hyperactivity disorder

Progress in Neuropsychopharmacology & Biological Psychiatry 98 (2020) 109796

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Altered resting functional network topology assessed using graph theory in youth with attention-deficit/hyperactivity disorder

T

⁎

Yanpei Wanga, Chenyi Zuob, Qinfang Xua,c, , Shuirong Liaod, Maihefulaiti Kanjie, ⁎ Daoyang Wangb, a

State Key Laboratory of Cognitive Neuroscience and Learning, Beijing Normal University, Beijing, China College of Educational Science, Anhui Normal University, Wuhu, China c Jiangsu Provincial Key Laboratory of Special Children's Impairment and Intervention, Nanjing Normal University of Special Education, Nanjing, China d School of Psychology, Beijing Normal University, Beijing, China e College of Educational Science, Xinjiang Normal University, Uramqi, China b

A R T I C LE I N FO

A B S T R A C T

Keywords: Attention-deficit/hyperactivity disorder Functional connectivity Topology

Notwithstanding an extensive literature about attention-deficit/hyperactivity disorder (ADHD) and brain structure and function, the controversy of ADHD resulting from dysfunction or developmental delay remains unclear. Graph analysis studies have reached consensus about the pattern of increased integration and decreased randomness during childhood and early adulthood. Here, we hypothesized that ADHD is a neurodevelopmental disorder resulting from developmental delay and would show a pattern of decreased integration and increased randomness during childhood and early adulthood compared with typically developing children. To test this hypothesis, publicly available resting-state fMRI data from 102 children with ADHD and 143 typically developing controls (TDC) were compared using graph theoretical analysis. Functional connectivity was estimated using Pearson correlation analysis, and network topology was characterized using small-world (SW) and minimum spanning tree (MST) properties. The mean strength of global connectivity was significantly weaker in those with ADHD and was related to ADHD diagnosis scores. Significant group differences were observed for SW (clustering coefficient, path length, global and local efficiency) and MST (leaf number, kappa and hierarchy) topology. In addition, except for global efficiency, all of these parameters showed significant correlations with ADHD-related disability. The topology of SW and MST showed less integration and more randomness, which confirmed that ADHD is a disorder associated with developmental delay. Moreover, the topology of resting-state functional networks in children with ADHD that show abnormalities was associated with the degree of disability, which can be considered neurological hallmarks of neurodevelopmental disorders and may facilitate the evaluation and monitoring of clinical status in individuals with ADHD.

1. Introduction Attention-deficit/hyperactivity disorder (ADHD) is one of the most common psychiatric disorders of childhood. According to the fifth edition of the Diagnostic and Statistical Manual of Mental Disorders (Association AP, 2013), ADHD is characterized by inattentiveness and/ or hyperactivity/impulsivity. ADHD typically commences in childhood and persists into adolescence and adulthood(Faraone et al., 2003) and affects 3–5% of school-aged children (Spencer et al., 1998). Children with ADHD display difficulties in behaviour control and/or in the focusing of attention, resulting in adverse consequences in terms of academic performance and social function. However, unlike the traditional representation of ADHD, the symptoms of ADHD are spread among a ⁎

wide range of non-motor functions. The introduction of advanced and non-invasive neuroimaging techniques has provided new opportunities for the study of ADHD in terms of structural and functional brain organization. In addition, the existing neuroimaging data support the multisystem pathophysiology of ADHD. The data generated by modern network science suggest that the human brain is a complex system consisting of interacting units. Brain network organization can be characterized by a number of metrics that can estimate functional integration and separation, quantification of brain region centrality, and test resilience against attack. Previous studies have found that the normal adult brain network of organization is an intermediate structure between two extremes: (1) a random network; (2) a regular network, which has highly ordered local

Corresponding authors at: State Key Laboratory of Cognitive Neuroscience and Learning, Beijing Normal University, Beijing, China. E-mail addresses: [email protected] (Q. Xu), [email protected] (D. Wang).

https://doi.org/10.1016/j.pnpbp.2019.109796 Received 13 June 2019; Received in revised form 22 October 2019; Accepted 24 October 2019 Available online 30 October 2019 0278-5846/ © 2019 Elsevier Inc. All rights reserved.

