RESEARCH

Dynamic connectivity and the effects
of maturation in youth with attention
deficit hyperactivity disorder

Nina de Lacy

1

and Vince D. Calhoun

2,3

1

Department of Psychiatry and Behavioral Science, University of Washington, Seattle, WA, USA
2The Mind Research Network, Albuquerque, NM, USA
3Department of Electrical and Computer Engineering, University of New Mexico, Albuquerque, NM, USA

a n o p e n a c c e s s

j o u r n a l

Keywords: ADHD, Functional network connectivity, Dynamic connectivity, Cortical,
Subcortical,

ICA

ABSTRACT

The analysis of time-varying connectivity by using functional MRI has gained momentum
given its ability to complement traditional static methods by capturing additional patterns
of variation in human brain function. Attention deficit hyperactivity disorder (ADHD) is a
complex, common developmental neuropsychiatric disorder associated with heterogeneous
connectivity differences that are challenging to disambiguate. However, dynamic
connectivity has not been examined in ADHD, and surprisingly few whole-brain analyses
of static functional network connectivity (FNC) using independent component analysis (ICA)
exist. We present the first analyses of time-varying connectivity and whole-brain FNC using
ICA in ADHD, introducing a novel framework for comparing local and global dynamic
connectivity in a 44-network model. We demonstrate that dynamic connectivity analysis
captures robust motifs associated with group effects consequent on the diagnosis of ADHD,
implicating increased global dynamic range, but reduced fluidity and range localized to the
default mode network system. These differentiate ADHD from other major neuropsychiatric
disorders of development. In contrast, static FNC based on a whole-brain ICA decomposition
revealed solely age effects, without evidence of group differences. Our analysis advances
current methods in time-varying connectivity analysis, providing a structured example of
integrating static and dynamic connectivity analysis to further investigation into functional
brain differences during development.

AUTHOR SUMMARY

Neuropsychiatric disorders represent a central field of inquiry in network neuroscience,
akin to lesional analysis of complex brain system dynamics. The prevalence of these
conditions increases from mid-childhood to peak in adolescence and regress thereafter,
challenging our ability to disambiguate maturational and connectivity effects. ADHD is a
paradigmatic example, and the most common neuropsychiatric disorder of development.
Here we present the first whole-brain analysis of time-varying connectivity in ADHD.
Building on leading-edge methods in dynamic connectivity, our novel approach analyses
time-varying connectivity on both a global brain basis, and within local network systems.
This framework demonstrates that analysis of time-varying connectivity offers additional
ways to characterize group and maturational effects in ADHD that are extensible to other
developmental neuropsychiatric disorders.

Citation: de Lacy, N., & Calhoun, V. D.
(2019). Dynamic connectivity and the
effects of maturation in youth with
attention deficit hyperactivity disorder.
Network Neuroscience, 3(1), 195–216.
https://doi.org/10.1162/netn_a_00063

DOI:
https://doi.org/10.1162/netn_a_00063

Supporting Information:
https://doi.org/10.1162/netn_a_00063

Received: 6 December 2017
Accepted: 5 June 2018

Competing Interests: The authors have
declared that no competing interests
exist.

Corresponding Author:
Vince Calhoun
vcalhoun@mrn.org

Handling Editor:
Lucina Uddin

Copyright: © 2018
Massachusetts Institute of Technology
Published under a Creative Commons
Attribution 4.0 International
(CC BY 4.0) license

The MIT Press

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Dynamic connectivity in ADHD

Intrinsic connectivity:
Refers to functional connectivity as
measured during task-free states such
as the wakeful resting state. It is
inferred that this represents the
spontaneous, or intrinsic, activity of
the brain.

INTRODUCTION

Historically, connectivity analysis of resting-state functional MRI (fMRI) data has largely pro-
ceeded by computing mean correlations between networks (or nodes) of interest across time
courses. This provides an averaged snapshot of “static” functional network connectivity (sFNC),
and superordinate approximation of underlying dynamic states (Ciric, Nomi, Uddin, & Satpute,
2017). Motivated by demonstrations that intrinsic connectivity fluctuates over the time series,
methods have been in development since 2010 (Chang & Glover, 2010; Sakoglu et al., 2010)
to delineate time-varying or dynamic functional network connectivity (dFNC) in resting-state
fMRI, and capture brain network activity in richer detail. Concomitantly, secondary measures
of dynamism have intuitive biological appeal as potential corollaries of cognitive control and
flexibility (Nomi et al., 2017) to examine how the brain switches among prototype connec-
tivity states over the time course of fMRI observations. In adults, state-dependent variability
in intrinsic dFNC between fronto-parietal and default mode networks (DMN) is associated
with reduced cognitive flexibility (Douw, Wakeman, Tanaka, Liu, & Stufflebeam, 2016), and
dFNC variation permits automated identification of individual subjects and predicts fluid intel-
ligence and executive function performance (Liu, Liao, Xia, & He, 2018). Initial investigations
of the development of dynamism in youth, when cognitive control networks undergo con-
siderable refinement entraining behavioral maturation, suggests increasing age is associated
with increased variability in the time allocated to each state (Marusak et al., 2017) and greater
switching fluidity in executive regions (Chai et al., 2017).

Although dynamic methods have yielded intriguing results in other developmental
neuropsychiatric disorders (Damaraju et al., 2014; de Lacy, Doherty, King, Rachakonda, &
Calhoun, 2017) revealing transient internetwork dysconnectivity that may be obscured by
time-averaging, to date they have not been published in ADHD. This omission is remarkable
given ADHD’s status as one of the most common neuropsychiatric developmental disorders
and ample evidence of deficits in multiple executive functions (Mueller, Hong, Shepard, &
Moore, 2017). Concomitantly, research in multiple fields suggests ADHD may be a convergent
phenotype encompassing heterogeneous mechanisms (Gallo & Posner, 2016). Structural imag-
ing studies have tended to support delayed maturation (Hoogman et al., 2017), with task-based
region of interest studies suggesting lagging strengthening of fronto-parieto–striatal-cerebellar
connections, with DMN, fronto-parietal, and ventral attention networks commonly implicated
(Cortese et al., 2012; Hart, Radua, Mataix-Cols, & Rubia, 2012; Hart, Radua, Nakao, Mataix-
Cols, & Rubia, 2013).

