Faculty of Social and Behavioural Sciences
Graduate School of Childhood Development and Education
Comparing the functional brain network between children with
attention-deficit hyperactivity disorder and typically developing children
Research Master of Child Development and Education Thesis 2
Student Anna Ridderinkhof Supervisors B. Zijlstra and T. Janssen Date 22 July 2014
Abstract
A new approach to study the brain network is based on graph theory. Thereby, a
small-world network is described as the most efficient network. First, it is investigated whether
the functional brain network of children with attention-deficit hyperactivity disorder
(ADHD) and of typically developing children shows characteristics of a small-world
network. Second, the functional brain network is compared between children with ADHD
and typically developing children. EEG-data during resting state with eyes closed is
analyzed. The findings indicate that the functional brain network of all investigated
frequency bands shows characteristics of a small-world network for children with ADHD
and for typically developing children. The main differences found in the topological
organization are a higher local connectivity in the theta frequency band for children with
ADHD compared to typically developing children, and a higher local connectivity in the
alpha frequency band for girls with ADHD compared to typically developing girls. No
differences were found in the delta and beta frequency band. The results imply that the
topological organization of the functional brain network is altered in children with
ADHD compared to typically developing children and that the effect of gender is
important to incorporate when investigating the functional brain network.
Introduction
Attention-deficit hyperactivity disorder (ADHD) includes symptoms of
inattention, impulsivity, and hyperactivity (American Psychiatric Association, 2000). The
worldwide prevalence of ADHD in children aged 18 and younger is 5.29% (Polanczyk,
de Lima, Horta, Biederman, & Rohde, 2007). Children with ADHD may develop
secondary problems in education and in social relationships, for example poor school
performance, troubles in making and maintaining peer relationships, and conflictual
relationships with parents due to difficulties in conforming to parental expectations (Carr,
1999).
Several models about the underlying neurobiology of ADHD have been
suggested. Barkley (1997) described an influential theoretical model whereby impaired
behavioral inhibition was hypothesized as the core deficit of ADHD. This may lead to
disruptions in the executive functions that depend on inhibition for an effective
execution. However, this model does not take into account the heterogeneity among
children with ADHD (Nigg, Willcutt, Doyle, & Sonuga-Barke, 2005). Castellanos,
Sonuga-Barke, Milham, and Tannock (2006) proposed a model, which suggests that
inattention symptoms are associated with deficits in ‘cool’ executive functions and that
hyperactivity and impulsivity symptoms are associated with deficits in ‘hot’ executive
functions. ‘Cool’ executive functions are defined as solving abstract and decontextualized
problems and associated with the dorsolateral prefrontal cortex (DLPFC). ‘Hot’ executive
functions are defined as solving problems characterized by high affective involvement
and associated with the orbital and medial prefrontal cortex (OMPFC). OMPFC pathways
forms the link between motivation and emotion on the one hand and cognition and motor
processes on the other hand. The model of Castellanos and colleagues (2006) indicates
that widespread brain networks might be affected in children with ADHD. In addition,
abnormalities are found in brain regions of the fronto-striatal circuitry consisting of the
dorsolateral prefrontal cortex (DLPFC), ventrolateral prefrontal cortex (VLPFC), dorsal
anterior cingulate cortex (dACC), and striatum (Bush, Valera, & Seidman, 2005). These
regions function within a network. Therefore, connectivity between these regions might
be affected as well (Bush et al., 2005).
Investigation of functional and anatomical brain connectivity in ADHD based on
functional magnetic resonance imaging (fMRI) and diffusion tensor imaging (DTI)
indeed revealed abnormalities in brain networks. Reduced anatomical connectivity is
found in various brain areas. This may affect long-range integrated information
processing in ADHD, since connectivity areas in the brain that are found to have reduced
anatomical connectivity also show altered functional connectivity. This is, for example,
found in the anterior limb of the internal capsule and the corpus callosum (Konrad &
Eickhoff, 2010). Differences are also found within the default mode network (DMN).
The DMN is identified using fMRI techniques and includes the precuneus, posterior
cingulate cortex (PCC), medial prefrontal cortex (MPFC), and ventral anterior cingulate
cortex (vACC). The DMN is mainly activated during resting state and is attenuated
during attention demanding tasks (Fransson, 2005). Empirical evidence remains
inconclusive and suggests that the DMN may either be hypo- or hyperconnected in
ADHD (Konrad & Eickhoff, 2010). For example, Castellanos and colleagues (2008)
precuneus and posterior cingulate cortex, and between the precuneus and the medial
prefrontal cortex and posterior cingulate cortex using resting state fMRI in adults with
ADHD compared to a matched control group. However, Tian and colleagues (2006)
found increased functional connectivity using resting state fMRI between the dorsal
anterior cingulate cortex (dACC) and various brain areas in children with ADHD
compared to a control group. Enhanced activity during resting state fMRI in basic
sensory and sensory-related cortices was also found (Tian et al., 2008).
