–periphery block structure under the static network. Red is the different core block and blue is the periphery block. (b) Core–periphery block structure in four states of the dynamic network.

In state 1, there was a core–periphery relationship for module 2 and module 10, module 7 and module 10, with core blocks for modules 2 and 7 being connected by periphery block #10. State 2 showed the three core blocks (module 3, module 4, and module 9) sharing the same periphery block #10. State 3 showed the five core blocks (module 2, module 3, module 4, module 6, and module 7) connected by periphery block #10. Module 6 was composed of regions of the Supplementary motor area (SMA), Median cingulate and paracingulate gyri (DCG), Temporal pole: superior temporal (TPOsup), Middle temporal gyrus (MTG), and Inferior temporal gyrus (ITG). State 4 showed the four core blocks (module 1, module 4, module 7, and module 8) connected by periphery block #10. Module 1 contained a subset of nodes of the AN and Module 8 was mainly located in the default mode network (SMN).

Group Differences on Core–Periphery Block Connections

We want to explore how the core–periphery block structure of ADHD can be anomalous, such as a core block or a periphery block, or an abnormal interaction between the core block and the periphery block. In the static network, as shown in Figure 5a, the intra-block CS of ADHD is significantly lower than HC in core block #3 ( $p < . 01$ , FDR-corrected). At the same time, in the low connectivity state 3 (Figure 5e), we also found that the intra-block CS of core block #3 is significantly lower than HC ( $p < . 01,$ FDR-corrected). In low connectivity state 4, the periphery block #10 intra-block CS is stronger than HC, but the difference is not significant. As shown in Figure 5c and d, in the high connectivity state 2, the CS between core block #9 and periphery block #10 ( $p = . 028,$ FDR-corrected) and between core block #4 and periphery block #10 is significantly enhanced than HC ( $p = . 031,$ FDR-corrected).

Figure 5.

Differences in CS between ADHD patients and HC in core–periphery block structures: (a) The difference in core block #3 in the static network. (b) The difference in periphery block #10 in low connectivity state 4 of dynamic networks. (c and d) The differences between core block #4 and periphery block #10 and between core block #9 and periphery block #10 in high connectivity state 2. (e and f) The differences in core block #3 and core block #6 in low connectivity state 3 (*p < .05, **p <. 01, FDR-corrected).

Group Differences in Nodes or Edges

We analyzed the difference in edges between ADHD and HC, as shown in Figure 6a, the circle represents the nodes within core block #3, and the blue line represents the different edges between the nodes. We obtained seven different edges within core block #3, mainly concentrated in the SOG and SPG, and ADHD was significantly lower than HC. In addition, we used the DI to further quantify the observed core block change. As shown in Figure 6b, we found a significant positive $a$ value indicating that ADHD preferentially attacks the low connectivity edges ( $a = . 30, p = 1.10 e - 6$ ). The orange nodes represent low connectivity edges, and blue nodes for high connectivity edges. The red nodes are different edges, and we found that the edges with differences are all low connectivity edges in HC. Similarly, in state 3, there are three different edges within core block #3 (Figure 6c). The DI is also a significant positive $a$ value ( $a = . 33$ , $p = 5.41 e - 6$ ; Figure 6d), which is consistent with the results of the static network.

Figure 6.

Differences in brain regions and edges in core block: (a) Different edges within core block #3 in the static network. (b) The slope of the regression line in gray measures the DI = 0.3. Blue nodes represent high connectivity edges, and orange nodes represent low connectivity edges. The red nodes are different edges. (c) Different edges within core block #3 in state 3 of dynamic networks. (d) The slope of the regression line in gray measures the DI. The thickness of the line is the t value of the different edges.

In state 3, we found that ADHD has a significantly lower connection between the SMA.R and MTG. L ( $p < . 01$ ) and a significantly stronger connection between DCG.R and ITG. R ( $p < . 01$ ) within core block #6 (Figure 7a), but there is no significant difference between ADHD and HC in the connection of the entire core block (Figure 5f). The two edges have some compensation, resulting in no significant change in ADHD on the module. In state 4, as shown in Figure 7b, three different edges were obtained within the periphery block.

Figure 7.

Differences in brain regions and edges in the special core block and the periphery block: (a) different edges within core block #6 in state 3 and (b) different edges within periphery block #10 in state 4.