Studies in intrinsic FNC highlight key control networks and the DMN in ADHD, including
relationships among DMN nodes. These networks play important roles in task-switching and
“task-negative” states (Dosenbach et al., 2006, 2007). Although the relationship between con-
trol network roles and dFNC is largely undefined, this backdrop motivated our inquiry into
time-varying connectivity in ADHD. We aimed to compare maturational effects, and those
accruing from group membership, or diagnosis of ADHD, in a whole-brain analysis encom-
passing a full set of brain networks and dynamic measures. Because prior work has implicated
disrupted connectivity among DMN nodes and the fronto-parietal network, we chose to es-
timate a higher order model. Higher order models enable the separation of right versus left
fronto-parietal networks (Smith et al., 2009), and DMN subnetworks are increasingly under-
stood as having differentiable functional emphases (Andrews-Hanna, Reidler, Sepulcre, Poulin,
& Buckner, 2010). Furthermore, control networks, rich in association cortex, likely share multi-
functional brain nodes to enable switching processes. Thus, techniques like ICA that allow
individual nodes to participate in multiple networks support the discrimination of effects in

Network Neuroscience

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Dynamic connectivity in ADHD

control networks (Craddock, James, Holtzheimer, Hu, & Mayberg, 2012; Sepulcre, Sabuncu,
& Johnson, 2012). To date, no published studies have examined dFNC in ADHD, or static FNC
in a whole-brain ICA parcellation including subcortical regions, despite the prominent involve-
ment of the latter in ADHD that is consistently demonstrated using task imaging. We aimed to
address these gaps by analyzing sFNC and dFNC using a high-order ICA parcellation in a large
age- and gender-matched subject sample drawn from the ADHD-200 repository, examining
the effects of maturation and group (Figure 1).

Given evidence of altered DMN function in ADHD, and control network roles in func-
tional configuration switching, we hypothesized that altered dynamism would be most prev-
alent within the DMN or in dFNC involving DMN subnetworks. We used ICA to estimate a
44-network model (Supporting Information Table S1, de Lacy & Calhoun, 2019) in 504 youth:
252 with ADHD and 252 with typical development (TD). We analyzed sFNC in a multivari-
ate framework including group, age, IQ-level, gender, site, and residual motion effects, after
determining comorbid diagnoses, medication usage, and handedness did not produce signifi-
cant effects within the ADHD group. We then employed the k-means algorithm on windowed
connectivity matrices (wFNC) to estimate four, five, and six brain states, identifying group dif-
ferences in dFNC and measures of dynamic fluidity in this native state space. We removed
the effects of gender, IQ-level, motion, and site by using the general linear model, succes-
sively including and then removing the effect of age. Finally, we identified four, five, and six
prototype connectivity clusters by applying the temporal ICA (tICA) algorithm to wFNC. We
discretized these to delineate a “meta-state” space and computed higher dimensional measures
of dynamic fluidity and range, again with and without age effects and after removing variance
attributable to IQ-level, gender, site, and motion. Five-state solutions are presented, and 4- and
6-state results reported. In addition, replication analyses were performed in a subsample of
444 subjects who were additionally matched for head motion in a 5-state solution.

We also present a novel increment to our prior work in dynamic methods by analyzing
not only global, but also local, measures of whole-brain dynamism. We hypothesized that
subjects with ADHD would exhibit decreased dynamism within the DMN system associated
with group effects.

RESULTS

Group Differences in Static FNC Are Not Detectable in ADHD Versus TD Youth

Our analysis of static (averaged) FNC across all functional brain networks detected no sig-
nificant difference in any pairwise correlation between ADHD and TD youth. Furthermore,
there was no significant interaction of group with any other covariate including age and
gender. These findings were replicated in the motion-matched sample. To examine the poten-
tial effects of comorbid diagnosis, history of prior or current medication usage, and handedness
on sFNC, we performed an additional multivariate analysis in ADHD youth. By restricting the
subject selection to ADHD youth, we took a conservative approach, reasoning any such effects
would not be “diluted” by the presence of TD youth and including all subjects with a history of
current or prior medication usage. We did not detect effects of comorbid diagnosis, medication
usage, or handedness in sFNC, or interaction of these variables with group or age.

Comparison of Maturational Effects in ADHD and TD Youth Shows Directional Differences in
Control Networks and DMN Subnetworks

To explore the effects of maturation in sFNC, we analyzed age effects in all subjects together
and in the ADHD and TD groups separately. Analysis of the effects of increasing age in sFNC

Network Neuroscience

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Dynamic connectivity in ADHD

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Figure 1. Computational Pipeline. A schematic of the computational pipeline illustrates steps in the preparation of the outcome measures of
sFNC, dFNC, and dynamism. Preprocessed fMRI were submitted to spatial group ICA to extract 44 intrinsic networks, from which thresh-
olded spatial maps are prepared via back reconstruction using the group information–guided ICA (GIG-ICA) algorithm. Pearson pairwise
correlations averaged over the time courses for these spatial maps were analyzed using a multivariate analysis of covariance (MANCOVA)
to form the basis for the static FNC analysis. In the dynamic pipelines, a sliding window approach to the intrinsic network (IN) time courses
formed windowed FNC that were clustered using k means to estimate brain states, on which four measures of dynamism were computed in
the native state space. Similarly, windowed FNC were clustered using the temporal ICA (tICA) algorithm to identify prototype connectivity
patterns that were discretized to form the basis for four measures of dynamism computed in the meta-state space.

Network Neuroscience

198

Dynamic connectivity in ADHD

Segregation:
Refers to brain regions or networks
that exhibit anti-correlated functional
connectivity.