Although reduced connectivity in various brain areas and abnormalities in the
DMN are found in ADHD (Castellanos et al., 2008; Konrad & Eickhoff, 2010; Tian et
al., 2008), the topological organization of networks in the whole brain is scarcely
investigated. A useful approach to study the topological organization of whole brain
networks came from advances in modern graph theory (Stam & Reijneveld, 2007). In
graph theory a graph is an abstract representation of a network that consists of nodes and
connections between them, called edges. The connectivity in a graph can be expressed in
the clustering coefficient C and in the path length L. The clustering coefficient is the
likelihood that neighbors of a node are also connected with each other. The path length of
a graph is the average of the shortest paths of connections between all pairs of nodes. A
network wherein all neighbors of a node are also connected with each other is called a
regular network. A regular network is characterized by high clustering and thereby a high
local connectivity, but a high path length and thereby low global connectivity. A network
wherein all nodes are connected randomly with each other is called a random network. A
random network is characterized by a low path length and thereby a high global
graph theory the most optimal complex network is characterized by high local and high
global connectivity with the combination of a high clustering, like a regular network, and
a low path length, like a random network. This most optimal network is called a
small-world network (Watts & Strogatz, 1998). A small-small-world network can be described as a
regular network with a few randomly wired edges, whereby the characteristics of a high
clustering and a low path length are present. Figure 1 shows the transition of a graph
from a regular to a random network, with a small-world network in between. Many
complex networks of various types are found to have the characteristics of a small-world
network. For example the social network of film actors connected by acting in the same
movie and the neural network of the worm C. elegans (Watts & Strogatz, 1998).
Figure 1. Transition of a graph from a regular network to a random network by
increasing the probability of randomly rewired edges to another node in the network. For
intermediate values of p, the graph shows the characteristics of a small-world network: a
high clustering and a short path length. Reprinted from Watts and Strogatz (1998).
Theoretical arguments for investigating the small-world network properties of the
connectivity in the brain are 1) The brain is a complex network and small-world
properties are found in many complex networks. 2) In the brain information is processed
both in specialized regions and in large-scale distributed systems for integration. This is
analogous to high clustering and short path lengths, respectively. 3) Small-world
networks are associated with high global efficiency as well as with high local efficiency.
It is likely that the brain evolved to maximize efficiency of information processing
(Bassett & Bullmore, 2006). Previous studies investigating the brain functional
connectivity in humans using electroencephalography (EEG), magnetoencephalography
(MEG), or fMRI have indeed found characteristics of a small-world network in the brain
(for review, see Bassett & Bullmore, 2006 and Stam & Reijneveld, 2007). By analyzing
the topological organization of networks in the whole brain using EEG, MEG, or fMRI
data it is assumed that functional connectivity between brain regions is reflected by
statistical interdependencies between time series of neuronal activity or related metabolic
measures recorded from different brain areas (Stam & Reijneveld, 2007). The topological
structure of the functional connectivity between brain regions over the whole brain is
modeled as a complex network with the use of graph theory. This is called the functional
brain network.
Since a small-world network is the most optimal organization of a complex
network, divergences from a small-world brain network may be related to ADHD.
Discrepancies from an optimal small-world network have been demonstrated in the
functional brain networks of neurological and psychiatric patients. For example in
beta band MEG was found and the functional brain network was found to display a more
random large-scale structure in the lower alpha band MEG compared to non-demented
control subjects (Stam et al., 2009). In children with autism an increased path length in
broad band EEG and reduced clustering in theta-alpha band EEG was found, compared to
a control group of children (Boersma et al., 2013).
A few studies investigated small-world network characteristics of functional brain
networks in children with ADHD. Wang and colleagues (2009) used global efficiency as
a measure for the efficiency of information propagation over the whole network, which is
comparable to the measure path length. Local efficiency was used as a measure of the
average efficiency of information exchanged within subgraphs included in the whole
network, which is comparable to the measure clustering. Using fMRI they found that the
global efficiency of the functional brain networks of boys with ADHD and of typically
developing boys was lower than in generated random networks and higher than in
generated regular networks. The local efficiency of the functional brain networks of boys
with ADHD and of typically developing boys was higher than in generated random
networks and lower than in generated regular networks. These results suggest a
small-world like structure of the functional brain networks of boys with ADHD and of typically
developing boys. However, the functional brain network of boys with ADHD was found
to have a significantly increased local efficiency and a trend towards a decreased global
efficiency compared to the control group. These results were interpreted to reflect the
tendency of a shift toward a regular structure of the efficiency in the functional brain
network of boys with ADHD (Wang et al., 2009). Furthermore, altered nodal efficiency
of the communication efficiency between a specific node and all other nodes in the
network and can be investigated when using fMRI because of its high spatial resolution.
Decreased nodal efficiency was found in the medial prefrontal, temporal, and occipital
cortex regions and increased nodal efficiency was found in the inferior frontal cortex and
subcortical regions.
Ahmadlou, Adeli, and Adeli (2012) found differences in functional brain
networks in children with ADHD compared to control children using EEG. In the
left-hemisphere the network of children with ADHD in the delta band showed lower path
lengths and higher clustering than the network of children without ADHD. No
differences were found in the whole brain network in the delta band and in the other EEG
frequency bands.
Those initial results indicate that the functional brain network of children with
ADHD might be altered compared to the functional brain network of typically developing
children. The study of Wang and colleagues (2009) implies that the functional brain
network of children with ADHD may be shifted to a more regular structure compared to
the functional brain network of typically developing children. In contrast, the
combination of higher clustering and lower path lengths found by Ahmadlou and
colleagues (2012) imply a more small-world structure in the left-hemisphere of the
functional brain network of children with ADHD compared to the functional brain
network of typically developing children. More studies are necessary to draw conclusions
about the abnormalities in the functional brain network of children with ADHD.
