Altered small‐world brain functional networks in children with attention‐deficit/hyperactivity disorder

INTRODUCTION

Attention‐deficit/hyperactivity disorder (ADHD), as one of the most commonly diagnosed childhood neurobehavioral disorders, is characterized by developmentally inappropriate symptoms of excessive inattention, impulsivity, and hyperactivity [American Psychiatric Association, 1994). Arising in childhood and persisting into adolescence and adulthood [Faraone et al., 2003], ADHD affects ˜3–5% of school‐age children [Spencer et al., 1998]. Children with ADHD have difficulties controlling their behaviors or focusing their attentions which result in an adverse effect on academic performance and social function.

Structural and functional neuroimaging studies have shown that the pathophysiology of ADHD is associated with regional abnormalities involving frontal, parietal, temporal, occipital, and subcortical regions [Bush et al., 2005; Seidman et al., 2004, 2005]. The involved regions have been identified as the components of various functional networks, such as fronto‐striatal [Castellanos et al., 2006], fronto‐parietal [Dickstein et al., 2006], and fronto‐temporal‐parietal circuits [Smith et al., 2006]. The regional abnormality may be associated with the dysfunction of the corresponding networks [Bush et al., 2005; Seidman et al., 2004]. Moreover, recent neuroimaging studies have found that ADHD patients showed anatomical [Ashtari et al., 2005; Hill et al., 2003; Hynd et al., 1991; Semrud‐Clikeman et al., 1994] and functional [Castellanos et al., in press; Murias et al., 2007; Tian et al., 2006] connectivity abnormalities involving frontal and subcortical regions. Although there are extensive researches on ADHD‐related abnormalities in widespread regions and the connectivity, very few studies have yet investigated the topological organization of functional networks in the whole brain in ADHD.

Recent advances in graph theoretical approaches have allowed us to characterize topological properties of complex networks. Using these approaches, Watts and Strogatz [1998] have shown that graphs with densely local connections and few long connections can be characterized as small‐world networks. Such a topology has been demonstrated in many complex networks, including social, economical, and biological networks [for a review, see Boccaletti et al., 2006]. Moreover, several recent studies have demonstrated the small‐world topology in large‐scale structural [Hagmann et al., 2007; He et al., 2007; Hilgetag et al., 2000; Sporns and Zwi, 2004] and functional [Achard et al., 2006; Bassett et al., 2006; Ferri et al., 2007; Micheloyannis et al., 2006a; Salvador et al., 2005a; Stam, 2004; Stephan et al., 2000] brain networks in humans and nonhuman primates. There is also increasing evidence that the small‐world properties of brain networks are affected by normal aging [Achard and Bullmore, 2007] and brain diseases, such as schizophrenia [Micheloyannis et al., 2006b], Alzheimer's disease [Stam et al., 2007], epilepsy [Ponten et al., 2007], spinal cord injury [De Vico Fallani et al., 2007], and brain tumor [Bartolomei et al., 2006]. Small‐world is an attractive model for the description of complex brain networks, since it provides a quantitative insight into relevant network parameters governing fundamental organization of the brain. In the current study, we hypothesize that the small‐world properties of brain functional networks would be altered in children with ADHD.

To test this hypothesis, we used functional magnetic resonance imaging (fMRI) to construct brain functional networks of both ADHD children and normal controls during the resting state. The spontaneous low‐frequency fluctuation (LFF) measured by resting‐state fMRI is highly synchronous between different brain regions and is physiologically meaningful [Achard and Bullmore, 2007; Achard et al., 2006; Biswal et al., 1995; Fox et al., 2005; Greicius et al., 2003; Jiang et al., 2004; Kiviniemi et al., 2000, 2004; Seeley et al., 2007]. Moreover, recent studies have suggested that the LFF can be employed to characterize the pathophysiological changes of brain disorders [Anand et al., 2005; Cao et al., 2006; Tian et al., 2006; Wang et al., 2006; Greicius et al., 2007; Zang et al., 2007]. In this study, we measured functional connectivity [Friston et al., 1993] by calculating correlations between the time series of any pair of the 90 cortical and subcortical regions of the whole brain during the resting state and then obtained a set of interregional correlation matrices. The resulting correlation matrices were further thresholded into undirected graphs to construct brain functional networks. Finally, the topological properties of the networks were characterized by graph theoretical approaches, and the differences between two groups were further statistically evaluated.