Figure 2. Maturational effects in static FNC among 44 INs in youth with ADHD vs. TD. Age effects
in static connectivity in 252 subjects with TD and 252 with ADHD ages 7–17 was determined by
computing Pearson pairwise correlations averaged across fMRI time courses among 44 INs obtained
from ICA. In A, significant (α < 0.01 corrected for false discovery rate [FDR]) age effects are dis- played for all 504 subjects, where B and C show significant (α < 0.05, corrected for FDR) age effects for TD and ADHD youth, respectively. in the entire subject group (Figure 2A) and in TD youth (Figure 2B) revealed several themes consistent with current understanding of connectivity changes in this developmental period. We observed age-driven strengthening in positive connectivity among networks within the same task-positive functional domains (network clades on the diagonal), except for the early maturing sensorimotor networks. Second, we found generally increasing anticorrelation be- tween default mode subnetworks and noncontrol task-positive networks, indicating matura- tional segregation. Third, sFNC between task-positive control and DMNs showed a mixture of effects. Strengthening positive connectivity with increasing age was present involving dorsomedial and orbitofrontal (OFC) nodes with DMN, and between the ventral frontal portion of the ventral attention network, right fronto-parietal control network, and anterior cingulate portion of the cingulo-opercular network with precuneus subnetworks. In contrast, connectiv- ity between the dorsal attention network and the DMN showed increasing anticorrelation with increasing age. Finally, among the task-positive control group itself, maturational segregation was also seen between the dorsal attention network and OFC, and between the dorsolateral prefrontal cortex and both OFC- and dorsomedial-anchored networks. In youth with ADHD, we found increasing anticorrelation in fewer (sub)networks, which may be appreciated in Figure 2C where many more pairwise FNC cells are empty (black). Within the DMN system, youth with ADHD displayed increasing positive correlation be- tween two DMN subnetworks anchored in the medial prefrontal cortex (intrinsic networks [INs] 16 and 18). Similarly, maturational effects in task-positive control networks and between task-positive and default mode subsystems differed in affected subjects. Task-positive control network relationships during typical development were characterized by increasing anti- correlation between subnetworks anchored in the prefrontal cortex: the dorsolateral prefrontal (IN6) with OFC (IN3), and dorsomedial prefrontal (IN4) cortices, and between the dorsal at- tention network (IN2) and OFC subnetwork (IN 3). This maturation segregation in prefrontal circuits was not observed in youth with ADHD. Instead, we detected increasing positive cor- relation with age between prefrontal circuits (IN6 and 7) and the anterior cingulate portion of the cingulo-opercular network (IN10), the ventral attention network (IN1) with right fronto- parietal control network (IN11), and dorsomedial prefrontal and temporo-limbic anchored circuits (IN 4 and 8). Maturation-driven strengthening of positive correlation between the dorsal attention network (IN2) and frontal cingulo-opercular network (IN 5) was common to subjects Network Neuroscience 199 l D o w n o a d e d f r o m h t t p : / / d i r e c t . m i t . / / t e d u n e n a r t i c e - p d l f / / / / / 3 1 1 9 5 1 0 9 2 3 6 4 n e n _ a _ 0 0 0 6 3 p d . t f b y g u e s t t o n 0 7 S e p e m b e r 2 0 2 3 Dynamic connectivity in ADHD L1 span: Refers to the maximal L1 distance achieved between occupied meta-states. with TD and ADHD. There was no interaction of motion with these effects. In the motion- matched sample, most effects for each of the three analyses were replicated, as shown in Supporting Information Figure S1 (de Lacy & Calhoun, 2019). There were some differences, for the most part effects that did not appear in these smaller samples that were present in the larger samples without motion matching. Increased Global Dynamic Meta-State Span Was a Robust Predictor of ADHD Diagnosis Versus TD We computed five measures of dynamic fluidity across the native (dwell time, fraction of time, state switching) and meta-state (L1 span, state switching) subspaces globally among all net- works, and locally within network groups (Table 1). In the global analysis, where dynamism was examined among all networks on a whole-brain basis, L1 state span was significantly in- creased (α < 0.05, corrected for false discovery rate [FDR]) in ADHD>TD after age variance
was removed. This finding was quite robust, being replicated in the 4-state and 6-state analy-
ses, when window size was varied to 20TR or 30TR (where TR is the repetition time of the MRI
acquisition sequence) across each of the 4-, 5-, and 6-state solutions, and in the motion-
matched sample (Supporting Information Table S1, de Lacy & Calhoun, 2019). Other global
meta-state measures of fluidity were significantly reduced (number of states achieved)
or were reduced and narrowly missed significance (meta-state switching) in the 5-state analysis
(Table 1) and in the motion-matched sample (Supporting Information Table S1), without rep-
lication in the 4-state and 6-state analysis.

Local Dynamic Fluidity Was Decreased Within the DMN System in ADHD

When we examined dynamism measures on a local basis (among subnetworks associated
with the same neurocognitive function) in the native state space, we discovered significantly
reduced dwell time in one state (State 2) in subjects with ADHD versus TD within the DMN

Table 1. Global and local intrasystem dynamic fluidity and range measures in subjects with ADHD and TD.

Native space

Meta-state space

Fraction
of time

State
switching

Number
of states

State
switching

IN group

Global
Task-positive control

Dwell time

0.122-0.936
0.117-0.896

0.323-0.911
0.414-0.626

DMN

Subcortical

Visual
Sensorimotor

0.012*-0.756

0.255-0.682

0.207-0.786

0.783-0.827

0.134-0.926
0.208-0.515

0.195-0.830
0.557-0.866

Cognitive processing

0.500-0.970

0.999

0.349
0.157

0.470

0.542

0.780
0.347

0.332

0.046
0.135

0.040

0.323

0.465
0.504

0.890

0.059
0.144

0.060

0.443

0.487
0.634

0.632

L1 span

0.010*
0.501

0.090

0.702

0.053
0.470

0.579

Total
L1 distance

0.475
0.285

0.036*

0.774

0.942
0.720

0.853

Note. Statistical significance level (p value or α value) is displayed for differences in ADHD>TD for each measure of fluid dynamism
in the 5-cluster analyses for global and within-system, network groupings. These values represent results after variance attributable
to age was removed using the general linear model. Significant ( p < 0.05 or α < 0.05, corrected for FDR) differences are highlighted in blue (ADHDTD). A red asterisk next to a value indicates a statistically significant solution was replicated
to the same level of significance in 4-cluster and 6-cluster sensitivity analyses. Dwell time p values are shown in a range, indicating
the lowest and highest p values in all five states. The DMN was the only system in which dwell time was significant, in only one state
represented by the specific lower bound p value shown.

Network Neuroscience

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Dynamic connectivity in ADHD

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Functional connectivity:
Refers to the strength of connections
between brain regions or networks
that share neurocognitive, or
functional, properties. More
specifically, temporal correlation is
assessed using statistical methods.
Regions or networks may exhibit
positively correlated or negatively
correlated (anti-correlated)
relationships.

L1 distance:
Refers to the L1 norm or Minkowski
distance which is a metric that
computes the distance between two
points as the sum of the absolute
differences of their Cartesian
coordinates.