Progress in Neuropsychopharmacology & Biological Psychiatry 98 (2020) 109796

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with our hypothesis. We thought the authors may have had some limitations in that study: (1) they used a small sample, which may have led to results that were not robust. We used publicly available resting functional MRI data from the Peking University cohort, including 102 ADHD children and 143 typically developing controls (TDC). (2) They used the AAL90 structural atlas and not a functional atlas. Some studies have found that the functional and structural definitions of brain regions do not correspond one to one (Chen and Deem, 2015; Chen et al., 2013). We use the Power 264 atlas to define the nodes of the brain networks, which is a widely used functional atlas derived from functional MRI data based on a very large sample size (Power et al., 2011). (3) They set a range of cost thresholds from 0.05 to 0.5 to construct the small world, and the differences between ADHD children and TDC mainly exists at the cost of 0.15, which may lose some signal below 0.15 and not result in obtaining a unique result. We used the connectivity strength between each pair of brain regions as an edge to construct a small world and compare the observed network to generated randomized networks to normalize. (4) They did not distinguish between positive and negative connections. We only retained the edges with a positive correlation for the analysis. (5) They only compared the difference between the two groups, which is not connected with the severity of the ADHD diagnosis. Therefore, we computed the Pearson correlations between the properties of the small world and ADHD diagnosis features to ensure that the differences between the ADHD and TDC groups were caused by ADHD. A previous study found that when the brain network changed from a regular to a random topological structure, the diameter and leaf fraction of the MST were strongly related to the path length of the SW and the degree of scale-free networks that were rewired to random networks (Tewarie et al., 2015b). An analysis of the MST could avoid methodological biases, which is particularly suitable for comparisons of brain networks. Therefore, we also constructed MSTs to explore the alterations in brain networks in ADHD youth. The aim of the present study was to explore the alterations in resting functional network connectivity or topology in children with ADHD. Increasing evidence has demonstrated that ADHD is a developmental disorder associated with developmental delay and that maturation during childhood results in a shift from a random towards more regular networks. We hypothesized that the changes in the functional network in ADHD youth would show a shift towards more random networks. This aim was achieved by using graph theoretical analysis of publicly available resting functional MRI data from 102 ADHD children and 143 typically developing controls (TDC). The topologies of frequency-specific MSTs and the small-world properties (SW) of brain functional networks were characterized, and group comparisons were performed. An analysis was then conducted to determine the correlations between the SW and MST parameters and ADHD-related disability, as measured using the ADHD symptom score. We supposed that children with ADHD would display alterations in the topology of the SW and MST, which would be associated with ADHD features.

connections (Stam, 2014). To date, many graph theoretical studies have focused on the intermediate topological structures between random and regular networks (Bullmore and Sporns, 2012), which are called smallworld (SW) networks. Subsequent research has shown that many types of real networks have small-world features (Strogatz, 2001). Researchers have defined cluster coefficients and path lengths as measures to characterize the topological properties of complex networks (Strogatz, 2001). The cluster coefficient is a measure of the local interconnectedness of the graph, whereas the path length is an indicator of its overall connectedness. Optimal networks feature a high cluster coefficient (i.e., many local connections) and a short path (corresponds to limited random long-distance connections). SW networks have a good balance between limited long-distance and dense local connections to ensure optimal efficiency in the whole-brain network, and these networks are sensitive to neurobiological alterations during normal and deviant development (Stam, 2014). Increasing evidence suggests that the small-world properties of the brain network influence maturation and brain diseases, such as Parkinson's disease (Olde Dubbelink et al., 2013), schizophrenia (Fornito et al., 2011), and autism (Boersma et al., 2013a). The small world has been an excellent model for describing brain networks since it put forward quantitative insights into network parameters governing the fundamental organization of the brain. Increasingly, brain researchers are applying graph theoretical approaches to characterize network topology. It is difficult to compare networks across different groups and conditions in graph theoretical studies. Therefore, before the analysis of graphs, a normalization step is generally necessary, which is performed through a threshold in the matrix of functional connectivity and/or comparing the observed network to randomized networks generated from the observed network. However, these processing steps cannot provide a unique or consistent result (Langer et al., 2013). To solve the problem, a so-called minimum spanning tree (MST) may be a good choice, which is derived from a weighted network (Olde Dubbelink et al., 2013). The MST is an acyclic sub-network that connects all nodes with the minimum possible link weight. In the MST, all networks have the same number of nodes and connections. The small world is sensitive to alterations in connection strength (for weighted networks) or link density (for unweighted networks), therefore, it involves a normalization step. The MST overcome these methodological limitations and is insensitive to alterations in connection strength or link density. In addition, Tewarie et al. have used simulations to test the MST characteristics and found that they were equally sensitive to alterations in network topology as the conventional graph theoretical measures (including small world)(Tewarie et al., 2015b). To date, only a few brain imaging studies have constructed MST and showed sensitivity to brain disease, such as Alzheimer's disease (Çiftçi, 2011) and epilepsy (Ortega et al., 2008). In addition, MST analysis has been successfully applied to investigate brain maturation in a whole-brain network study and captured the developmental changes in network topology (Boersma et al., 2013b). Some resting functional studies have identified functional network changes in ADHD adults, which showed a shift towards more regular networks (Ahmadlou et al., 2012; Cao et al., 2014; Liu et al., 2015; Wang et al., 2009). Recent graph analysis studies have confirmed a shift from a more random to a more regular small-world topological structure during maturation (Boersma et al., 2013b; Liu et al., 2015; Smit et al., 2016). ADHD is a developmental disorder that is associated with developmental delay (Shaw et al., 2007). This suggests that maturational delay would be reflected by a more random network in ADHD during childhood, rather than by a more regular network (Boersma et al., 2013b; Liu et al., 2015; Smit et al., 2016). Wang and colleagues found that the small-world properties of brain functional networks were altered in children with ADHD(Wang et al., 2009), which was the first study to reveal the topological properties of brain functional networks in children with ADHD using resting-state fMRI. However, they found a shift in the topology towards regular networks, which was inconsistent