In Figure 8a, between the core block #4 and the periphery block #10, we found two different edges, and ADHD was significantly higher than HC. To quantify the observed change between the core block and the periphery block, we found a significant negative $a (a = - . 31, p = 3.98 e - 4)$ value between the core block and the periphery block, indicating that the connection between the ADHD core block and the periphery block has been reorganized (Figure 8b). In the connection of core block #9 to the periphery block #10, we found four significantly enhanced edges (Figure 8c). On the DI, a significant negative $a (a = - . 155, p = . 003)$ value was also found (Figure 8d).

Figure 8.

Differences in brain regions and edges between the core block and periphery block: (a) Different edges between core block #4 and periphery block #10. (b) DI between #4 and #10. The slope of the regression line in gray measures the DI = −0.31. (c) Different edges between core block #9 and periphery block #10. (d) The slope of the regression line in gray measures the DI = −0.155 between core block #9 and periphery #10.

Relationship Between Core–Periphery Measures and Clinical Variables

In this study, a partial correlation was used to investigate the relationship between core–periphery characteristics and ADHD symptoms with significant differences between groups. Figure 9a and b showed the intra-block CS of core block #3 were significantly positively correlated with WAIS_MR scores in static work and state 3 respectively. Figure 9c showed that the CS between core block #4 and periphery block #10 was significantly positively correlated with WAIS_VOC scores. The CS between core block #9 and periphery block #10 was significantly positively correlated with the WAIS_MR score as shown in Figure 9d.

Figure 9.

Correlation of clinical features: (a) Correlation between WAIS_MR scores and intra-block CS of core block #3 in the static network. (b) Correlation between WAIS_MR scores and intra-block CS of core block #3 in state 3. (c) Correlation between WAIS_VOC Scores and the CS between core block #4 and periphery block #10. (d) Correlation between WAIS_MR scores and the CS between core block #9 and periphery block #10.

Discussion

The Core–Periphery Structure Based on WSBM

The brain itself was a dynamic process and we used both static and dynamic functional connectivity to analyze abnormalities in the core–periphery structures of ADHD. Hence, we leveraged recent methodological advances in community detection algorithms WSBM to identify optimal community structure. Unlike other common methods,WSBM is sensitive to core–periphery structure and can detect core–periphery pairs (Tooley et al., 2022). Importantly, in both static and dynamic networks we found that different core blocks were connected by the common periphery block #10 in ADHD and HC, forming a “core–periphery pattern.” This “core–periphery pattern” may provide a means by which cores can transiently communicate with one another (Gu et al., 2020). In this paper, we found some core–periphery pairs, such as core block #3 and periphery block #10, core block #9, and periphery block #10. Core block #6 and core block #8 consisted mainly of the temporal lobe, SMA, and insula, and core block #4 was located mainly in the occipital lobe. These findings are consistent with previous studies on the core–periphery of brain networks (Iandolo et al., 2021; Shen et al., 2021). Some studies also using intrinsic functional connectivity analysis have reported network centrality in the visual (L. Wang et al., 2009) and sensorimotor cortex (An et al., 2013; Di Martino et al., 2013), which corresponds to our core block #3 and core block #9. Periphery block #10 was mainly located in the AN. Sepulcre et al. (2012) found that neurotypical adults display functional connectivity streams that can be traced from primary sensory circuits to attention networks, consistent with the interaction between our core and periphery. Further analyses were based on this core–periphery pattern.

Decreased Intra-Block CS of Core Block in ADHD

In the static network, we found that the intra-block CS of core block #3 of ADHD was significantly reduced. Core block #3 was located mainly in the occipital and SPG, thus indicating a reduced connection of the occipital lobe as well as the SPG. Previous studies (C. Tang et al., 2018; Y. Tang et al., 2022) found that ADHD has smaller connections in both the occipital and parietal lobes. Another study (Silk et al., 2008) reported that ADHD exhibits deactivation of parietal and occipital regions during spatial tasks and we reached the same conclusion in core block #3. The core block is a high-density connected module that is responsible for specialized information processing and is considered the basis of cognitive processes (Betzel et al., 2018). Core block #3 was primarily responsible for visual processing, and visual function is known to play an important role in the pathogenesis of ADHD symptoms (Lin et al., 2021). From the perspective of integration and segregation, that is, the local segregation of the core block #3 was weakened resulting in the information transmission efficiency of the core block being reduced. Several studies (Qian et al., 2019) have shown a reduction in ADHD modular segregation in functional networks. We came to the same conclusion on core block #3, that is, ADHD core block #3 had a reduced degree of segregation.