Figure 3. Brain states and local dwell time within the DMN system in ADHD vs. TD. Dynamic
functional connectivity across five brain states was estimated with k-means clustering of windowed
FNC from the ICA timecourses within the DMN system. The DMN system was represented in seven
subnetworks, INs 13-19. See Supporting Information Table S1 (de Lacy & Calhoun, 2019) for further
description of each subnetwork. The dwell time within each state was computed for each subject.
Significant FNC differences between all combinations of DMN subnetworks, and significant differ-
ences in dwell time in ADHD>TD, were examined with two-sample t tests at a significant level of
α < 0.05, corrected for FDR. system (Table 1 and Figure 3) that was characterized by high levels of connectivity among DMN INs. This finding was also present in the motion-matched sample (Supporting Information Table S1, de Lacy & Calhoun, 2019) and was replicated in the 6-state analysis. A directionally similar effect was present in the 4-state analysis, but missed significance at α = 0.128. In addition, we found significantly (α < 0.05, corrected for FDR) reduced L1 distance within the DMN system (Table 1), replicated in the 6-state analysis but not the 4-state analysis. Another measure of fluidity, meta-state switching, was significantly reduced in the 5-cluster analysis, very narrowly missing significance in the 4-state (α = 0.059) but not 6-state analysis. These latter two findings were not present in the motion-matched sample (Supporting Information Table S1, de Lacy & Calhoun, 2019). Across all meta-state measures there was a generalized finding of reduced fluidity and range in ADHD versus TD within the DMN system, in every case either significant or narrowly missing significance. However, when subjects were motion-matched, no effect approached significance, although directionally there continued to be consistently reduced dynamism in ADHD. Differences in intrasystem dynamic fluidity never approached statistical significance Network Neuroscience 201 Dynamic connectivity in ADHD in any other neurocognitive system (Table 1) in either the original or motion-matched subject samples. We identified no significant (α < 0.05, corrected for FDR) differences in any measure of local fluidity or range between the DMN system and other network systems in ADHD (Table 2). However, some interesting general trends emerged that did not reach statistical sig- nificance in the original sample. We observed consistently reduced dynamism between the DMN and subcortical and sensorimotor systems, and consistently increased dynamism with task-positive control networks in ADHD versus TD across all meta-state measures. Similar trends were present in the 4-state and 6-state analyses. In the motion-matched sample, there was consistently increased dynamism between the DMN and all other neurocognitive systems in ADHD versus TD across all meta-state measures. In the case of task-positive control net- works and DMN subnetworks, these achieved statistical significance in the number of states and state-switching measures (Supporting Information Table 2, de Lacy & Calhoun, 2019). Transient DMN-Striato-Thalamic Hyperconnectivity Associated with a Diagnosis of ADHD Was Revealed by Local dFNC Analysis We identified a single, robust finding in analysis of FNC within five brain states that replicated in the 4-state and 6-state analysis. In local dFNC between the DMN and subcortical systems, subjects with ADHD displayed significant hyperconnectivity between a posterior cingulate- anchored subnetwork of the DMN (IN14), and the basal ganglia-thalamic network (IN30). This was a transient phenomenon that appeared in one brain state (Figure 4). Of note, this was not detectable in the sFNC whole-brain analysis of either group or maturational effects, further suggesting it is a local dynamic feature attributable to the effect of ADHD diagnosis. In each of the 4-, 5-, and 6-state analyses, this functional state was characterized by strong correlations among DMN subnetworks, suggesting it corresponds to DMN activation. Additionally, while anticorrelation between the DMN and striatal/cerebellar subnetworks is common among dFNC states, it was significantly stronger in this state. In the motion-matched sample of 444 youth, this effect also appeared, similarly in a state where there were strong correlations among DMN subnetworks and anticorrelation between DMN and subcortical subnetworks. Interestingly, in Table 2. Local DMN intersystem dynamic fluidity and range measures in subjects with ADHD and TD. Native space Meta-state space IN groups Dwell time Fraction of time State transitions Number of states State switching L1 Span Total L1 distance DMN x task-positive control DMN x sensorimotor 0.337-0.867 0.149-0.793 0.829-0.986 0.974 DMN x visual 0.281-0.912 0.988 DMN x subcortical 0.108-0.888 0.820-0.964 DMN x cognitive processing 0.186-0.852 0.333 0.769 0.353 0.521 0.155 0.910 0.602 0.424 0.459 0.509 0.618 0.602 0.402 0.466 0.550 0.664 0.467 0.345 0.712 0.079 0.510 0.831 0.166 0.666 0.311 0.912 Note. Statistical significance level (p value or α value) is displayed for differences in ADHD>TD for each measure of fluid dynamism
in the 5-cluster analyses for cross-system grouping between the DMN group and every other network group. All values represent
two-sample t tests performed at p < 0.05 or α < 0.05, corrected for FDR. These values represent results after variance attributable to age was removed using the general linear model. All results replicated to the same level of significance in the 4-state and 6-state analyses with the exception of a significant difference in dwell time between the DMN and visual system in State 2 in the 4-state analysis. Dwell time and fraction of time values are shown in a range, indicating the lowest and highest bounds for each of the five states. Network Neuroscience 202 l D o w n o a d e d f r o m h t t p : / / d i r e c t . m i t . / / t e d u n e n a r t i c e - p d l f / / / / / 3 1 1 9 5 1 0 9 2 3 6 4 n e n _ a _ 0 0 0 6 3 p d . t f b y g u e s t t o n 0 7 S e p e m b e r 2 0 2 3 Dynamic connectivity in ADHD Dynamic connectivity: Refers to the phenomenon of functional connectivity changing over time. Analysis of this time-varying connectivity is commonly performed using functional MRI, but the phenomenon has been observed using other experimental modalities. Figure 4. Transient hyperconnectivity between the posterior DMN and striato-thalamic network in dFNC states. Dynamic functional connectivity across five brain states was estimated with k-means clustering of windowed FNC from the ICA timecourses in global and local intrinsic connectivity systems. In the global analysis, differences in FNC between subjects with ADHD and TD were examined across all networks considered simultaneously. In local analyses, differences were com- puted within subnetworks of each functional system and between the DMN system and every other system. Significant FNC differences between any combination of intrinsic network systems were examined with two-sample t tests at a significant level of α < 0.05, corrected for FDR. the motion-matched subsample there were additional significant effects extending across all states, the majority also being hyperconnectivity, with 60% of all effects involving the same basal ganglia-thalamic network. These may be inspected in Supporting Information Figure S2 (de Lacy & Calhoun, 2019). We also identified significant group differences in localized dynamic connectivity in the native state space. Specifically, we found evidence of hyperconnectivity between two cognitive processing networks when local dFNC was analyzed within the cognitive processing network group: IN38, a network anchored in retrosplenial/parahippocampal cortex associated with memory and perceptual areas, and IN4, associated with expressive speech. This finding was not replicated in the 4-state or 6-state analysis, or in the motion-matched sample. Other than these findings, there were no significant differences in dFNC in any other of the global or local measures of dynamic connectivity. In the motion-matched sample, we also detected significant differences in dFNC between DMN subnetworks and visual networks, which may be viewed in Supporting Information Figure S3 (de Lacy & Calhoun, 2019). DISCUSSION Notwithstanding its interest to the neuroimaging research community, surprisingly few stud- ies have been published in youth with ADHD utilizing ICA to assess intrinsic connectivity between large-scale networks. In intrinsic sFNC, a combination of group and maturational effects have been identified. A trio of studies in the ADHD-200 data by the same group repre- sents the largest body of work to date. These use a grid-based 907-seed parcellation restricted to cortex, in 133 youth with ADHD and 288 TD subjects (the latter skewing older and female), Network Neuroscience 203 l D o w n o a d e d f r o m h t t p : / / d i r e c t . m i t . / t / e d u n e n a r t i c e - p d l f / / / / / 3 1 1 9 5 1 0 9 2 3 6 4 n e n _ a _ 0 0 0 6 3 p d t . f b y g u e s t t o n 0 7 S e p e m b e r 2 0 2 3 Dynamic connectivity in ADHD Scrubbing: Is a method used in functional MRI to address unwanted ’noise’ accruing from head otion during the acquisition of sequential MRI volumes. Individual volumes where large head motion is present are removed from the signal. performing scrubbing in up to 60% of frames to examine sFNC. Collectively, they identified group effects in hypoconnectivity of the DMN with fronto-parietal control, ventral attention and visual networks, and within-DMN. In a separate study, maturational lag was identified in these same network pairs (C. Sripada et al., 2014; Sripada, Kessler, & Angstadt, 2014). Using joint-ICA, hyperconnectivity was seen in DMN, again with ventral attention and fronto-parietal control, and also the dorsal attention network (Kessler, Angstadt, Welsh, & Sripada, 2014). A separate group performed one of the few extant analyses using ICA, in 40 age- and gender- matched children in 12 networks, finding altered maturational connectivity maturation be- tween salience and sensorimotor networks, and anterior-posterior nodes of the DMN (Choi, Jeong, Lee, & Go, 2013). In addition, a specific contribution of connectivity-driven studies fo- cused on internetwork relationships has been the generation of the “Default mode network interference hypothesis” in ADHD. This proposes that attenuated DMN deactivation in task- demanding states and reduced segregation between the DMN and task-positive control net- works may be associated with deficits in the appropriate functioning of the latter (Castellanos & Aoki, 2016; Castellanos & Proal, 2012; Sonuga-Barke & Castellanos, 2007). It has been further suggested that this results from abnormally reduced suppression of medial prefrontal DMN nodes (Fassbender et al., 2009). Using an ICA-based functional parcellation, we could not attribute sFNC differences to group (ADHD) effects as detected by (Sripada et al., 2014), even though we used the same underlying dataset, in either our original or motion-matched sample. This latter discrepancy may be due to methodologic and subject-selection differences. We constructed an approxi- mately age- and gender-matched subject sample, since older age and female gender are both protective factors, and may therefore artificially magnify ADHD>TD differences. In addition,
we used ICA to obtain a data-driven functional parcellation rather than a post hoc assignment
of edges to spatial maps, addressing motion via regression of motion parameters, selective de-
spiking, removal of motion artifact via the ICA decomposition, and controlling for motion in
the statistical analysis, rather than scrubbing.