2. Materials and methods 2.1. Participants The present study was performed using publicly available data from the ADHD-200 Consortium (http://fcon_1000.projects.nitrc.org/indi/ adhd200/). The ADHD-200 dataset contains functional and anatomical MRI data from eight institutions. For the purposes of the present study, 245 participants between the ages of 8–17 years (11.702 ± 1.958) were selected from the Peking University cohort. This dataset comprised 102 children with ADHD and 143 TD controls. ADHD patients were identified in clinical practice using the Computerized Diagnostic Interview Schedule IV (C-DIS-IV). Prior to inclusion in the Peking University cohort, all participants (ADHD and TD) were evaluated using the Schedule for Affective Disorders and 2

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Fig. 1. Graph and functional connectivity analysis pipeline. Schematic overview of the formation of individual functional brain networks using two different methods, i.e. construction of weighted graphs and minimum spanning trees (MST). After MRI recording (A), data from the MRI (B) were projected onto an functional framework of 264 brain regions, (C). Functional connectivity between all pairs of brain regions was assessed by means of the Pearson correlation (D). For weighted network analysis, a weighted graph (E) was constructed from the Pearson correlation. For MST analysis, the MST matrix was derived from the correlation matrix by Kruskal's algorithm (D'), with concurrent MST construction (E'). Finally, network measures were computed for both the weighted graph (F) and the minimum spanning tree (Olde Dubbelink et al., 2013).

relevant guidelines and regulations.

Schizophrenia for School-age Children-Present and Lifetime Version (KSADS-PL). In all cases, this was completed with the assistance of one parent. A dimensional evaluation of ADHD symptoms was performed using the ADHD Rating Scale (ADHD-RS) IV. Additional inclusion criteria for the Peking University cohort included the following: (i) no lifetime history of inpatient psychiatric treatment; (ii) no history of neurological disorders that could impact brain function; (iii) no current use of psychotropic medications; and (iv) a score of > 80 for the fullscale Wechsler Intelligence Scale for Chinese Children-Revised (WISCCR). Psychostimulant medications were withheld for a minimum of 48 h prior to fMRI scanning. The Peking University study was approved by the Research Ethics Review Board of the Institute of Mental Health, Peking University. Informed consent was obtained from all participants and parents. All methods were performed in accordance with the

2.2. MRI dataset High-resolution whole-brain structural images were obtained for each subject on a SIEMENS TRIO 3-Tesla scanner using a 3D T1weighted spoiled gradient-recalled sagittal MRI sequence. The following parameters were used: 1700/3.92 ms (TR/TE), 176 slices, 1.0/ 0 mm (thickness/gap), 256 × 256 mm (FOV), 256 × 256 (resolution), 12° (flip angle). During acquisition of resting-state fMRI data, subjects were told not to concentrate on anything in particular, but to just relax with their eyes closed. Functional images were obtained axially using the echo planar imaging (EPI) sequence, and the parameters were 2000/30 ms (TR/TE), 30 slices, 4.5/0 mm (thickness/gap), 3

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coefficient indicates that the neighbours of a node are often also directly connected to each other, that is, they form a cluster. To determine whether a network has small-world properties, the values of L and C must be normalized by generated random networks (Watts and Strogatz, 1998). Small-world networks are characterized by path lengths that are similar to those of comparable random networks (Lrandom) but with increased cluster coefficients (Crandom): λ = L/ Lrandom ≈ 1 and γ = C/Crandom > 1(Humphries et al., 2005). Random clustering coefficient and path length derived from the mean of those values from 100 random networks. Each random network was generated by randomly reshuffling the edge weights in the original network (Maslov and Sneppen, 2002), which ensures that the node degree and node distribution of the random network is similar to the original network.