MATERIALS AND METHODS

Functional Connectivity Matrix and Graph Construction

To measure the functional connectivity among regions, the brain was first parcellated into 90 anatomical regions of interest (45 in. each hemisphere, see Table I) using the anatomical automatic labeling (AAL) template [Tzourio‐Mazoyer et al., 2002]. The mean time series of each region was then obtained by averaging the time series of all voxels in the region. Several sources of variance of BOLD signal were further removed from the mean time series using a multiple linear regression model. The regressors consisted of the estimated profiles of head motion (three for translation and three for rotation) and the global brain activity [Fox et al., 2005]. The residuals of this regression were then used to substitute for the raw mean time series of the corresponding regions. Pearson's correlation coefficients between the residual time series of each possible pair of the 90 regions were further computed to produce a symmetric correlation matrix (i.e., functional connectivity matrix) for each subject.

Table I.

Regions of interest in an entire human brain functional network

Region	Abbrevation	Region	Abbrevation
Precentral gyrus	PreCG	Lingual gyrus	LING
Superior frontal gyrus (dorsal)	SFGdor	Superior occipital gyrus	SOG
Orbitofrontal cortex (superior)	ORBsup	Middle occipital gyrus	MOG
Middle frontal gyrus	MFG	Inferior occipital gyrus	IOG
Orbitofrontal cortex (middle)	ORBmid	Fusiform gyrus	FFG
Inferior frontal gyrus (opercular)	IFGoperc	Postcentral gyrus	PoCG
Inferior frontal gyrus (triangular)	IFGtriang	Superior parietal gyrus	SPG
Orbitofrontal cortex (inferior)	ORBinf	Inferior parietal lobule	IPL
Rolandic operculum	ROL	Supramarginal gyrus	SMG
Supplementary motor area	SMA	Angular gyrus	ANG
Olfactory	OLF	Precuneus	PCUN
Superior frontal gyrus (medial)	SFGmed	Paracentral lobule	PCL
Orbitofrontal cortex (medial)	ORBmed	Caudate	CAU
Rectus gyrus	REC	Putamen	PUT
Insula	INS	Pallidum	PAL
Anterior cingulate gyrus	ACG	Thalamus	THA
Middler cingulate gyrus	MCG	Heschl gyrus	HES
Posterior cingulate gyrus	PCG	Superior temporal gyrus	STG
Hippocampus	HIP	Temporal pole (superior)	TPOsup
Parahippocampal gyrus	PHG	Middle temporal gyrus	MTG
Amygdala	AMYG	Temporal pole (middle)	TPOmid
Calcarine cortex	CAL	Inferior temporal gyrus	ITG
Cuneus	CUN

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The regions are described by Tzourio‐Mazoyer et al. (2002), and the abbreviations are provided according to Salvador et al. (2005a) and Achard et al. (2006).

To investigate the properties of brain functional networks, each correlation matrix was thresholded into a binary graph (i.e., network), where nodes represent brain regions and edges represent undirected connections. In this study, network cost was adopted as a threshold measurement since it concisely couples with network efficiency (see the following section for the definition of efficiency measures), thus providing a biologically meaningful description of the performance of a network [Achard and Bullmore, 2007; De Vico Fallani et al., 2007; Latora and Marchiori, 2001]. C _G, the cost of a graph G, is defined in (1)

(1)

where N and K are the total number of nodes and edges in the graph G, respectively. N(N − 1)/2 is the number of all the possible edges in the G. C _G measures how expensive it is to build a network. It needs to note that the selection of different cost thresholds may lead to graphs with distinct topologies: high thresholds yield sparser graphs and low thresholds yield denser ones. However, since there is no definitive way currently to select a precise threshold in complex brain networks studies [Achard and Bullmore, 2007; Bassett et al., 2006; He et al., 2007], in the present study, we thus investigated the properties of the networks over a wide range of threshold values. This can allow us to explore the differences in network properties between two groups at each threshold level. Here, the range of cost threshold was set from 0.05 to 0.5 to make (1) the small‐world attributes estimable [i.e., the mean degree k of the graph is greater than the log of the number of nodes (N = 90); Watts and Strogatz, 1998. Note that k is the average of the degree over all nodes, where the degree of a node represents the number of connections to that node], and (2) the resulting matrices have sparse properties. Such a criteria of threshold selection has been utilized in several recent studies [Achard and Bullmore, 2007; Achard et al., 2006; He et al., 2007].