From the edge perspective, we found a significant reduction in the connection between the SOG and MOG within core block #3, and we further concluded the reduction in core block segregation was caused by these abnormal connections. The SOG and MOG were located in the occipital lobe, which directs the processing of visual information, the maintenance of attention and inhibition of indifferent stimuli (Sripada et al., 2014), whereas dysfunction in the ability to inhibit foreign and indifferent stimuli is a core symptom of ADHD (Buffalo et al., 2010). Meanwhile, only in state 3 we found the core block #3 disrupted, consistent with the static network results. In this study, State 3 was a low connectivity configuration characterized by low levels of connectivity, so we hypothesized that core block #3 was primarily caused by disruptions to the low connectivity edges. Furthermore, the intra-block CS of core block #3 was detected to be significantly positively correlated with the WAIS_MR. These correlations suggested that the intra-block CS in core block #3 was sensitive to the severity of ADHD disease.

Increased CS Between Core and Periphery Blocks in ADHD

In the high connectivity state of the dynamic network, our results indicated increased functional connectivity between the core blocks and the periphery block, which was manifested as core block #4 and periphery block #10, core block #9 and periphery block #10. Core block #4 was mainly located in the VN, and core block #9 was mainly located in the SMN, which indicated that the VN and AN, and the SMN and AN were hyperconnected. Our results partially align with previous studies of ADHD (Choi et al., 2013; Kebets et al., 2019), suggesting the altered connections between AN and SMN. Zhu et al. (2023) have found that the connection between the VN and the AN is abnormal in different states of the dynamic network. The interaction of the core and periphery reflects an efficient integration (Iandolo et al., 2021), we believed that the increased core–periphery connectivity in the high connectivity state may reflect enhanced integration of ADHD. Zhu et al. (2023) found enhanced integration of ADHD networks in dynamic connectivity. R. F. Betzel et al. (2018) reported that the core–periphery structure reflects the capacity for information to be broadcast from a core to a periphery. Our results suggested that the core broadcasted information to the periphery too actively. In addition, our observations supported the notion that the sensory cortex, as the core, tended to compensate for directed attention networks (Fassbender & Schweitzer, 2006). Furthermore, WAIS_VOC scores and WAIS_MR scores were positively correlated with the connection between the core–periphery. These results suggested that enhanced connectivity between core and periphery blocks was associated with cognitive performance and intelligence in ADHD. Moreover, we only found increased integration between core–periphery in dynamic analysis, which indicated the changes in the connectivity between the core–periphery of ADHD patients were difficult to recognize by static analysis. Therefore, dynamic analysis encompasses the capacity for more fine-grained conclusions (Allen et al., 2014).

In the interaction of core block #4 with periphery block #10, the connection between the FFG. R and ORBmid.L and between the IOG.L and PCG.R were significantly enhanced. (Su et al., 2023) have shown that the PCG and IOG had abnormal brain connections. Q. Lin et al. (2023) found abnormalities in the orbitofrontal and FFG. The connection between the STG.L and ORBmid.L, and between the INS.L and ORBmid.L were significantly enhanced in the interaction between core block #9 and periphery block #10. Some studies (Q. Lin et al., 2023; Y. Tang et al., 2022) have revealed that these brain regions are abnormal. W. Wang et al. (2013) revealed the functional connection enhancement of the INS.L in ADHD. We further concluded that the integration enhancement between core–periphery was caused by these nodes and edges. The FFG and ORBmid are important regions for VN and AN respectively. VN interacts with AN to maintain attention(Shulman et al., 2009) and suppress attention to irrelevant stimuli (Capotosto et al., 2009). Failure to ignore extraneous stimuli is one of the core symptoms of ADHD (Castellanos & Proal, 2012). The INS and STG are important regions for SMN. The SMN-AN interaction is important for movement control and attentional regulation, which is known to be abnormal in ADHD (Carmona et al., 2015). Thus, exposing symptoms of ADHD hyperactivity and attention deficits. The PCG was the main region of DMN, and the enhanced activity of DMN may be related to the inability to concentrate in ADHD patients. Thus, abnormalities in the interaction between the core and periphery may provide a new perspective on the clinical symptoms of ADHD.