220 × 220 mm (FOV), 64 × 64 (resolution), 90° (flip angle), 236 total time points. Other series have no relation to the present study are not described here. 2.3. Data processing Image preprocessing was performed using the DPARSF data processing assistant for rsfMRI (Yan and Zang, 2010). Preprocessing comprised the following steps: (1) discarding the first ten volumes; (2) slice timing to correct for temporal offsets; (3) realignment of each volume for head movement; (4) spatial normalization to MNI space (NewSegment + DARTEL) and then resampled to 3-mm isotropic voxels; (5) spatial smoothing with a 4-mm 3D full-width half-maximum kernel; (6) detrending to remove linear trends due to scanner drift; (7) temporal bandpass filtering (0.01–0.1 Hz) to remove low-frequency drift and high-frequency physiological noises; and (8) regressing out whole brain and white matter signals and twenty-four motion parameters. We used framewise displacement (FD) (the Euclidean distance between consecutive time points based on six rigid body motion parameters) to quantify head motion. We excluded the subject with FD > 0.25 mm and one subject were not included in the further analysis for head motion. The FD was also included as a covariate in all analyses to control for any residual motion confounds.For any instance of FD > 0.25 mm, the time point as well as the preceding and following time points were censored. When two censored time points occurred within 10 time points of each other, all time points between them were also censored. The average number of censored time points per participant did not differ between them.

2.6. Minimum spanning tree reconstruction The minimum spanning tree of an undirected weighted network is a unique acyclic sub-graph that connects all the nodes with the minimum possible link weight. In our analysis, we used the maximum connection strength (correlation matrix) as the edge to construct an acyclic subnetwork, equivalent to a minimum spanning tree obtained by using the Kruskal algorithm (Kruskal, 1956). Briefly, all connections are arranged in descending order, then starting from the strongest strength edge, consecutive high strength links were added until all nodes (n) were connected and formed an acyclic sub-network consisting of n-1 edges (Fig. 1). If adding a link resulted in the formation of a cycle, this link was skipped. In terms of the information about the topological properties of the minimum spanning tree, we can compute several measures to characterize the topology of the tree, including the normalized leaf fraction, kappa (degree of divergence), betweenness centrality and hierarchy. The normalized leaf number is defined as the number of nodes with a degree of 1 divided by the maximum number of leaves possible given the size of the tree and is used to measure the integration in the network (Tewarie et al., 2015b). A decreased value in the normalized leaf number indicates a decreased global efficiency. Previous studies have found that leaf number is an important network parameter during development and is sensitive to changes with ageing (Smit et al., 2016), autism (Boersma et al., 2013a) and Parkinson's disease (Olde Dubbelink et al., 2013). Kappa, also called the degree of divergence, is used to measure the broadness of the degree distribution. A decreased value of kappa indicates a decrease in highly connected nodes or “hubs”. Betweenness centrality (BC) of a node is defined as the number of the shortest paths between any two nodes that pass it, divided by the total number of shortest paths in the network. If BC = 0, the node is a leaf node; if BC = 1, the node is a central node in a star-like network. The BC of a node ranges between 0 and 1. We usually use BCmax, which is the BC of the node with the highest BC in the tree, to measure the BC of the tree. A decreased value of BCmax in the tree indicates a decreased global efficiency and a decreased “hub” strength. Hierarchy is an indicator of the balance between efficient communication paths and overload of hub nodes, which is defined as:

2.4. Graph and functional connectivity analysis Graph analysis was performed using Gretna software (Wang et al., 2015) for the extracted BOLD time series data (https://www.nitrc.org/ projects/gretna) and Brain connectivity toolbox (Rubinov et al., 2009) for small-world and minimum spanning tree topology (https://www. nitrc.org/projects/bct/). To measure functional connectivity, the brain was parcellated into 264 functional regions of interest (ROIs) that were previously defined by Power et al., which has been widely used in functional connectivity studies (Power et al., 2011). ROIs were defined as 6-mm radius spheres around these MNI coordinates. We extracted BOLD time series from each of the voxels in each ROI and averaged all voxels in the respective ROI as the signal. The functional connectivity between each pair of ROIs was then computed by means of a Pearson correlation. We used the correlations to construct small-world networks and to compute the network properties in the extracted BOLD time series data. Graph and functional connectivity analysis pipelines are shown in Fig. 4. 2.5. Small world properties To approximate a Gaussian distribution, the Pearson correlation coefficients in the resulting 264 × 264 matrix were transformed by Fisher's r-to-z. This matrix represented the strength of the functional connectivity between all 264 areas in the whole brain and served as an adjacency matrix for graph analysis. The small-world parameters, the clustering coefficient (C) and path length (L), were calculated in terms of Watts and Strogat (Watts and Strogatz, 1998) (Fig. 1). Briefly, the characteristic path length is defined as the average shortest path connecting any two nodes in the graph. The path length is used to measure how well a network is connected, and a small value indicates an average short distance between any two nodes. The cluster coefficient is defined as the number of actual edges connecting the neighbours of a node divided by the maximum number of edges possible between neighbouring nodes. The cluster coefficient of a network is used to measure how many local clusters exist in the network. A high cluster

TH =

L 2mBCmax.

where L is the leaf number; m is the number of vertices −1; and BCmax is the maximum value of betweenness centrality. The value of the hierarchy ranges between 0 and 1. If leaf number = 2, tree is a line-like topology, hierarchy approaches 0. If leaf number = m, tree is a star-like topology, tree hierarchy approaches 0.5. When the numbers are between 2 and m, the tree hierarchy can have higher values (Olde Dubbelink et al., 2013).