In this study it is investigated whether the functional brain network of children
with respect to characteristics of a small-world network. First, it is investigated whether
the functional brain network of children with ADHD and of typically developing children
show characteristics of a small-world network. Second, it is investigated whether the
functional brain network of children with ADHD differs from the functional brain
network of typically developing children. The functional brain network is examined in
brain activity measured with EEG during resting state with eyes closed, separated into the
frequency bands delta, theta, alpha and beta. The effect of gender and interaction effect of
gender and ADHD on the functional brain network is also investigated, since previous
research shows gender differences in the topological organization of the functional brain
network (Boersma et al., 2011; Tian, Wang, Yan, & He, 2011).
It is hypothesized that the functional brain network of children with ADHD and of
typically developing children show characteristics of a small-world network. Previous
studies have shown that the brain can be viewed as a complex network with small-world
network characteristics (Bassett & Bullmore, 2006; Stam & Reijneveld, 2007; Wang et
al., 2009). It is furthermore hypothesized that the functional brain network of children
with ADHD diverges from the functional brain network of typically developing children.
There is no specific hypothesis about the direction of the differences. Hereby it is
considered that the DMN that is, among other brain activity, activated during rest may
either be hypo- or hyperconnected (Konrad & Eickhoff, 2010). In addition, the results
found in previous studies that investigated the small-world network characteristics of the
functional brain network in children with ADHD during rest are inconsistent (Ahmadlou
Method Procedure
This study is part of the research project Braingymnastics conducted at the Free
University of Amsterdam (Vrije Universiteit Amsterdam, VU) that investigates primarily
the effectiveness of neurofeedback training and sports in comparison to treatment with
methylphenidate in a randomized controlled trial. Secondarily, Braingymnastics
compares children with ADHD to typically developing children to investigate
fundamental questions about the nature of ADHD. Braingymnastics has been approved
by the Medical Ethical Committee of the VU (Medisch Ethische Toetsingscommissie,
METC). The present study falls within the second aim by investigating differences in the
functional brain network between children with ADHD and typically developing children
using EEG data. The pre-treatment measuring points of children with ADHD were used.
All children with ADHD had not used medication for ADHD before and did not use
medication at the time of the measurement. Typically developing children were measured
once. For all children EEG recordings, an IQ score, and age were obtained. Informed
written consent of one parent was acquired.
Sample
The sample of this study consists of a group of 48 children with ADHD and a
comparison group of 48 typically developing children aged between 7 and 13 years old.
Children with ADHD were recruited via child- and adolescent psychiatric institutions and
hospitals sited in Amsterdam, Rotterdam, and surroundings. Children of the comparison
group were recruited via sports clubs and elementary schools in large cities in the
ADHD according to the DSM-IV-TR criteria (American Psychiatric Association, 2000)
by a qualified psychologist of the involved psychiatric institutions and hospitals. Children
with comorbid disorders were also included to obtain a representative group of the
clinical population. Children of the comparison group were excluded when they had a
score above the clinical threshold on the Dutch version of the Disruptive Behavior
Disorders rating scale (DBD Rating Scale; Pelham, Gnagy, Greenslade, & Milich, 1992;
in Dutch: Vragenlijst voor Gedragsproblemen bij kinderen; VvGK; Oosterlaan, Scheres,
Antrop, Roeyers, & Sergeant, 2000). Parents and teachers of the children completed the
VvGK. Inclusion criterion for both groups was a sufficient knowledge of the Dutch
language. Exclusion criteria for both groups were severe physical or cognitive disabilities
and neurological disorders, because this could interfere with the measurements.
To diminish the influence of gender and intelligence on differences between the
two groups, the groups were selected out of a group of 115 children with ADHD and 97
typically developing children. Children with an IQ-score lower than 75 or higher than
125 were excluded from both groups. In total 24 girls with ADHD had participated in the
research project Braingymnastics. Therefore, the first 24 participating boys with ADHD
were selected to form, together with the 24 girls with ADHD, the ADHD group. To form
a typically developing comparison group, the first 24 typically developing boys and the
first 24 typically developing girls were selected. The order of participation was based on
the order of measurement date. The ADHD group and the typically developing
Variables
Brain activity. Brain activity was measured with EEG during a resting period of
3 minutes. Children sat in a chair in a Faraday room and were instructed to have their
eyes closed. An EEG-cap with 128 channels with the ABC layout system was used,
whereby the EEG activity was measured with a sample frequency of 512 Hz.
Age. Age in months at measuring point was used.
Intelligence. A short version of the Dutch Wechsler Intelligence Scale for
Children-Third Edition (WISC-III; Kort et al., 2005) was used to assess a score indicating
intelligence. The short version consisted of the subtests arithmetic, block design,
vocabulary, and picture arrangement. For each subtest a standard score was computed
with a range from 1 till 19. A standard score of 10 represents the average for each age
category. Subsequently, a total IQ-score was estimated based on the standard scores.