Our analysis of maturational effects in sFNC in youth was consistent with the established
literature, with increasing positive connectivity among task-positive control networks and
between these networks and other task-specific networks such as visual or sensorimotor net-
works, and increasing anticorrelation between DMNs and task-specific networks. We also per-
formed an exploratory comparative analysis by splitting the subject group into TD and ADHD
groups with equal power that were approximately balanced for age and gender. These analy-
ses showed directional differences. In youth with ADHD, the maturational segregation seen in
TD among certain posterior subnetworks of the DMN was not present, congruent with recent
work (Mills et al., 2017), but instead age-related strengthening between medial prefrontal cor-
tical subnetworks was identified. In TD, there was a general theme of strengthened coupling
between the DMN and large-scale circuits anchored in dorsomedial and orbitofrontal cortex.
In ADHD, the former was also present, but orbitofrontal maturational strengthening with DMN
was not. The OFC is linked to reward-based decision-making and impulsivity, both consistent
parts of the ADHD phenotype (Mueller et al., 2017). Similarly, in ADHD youth we found mat-
urational strengthening of positive couplings between precuneus and the anterior cingulate
node of the cingulo-opercular network as in TD youth, but the increasing maturational corre-
lation seen in TD youth between the ventral frontal portion of the ventral attention network and
the right fronto-parietal control network was not present in ADHD. These latter networks have
been consistently linked with ADHD and these findings may link to recent research demon-
strating a differentiated pathway of precuneus functional development from the rest of the
DMN (Yang et al., 2014). Finally, segregation of the dorsal attention network with dorsolateral

Network Neuroscience

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Dynamic connectivity in ADHD

prefrontal cortex was present in TD youth, but not those with ADHD. As we note previously,
it has been suggested that higher motion may be a trait difference in ADHD, but this is not a
settled issue and therefore motivated our replication analyses in a motion-matched subsample.
This replication analyses in sFNC in a motion-matched subsample reassuringly detected very
similar effects with minor selected differences which may be due to motion differences, or to
reduced power in this smaller sample. Overall, our high-order model provides additional detail
on connectivity maturation among subnetworks of the larger networks commonly considered
in lower order models, showing directionally divergent patterns of sFNC maturation, but no
identifiable group effects, in youth with ADHD and TD.

In contrast, our analysis of time-varying intrinsic connectivity based on ICA-derived net-
works demonstrated group differences associated with ADHD diagnosis. We identified tran-
sient hyperconnectivity between the basal ganglia-thalamic network (IN30) and a subnetwork
of the DMN anchored in the posterior cingulate (IN14). This phenomenon was robust to vari-
ance in analytic parameters and provides the first conceptual link between decades of struc-
tural and task-based findings in ADHD implicating the striatum, and dynamic connectivity.
Furthermore, in the motion-matched subsample even more dFNC effects were detected, the
preponderance involving the same basal ganglia-thalamic network. Of note, the effect in the
original sample occurred in a distinctive brain state where maximal anticorrelation obtained
between the DMN and subcortical system generally, and strong positive connections were
observed within the DMN system. In the motion-matched subsample, the largest number of
dFNC differences were also in this state. An intriguing conceptual parallel is present in our
earlier work in schizophrenia, where we identified that thalamico-cortical dFNC differences
with TD existed in states with the strongest cortical-subcortical anticorrelations (Damaraju
et al., 2014). Similarly, in autism we found dFNC differences occurred in states exhibiting
greater anticorrelation between the DMN and other network systems (de Lacy et al., 2017).
Although the specific networks involved differ among these conditions, these findings suggest
that dynamic configuration states where the DMN is more anticorrelated with task-positive
networks may represent increased vulnerability to transient dysconnectivity phenomena asso-
ciated with neuropsychiatric conditions.

Our analysis of global measures of dynamism provided further group-specific effects. In
particular, we identified a significantly increased global meta-state span in ADHD>TD. This
finding suggests that subjects with ADHD traverse a larger whole-brain state space to instantiate
basal connectivity patterns, perhaps representing a more inefficient dynamic “search process.”
We believe the higher dimensional meta-state measures are generally less susceptible to dis-
tortion than those native state spaces, and since this measure was quite robust to variations of
our analytic parameters and appeared in the motion-matched sample. It differentiates ADHD
from at least one other neuropsychiatric condition (Miller et al., 2016), and may offer a con-
nectivity motif with specificity for ADHD. In this study, we introduced a novel increment of
our prior work in dynamic analysis by introducing local measures of dynamism within network
systems. These were developed to test for dynamic effects that localized to the DMN system,
and they produced three significant results. In every case, dynamism was significantly reduced
in ADHD2 standard deviations from the mean DVARS were eliminated from consideration.

Construction of Subject Sample

Our goal was to create a subject sample that was approximately representative of the youth
population with ADHD in terms of age distribution, handedness, comorbidities, gender, and
head motion while preserving statistical power given the effect size in resting-state imaging.
Subjects passing imaging quality control criteria were selected to create an approximately
age- and gender-matched sample of 252 youth with ADHD and 252 TD youth, ages 7.0–17.9,
with demographic characteristics summarized in Table 3.