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Table 1 Subject characteristics. Group Age a

Full IQ FD

Table 2 Group differences in network parameters. N

TDC ADHD TDC ADHD TDC ADHD

143 102 142 102 143 102

TDC ADHD

143 102

Gender

Handedness a TDC ADHD

142 102

Mean 11.428 12.085 118.000 106.029 0.145 0.182 female/male 59/84 12/90 left/right 1/141 2/100

SD 1.856 2.040 13.151 13.105 0.058 0.091

t-value −2.622

⁎⁎

Functional connectivity

⁎⁎⁎

7.023

SW

Gamma

−3.695⁎⁎⁎

Lambda

χ2 25.16⁎⁎⁎

Global efficiency Local efficiency

χ2 0.77

MST

Leaf Kappa

* p < 0.05, ** p < 0.01, *** p < 0.001. a Data not available for one TD children; sex dummy variable: females = 0; males = 1).

Hierarchy Betweenness centrality

2.7. Statistical analysis

Group

N

Mean

SD

F-value

Cohen's d

TDC ADHD TDC ADHD TDC ADHD TDC ADHD TDC ADHD TDC ADHD TDC ADHD TDC ADHD TDC ADHD

143 102 143 102 143 102 143 102 143 102 143 102 143 102 143 102 143 102

9.204 8.963 1.500 1.487 1.261 1.252 0.195 0.193 0.136 0.132 0.430 0.421 1.706 1.670 1.344 1.304 0.610 0.615

0.871 0.992 0.075 0.075 0.037 0.040 0.012 0.015 0.015 0.017 0.024 0.023 0.098 0.099 0.115 0.103 0.039 0.037

14.307

0.262

5.401

0.174

8.173

0.236

11.117

0.150

13.309

0.253

6.332

0.382

16.869

0.367

5.300

0.364

0.650

−0.131

* p < .05, in bold font: p < .05 FDR corrected. The mean and SD of functional connectivity was divided by 10−2 and hierarchy by 10−3.

Statistical group differences between the ADHD children and typically developing children in age, sex, handedness and IQ were determined using t-tests. To account for these differences, group differences in global mean correlations and MST and small-world properties were evaluated using ANCOVA, with age, sex, FD and IQ as covariates. Moreover, a partial correlation coefficient was computed to assess the relationship between ADHD diagnosis scores and the network parameters in the small-world and minimum spanning tree topology. Statistical analyses were performed using SPSS 21 (IBM, Armonk, New York). Throughout, multiple comparisons were controlled using the false discovery rate (p < 0.05) (Genovese et al., 2002).

Table 3 Pearson correlations between network parameters and disability score.

3. Results 3.1. Group characteristics

Pearson's rho

ADHD

Inattentive

HyperImpulsive

Functional connectivity SW Gamma Lambda Global efficiency Local efficiency MST Leaf Kappa Hierarchy Betweenness centrality

−0.152 −0.156 −0.167 −0.112 −0.156 −0.167 −0.186 −0.177 0.085

−0.150 −0.149 −0.164 −0.112 −0.158 −0.202 −0.205 −0.189 0.071

−0.129 −0.135⁎ −0.142⁎ −0.097 −0.129 −0.097 −0.135⁎ −0.136⁎ 0.092

In bold font: p < 0.05 FDR corrected. ⁎ p < 0.05.

Table 1 summarizes the characteristics of the ADHD and TD children. Compared with the controls, the ADHD group showed a higher mean age (ADHD: mean = 12.085; TD: mean = 11.428, t = −2.622, p = 0.009), a lower mean IQ (ADHD: mean = 106.029; TD: mean = 118.000, t = 7.023, p < 0.001) more males (χ2 = 25.16, p < 0.001) and more head motion (ADHD: mean = 0.182; TD: mean = 0.145, t = −3.695, p < 0.001). No significant difference was observed in handedness between the two study groups, as detailed in Table 1. In the subsequent analyses, age, sex, FD and IQ were used as covariates.

with ADHD diagnosis scores, as detailed in Table 3. In addition, we found significant differences in global efficiency (ADHD: mean = 0.193; TD: mean = 0.195, F (1,239) = 11.117, p = 0.001) and local efficiency (ADHD: mean = 0.132; TD: mean = 0.136, F (1,239) = 13.309, p < 0.001), as detailed in Table 2, but only local efficiency was correlated with ADHD diagnosis scores, as detailed in Table 3 and Fig. 3. 3.4. MST topology

After controlling for age, sex, FD and IQ using ANCOVA (with age, sex, FD and IQ as covariates), a significant group difference was observed for the global mean correlation (ADHD: mean = 9.204 × 10−2; TD: mean = 8.963 × 10−2, F (1,239) = 14.307, p < 0.001), as detailed in Table 2. A significant correlation was found between global mean correlation and ADHD diagnosis scores, as detailed in Table 3 and Fig. 2.