Data analysis
Pre-processing. EEG-data was pre-processed using BrainVision Analyzer
software (www.brainproducts.com). The reference was set to linked-ears. An infinite
impulse response (IIR) filter was applied with the low cut off set on 0.1 Hz, the high cut
off on 40 Hz and a notch filter on 50 Hz. The EEG-data was then imported in the
software programme BrainWave version 0.9.93 developed by C. J. Stam (available at:
http://home.kpn.nl/stam7883/ brainwave.html). Seven epochs of EEG recordings of eight seconds each were manually selected for each participant, whereby selections were made
to minimize artifacts in the EEG-data that was used for further analyses. Thereafter, the
EEG-data was separated into the frequency bands delta (0.5 – 3.5 Hz), theta (3.5 – 7.5
Graph construction. BrainWave was used for graph construction. By the
construction of graphs based on the EEG-data, every channel of the 128 EEG-channels
was modelled as a node in the functional brain network. The connections between the
channels were modelled as the edges in the functional brain network. Weighted graphs
were constructed, which means that the strength of the connections was incorporated in
the graph construction, instead of using a threshold to set the maximum number of
connections as in unweighted graphs. The connections between the channels within the
epochs were measured with the phase lag index (PLI; Stam, Nolte, & Daffertshofer,
2007). The PLI is a measure of phase synchronization between two time series, which
represents the strength of the connection between two channels. The PLI has, compared
to other measures, strongly diminished bias of activity from one cortical source that is
measured by multiple channels (volume conduction) and of reference electrodes, because
it measures the nonzero phase lag between two time series. Nonzero phase lags cannot be
explained by volume conduction. Therefore, the PLI is more likely to reflect true
interaction between the underlying systems than other available measures of statistical
interdependencies between time series. Stam, Nolte, and colleagues (2007) give a
detailed mathematical description. The PLI’s were computed between all possible
combinations of two time series of all 128 channels, for each frequency band and for each
epoch separately. Connectivity matrices were then created with the PLI’s of all pairwise
combinations of channels per frequency band and per epoch.
The variables mean PLI, clustering coefficient, path length, normalized clustering
coefficient, and normalized path length were then computed, based on the description of
of BrainWave for weighted graphs. The clustering coefficient (Cw) and the path length
(Lw) were estimated from the connectivity matrices and averaged over the seven epochs
per participant. PLI’s were also averaged over the seven epochs per participant, and
thereby the mean PLI variable was calculated. Fifty random networks with the same
number of nodes and strength of connections were generated per epoch, by randomly
shuffling the cells of the original connectivity matrix of that epoch. Thereby, the mean
strength of the correlations and the symmetry of the matrices where preserved (Stam &
Reijneveld, 2007). From these random matrices, the average clustering coefficient and
the average path length of the generated random networks (Cr and Lr, respectively) were
obtained. The ratio was calculated between the observed clustering coefficient of the
participants and the clustering coefficient of the generated random networks. This ratio
was called the normalized clustering coefficient gamma. The ratio between the observed
path length of the participants and the path length of the generated random networks was
calculated. This ratio was called the normalized path length lambda. The functional brain
network shows characteristics of a small-world network when gamma is larger than one
and lambda does not differ from one (Stam & Reijneveld, 2007). A variable
small-world-ness was computed as a ratio between gamma and lambda. This variable is a quantitative
measure of small-world-ness. A small-world-ness value larger than one indicates that the
functional brain network shows characteristics of a small-world network (Humphries &
Gurney, 2008).
Statistical analysis. To answer the first research question whether the functional
brain network shows characteristics of a small-world network, it was tested whether the
variable was considered to be significantly larger than one when the mean minus two
times the standard error of the mean was larger than one. This was tested for each
frequency band for both groups.
To answer the second research question whether the functional brain network
differs between children with ADHD and typically developing children, the clustering
coefficient, the path length, gamma, lambda, and the small-world-ness variable were
compared between the two groups for all frequency bands using ANOVA. In addition,
the variables were compared between boys and girls and interaction effects were tested.
Because outliers were found in the solution the assumptions of ANOVA were violated.
Therefore, a permutation test was applied to the ANOVA (Anderson & ter Braak, 2003),
which does not assume a normal distribution of residuals. An exact permutation test was
used, whereby the values where randomly rearranged without replacement over the two
groups 5000 times. Each time the randomly arranged groups were compared and the
values were stored. A p-value was obtained, representing the percentage of simulated
F-values that was equal to or higher than the obtained F-value of the ANOVA test on the
observed data. For each comparison a significance level of α = 0.05 was used.
Results Small-world-ness
In Table 1 the means and standard deviations of all variables are displayed. For
the ADHD group the small-world-ness variable differed significantly from one in the
frequency bands delta (1.04, SE=0.005), theta (1.04, SE=0.005), alpha (1.03, SE=0.007),
and beta (1.05, SE=0.006). The small-world-ness variable differed also significantly from
SE=0.004), alpha (1.02, SE=0.006), and beta (1.03, SE=0.005). This indicates that the
functional brain network shows characteristics of a small-world network for both groups
and for all investigated frequency bands.
Table 1.
Means and standard deviations (SD).