Increased Intra-Block CS of Periphery Block in ADHD

In both static and dynamic networks, we found that periphery block #10 was identical and had different core blocks connected. The periphery block #10 included portions of the frontal lobe, suggesting that this region had an important mediating role in the mesoscale network function of the resting-state brain in ADHD (Salmi et al., 2009). In State 3, we found that the intra-block CS of the periphery block was not significantly different between groups, but for further research, we found the ORBmid.L and ANG.L, the ORBmid.R and ANG.R, the IPL. R and ANG.R connectivity was significantly enhanced. Ji and Zhang (2022) found that the important brain regions that distinguish ADHD from healthy controls include ORBmid. Q. Lin et al. (2023) found the functional connection enhancement of the ANG in ADHD. The ORBmid belongs to the frontal lobe and is mainly related to thinking functions (Ji & Zhang, 2022). Abnormal ORBmid connections may precisely reflect some of the disorders in the frontal lobe function of ADHD patients. The ANG participates in language processing (Friederici, 2011), abnormal connectivity of the ANG may affect the language ability of ADHD.

The predominant feature of state 3 is a low connectivity state. Enhanced connectivity of periphery block #10 in ADHD patients may be due to a lower connectivity state, could be interpreted as a potential compensatory mechanism of intrinsic brain networks resulting in stronger synchrony (Kim et al., 2017). In addition, the enhanced connectivity of the periphery block echoes the previously reported trend of compensation from the core block to the periphery block.

DI of Core–Periphery in ADHD

To quantify the observed changes in the core–periphery block structure, we calculated the DI of core block #3 is $a = . 3$ , which represents the degree of edge disruption within the core block (Guillon et al., 2019). We found a significant positive $a$ value implying that the low connectivity edges in HC were disrupted and converted to lower connectivity edges in ADHD. The edges we found with differences within core block #3 were all exactly the low connectivity edges in HC (Figure 6b, d), resulting in a decrease in overall connectivity for core block #3, further demonstrating that our results are reasonable.

In the connection between core block #4 and periphery block #10, we calculated the DI between the core and the periphery as $a = - . 31$ as a negative value. In the connection between core block #9 and periphery block #10, we also found a significant negative value for the DI, implying that reorganization had occurred between the core and the periphery (Guillon et al., 2019). These results mean that the high connectivity edges in HC turn to low connectivity edges in ADHD, while the low connectivity edges turn to high connectivity edges in ADHD (J. Wang et al., 2016). We found that the disrupted edges between core–periphery were all low connectivity edges in HC and that these edges significantly increase to become high connectivity edges in ADHD (Figure 8b, d), while no significant differences were found for the high connectivity edges, resulting in enhanced connectivity between the core and the periphery at the mesoscale.

Conclusion

The current study used the WSBM algorithm to investigate alterations of core–periphery community structure in the functional brain networks of ADHD. In this study, the CS of the core block mainly located in the occipital lobe and SPG reduced in ADHD. Enhanced connectivity between the core and periphery block, specifically between core block located mainly in the VN and periphery block located mainly in the AN and between core block mainly located in the SMN and periphery block located mainly in the AN. Connectivity enhancement of periphery block mainly located in the AN. These results suggested abnormalities in the core–periphery structure of ADHD. Moreover, core–periphery abnormalities were clearly associated with ADHD symptoms. Our results support a core–periphery view of community structures and provide new evidence to explain the physiological deficits caused by this class of neurological disorders.

Footnotes

Declaration of Conflicting Interests

The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding

The author(s) disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: This work was supported by the National Natural Science Foundation of China (Grant Nos 61906130, 62176177, and 61873178).

ORCID iDs

Dandan Li

Bin Wang

Author Biographies

Dandan Li is an associate professor and an associate supervisor in the college of Computer Science and Technology of Taiyuan University of Technology. She received the Ph.D. degree from China University of Geosciences (Beijing) in 2014. Dr. Li is mainly engaged in the research of brain science and intelligent information processing.

Dianni Hou is currently studying at Taiyuan University of Technology and is studying for a master’s degree. Her major is computer technology, and her main research content is brain science and intelligent computing.

Yating Zhang is currently studying at Taiyuan University of Technology and is studying for a master’s degree. Her major is computer technology, and her main research content is brain science and intelligent computing.

Yao Zhao is currently studying at Taiyuan University of Technology and is studying for a master’s degree. His major is computer technology, and his main research content is brain science and intelligent computing.