Age and IQ for this sample were normally distributed, with skew and kurtosis between −3.5
and +3.5. Subjects had full-scale IQ (FSIQ) ranging from 73 to 153 with a mean of 110. There
was no significant difference in FSIQ between groups. Our sample contains 3:1 male-to-female
ratio and is weighted toward children over 11 years old, directionally similar to the distribution
of clinical incidence of ADHD in the population. Within the younger age bands, we included a
slightly greater proportion of females given our desire to include more younger subjects and the
relative paucity of male controls available at this age. Our 504 subjects came from the Peking,
KKI, NYU, and Pittsburgh sites in the ADHD-200 repository. Individual variables (regressors)
were constructed for each site. A list of included subjects with their ID codes, corresponding
to that given in the ADHD-200 repository key, may be inspected in Supporting Information
Table S3 (de Lacy & Calhoun, 2019).

Table 3. Demographic characteristics of subjects.

Typically developing

ADHD

Age group
7–8.99
9–10.99
11–12.99
13.0–14.99
15.0–17.99
Total

Number
38
72
65
51
26
252

% Male
52.6
62.5
78.5
94.1
80.8
73.4

Number
40
73
60
54
25
252

% Male
65.0
71.2
80.0
94.4
80.0
78.1

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Dynamic connectivity in ADHD