ADHD group Comparison group
Total Boys Girls Total Boys Girls
Mean (SD) Mean (SD) Mean (SD) Mean (SD) Mean (SD) Mean (SD)
n 48 24 24 48 24 24 Age 10.15 (1.75) 10.45 (1.96) 9.84 (1.47) 10.07 (1.22) 9.93 (1.06) 10.20 (1.36) IQ 98.33 (12.31) 100.38 (12.53) 96.29 (12.00) 101.32 (10.91) 103.35 (9.64) 99.29 (11.90) Delta Mean PLI 0.178 (0.015) 0.180 (0.018) 0.175 (0.012) 0.173 (0.015) 0.176 (0.017) 0.169 (0.011) Cw 0.195 (0.017) 0.197 (0.020) 0.194 (0.013) 0.190 (0.016) 0.194 (0.018) 1.869 (0.013) Lw 4.710 (0.290) 4.676 (0.318) 4.744 (0.261) 4.795 (0.290) 4.759 (0.341) 4.831 (0.229) Gamma 1.092 (0.020) 1.086 (0.015) 1.097 (0.023) 1.096 (0.018) 1.094 (0.019) 1.098 (0.017) Lambda 1.056 (0.024) 1.057 (0.021) 1.054 (0.027) 1.056 (0.026) 1.059 (0.029) 1.052 (0.022) Small-world- ness 1.036 (0.033) 1.029 (0.026) 1.043 (0.038) 1.040 (0.032) 1.036 (0.038) 1.045 (0.025) Theta Mean PLI 0.134 (0.017) 0.141 (0.020) 0.128 (0.011) 0.129 (0.011) 0.128 (0.011) 0.130 (0.011) Cw 0.150 (0.019) 0.156 (0.023) 0.144 (0.013) 0.143 (0.012) 0.142 (0.013) 0.143 (0.012) Lw 6.304 (0.547) 6.118 (0.559) 6.490 (0.476) 6.535 (0.503) 6.599 (0.584) 6.470 (0.408) Gamma 1.109 (0.028) 1.100 (0.016) 1.117 (0.035) 1.097 (0.018) 1.095 (0.014) 1.098 (0.022) Lambda 1.070 (0.023) 1.067 (0.019) 1.073 (0.026) 1.071 (0.012) 1.076 (0.021) 1.067 (0.018) Small-world- ness 1.038 (0.036) 1.033 (0.023) 1.043 (0.045) 1.025 (0.027) 1.019 (0.027) 1.031 (0.027)
Table 1, part 2
ADHD group Comparison group
Total Boys Girls Total Boys Girls
Mean (SD) Mean (SD) Mean (SD) Mean (SD) Mean (SD) Mean (SD) Alpha Mean PLI 0.186 (0.079) 0.203 (0.088) 0.169 (0.067) 0.167 (0.050) 0.165 (0.045) 0.169 (0.056) Cw 0.212 (0.087) 0.230 (0.098) 0.195 (0.072) 0.189 (0.054) 0.188 (0.049) 0.190 (0.060) Lw 5.324 (1.391) 5.047 (1.476) 5.602 (1.271) 5.594 (1.050) 5.572 (0.999) 5.615 (1.120) Gamma 1.137 (0.042) 1.127 (0.040) 1.147 (0.043) 1.128 (0.034) 1.134 (0.032) 1.122 (0.035) Lambda 1.104 (0.053) 1.108 (0.071) 1.101 (0.027) 1.106 (0.043) 1.108 (0.040) 1.104 (0.047) Small-world- ness 1.032 (0.051) 1.021 (0.059) 1.044 (0.039) 1.023 (0.045) 1.026 (0.042) 1.019 (0.047) Beta Mean PLI 0.082 (0.013) 0.081 (0.012) 0.083 (0.014) 0.079 (0.009) 0.077 (0.008) 0.081 (0.010) Cw 0.092 (0.016) 0.091 (0.014) 0.093 (0.018) 0.088 (0.011) 0.086 (0.009) 0.090 (0.012) Lw 10.118 (1.205) 10.224 (1.068) 10.011 (1.342) 10.385 (0.950) 10.611 (0.799) 10.159 (1.047) Gamma 1.111 (0.031) 1.106 (0.030) 1.116 (0.031) 1.102 (0.021) 1.101 (0.025) 1.102 (0.016) Lambda 1.058 (0.027) 1.059 (0.024) 1.057 (0.031) 1.064 (0.028) 1.066 (0.032) 1.061 (0.024) Small-world- ness 1.052 (0.039) 1.046 (0.037) 1.058 (0.040) 1.034 (0.035) 1.036 (0.042) 1.040 (0.027) Between-group differences
In Table 2 the statistics of the variables wherefore significant or near significant
differences were found between the children with ADHD and typically developing
children (group effect), between boys and girls (gender effect), or for the interaction
effect (group x gender) are displayed. The statistics of all comparisons can be found in
Table 2.
Statistics of variables with significant (*) or nearly significant (#) effects.
Mean PLI in the theta band. A nearly significant effect of group was found on
mean PLI in the theta band, whereby the trend was towards a higher mean PLI for the
children with ADHD compared to the children in the comparison group. An effect of
gender was found, whereby boys had a significant higher mean PLI in the theta band than
girls. The interaction effect of group x gender was also found to be significant. Post-hoc
tests showed that mean PLI in the theta band was higher for boys in the ADHD group
than for boys in the comparison group (F (1, 46) = 7.06, p = 0.007) and girls in the
ADHD group (F (1, 46) = 7.66, p = 0.007) (Figure 2). No significant differences were
found between girls in the ADHD group and girls in the comparison group (F (1, 46) =
0.25, p = 0.634) and between boys and girls within the comparison group (F (1, 46) =
0.13, p = 0.631).