Xiaohong Cui is an associate professor in the college of Computer Science and Technology of Taiyuan University of Technology. Her research focuses on brain science and intelligent computing

Yan Niu, Doctor Degree of Engineering, lecturer. Worked in Tai Yuan University of Technology. Her research interests include brain science and intelligent computing

Jie Xiang is a professor and doctoral supervisor in the college of Computer Science and Technology of Taiyuan University of Technology. She received the M.S. degree and the Ph.D. degree in computer science and technology from Taiyuan University of Technology. Jie is mainly engaged in brain science and intelligent computing, intelligent information processing and big data management and analysis.

Bin Wang is a professor and doctoral supervisor in the college of Computer Science and Technology of Taiyuan University of Technology. He received the Ph. D. Degree in Okayama University, Japan, in 2013. He is mainly engaged in the study of brain cognitive function and the diagnosis of mental diseases.

References

Aicher

Jacobs

A. Z.

Clauset

(2015). Learning latent block structure in weighted networks. Journal of Complex Networks, 3(2), 221–248.

Allen

E. A.

Damaraju

Plis

S. M.

Erhardt

E. B.

Eichele

Calhoun

V. D.

(2014). Tracking whole-brain connectivity dynamics in the resting state. Cerebral Cortex, 24(3), 663–676.

Cao

X. H.

Cao

Q. J.

Sun

Yang

Zou

Q. H.

Katya

Zang

Y. F.

Wang

Y. F.

(2013). Methylphenidate normalizes resting-state brain dysfunction in boys with attention deficit hyperactivity disorder. Neuropsychopharmacology, 38(7), 1287–1295.

Baniqued

P. L.

Gallen

C. L.

Kranz

M. B.

Kramer

A. F.

D’Esposito

(2019). Brain network modularity predicts cognitive training-related gains in young adults. Neuropsychologia, 131, 205–215.

Betzel

R. F.

Bassett

D. S.

(2017). Multi-scale brain networks. Neuroimage, 160, 73–83.

Betzel

R. F.

Medaglia

J. D.

Bassett

D. S.

(2018). Diversity of meso-scale architecture in human and non-human connectomes. Nature Communications, 9(1), 346.

Borgatti

S. P.

Everett

M. G.

(1999). Models of core/periphery structures. Social Networks, 21(4), 375–395.

Buffalo

E. A.

Fries

Landman

Liang

Desimone

(2010). A backward progression of attentional effects in the ventral stream. Proceedings of the National Academy of Sciences of the USA, 107(1), 361–365.

Capotosto

Babiloni

Romani

G. L.

Corbetta

(2009). Frontoparietal cortex controls spatial attention through modulation of anticipatory alpha rhythms. Journal of Neuroscience, 29(18), 5863–5872.

10.

Carmona

Hoekzema

Castellanos

F. X.

Garcia-Garcia

Lage-Castellanos

Van Dijk

K. R. A.

Navas-Sanchez

F. J.

Martinez

Desco

Sepulcre

(2015). Sensation-to-cognition cortical streams in attention-deficit/hyperactivity disorder. Human Brain Mapping, 36(7), 2544–2557.

11.

Castellanos

F. X.

Proal

(2012). Large-scale brain systems in ADHD: Beyond the prefrontal-striatal model. Trends in Cognitive Sciences, 16(1), 17–26.

12.

Choi

Jeong

Lee

S. W.

H. J.

(2013). Aberrant development of functional connectivity among resting state-related functional networks in medication-naive ADHD children. PLoS One, 8(12), e83516.

13.

Di Martino

Zuo

X.-N.

Kelly

Grzadzinski

Mennes

Schvarcz

Rodman

Lord

Castellanos

F. X.

Milham

M. P

. (2013). Shared and distinct intrinsic functional network centrality in autism and attention-deficit/hyperactivity disorder. Biological Psychiatry, 74(8), 623–632.

14.

Ding

Xiang

Cui

Wang

Cheng

Wang

(2022). Abnormal dynamic community structure of patients with attention-deficit/hyperactivity disorder in the resting state. Journal of Attention Disorders, 26(1), 34–47.

15.

Fair

D. A.

Posner

Nagel

B. J.

Bathula

Dias

Mills

K. L.

Blythe

M. S.

Giwa

Schmitt

C. F.

Nigg

J. T.

(2010). Atypical default network connectivity in youth with attention-deficit/hyperactivity disorder. Biol Psychiatry, 68(12), 1084–1091.

16.

Faskowitz

Yan

Zuo

X. N.

Sporns

(2018). Weighted stochastic block models of the human connectome across the life span. Scientific Reports, 8(1), 12997.