The clinically diagnosed ADHD population is enriched for left-handedness, although its
significance is disputed (Ghanizadeh, 2013). We retained this characteristic, and there was
a significant difference in handedness scores between groups (p = 0.003) with more left-
handedness in the ADHD group. Similarly, in the ADHD group, 96 subjects (38%) reported
past or present comorbidity with specific learning disorders, oppositional defiant disorder,
depression, anxiety disorders, and Tourette’s syndrome, approximately equivalent to the gen-
eral population with ADHD. No subjects reported autism, schizophrenia or psychotic symp-
toms. Instruments used to make diagnoses of ADHD and comorbidities varied across site—a
limitation—and these may be inspected at http://fcon_1000.projects.nitrc.org/indi/adhd200/.
Fifty-nine subjects in our sample with ADHD were reported to not be naïve to psychoactive
medications. Of these, three subjects in the Pittsburgh sample were reported to be taking medi-
cations at the time of scanning, but otherwise psychostimulants were withheld at least 24 hours
prior to scanning. Subjects with ADHD are also known to have higher rates of head motion
during MRI scanning and this has been proposed as a genuine trait, and perhaps genetic, differ-
ence (Couvy-Duchesne et al., 2016). Group differences in DVARS, the frame-to-frame measure
of head motion, were significant at p < 0.05, with ADHD subjects having more head motion. Overall, our desire was to fashion a subject sample resembling clinical populations; there- fore, we erred on the side of retaining differences in motion, handedness, comorbidities, and medication usage, and modeling these variables statistically. However, since the attribution of head motion differences to a trait difference in ADHD is not a settled question, we also created a subsample of 444 subjects (222 with ADHD and 222 with TD) that were further matched for head motion, quantified as DVARS score. The subjects that were omitted from the original sample to create this motion-matched subsample are detailed in Supporting Information Table S4 (de Lacy & Calhoun, 2019) Using a two-sample t test, we verified there was no significant difference in DVARS between subjects with ADHD and TD in the motion- matched subsample (p = 0.44). All methods detailed below were applied similarly to each subject sample, with any exceptions noted. l D o w n o a d e d f r o m h t t p : / / d i r e c t . m i t . t / / e d u n e n a r t i c e - p d l f / / / / / 3 1 1 9 5 1 0 9 2 3 6 4 n e n _ a _ 0 0 0 6 3 p d . t f b y g u e s t t o n 0 7 S e p e m b e r 2 0 2 3 Group Spatial Independent Component Analysis After processing the fMRI data, we performed ICA using the Group ICA of fMRI Toolbox (GIFT) developed in our group and widely used in ICA of fMRI (Calhoun & Adali, 2012; Calhoun, Adali, Pearlson, & Pekar, 2001), using an established pipeline (Allen et al., 2011). Resting-state scans were first prewhitened and despiked (using 3dDespike) followed by a subject-specific data reduction principal component analysis retaining 63 principle compo- nents with the objective of stabilizing back reconstruction and retaining maximum variance at the individual level (Erhardt et al., 2011). A relatively high-order 60-component group ICA was then performed using the Infomax algorithm with best run selection from 10 randomly initial- ized analyses (Himberg, Hyvarinen, & Esposito, 2004; Li, Adali, & Calhoun, 2007). Aggregate spatial maps were estimated as the centrotypes of component clusters to reduce sensitivity to initial algorithm parameters. Single-subject images were concatenated in time to perform the single-group ICA estimation and subject-specific spatial maps estimated using back recon- struction (Erhardt et al., 2011) with the group information–guided ICA (GIG-ICA) algorithm (Du et al., 2016), an approach which we have shown captures individual subject variability well (Allen, Erhardt, Wei, Eichele, & Calhoun, 2012). GIG-ICA estimates single-subject images and time courses from the single (all subjects) group ICA estimation, thereby allowing individual variation in spatial maps. The resulting independent components were scaled by converting each subject component image and timecourse to z-scores. Network Neuroscience 208 Dynamic connectivity in ADHD Sorting Components from the Spatial ICA As is standard in ICA analysis, components were sorted using a semimanual process into two groups: (1) gray matter networks and (2) artifactual noise components. All gray matter networks were included in the study, and all noise components such as the effects of blood pulsations and motion were discarded. Sorting was performed using a combination of expert visual in- spection and quantitative metrics. For each of the 60 components we computed the spectral metrics of (1) fractional amplitude of low-frequency fluctuations (fALFF) and (2) dynamic range (Allen et al., 2011). fALFF is the ratio of the integral of spectral power below 0.10 Hz to the in- tegral of power between 0.15 and 0.25 Hz. Dynamic range is the difference between the peak power and minimum power at frequencies to the right of the peak. Generally, components representing brain networks have higher values in these spectral metrics, whereas noise com- ponents (such as signals accruing from cerebrospinal fluid, vascular pulsations, white matter, or head motion) have lower values, although there are currently no absolute cutoff points for inclusion or exclusion. Components were visually inspected by both authors to determine their correspondence with gray matter. Components with poor overlap with cerebral gray matter or low spectral metrics were discarded. The remaining 44 components represented the intrinsic networks (INs) used in this study, and the coordinates in Montreal Neurologic space associ- ated with their top three peak intensities may be inspected in Supporting Information Table S5 (de Lacy & Calhoun, 2019). Discarded artifactual components may be inspected in Supporting Information Table S6 (de Lacy & Calhoun, 2019). Construction of Intrinsic Network Spatial Maps We constructed network spatial maps by selecting voxels that represented the strongest and most consistent coactivations for each of the 44 gray matter INs included after the sorting process by performing a voxelwise one-sample t test on the individual subject time courses and thresholding individual voxels at (mean + 4 SD), again following an established pipeline (Allen et al., 2011) using GIFT. Thus, these spatial maps represent the brain regions most associated with each component’s time course, instantiated in thresholded brain maps. This procedure enabled us to construct a group spatial map for each of the networks assembled from the relevant individual subject time courses. These spatial maps were used to attribute the neuro- cognitive labels for each IN, and served as the inputs for the sFNC analysis to construct the sFNC matrices (Figure 5). Functional Intrinsic Network Attribution and Grouping The primary neurocognitive function of each IN spatial map was attributed by visual inspection and quantitative comparisons by using three methods. First, we determined the coordinates in Montreal Neurologic Space (MNI) associated with peak intensities for each of the 44 INs. The top three coordinates were compared with the literature. We found multiple literature-based confirmatory sources that gave specific Talairach or MNI coordinates and associated these with network labels for all networks in the task-positive network group, the DMN, and pri- mary sensorimotor and visual networks (Dosenbach et al., 2007; Dosenbach et al., 2006; Fox et al., 2005; Laird et al., 2011; Seeley et al., 2007; Smith et al., 2009; Spreng, Sepulcre, Turner, Stevens, & Schacter, 2013; Vernet, Quentin, Chanes, Mitsumasu, & Valero-Cabre, 2014), but not for INs in the subcortical or cognitive processing groups. Second, the neurocognitive func- tion of the top five spatial locations in each IN were examined using the Brodmann Interactive Atlas (http://www.fmriconsulting.com/brodmann/Interact.html). Third, network correlations with reverse inference maps of regional activations associated with specific neurocognitive Network Neuroscience 209 l D o w n o a d e d f r o m h t t p : / / d i r e c t . m i t . t / / e d u n e n a r t i c e - p d l f / / / / / 3 1 1 9 5 1 0 9 2 3 6 4 n e n _ a _ 0 0 0 6 3 p d . t f b y g u e s t t o n 0 7 S e p e m b e r 2 0 2 3 Dynamic connectivity in ADHD l D o w n o a d e d f r o m h t t p : / / d i r e c t . m i t . / t / e d u n e n a r t i c e - p d l f / / / / / 3 1 1 9 5 1 0 9 2 3 6 4 n e n _ a _ 0 0 0 6 3 p d . t f b y g u e s t t o n 0 7 S e p e m b e r 2 0 2 3 Figure 5. Intrinsic networks grouped by associated neurocognitive function. Forty-four functional networks were identified and analyzed from whole-brain resting-state functional MRI data in 504 age- and gender-matched subjects 7–17 years old: 252 typically developing youth and 252 with ADHD. Networks are shown grouped into domains. Top constituent anatomic regions for each network and an attribution of its function may be inspected in Supporting Information Table S1 (de Lacy & Calhoun, 2019). functions were inspected in Neurosynth (Yarkoni, Poldrack, Nichols, Van Essen, & Wager, 2011). Static Functional Network Connectivity Analysis We performed a multivariate analysis of covariance (MANCOVA) using the MANCOVAN tool- box in GIFT to compare the effects of age with other possible predictors of variance in the same set of network maps for (1) all 504 subjects, (2) the 252 TD subjects, and (3) the 252 subjects with ADHD using an established method (Allen et al., 2011). To optimize for the large dimen- sions of the data, but enable statistical testing at each voxel, predictors were submitted to the MANCOVA with an F test at each iteration to produce a final reduced model for each outcome measure and network before univariate testing of significant predictors was performed on the original model. Nuisance regressors composed of individual sites, DVARS measure, and the six realignment parameters and their six first derivatives were regressed from the analysis by using the general linear model, prior to computing Pearson correlations between IN spatial maps. Network Neuroscience 210 Dynamic connectivity in ADHD Each site was modeled as an individual regressor. We used age, gender, FSIQ-level, scan site, and DVARS measure as predictors for all three analyses. For the first analysis of the combined group of 504 subjects, group or diagnosis of ADHD was also added as a predictor. Although we did remove the effects of DVARS measure and site prior to computing FNC matrices, we retained these as predictors in the MANCOVA to test for any residual effects of motion or site on results obtained in the statistical testing. For example, we tested for group × DVARs inter- actions. Significant effects were computed for both positively correlated voxels in each net- work and for voxels with anticorrelated time courses. We