After controlling for age, sex, FD and IQ, using ANCOVA (with age, sex, FD and IQ as covariates), significant group differences were found for MST leaf (ADHD: mean = 0.421; TD: mean = 0.430, F (1,239) = 6.332, p = 0.013), kappa (ADHD: mean = 1.670; TD: mean = 1.706, F (1,239) = 16.869, p < 0.001) and hierarchy (ADHD: mean = 1.304; TD: mean = 1.344, F (1,239) = 5.300, p = 0.022) measures, but not betweenness centrality, as detailed in Table 2. In addition, leaf, kappa and hierarchy measures were significantly associated with ADHD diagnosis scores, as detailed in Table 3 and Fig. 4.

3.3. Small-world topology

4. Discussion

After controlling for age, sex, FD and IQ, using ANCOVA (with age, sex, FD and IQ as covariates), significant group differences were found for both the normalized clustering coefficient (ADHD: mean = 1.487; TD: mean = 1.500, F (1,239) = 5.401, p = 0.021) and normalized path length (ADHD: mean = 1.252; TD: mean = 1.261, F (1,239) = 8.173, p = 0.005), as detailed in Table 2, which also significantly correlated

The present study applied weighted graphs and minimum spanning trees to analyse resting functional MRI data and demonstrated largescale changes in functional brain network organization in children with ADHD. Consistent with previous reports, we found an economical small-world configuration in both the ADHD and TD groups (Wang et al., 2009). Since Watts and Strogatz (1998) quantitatively described

3.2. Functional connectivity

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Fig. 2. Scatter plots for correlation between functional connectivity strength and ADHD diagnosis score (including inattentive, hyperimpulsive and ADHD diagnosis score).

connections in the present study. Finally, but most importantly, they only compared the differences between ADHD and controls, but they did not further ensure that the difference was related to the severity of ADHD. To clarify this problem, we explored the correlations between the different features of the two study groups. However, we found that global efficiency was not related to the ADHD diagnosis score, which suggested that global efficiency may not reflect the ADHD features in the brain networks. We found that both the normalized clustering coefficient and path length were negatively associated with the ADHD diagnosis score, which suggested that the normalized clustering coefficient and path length were effective parameters for capturing the ADHD diagnosis and indicated that a lower clustering coefficient and path length, that is, a shift of the topology towards a random network, were associated with more ADHD diagnosis features. Smit and colleagues have confirmed that connectivity alterations were accompanied by a decrease in the clustering coefficient and that the path length reflected increased network randomness or decreased order (Smit et al., 2012). These alterations may have resulted from the loss of localized information integration and the randomness of the overall connections, and hence, we provided the first evidence for the brain developmental delay in individuals with ADHD from the perspective of global organization of brain functional networks by using resting-state fMRI. In addition, a recent study used a similar approach with the present study, although they only analyzed the frontal-parietal attention network (Wang et al., 2019), they observed similar results with us, that is, the topology of small world showed less integration and more randomness. To avoid methodological biases and further test whether ADHD was a disorder related to developmental delay, we constructed the MST and observed lower leaf, kappa and hierarchy measures in the ADHD children, which indicated a decentralized tendency; that is, a shift from a more star-like topology towards a more line-like organization. To our knowledge, this is the first study that used MST in resting-state fMRI to study ADHD. We used leaf, kappa, hierarchy and betweenness measures as the core analysis index, which have been widely used with other technologies, such as EEG and MEG. Leaf usually means the numbers of nodes with one degree in the MST, which is divided by the total number of nodes to normalize. Previous studies have found that leaf is a measure of global integration in the network and that a decreased value corresponded to decreased global efficiency (Tewarie et al., 2015b). In addition, the leaf measure has been strongly related to the path length in small-world topology (Stam, 2014), which was confirmed by our data. We found that the leaf measures were significantly associated with path length (r = 0.24, p = 1.48 × 10−4) and global efficiency (r = − 0.22, p = 0.001) and that fewer leaves in ADHD were negatively related to the ADHD diagnosis scores, which indicated that ADHD may involve less global integration. Kappa, that is, the degree of divergence, measures the broadness of the degree distribution, and a