Group effect Gender effect Interaction effect group x gender F value Partial eta square p-value permutation test F value Partial eta square p-value permutation test F value Partial eta square p-value permutation test Theta Mean PLI 3.71# 0.04 0.058 4.28* 0.04 0.034 6.16* 0.06 0.014 Cw 5.73* 0.06 0.015 2.64 0.03 0.105 4.68* 0.05 0.028 Lw 4.87* 0.05 0.031 1.35 0.01 0.250 5.77* 0.06 0.020 Gamma 6.60* 0.07 0.012 4.67* 0.05 0.033 2.07 0.02 0.158 Small- world-ness 3.94# 0.04 0.051 2.95 0.03 0.084 0.00 0.00 0.954 Alpha Gamma 1.32 0.01 0.255 0.32 0.00 0.571 4.47* 0.05 0.038
Figure 2. Interaction effect of group x gender on mean PLI in the theta band.
Figure 3. Interaction effect of group x gender on Cw in the theta band.
Cw in the theta band. An effect of group was found on Cw in the theta band,
whereby children with ADHD had a significantly higher Cw than children in the
tests revealed that Cw in the theta band was higher for boys in the ADHD group than for
boys in the comparison group (F (1, 46) = 7.75, p = 0.004) and girls in the ADHD group
(F (1, 46) = 5.19, p = 0.022) (Figure 3). No significant differences were found between
girls in the ADHD group and girls in the comparison group (F (1, 46) = 0.04, p = 0.836)
and between boys and girls in the comparison group (F (1, 46) = 0.23, p = 0.631).
Lw in the theta band. A significant effect of group was found on Lw in the theta
band, whereby children with ADHD had a significantly lower Lw than children in the
comparison group. The interaction effect group x gender was also found to be significant.
Post-hoc tests showed that Lw in the theta band higher for girls in the ADHD group than
for boys in the ADHD group (F (1, 46) = 6.17, p = 0.017) and higher for boys in the
comparison group than for boys in the ADHD group (F (1, 46) = 8.50, p = 0.006) (Figure
4). No significant differences were found between girls in the ADHD group and girls in
the comparison group (F (1, 46) = 0.03, p = 0.881) and between boys and girls in the
comparison group (F (1, 46) = 0.79, p = 0.373).
Figure 4. Interaction effect group x gender on Lw in the theta band.
Gamma in the theta band. A significant effect of group was found on gamma in
the theta band, whereby children in the ADHD group had a significantly higher gamma
than children in the comparison group (Figure 5). A significant effect of gender was also
found. Girls had a significantly higher gamma than boys. No significant interaction effect
of group x gender was found.
Figure 5. Group and gender effects on gamma in the theta band.
Small-world-ness in the theta band. A nearly significant effect of group was
found on small-world-ness in the theta band, whereby the trend was towards a higher
small-world-ness for the children in the ADHD group as compared to the children in the
comparison group (Figure 6). No effect of gender and no interaction effect of group x
Figure 6. Trend of a group effect on small-world-ness in the theta band.
Gamma in alpha band. No effects of group and gender were found on gamma in
the alpha band. The interaction effect of group x gender was found to be significant.
Post-hoc tests showed that gamma in the alpha band was significantly higher for girls in the
ADHD group than for girls in the comparison group (F (1, 46) = 4.99, p = 0.031) (Figure
7). No significant differences were found between boys in the ADHD group and boys in
the comparison group (F (1, 46) = 0.50, p = 0.493), between boys and girls in the ADHD
group (F (1, 46) = 2.98, p = 0.088), and between boys and girls in the comparison group
(F (1, 46) = 1.51, p = 0.225).
No significant effects of group, gender or the interaction between group and
Figure 7. Interaction effect of group x gender on gamma in the alpha band.
Discussion
In the present study the functional brain network of children with ADHD is
investigated and compared to the functional brain network of typically developing
children, whereby graph theory was applied to EEG data recorded when children were in
rest with their eyes closed. It was found that the functional brain network of both ADHD
children and typically developing children shows the characteristics of a small-world
network over all investigated frequency bands. This finding is in agreement with previous
research that found characteristics of a small-world network in the brain (for review, see
Bassett & Bullmore, 2006 and Stam & Reijneveld, 2007). Small-world networks are the
most optimal complex networks, because of the combination of high local connectivity
and high global connectivity (Watts & Strogatz, 1998). With this finding, the present
processing with the combination of high clustering and low average path length in the
topological structure of the functional connections (Bassett & Bullmore, 2006).
Although both children with ADHD and typically developing children showed
efficient small-world network characteristics, differences in the functional brain network
were also found. Mean synchronization (mean PLI) in the theta frequency band was
significantly higher for boys than for girls and significantly higher for boys with ADHD
compared to girls with ADHD and compared to typically developing boys. A tendency of
a higher mean synchronization was found for children with ADHD compared to typically
developing children. The clustering coefficient was significantly higher and the path
length was significantly lower for children with ADHD compared to typically developing
children in the theta frequency band as well. Investigation of the interaction effect of
group with gender revealed that the clustering coefficient was significantly higher and the
path length was significantly lower only for boys with ADHD compared to typically
developing boys, and not for girls with ADHD compared to typically developing girls.