corrected for FDR at α = 0.01 for the 504-subject model and α = 0.05 for the smaller models of 252 subjects, given their reduced power. To assess for possible effects of handedness, presence of comorbid diagnosis, and medica- tion usage, we constructed an additional multivariate analysis in the original ADHD group of 252 subjects, where sensitivity to these effects would be larger than if diluted by the addition of TD controls. We used age, gender, FSIQ-level, scan site, DVARS, handedness, presence of comorbid diagnosis, and medication usage as predictors and otherwise duplicated our multivariate methodology. Comprehensive meta-analysis of fMRI studies suggests that ADHD- related dysfunction is present regardless of comorbid psychiatric conditions or history of stim- ulant treatment (Cortese et al., 2012). Computation of Brain States in Native State Space To identify dynamic brain states, we adopted the framework (Allen et al., 2014; Sakoglu et al., 2010) of deriving a small number of stable FNC states from fMRI time courses by applying a clustering algorithm to a succession of FNC windows. First, subject time courses were de- trended and despiked to remove outliers by using 3dDespike in the AFNI software, and filtered using a fifth-order Butterworth low-pass filter with a high-frequency cutoff of 0.15 Hz. After regression of six head motion parameters and their first temporal derivatives from the time courses, windowed covariance matrices were assembled using a sliding window approach instantiated in the temporal dFNC toolbox in GIFT, where a tapered rectangular window was created by convolving a rectangle (width = 25 TRs) with a Gaussian and slid in steps of 1 TR. Windowed FNC covariance matrices (wFNC) were estimated using a graphical LASSO method (Friedman, Hastie, & Tibshirani, 2008) as detailed in (Allen et al., 2014). The window size was selected based on previous studies demonstrating window sizes in the range of 40–60 s, which produce reasonable and robust results (Allen et al., 2014; Damaraju et al., 2014; de Lacy et al., 2017). Since this is multisite data, the TR varies among the four sites with a range of 1.5 to 2.5 s, and our algorithm incorporated this. Successive wFNC were then concatenated to form an array representing a state transition vector, or how the FNC state changed as a function of time for each subject. Subsequently, the k-means algorithm with city distance function was applied to this state transition vector to derive stable dynamic states, initializing the cluster- ing of data from all subjects with cluster centroids that were first clustered using a subset of windows with local maxima in FC variance as in Allen et al. ( 2014) followed by clustering of the entire set of windows after initialization with the previous cluster solution. The subsam- pling procedure was performed to improve performance and reduce computational demand; previous results show that the solution improves results (Allen et al., 2014). We computed the number of clusters in the data by using the Elbow criterion and the Bayes information criterion (Supporting Information Figure S1, de Lacy & Calhoun, 2019). The former produced a cluster number of four, and the latter of six. We presented the average solution of five clusters, but also reproduced the analyses using the same methods for four- and six-cluster solutions and report all results throughout. In addition, we applied a threshold concept requiring that a given FNC Network Neuroscience 211 l D o w n o a d e d f r o m h t t p : / / d i r e c t . m i t . t / / e d u n e n a r t i c e - p d l f / / / / / 3 1 1 9 5 1 0 9 2 3 6 4 n e n _ a _ 0 0 0 6 3 p d . t f b y g u e s t t o n 0 7 S e p e m b e r 2 0 2 3 Dynamic connectivity in ADHD covariance matrix be present in a minimum number of 10 windows for each subject included. Finally, we also performed a sensitivity analysis on the window size for the global 44-network dynamic models, analyzing each of the 4-, 5-, and 6-state solutions with window sizes of 20TR and 30TR. Generally, our framework fixes the number of clusters for all subjects since we believe allowing cluster number to vary among subjects could introduce model bias, since mathematically the results of computations in secondary metrics could be influenced by dif- ferences in cluster number. For example, it may be appreciated that comparing the fraction of total scan time two subjects spent in a state might differ for spurious reasons if one subject was moving among five clusters (states), and the other among four. Instead, our approach allows for potential differences in “dynamic biology” by permitting subjects to not enter (be present in) any given cluster. We computed the number of subjects from each group (TD vs. ADHD) in each state for every permutation of the analysis. Although these were in some cases different, this difference did not reach statistical significance tested at α < 0.05, corrected for FDR. In the motion-matched sample, we performed similar procedures for a five-cluster analysis with window size of 25TR, representing the primary analytic parameters presented for the original sample. Measures of Dynamism in Native State Space We computed four measures of functional dynamism in the native state space, that is, on the stable brain states computed with k means. These included three measures of fluidity: the number of times each subject moved between these states during their individual time courses, the average time (in windows) they spent in each of the states once entering that state (dwell time), and the fraction of their total time course spent in each state. We also computed FNC between pairwise INs within each state. Computation of Prototype Connectivity Patterns in Meta-State Space To create prototype connectivity patterns (CPs) for use in higher dimensional measures of dy- namism, we followed a similar method but in this case preferred the use of the tICA algorithm (Miller et al., 2016). After creating wFNC series as detailed above, the tICA algorithm was ap- plied to the individual arrays of FNC covariance matrices by using the city method and the algorithm iterated a maximum of 200 times before convergence. We chose the tICA algorithm since its decomposition produces CPs whose weights in the wFNC are maximally temporally mutually independent. However, we have previously demonstrated that results using our dy- namic measures (below) are stable if other clustering measures such as k means, spatial ICA, and principal component analysis are used (Miller et al., 2016). CPs formed the analytic sub- strate for the remainder of the study. High-Dimension Measures of Dynamism in Meta-State Space We computed four measures of dynamism in the higher dimensional meta-state space by using the same procedure as detailed by Miller and colleagues (Miller, Yaesoubi, & Calhoun, 2014; Miller et al., 2016). Here, the time-varying, additive contributions made by CPs to each ob- served wFNC over the subject time courses are discretized. A five-dimensional weight vector is obtained representing the contribution of each CP to each wFNC matrix by regressing the FNC estimate onto the tICA cluster centroid. Real-valued weights accruing from this computation are then replaced by a value in ± (1, 2, 3, 4) according to the signed quartile into which each weight falls. The resulting discretized vectors are termed meta-states. Four measures of dy- namism were computed for these meta-states. Discretization of the CP contributions to wFNC Network Neuroscience 212 l D o w n o a d e d f r o m h t t p : / / d i r e c t . m i t . / / t e d u n e n a r t i c e - p d l f / / / / / 3 1 1 9 5 1 0 9 2 3 6 4 n e n _ a _ 0 0 0 6 3 p d t . f b y g u e s t t o n 0 7 S e p e m b e r 2 0 2 3 Dynamic connectivity in ADHD = 32,768 possible meta-states (and similarly, 84 constructs a state space comprised of 85 and 86 possible states in the sensitivity analysis), which subjects may occupy over time. Two metrics describe the fluidity with which subjects traverse the meta-state space: the number of distinct meta-states passed through by each individual and the number of times each subject switches between meta-states. The remaining two metrics describe the high-dimension dynamic range 1 achieved by subjects: the maximal L span achieved between occupied meta-states, and the total distance “traveled” by an individual through the state space (sum of all L distances). 1 Local and Global Measures of Dynamism In this work, we introduce the concept of local versus global analysis of brain dynamism as observed in fMRI. Here, we applied the concepts of dFNC and meta-state analysis not only to the global set of INs but also to subsets of INs grouped by neurocognitive attribution. The formation of a high-order connectivity model with 44 networks is particularly tractable for this approach since it allows the examination of dynamism among subnetworks of the same system. In this procedure, the above pipeline was repeated in the same fashion for (1) the overall group of 44 networks, (2) within each of the six groups of INs when grouped by their dominant neurocognitive attribution (e.g., among 7 subnetworks of the default mode system), and (3) between the default mode system and each of the other functional system groups (e.g., among the default mode subnetworks and the sensorimotor networks). Dynamic Statistical Analysis Group differences in each measure of dynamic connectivity between TD subjects and subjects with ADHD were calculated using two-sample t tests. These were computed at a significance level of α < 0.05, corrected to control FDR where multiple comparisons obtained. We per- formed this analysis using the general linear model to disambiguate the effects of maturation (age) versus group effect of ADHD>TD. Variance associated with site, DVARS measure, IQ-
level, and gender was removed by regression using the general linear model from the correla-
tion values prior to performing clustering. The analysis was then repeated, removing variance
associated with site, DVARS measure, IQ-level, gender, and age using the general linear model.

ACKNOWLEDGMENTS

The authors would like to thank B. Ernesto Johnson for his assistance with figure preparation.

AUTHOR CONTRIBUTIONS

Nina de Lacy: Conceptualization; Formal analysis; Investigation; Writing – original draft. Vince
Calhoun: Supervision; Writing – review & editing.

FUNDING INFORMATION

Nina de Lacy, National Center for Advancing Translational Sciences (http://dx.doi.org/
10.13039/100006108), Award ID: KL2TR000421 and KL2TR002317. Vince Calhoun, Na-
tional Institutes of Health (http://dx.doi.org/10.13039/100000002), Award ID: 2R01EB005846.
Vince Calhoun, National Institutes of Health (http://dx.doi.org/10.13039/100000002), Award
ID: P20GM103472. Vince Calhoun, National Institutes of Health (http://dx.doi.org/10.13039/
100000002), Award ID: R01EB020407. Vince Calhoun, National Science Foundation (http://dx.
doi.org/10.13039/100000001), Award ID: 153906.

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