Efficiency of Small‐World Networks

For a given binary graph G with a wiring cost C _G, we can evaluate its small‐world attributes. Originally, Watts and Strogatz [1998] proposed clustering coefficient (C _p) and shortest path length (L _p) to quantify small‐world properties of a network. Recent studies have indicated that, in small‐world analysis, efficiency measure has a number of technical and conceptual advantages over conventional C _p and L _p measures, since it provides a single measure to analyze both the local and the global behavior of a network and can also deal with either the disconnected or nonsparse graphs or both [Latora and Marchiori, 2001]. Recently, Achard and Bullmore [2007] applied the efficiency metric for the first time to investigate human brain functional networks. They found that human brain functional networks exhibited economical small‐world properties and that the economical performance of these networks was affected by normal aging and a dopamine receptor antagonist. Using the efficiency measures, in this study, we investigated brain functional networks in the ADHD and control boys. Briefly, the efficiency of a graph G in (2) is defined as the inverse of the harmonic mean of the minimum path length, L_i,j (i.e., the shortest length of the path from node i to node j) [Latora and Marchiori, 2001].

(2)

According to the definition, L_i,j would be infinite if there is no path between node i and node j, thus contributing nothing to the sum. When the graph G represents a whole network, E(G) measures the global efficiency, E _glob(G), of the network that quantifies the efficiency of information propagation over it. When considering a subgraph of the whole graph G, such as G_i, which is composed of the nearest neighbors of node i, E(G_i) indicates the efficiency of the subgraph G_i, measuring how efficient the information is exchanged in the subgraph. Thus, the local efficiency, E _loc(G), of the whole network is defined in (3) as the average of the efficiency E(G_i) over all subgraphs included in the network [Latora and Marchiori, 2001].

(3)

Besides the two global metrics, E _glob(G) and E _loc(G), in this study, we also investigated regional nodal efficiency in (4), E _nodal(G,i), defined as the inverse of the harmonic mean of the minimum length of path between node i and all other nodes in a graph [Achard and Bullmore, 2007]. E _nodal(G,i) measures the communication efficiency between a node i and all the other nodes in the network G.

(4)

Statistical evaluation of small‐world properties requires comparable regular and random networks [Watts and Strogatz, 1998]. In this study, we generated populations of regular networks (n = 100) and random graphs (n = 100) that preserved the same number of nodes and edges, respectively. The efficiency of G was compared with that of random graphs, G _rand, and regular graphs, G _reg. The graph G would be considered a small‐world if it met the following conditions [Achard and Bullmore, 2007]:

(5)

In the present study, we also measured the cost efficiency as the difference between global efficiency and cost, i.e., E _glob(G) − C _G, which would be positive in the case of an economical network [Achard and Bullmore, 2007].

RESULTS

DISCUSSION

This is the first study, to our knowledge, to investigate small‐world properties of brain functional networks in children with and without ADHD. We found that brain functional networks exhibited economical small‐world topology in both groups. An altered functional network, however, was found in the brain of ADHD. In particular, a tendency of shift toward regular networks was demonstrated in ADHD when compared with normal controls. Moreover, our study revealed that nodal efficiency was profoundly affected at several regions of prefrontal, temporal, and occipital cortices, which were compatible with previous studies in ADHD. Our results suggested that the widely distributed functional brain networks are altered in ADHD, thus providing further evidence for brain dysfunction associated with this disease [Bush et al., 2005; Seidman et al., 2004].

Since small‐world networks were quantitatively described by Watts and Strogatz [1998], human brain functional networks with a small‐world configuration have been validated by using various imaging techniques, such as MEG, EEG, and fMRI [for reviews, see Bassett and Bullmore, 2006; Stam and Reijneveld, 2007]. In agreement with these previous findings, in the present study, we also observed the features of small‐world architecture in the functional brain networks in children both with and without ADHD using the resting‐state fMRI (see Fig. 1), thus providing further support for the opinion that small‐world brain networks have the ability to display tolerance in the face of developmental aberration or disease [Achard et al., 2006]. Moreover, the functional networks with small‐world features were also found to show economical properties (see Fig. 2), consistent with previous studies [Achard and Bullmore, 2007]. Together, these findings supported the standpoint that brain networks might have been evolved to maximize cost efficiency of parallel information processing, i.e., high efficiency of parallel information transfer at low cost [Kaiser and Hilgetag, 2006; Sporns et al., 2004].