the topology of small-world networks(Watts and Strogatz, 1998), human brain functional networks organized with small-world networks have been verified by various imaging techniques, such as EEG, fMRI and MEG (Bullmore and Sporns, 2012; Stam, 2014). In accordance with previous reports, small-world architecture features were observed in the two study groups, which suggests that small-world brain networks are tolerant to developmental aberration (Achard et al., 2006). Although both study groups had economical properties of small-world networks, which have been confirmed by a previous study (Achard and Bullmore, 2007) the topology of the brain networks in the ADHD group differed from the typically developing control group. Many reports have confirmed widely distributed alterations throughout the functional brain networks in ADHD, which provided evidence to support the notion that ADHD is associated with brain dysfunction(Bush et al., 2005; Seidman et al., 2004). We found that both the normalized clustering coefficient and path length were smaller in ADHD children than in typically developing children. The normalized parameters were the observed networks divided by random networks derived from the observed networks, and values closer to 1 indicated a trend towards a random network. That is, the children with ADHD may have a shift towards random networks. Previous studies have confirmed a shift from a more random to a more regular smallworld topological structure during maturation (Boersma et al., 2013b; Liu et al., 2015; Smit et al., 2016). As Shaw and colleagues (Shaw et al., 2007) have reported, ADHD is a developmental disorder associated with developmental delay, based on structural data. We have verified this view regarding the small-world topology derived from functional data. The random trend indicated that both the global and local features in the ADHD children were weaker. This result was not in accord with Wang and colleagues' work (Wang et al., 2009), which found an alteration towards regular networks in individuals with ADHD. To clarify this difference, we also computed the global and local efficiencies, and the results showed a decreased local efficiency and a decreased global efficiency in ADHD, which indicated a disorder-related shift in the topology towards random networks. We think the differences may have resulted from the following five reasons: First, by setting the threshold at cost from 0.05 to 0.5 in the functional connectivity matrix to normalize the differences among individuals, Wang and colleagues found an increased local efficiency in ADHD, but which was only significant at the cost of 0.15. In addition, the small sample size may have also affected the robustness of the result. To solve this problem, we used a large sample size from publicly available data. Second, they used the AAL 90 structural atlas to explore the functional relationship between brain regions, which could not reflect the transfer of information mode. Third, the positive and negative correlations between brain regions may have been confounded as the negative connections had not been clearly elucidated in the analysis. Therefore, we discarded the negative

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Fig. 3. Scatter plots for correlation between small world parameters (clustering coefficient, path length, global efficiency and local efficiency) and ADHD diagnosis score (including inattentive, hyperimpulsive and ADHD diagnosis score).

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Fig. 4. Scatter plots for correlation between minimum spanning tree parameters (leaf numbers, kappa, hierarchy and betweenness centrality) and ADHD diagnosis score(including inattentive, hyperimpulsive and ADHD diagnosis score).

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Author contributions

decreased value corresponds to a decrease in highly connected nodes or “hubs”. Lower kappa in ADHD suggested that ADHD may be associated with some “hub” brain region impairments, which were also significantly associated with the ADHD diagnosis scores. In addition, decreased kappa would reduce the resilience of the brain network against attack and spread of information across the tree (ease of synchronization). The tree hierarchy is a measure, which ranges from 0 to 1, of the balance between hub-overload and weak integration, and an optimal tree configuration corresponds to a value of approximately 0.5 (intermediate between a line-like and star-like topology). In our two study groups, the value of the hierarchy was close to zero, which indicated that the configuration in the two groups was a line-like topology. The smaller hierarchy in ADHD showed a disorder-related alteration towards a more line-like topology. The hierarchy measures showed a negative correlation with the ADHD diagnosis scores, which suggested that higher ADHD features indicated a tendency towards more line-like topology that may result in the disorder. All of the abnormalities in leaf, kappa and hierarchy in the ADHD children revealed a shift towards a more decentralized topology and a less integrated organization(Stam, 2014). In conventional graph analysis, this type of topology has been associated with a more random network (Tewarie et al., 2015a). Using MST analysis, a study based on a large sample (n = 1500) of individuals aged 5 to 71 years confirmed the pattern of increased integration and decreased randomness from childhood into early adulthood (Smit et al., 2016). Together with these findings, our results reconfirmed that ADHD was a disorder related to developmental delay. Above all, the MST could also depict the pattern of ADHD like small world. Based on the advantages of MST, we thought that MST is a more convenient and reliable method to depict the topological attributes of resting state fMRI networks, especially in ADHD. Despite the limitations of resting functional MRI analysis, our approach has several advantages over other techniques. In particular, compared with EEG, functional MRI has comparable temporal and a higher spatial resolution, which is not affected by field spread and volume conduction. In addition, the MST analysis avoids methodological biases and is suitable for the comparison of brain networks, which overcomes the use of arbitrary thresholds and normalization steps and can provide similar information about network topology as conventional graph measures. However, several limitations should be further addressed. First, our participants from the public data were not matched in age and IQ, although we controlled for these variables as covariates. Future studies should further explore the differences in the networks using matched participants. Second, previous studies have found that children with ADHD show sex differences in the brain structural characteristics(Wang et al., 2018); however, girls made up 29% of our participants. We used sex only as a covariate, and future studies could match participants by sex, further clarifying the sex differences in functional connectivity. Last, we thought and confirmed ADHD is a disorder of neurodevelopmental delay. However, the best approach to test this would be to conduct a longitudinal study, e.g. investigating functional connectivity in young kids and following them up into early adulthood.