17.

Fassbender

Schweitzer

J. B.

(2006). Is there evidence for neural compensation in attention deficit hyperactivity disorder? A review of the functional neuroimaging literature. Clinical Psychology Review, 26(4), 445–465.

18.

Friederici

A. D.

(2011). The brain basis of language processing: From structure to function. Physiological Reviews, 91(4), 1357–1392.

19.

Xia

C. H.

Ciric

Moore

T. M.

Gur

R. C.

Gur

R. E.

Satterthwaite

T. D.

Bassett

D. S.

(2020). Unifying the notions of modularity and core–periphery structure in functional brain networks during youth. Cerebral Cortex, 30(3), 1087–1102.

20.

Guillon

Chavez

Battiston

Attal

La Corte

Thiebaut

Schotten

Dubois

Schwartz

Colliot

de Vico Fallani

(2019). Disrupted core-periphery structure of multimodal brain networks in Alzheimer’s disease. Network Neuroscience, 3(2), 635–652.

21.

Henry

T. R.

Cohen

J. R.

(2019). Dysfunctional brain network organization in neurodevelopmental disorders. Connectomics, 83–100.

22.

Iandolo

Semprini

Sona

Mantini

Avanzino

Chiappalone

(2021). Investigating the spectral features of the brain meso-scale structure at rest. Human Brain Mapping, 42(15), 5113–5129.

23.

Zhang

(2022). Functional brain network classification based on deep graph hashing learning. IEEE Transactions on Medical Imaging, 41(10), 2891–2902.

24.

Kebets

Holmes

A. J.

Orban

Tang

Sun

Kong

Poldrack

R. A.

Yeo

B. T.

(2019). Somatosensory-motor dysconnectivity spans multiple transdiagnostic dimensions of psychopathology. Biological Psychiatry, 86(10), 779–791.

25.

Kim

Criaud

Cho

S. S.

Díez-Cirarda

Mihaescu

Coakeley

Ghadery

Valli

Jacobs

M. F.

Houle

Strafella

A. P.

(2017). Abnormal intrinsic brain functional network dynamics in Parkinson’s disease. Brain, 140(11), 2955–2967.

26.

Kyeong

Kim

J. J.

Kim

(2017). Novel subgroups of attention-deficit/hyperactivity disorder identified by topological data analysis and their functional network modular organizations. PLoS One, 12(8), e0182603.

27.

Leonardi

Van De Ville

(2015). On spurious and real fluctuations of dynamic functional connectivity during rest. Neuroimage, 104, 430–436.

28.

Lin

Wang

Chen

Liang

Wang

Zhao

Zhang

Xie

Yang

Huang

(2021). Functional connectivity of attention-related networks in drug-naive children with ADHD. Journal of Attention Disorders, 25(3), 377–388.

29.

Lin

Shi

Huang

Jiao

Kuang

Chen

Rao

Zhu

Liu

Huang

Lin

(2023). Functional brain network alterations in the co-occurrence of autism spectrum disorder and attention deficit hyperactivity disorder. European Child & Adolescent Psychiatry. Advance online publication. https://doi.org/10.1007/s00787-023-02165-0

30.

Lui

J. H.

Johnston

Lee

C. M.

Lee-Flynn

S. C.

(2013). Parental ADHD symptoms and self-reports of positive parenting. Journal of Consulting and Clinical Psychology, 81(6), 988.

31.

Park

J. L.

Hudec

K. L.

Johnston

(2017). Parental ADHD symptoms and parenting behaviors: A meta-analytic review. Clinical Psychology Review, 56, 25–39.

32.

Qian

Castellanos

F. X.

Uddin

L. Q.

Loo

B. R. Y.

Liu

Koh

H. L.

Poh

X. W. W.

Fung

Guan

Lee

T. S.

Lim

C. G.

Zhou

(2019). Large-scale brain functional network topology disruptions underlie symptom heterogeneity in children with attention-deficit/hyperactivity disorder. NeuroImage: Clinical, 21, 101600.

33.

Salmi

Rinne

Koistinen

Salonen

Alho

(2009). Brain networks of bottom-up triggered and top-down controlled shifting of auditory attention. Brain Research, 1286, 155–164.

34.

Sepulcre

Sabuncu

M. R.

Yeo

T. B.

Liu

Johnson

K. A.

(2012). Stepwise connectivity of the modal cortex reveals the multimodal organization of the human brain. Journal of Neuroscience, 32(31), 10649–10661.