Although both of ADHD and control groups had economical small‐world properties as elucidated earlier, the topology of the ADHD group was altered compared to the control group. A tendency of decreased global efficiency of the brain networks was found in ADHD over the whole cost range. It has been suggested that the global efficiency is affected by the loss of long‐range connections [Latora and Marchiori, 2001]. Structural and diffusion imaging studies found that the regions showing the ADHD‐related abnormality are associated with long fibers in ADHD children, such as the corpus callosum (connecting the left and right cerebral hemispheres) [Hill et al., 2003; Hynd et al., 1991; Semrud‐Clikeman et al., 1994] and the anterior limb of internal capsule (containing thalamocortical fibers and corticopontine fibers) [Ashtari et al., 2005]. The abnormalities may incur the disruption to the long‐range communication among parts of the brain. A recent research has also indicated abnormal long‐range connections (dorsal anterior cingulate and medial parietal lobe) in ADHD [Castellanos et al., in press]. All these abnormalities may contribute to the decreasing tendency of global efficiency of brain network in ADHD. In the current study, significantly increased local efficiency of the brain networks was also found in ADHD children compared to the controls. The underlying mechanisms of increased local efficiency of a network have been widely discussed in various studies. For example, De Vico Fallani et al. [2007] reported that increased local efficiency in spinal cord injured patients could be attributable to a functional reorganization (i.e. brain plasticity). Latora and Marchiori [2001] indicated that the higher the local efficiency of a network, the larger fault tolerance was the network at the face of external attack. We thus suspected that the higher value of local efficiency in ADHD observed here might suggest a kind of defense mechanism responsible for suppressing the disorder affection.

Although both the ADHD children and controls showed small‐world attributes in their brain functional networks, the increased local efficiency combined with slightly decreased global efficiency made their networks topology exhibit the tendency of a shift toward regular networks (see Fig. 1). It has been suggested that the small‐world structure reflects an optimal balance between local processing and global integration [Sporns and Tononi, 2002]. Therefore, any abnormal shift caused by brain diseases toward either random [Bartolomei et al., 2006; Micheloyannis et al., 2006b; Ponten et al., 2007] or regular [De Vico Fallani et al., 2007] networks may reflect a less optimal network organization. Though the biological causes of underlying the shift remain still unclear, the regular configurations in complex networks have been found to demonstrate low global coordination and slow information flow compared to small‐world arrangements [Barahona and Pecora, 2002; Lago‐Fernandez et al., 2000; Nishikawa et al., 2003; Strogatz, 2001]. Hence, our results suggested that the ADHD‐related network shift may reflect the abnormalities of network architecture.

As described by Achard and Bullmore [2007], the nodal efficiency measures the extent to which the node connects all other nodes of a network, which may indicate the importance of the nodal area in the whole brain network. Using this measure, we here found abnormal nodal efficiency in several regions, involving the prefrontal, temporal, occipital, and subcortical regions (Table II) that were, in general, concerned in ADHD studies. The orbital frontal cortex (OFC) is associated with executive function network [Makris et al., 2007]. The decreased nodal efficiency in the OFC was in accordance with several structural and functional imaging studies that have found cortical atrophy and reduced activity in this region in the ADHD patients [Lee et al., 2005; Makris et al., 2007], which might suggest the abnormalities of executive function in the patients. In addition, several regions belonging to temporal and occipital cortices were also found to have significant decreases in nodal efficiency (Table II), which were compatible with previous studies showing ADHD‐related structural and functional abnormalities in these regions [Castellanos et al., 2002; Durston et al., 2004; Schulz et al., 2004]. In contrast, the inferior frontal gyrus (IFG) exhibited significantly increased nodal efficiency. The IFG was critical for response inhibition [Aron et al., 2003], dysfunction of which has been considered as the core deficit in ADHD [Barkley, 1997; Schulz et al., 2004; Vaidya et al., 1998]. The greater nodal efficiency may thus reflect greater inhibitory effort in the ADHD children. Together, our findings of ADHD‐related changes in the nodal efficiency reported here suggest that the nodal roles in brain functional networks are profoundly affected by this disorder.

In addition to the efficiency measures aforementioned, in this study, we also investigated the degree distribution of brain functional networks of both the ADHD and controls groups. Our results demonstrated that the brain networks of both groups followed a truncated power‐law form (P(k) ∼ k ^a−1 e ${}^{\mathit{\text{k}}\text{/}\mathit{\text{k}}{}_{\text{c}}}$, where a is an estimated exponent and k _c is a cutoff degree) as opposed to scale‐free regime (see Fig. 6), consistent with previous studies [Achard et al., 2006; He et al., 2007]. Further statistical analysis indicated that there were no significant difference in the fitted parameters [a: t(37) = 0.412, P = 0.683; k _c: t(37) = −0.141, P = 0.889] between the two groups, implying that the degree distribution property of brain functional networks was not altered by this disorder. The truncated power‐law distribution shown here suggests that the human brain network includes some core regions but prevents the appearance of the huge hubs with many connections. Such a network structure has been demonstrated to be more resilient to targeted attacks, but equally resilient to random errors as compared to a scale‐free network [Achard et al., 2006; Albert et al., 2000]. Although physical constraints may account for the form of this degree distribution, it remains still unclear about the biological causes underlying this network topology and would be meaningful to further clarify the issue in future studies.