Yanpei Wang analyzed the data and wrote the draft of the paper. Chenyi Zuo and Qinfang Xu amend and proofread the draft of the paper. Qinfang Xu, Daoyang Wang, Shuirong Liao and Maihefulaiti Kanji participated in the discussion and offered some good ideas. All authors reviewed the manuscript. Ethical statement The present study was performed using publicly available data from the ADHD-200 Consortium (http://fcon_1000.projects.nitrc.org/indi/ adhd200/). Ethics Committee approval was obtained from the Institutional Ethics Committee of Beijing University. Declaration of Competing Interest The authors declare no competing financial or non-financial interests. Acknowledgements This research was supported by the National natural science foundation of China (No. 31662083). This research was supported by the provincial Natural science foundation for universities of Jiangsu, China (No. 16KJB180018). The authors acknowledge the contribution of ADHD-200 consortium organizers for sharing the raw data. References Achard, S., Bullmore, E., 2007. Efficiency and cost of economical brain functional networks. PLoS Comput. Biol. 3, e17. Achard, S., Salvador, R., Whitcher, B., Suckling, J., Bullmore, E.T., 2006. A resilient, lowfrequency, small-world human brain functional network with highly connected association cortical hubs. J. Neurosci. 26, 63–72. Ahmadlou, M., Rostami, R., Sadeghi, V., 2012. Which attention-deficit/hyperactivity disorder children will be improved through neurofeedback therapy? a graph theoretical approach to neocortex neuronal network of ADHD. Neurosci. Lett. 516, 156–160. Association AP, 2013. Diagnostic and statistical manual of mental disorders. BMC Med. 17, 133–137. Boersma, M., Kemner, C., De Reus, M.A., Collin, G., Snijders, T.M., Hofman, D., et al., 2013a. Disrupted functional brain networks in autistic toddlers. Brain Connect. 3, 41–49. Boersma, M., Smit, D.J., Boomsma, D.I., De Geus, E.J., Delemarre-van de Waal, H.A., Stam, C.J., 2013b. Growing trees in child brains: graph theoretical analysis of electroencephalography-derived minimum spanning tree in 5- and 7-year-old children reflects brain maturation. Brain Connect. 3, 50–60. Bullmore, E., Sporns, O., 2012. The economy of brain network organization. Nat. Rev. Neurosci. 13, 336–349. Bush, G., Valera, E.M., Seidman, L.J., 2005. Functional neuroimaging of attention-deficit/ hyperactivity disorder: a review and suggested future directions. Biol. Psychiatry 57, 1273–1284. Cao, M., Wang, J.H., Dai, Z.J., Cao, X.Y., Jiang, L.L., Fan, F.M., et al., 2014. Topological organization of the human brain functional connectome across the lifespan. Dev. Cogn Neurosci. 7, 76–93. Chen, M., Deem, M.W., 2015. Development of modularity in the neural activity of children’s brains. Phys. Biol. 12, 16009. Chen, Z., Liu, M., Gross, D.W., Beaulieu, C., 2013. Graph theoretical analysis of developmental patterns of the white matter network. Front. Hum. Neurosci. 7, 716. Çiftçi, K., 2011. Minimum spanning tree reflects the alterations of the default mode network during Alzheimer’s disease. Ann. Biomed. Eng. 39, 1493–1504. Faraone, S.V., Sergeant, J., Gillberg, C., Biederman, J., 2003. The worldwide prevalence of ADHD: is it an American condition? World Psychiatry 2, 104. Fornito, A., Yoon, J., Zalesky, A., Bullmore, E.T., Carter, C.S., 2011. General and specific functional connectivity disturbances in first-episode schizophrenia during cognitive control performance. Biol. Psychiatry 70, 64–72. Genovese, C.R., Lazar, N.A., Nichols, T., 2002. Thresholding of statistical maps in functional neuroimaging using the false discovery rate. Neuroimage 15 (4), 870–878. Humphries, M.D., Gurney, K., Prescott, T.J., 2005. The brainstem reticular formation is a small-world, not scale-free, network. P Roy Soc B-Biol Sci. 273, 503–511. Kruskal, J.B., 1956. On the shortest spanning subtree of a graph and the traveling salesman problem. P Am Math. Soc. 7, 48–50. Langer, N., Pedroni, A., Jancke, L., 2013. The problem of thresholding in small-world network analysis. PLoS One 8, e53199.

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