Stronger connections in the network of boys with ADHD, as shown by the higher
mean synchronization, might have resulted in the differences found in the clustering
coefficient and path length in the theta frequency band. The variables gamma and lambda
control for the strength of connections and are thereby defined as the normalized
clustering coefficient and normalized path length, respectively (Stam & Reijneveld,
2007). The normalized clustering in the theta frequency band was significantly higher for
children with ADHD compared to typically developing children, and higher for girls than
for boys. However, the normalized path length did not significantly differ between
there was no interaction effect on the normalized clustering and the normalized path
length. Therefore, it is likely that the higher clustering and lower path length for boys
with ADHD is a consequence of stronger connections in the network of the theta
frequency band of boys with ADHD, instead of a difference in the topological
organization of the network. The results indicate that the functional brain network of
children with ADHD has a higher local connectivity and an equal global connectivity in
the theta frequency band in comparison to the functional brain network of typically
developing children. This implies that the functional brain network of children with
ADHD shows more the characteristics of a small-world network than the functional brain
network of typically developing children. This is reflected by the tendency towards a
higher small-world-ness for children with ADHD in the theta frequency band.
In the alpha frequency band normalized clustering was higher for girls with
ADHD as compared to typically developing girls. This indicates that the functional brain
network of girls with ADHD has a higher local connectivity in the alpha frequency band
than the functional brain network of typically developing girls. Normalized path length
and small-world-ness in the alpha frequency band did not differ between children with
ADHD and typically developing children and not between boys and girls. In addition, the
functional brain network between children with ADHD and typically developing children
and between boys and girls did not differ in the delta and beta frequency band on all
investigated variables.
The results are surprising, because they imply that the functional brain network is
more efficient for children with ADHD than for typically developing children in the theta
girls in the alpha frequency band, since the combination of a higher local connectivity
and an equal global connectivity approaches more the characteristics of the optimal
small-world network as described by Watts and Strogatz (1998). Ahmadlou, Adeli and
colleagues (2012) also found stronger characteristics of a small-world network in the
functional brain network of children with ADHD compared to typically developing
children. However, they found differences in the left hemisphere in the delta frequency
band, rather than in the theta and alpha frequency band in the whole brain as in this study.
Wang and colleagues (2009) found an increased local efficiency in boys with ADHD,
which corresponds to the higher local connectivity for children with ADHD in the theta
frequency found in this study. In contrast, Wang and colleagues (2009) also reported a
trend towards a decreased global efficiency, which was not supported by the results of
this study where no difference in global connectivity was found in all frequency bands.
Despite of the similarities and differences in results between the studies, the results of
this study replicate the results of the former studies in the finding that the functional brain
network of children with ADHD differs from the functional brain network of typically
developing children.
Interestingly, most of the differences between children with ADHD and typically
developing children were found in the theta frequency band. A meta-analysis of
quantitative EEG research shows that children, adolescents, and adults with ADHD have
increased theta power brain activity, compared to children, adolescents, and adults
without ADHD (Snyder & Hall, 2006). The increased activity in the theta frequency band
may be related to the higher mean synchronization or to differences in the topological
This study did not incorporate an analysis of the power of the frequency bands and the
relation with the topological organization, but this is recommended for future studies of
the functional brain network of children with ADHD.
The effects of gender on the topological organization of the functional brain
network found in this study do not correspond with previous research. Boersma and
colleagues (2011) also used EEG recordings during rest with eyes closed to investigate
gender differences. They reported a higher mean synchronization in all frequency bands
for girls compared to boys. In contrast, in this study a higher mean synchronization for
boys was found in the theta frequency band. Furthermore, Boersma and colleagues found
a higher normalized clustering for girls in the alpha and beta frequency bands. In this
study a higher normalized clustering for girls was found in the theta frequency band.
Normalized clustering in the alpha frequency band was only found to be higher for girls
with ADHD compared to typically developing girls, and not compared to boys with
ADHD. Methodological differences could account for the differences in results. Boersma
and colleagues (2011) used only fourteen EEG channels compared to 128 channels in this
study and used a different synchronization measure. Moreover, because the present study
is mainly focused on the differences between children with ADHD and typically
developing children, the sample of boys and girls is not representative for the general
population of children, since half of the sample is diagnosed with ADHD.
This study was based on EEG data measured during resting state, a situation
wherein the DMN is mainly activated (Fransson, 2005). Previous studies suggest that the
functional connectivity of the DMN during resting state may either be decreased
findings of this study underpin that the functional connectivity is increased during resting
state in the brain of children with ADHD compared to typically developing children. The
observed differences reflect a stronger local functional connectivity in the theta frequency
band for children with ADHD and in the alpha frequency band for girls with ADHD
compared to typically developing children, but no increased or decreased connectivity
was found in the delta and beta frequency band. This is in contrast to the research that
shows a reduced anatomical and functional connectivity in ADHD in for example the
anterior limb of the internal capsule and the corpus callosum (Konrad & Eickhoff, 2010).