35.

Shaw

Malek

Watson

Greenstein

De Rossi

Sharp

(2013). Trajectories of cerebral cortical development in childhood and adolescence and adult attention-deficit/hyperactivity disorder. Biol Psychiatry, 74(8), 599–606.

36.

Shen

Aliko

Han

Skipper

J. I.

Peng

(2021). Finding core-periphery structures with node influences. IEEE Transactions on Network Science and Engineering, 9(2), 875–887.

37.

Shulman

G. L.

Astafiev

S. V.

Franke

Pope

D. L.

Snyder

A. Z.

McAvoy

M. P.

Corbetta

(2009). Interaction of stimulus-driven reorienting and expectation in ventral and dorsal frontoparietal and basal ganglia-cortical networks. Journal of Neuroscience, 29(14), 4392–4407.

38.

Silk

T. J.

Vance

Rinehart

Bradshaw

J. L.

Cunnington

(2008). Dysfunction in the fronto-parietal network in attention deficit hyperactivity disorder (ADHD): An fMRI study. Brain Imaging and Behavior, 2, 123–131.

39.

Sporns

(2016). Networks of the brain. MIT press.

40.

Sporns

Betzel

R. F.

(2016). Modular brain networks. Annual Review of Psychology, 67(1), 613–640.

41.

Sripada

C. S.

Kessler

Angstadt

(2014). Lag in maturation of the brain’s intrinsic functional architecture in attention-deficit/hyperactivity disorder. Proceedings of the National Academy of Sciences USA, 111(39), 14259–14264.

42.

Chen

Qian

Dai

Yan

Lin

Zhang

Liu

Zhao

Yang

(2023). Evaluation of individual-based morphological brain network alterations in children with attention-deficit/hyperactivity disorder: A multi-method investigation. European Child & Adolescent Psychiatry, 32, 2281–2289.

43.

Tang

Wei

Zhao

Nie

(2018). Different developmental pattern of brain activities in ADHD: A study of resting-state fMRI. Developmental Neuroscience, 40(3), 246–257.

44.

Tang

Zheng

Tian

(2022). Resting-state fMRI whole brain network function plasticity analysis in attention deficit hyperactivity disorder. Neural Plasticity, 2022, 4714763.

45.

Thilaga

Ramasamy

Nadarajan

Nandagopal

(2018). Shortest path based network analysis to characterize cognitive load states of human brain using EEG based functional brain networks. Journal of Integrative Neuroscience, 17(2), 253–275.

46.

Tooley

U. A.

Bassett

D. S.

Mackey

A. P.

(2022). Functional brain network community structure in childhood: Unfinished territories and fuzzy boundaries. NeuroImage, 247, 118843.

47.

Wang

Xian

(2016). Graph theoretical analysis reveals the reorganization of the brain network pattern in primary open angle glaucoma patients. European Radiology, 26, 3957–3967.

48.

Wang

Zhu

Zang

Cao

Zhang

Zhong

Wang

(2009). Altered small-world brain functional networks in children with attention-deficit/hyperactivity disorder. Human brain mapping, 30(2), 638–649.

49.

Wang

Yao

Jackson

Liu

Liang

(2013, 4–9 August). Dysfunctional neural activity and connection patterns in attention deficit hyperactivity disorder: A resting state fMRI study [Conference session]. The 2013 International Joint Conference on Neural Networks (IJCNN), Dallas, TX, United States (pp. 1–6). IEEE.

50.

Yeo

B. T.

Krienen

F. M.

Sepulcre

Sabuncu

M. R.

Lashkari

Hollinshead

Roffman

J. L.

Smoller

J. W.

Zöllei

Polimeni

J. R.

Fischl

Liu

Buckner

R. L.

(2011). The organization of the human cerebral cortex estimated by intrinsic functional connectivity. Journal of Neurophysiology, 106(3), 1125–1165.

51.

Yin

Mucha

P. J.

Cohen

J. R.

Zhu

Lin

(2022). Altered neural flexibility in children with attention-deficit/hyperactivity disorder. Molecular Psychiatry, 27(11), 4673–4679.

52.

Zhu

Wang

Zhang

Wang

Zou

(2023). Dynamic functional connectivity changes of resting-state brain network in attention-deficit/hyperactivity disorder. Behavioural Brain Research, 437, 114121.