In the present study, although IQ scores between two groups was significantly different, no significant correlations were found between IQ and the global, local, and nodal efficiency within each group, except the left lingual gyrus in the ADHD group. The result indicated that our finding of altered network efficiency in ADHD might not be accounted for by the IQ scores. However, using an EEG technique, Micheloyannis et al. [2006a] reported that the IQ was correlated with the topological parameters of brain networks during working memory tasks. Nonetheless, they did not find significant correlations during the no‐task or rest condition, consistent with the current study. These results suggest that the topology of brain networks during the rest state is greatly distinct from that during the task state. Future studies might be helpful to further clarify the relation between IQ and network topology.

Several issues need to be further addressed. First, in order to construct functional brain networks, the present study used a prior template (AAL) to parcellate the whole brain into 90 regions. Although such a template has been applied to several recent studies [Achard and Bullmore, 2007; Achard et al., 2006; Salvador et al., 2005a, 2005b], different parcellation schemes may affect our results. In future studies, other available templates [He et al., 2007; Toga et al., 2006] could be adopted to explore the effect of the templates on the networks architectures. Second, a wide range of cost thresholds were employed to investigate network efficiency, and results without correction were reported in this work. As discussed in the method section, different thresholds may lead to graphs with distinct topologies, but no definitive approach is available to determine a single precise threshold so far. Thus, the use of the wide range of thresholds is reasonable for this preliminary study. Moreover, while uncorrected results were reported here, the present study provided a meaningfully specific cost range (0.1–0.15) that could be employed in future to reduce the problem of multiple comparisons. In addition, the use of a large number of samples would be also important to increase the statistical power. Third, in this study, the brain functional networks were constructed based on the thresholded correlation matrices. It is also possible to construct the brain networks with continuous weighting that provides more detailed connectivity information between network nodes compared with the binary graphs [Achard and Bullmore, 2007; Barrat et al., 2004; Jiang et al., 2004; Latora and Marchiori, 2001]. However, the weighted models could lead to the complications of statistical features descriptions in graph theoretical analysis, thus the initial study confined itself to a simple binary connectivity analysis. In future studies, it would be interesting to apply efficiency and cost measurements to the weighted networks and further investigate their topological properties in ADHD. Fourth, in this work we used resting‐state fMRI to investigate brain functional networks. Previous work has suggested that spontaneous LFFs measured by BOLD fMRI probably reflect underlying anatomical connectivity of the cortex [Achard et al., 2006; Salvador et al., 2005a]. For example, in macaque cortex, Honey et al. [2007] have demonstrated that spontaneous neuronal dynamics at multiple temporal scales can be related to underlying anatomical connectivity. In human cortex, He et al. [2007] have also demonstrated that the structural brain networks constructed from cortical thickness data exhibit topological and anatomical similarity with the low‐frequency brain functional networks. Therefore, we suspected that the ADHD‐associated changes in topological organization found in this study may reflect the abnormality in structural brain networks in patients, which needs to be further studied in future. Finally, our results could be potentially influenced by the preprocessing approaches used in this study. To date, however, no systematic study is conducted to evaluate the effects of the preprocessing approaches on graphic properties. Nevertheless, there were evidences for the effect of frequency band on the graphs. For example, Salvador et al. [2005b, 2008] demonstrated that resting‐state functional connectivity between regions was related to specific frequency intervals: low‐frequency components associated with long‐distance connections and high‐frequency with short‐distance connections. Achard et al. [2006] also reported that brain functional networks exhibited small‐world properties at multiple time scales, but most salient in the low‐frequency interval (0.03–0.06 Hz). In the current study, we also investigated topological parameters of brain functional networks constructed by time series of other frequency band (lower than 0.0083 Hz or higher than 0.15 Hz) and found that there were no significant differences in E _glob, E _loc and E _nodal between the two groups. In future studies, it would be important to systematically analyze the effects of different preprocessing procedures on the topological properties of brain networks.

In summary, this is the first study to reveal the topological properties of brain functional networks in children with ADHD using the resting‐state fMRI. Our results provided further support for the presence of small‐world features in complex brain networks, and more importantly, we found that the disorder had a deleterious effect on the topological organization of brain functional networks. These findings were compatible with previous ADHD studies from structural and functional imaging, thus enhancing our understanding of the underlying pathophysiology of ADHD and discriminating the neuropathological state of mental disorders.