A limitation of investigating the topological organization in the functional brain
network is that diverse methodological choices made in the studies make it difficult to
interpret the differences in results between the studies. The reported results could depend
on the methodological choices, for example how much channels are included, which
synchronization measure is used, and if and what thresholding rule is used (Bassett &
Bullmore, 2006). In this study the choice was made to use all available 128 EEG
channels to base the modelling on recordings of a large group of brain regions. The
electromagnetic field that is related to neuronal activity is directly measured with EEG
and thereby the EEG technique has a high temporal resolution (Stam & Reijneveld,
2007). The PLI is used as synchronization measure, to diminish the bias of volume
conduction associated with the low spatial resolution of the EEG technique (Stam, Nolte,
et al., 2007). Weighted graphs are used opposed to unweighted graphs with a
thresholding rule. With unweighted graphs the problem raises that choosing one
thresholding rule would be arbitrary and with using a range of thresholds a large number
Compared to other EEG studies (e.g. Ahmadlou, Adeli, et al., 2012), the sample size of
this study is larger, which provides a higher statistical power that decreases the
probability of a Type II error.
Since this is one of the first studies that investigated the functional brain network
in children with ADHD compared to typically developing children, this study is highly
exploratory. This study could be replicated to investigate the validity and reliability of the
findings. Future research could also investigate the relation between differences in the
functional brain network and differences in the functional connections with the use of
imaging techniques. Another possibility is to compare the functional brain network
between children with ADHD and typically developing children during an activity.
Differences in the functional brain network between subtypes of ADHD can also been
studied, as well as the relation between the functional brain network and severity of
ADHD behaviour symptoms. Based on the gender effects and interaction effects found in
this study, it is recommended to take gender into account when investigating the
functional brain network of children with ADHD.
Overall, with this study it is supported that the topological organization of the
functional brain network shows the characteristics of a small-world network in typically
developing children and in children with ADHD. Moreover, this study revealed that
children with ADHD have a higher local connectivity than typically developing children
in the functional brain network of the theta frequency band, and that girls with ADHD
have a higher local connectivity than typically developing girls in the functional brain
network of the alpha frequency band. Thereby, it is supported that psychiatric disorders
brain network. The findings imply a more small-world structure in the functional brain
network of the theta frequency band for children with ADHD and of the alpha frequency
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Appendix 1
Table 1.
Statistics
Group effect Gender effect Interaction effect group x gender F value Partial eta square p-value permutation test F value Partial eta square p-value permutation test F value Partial eta square p-value permutation test Delta Mean PLI 2.58 0.03 0.116 3.75 0.04 0.053 0.16 0.00 0.696 Cw 2.01 0.02 0.154 2.34 0.02 0.129 0.34 0.00 0.562 Lw 2.04 0.02 0.156 1.40 0.01 0.234 0.00 0.00 0.974 Gamma 1.30 0.01 0.262 3.49 0.04 0.067 0.85 0.01 0.360 Lambda 0.00 0.00 0.952 1.01 0.01 0.316 0.19 0.00 0.672 Small- world-ness 0.42 0.00 0.514 3.20 0.03 0.069 0.10 0.00 0.750 Theta Mean PLI 3.71 0.04 0.058 4.28* 0.04 0.034 6.16* 0.06 0.014 Cw 5.73* 0.06 0.015 2.64 0.03 0.105 4.68* 0.05 0.028 Lw 4.87* 0.05 0.031 1.35 0.01 0.250 5.77* 0.06 0.020 Gamma 6.60* 0.07 0.012 4.67* 0.05 0.033 2.07 0.02 0.158 Lambda 0.06 0.00 0.807 0.13 0.00 0.711 3.14 0.03 0.081 Small- world-ness 3.94 0.04 0.051 2.95 0.03 0.084 0.00 0.00 0.954 Alpha Mean PLI 2.04 0.02 0.158 1.25 0.01 0.270 1.91 0.02 0.168 Cw 2.49 0.03 0.121 1.29 0.01 0.260 1.62 0.02 0.208 Lw 1.15 0.01 0.287 1.42 0.02 0.230 1.04 0.01 0.302 Gamma 1.32 0.01 0.255 0.32 0.00 0.571 4.47* 0.05 0.038 Lambda 0.03 0.00 0.873 0.25 0.00 0.627 0.04 0.00 0.855 Small- world-ness 0.99 0.01 0.328 0.65 0.01 0.423 2.36 0.02 0.139
Table 1, part 2
Group effect Gender effect Interaction effect group x gender F value Partial eta square p-value permutation test F value Partial eta square p-value permutation test F value Partial eta square p-value permutation test Beta Mean PLI 1.16 0.01 0.289 1.60 0.02 0.207 0.28 0.00 0.596 Cw 1.81 0.02 0.179 1.74 0.02 0.183 0.10 0.00 0.755 Lw 1.47 0.02 0.228 2.27 0.02 0.143 0.29 0.00 0.597 Gamma 3.18 0.03 0.080 0.93 0.01 0.342 0.80 0.01 0.368 Lambda 0.94 0.01 0.333 0.28 0.00 0.596 0.07 0.00 0.799 Small- world-ness 3.59 0.04 0.060 1.16 0.01 0.293 0.22 0.00 0.643
